MULTILAYER NETWORK RELATIONSHIPS AND CULTURE CONTACT IN 

MISSISSIPPIAN WEST-CENTRAL ILLINOIS, A.D. 1200 - 1450 

 
By 
 

Andrew James Upton 

Michigan State University 

in partial fulfillment of the requirements  

for the degree of  

Anthropology—Doctor of Philosophy 

A DISSERTATION 

Submitted to 

2019 

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

 

 

 
 
 
 
 
 
 
 
 
 

 

 

 

MULTILAYER NETWORK RELATIONSHIPS AND CULTURE CONTACT IN 

MISSISSIPPIAN WEST-CENTRAL ILLINOIS, A.D. 1200 - 1450 

ABSTRACT 

 
By 
 

 

 
 

Andrew James Upton 

This dissertation explores the impact of migration on structure and change in human 

social networks. Prior scholarship on intercultural contacts emphasizes interaction spheres, 

hybridization, technological transfer, or models of exchange as indicators for constructing 

borders and defining societal membership. The current study assesses how network relationships 

among complex and smaller-scale societies structured, and were restructured by, migration. In 

particular, I address the role of ceramic industry in the transformation of communal-scale 

interaction and identification networks through culture contact across the middle to late 

Mississippian transition in the Late Prehistoric central Illinois River valley (ca. 1200 – 1450 

A.D.).  

In this study, I draw on a body of contemporary social theory focused on parsing social 

structure across multiple types of interrelationships to investigate how both indigenous societies 

and migrant peoples approach intercultural social and economic relations. This theoretical 

framework posits that specific types of relationships act as sensitive features in explanations of 

group contact, continuity, or change, but that understanding of the entire social system is only 

approachable through analysis of how individual network layers influence and co-construct each 

other. Building on a recent formalism, I refer to the superpositioning of individual network layers 

as a multilayer social network. Through multilayer network analysis, expectations are offered 

that seek to characterize communal behavioral strategies in the negotiation of a multicultural 

 

social and economic environment following cultural contact. This dissertation thus offers 

theoretical and methodological means to investigate social settings in which disparate material 

culture traditions coexist or intermix in time and space through the comparative modeling of 

various networks of relationships that connect individuals and communities. 

Ceramic industry is parsed into three relational dimensions in this study: A model for 

assessing social interaction via the cultural transmission of ceramic artifact attributes is applied 

to a database representing technological characterizations of over 1,300 vessels. Networks of 

social identification are modeled from a database of stylistic designs incised or trailed onto the 

outflaring rim of over 490 plates primarily used in the serving of food. Networks of economic 

interactions related to ceramic industry are modeled through the compositional analysis of over 

580 ceramic vessels.  

Based on a comparative analysis of the structure of multiple network layers, I 

hypothesize that Oneota in-migration into the Mississippian central Illinois River valley resulted 

in a period of accommodative intercultural communal coexistence at the macro-regional scale. In 

social settings following culture contact characterized by accommodative coexistence, relational 

transaction costs are relatively moderate to low but heterogeneous or exclusive categorial 

identities delimit the extent of collective action or social movements. A breakdown of economic 

relationships and reduction in the social scale of shared categorical identities among 

communities are argued to be clear inflection points in delimiting social transformations to sub-

groups of relational networks that did share common categorical identities, identities that may 

have cross-cut cultural boundaries. 

 
 
 
 

 

 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 

Copyright by 
ANDREW JAMES UPTON 
2019 

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

For Sarah and my Mom and Dad; 

To Grandma and Papa 

 
 
 
 
 
 
 

v 

 

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

ACKNOWLEDGEMENTS 

 

This study, I hope, does justice to all those mentors, colleagues, peers, family, and friends 

who have contributed to my intellectual development and fanned my curiosity and skepticism 

over the course of my academic career. I am deeply grateful to all of you. I would be remiss to 

not acknowledge the following individuals and organizations in particular.  

 

First and foremost, I would like to thank my dissertation committee: Drs. Jodie 

O’Gorman, William Lovis, Lynne Goldstein, Michael Conner, and Susan Sleeper-Smith as well 

as my outside reader Dr. Matthew Peeples. Each of you have encouraged me to challenge my 

instincts, to think in a rigorous and skeptical way, and to broaden my theoretical and 

methodological perspectives. I owe an immense debt of gratitude to my advisor, Dr. Jodie 

O’Gorman for her unwavering support and her many contributions to my personal and 

professional development. Dr. Lovis, thank you for developing and reinforcing a scientific 

mindset in me and for opening the world of statistical analysis to me, for that I will be forever 

grateful. Dr. Goldstein, thank you for grounding me and for being an inspiring role model. Dr. 

Conner, thank you for your support and mentoring, and thanks to you and Katie for providing 

housing for me during my time at Dickson Mounds in Havana – I will remember that time 

fondly. Dr. Peeples, thank you for paving the way for this study, for reviewing the mountain of 

code I produced for it, and for being such a positive source of support – I truly could not have 

made it this far without him.  

 

My dissertation research was funded in part by a National Science Foundation Doctoral 

Dissertation Improvement Grant (1745150), a Wenner-Foundation Dissertation Fieldwork Grant 

(Gr. 9479), an individual grant from the Ruth Landes Memorial Research Fund, a program of the 

vi 

Reed Foundation, the R. Bruce McMillan Museum Internship with the Illinois State Museum at 

Dickson Mounds, the Graduate School, College of Social Science, and Department of 

Anthropology at Michigan State University, and the Field Museum of Natural History’s 

Elemental Analysis Facility National Science Foundation subsidy program. Many thanks to the 

Western Illinois Archaeological Research Center, Western Illinois University, and the Upper 

Mississippi Valley Archaeological Research Foundation for gracious access to collections used 

in this research and to Lawrence Conrad for his support of my research and many hours of 

discussion on Mississippian and Oneota occupations in west-central Illinois. Thanks to the 

Consortium for Archaeological Research for access to collections at Michigan State University. 

Thanks to Tom Emerson, Duane Esarey, Kjersti Emerson, Alexy Zelin, and Laura Kozuch for 

access to reports, photographs, and collections at the Illinois State Archaeological Survey. I owe 

many thanks to Dee Ann Watt, Alan Harn, Kelvin Sampson, and Drs. Michael Wiant and Bonnie 

Styles, for facilitating access to materials at the Illinois State Museum system and for assisting 

with my many destructive and other analysis requests. Many thanks to Dr. Jeremy Wilson and 

John Flood for their support and for providing access to materials at Indiana University Purdue 

University Indianapolis.  

Drs. Laure Dussubieux and Mark Golitko provided invaluable support in the collection of 

LA-ICP-MS data at the Field Museum and gave me a crash course on analytical chemistry and 

the analysis of compositional data. I am grateful to Matthew Peeples, Gianmarco Alberti, Hadley 

Wickham, Manlio De Domenico, Gábor Csárdi, and Matteo Magnani for creating the open-

source programming tools that made this dissertation research possible.  

 

I would like to acknowledge supervisors from the various careers paths I have taken 

while working on this study. Each of you not only contributed to my personal and professional 

vii 

development but also supported my research needs in countless ways: James Mack, Yonatan 

Eyal, Mary Horan, Justine Clark-Lomax, James Robertson, Erik Kreusch, Dan Reeves, Patricia 

Likins, and Brad Peters.  

 

Moral and academic support was instrumental from my peers at MSU: Frank and Nicole 

Raslich, Sylvia Galaty, Stefan Johnson, Nikki Klarmann, Jessica Yann, Sean Dunham, Kate 

Frederick; and from friends beyond Alex Ferko, David Armacost, Chris Robinson, Evan Jones, 

Emily Repp, Evonne Swallie, Courtney Mills, Rachael Crane, Tommy Hemmer, and scores of 

others. I offer sincerest apologies to any I have omitted.  

My parents, Bill and Joanne Upton, gave me the freedom to follow my dreams and to 

find my passions – I cannot express in words how grateful I am for that and for their undying 

love. Thanks to my brother Ian, sister Abby, and brother in-law Scott for everything they have 

done for me over the years. Many thanks to my grandparents, Jack Upton, Mary Lou Upton, Jean 

Streb and William Streb for your sacrifices, practical life advice, and support. I wish you all 

could have been here to see the completion of this work. And thanks to my extended family – to 

Bill and Annie Jones, the Lightles and the Santalucias, the Snyders (and Tyler), the Dieckmanns, 

the Permes, the Brezgers, and Jenny and Andy Kranz and Jessica, Jared and Megan Van Vooren. 

Nothing means more to me than having the love and support of my family.  

 

Finally, and most of all, I am thankful to Sarah for being the love of my life, an ever-

present source of inspiration, and for reminding me every day that there are more important 

things than the Late Prehistoric central Illinois River valley.  

 
 
 
 

viii 

TABLE OF CONTENTS 

 
 
CHAPTER 1  INTRODUCTION ............................................................................................... 1 
1.1 
Brief Introduction to the Research Problem .......................................................... 1 
1.2  Multicultural Social Interrelationships and Multilayer Social Network Analysis .. 2 
1.3 
The Case Study .................................................................................................... 5 
1.4 
Dissertation Organization ..................................................................................... 7 

 
CHAPTER 2  MULTILAYER SOCIAL NETWORKS AND INTERCULTURAL 

2.1 
2.2 
2.3 

2.4 

COMMUNAL COEXISTENCE ........................................................................ 10 
Introduction ....................................................................................................... 10 
Evolving Perspectives on Social Interaction and Identity Formation................... 10 
Social Systems as Multilayered, Relational Networks ........................................ 19 
2.3.1  Theory in Networks ..................................................................................... 20 
2.3.2  Multilayer Ties in Anthropological Archaeology .......................................... 28 
2.3.3  Social Transformation through Relational and Categorical Identification ..... 33 

Intercultural Communal Coexistence – Linking Culture Contact, Multilayer 
Social Network Analysis, and Archaeological Evidence..................................... 36 
2.4.1  Material Culture Correlates to Intercultural Communal Coexistence ............ 41 

 
CHAPTER 3  REGIONAL AND CULTURAL BACKGROUND: LATE PREHISTORY IN 

THE CENTRAL ILLINOIS RIVER VALLEY .................................................. 47 
Introduction ....................................................................................................... 47 
3.1 
Geographic Setting ............................................................................................ 48 
3.2 
The Mississippian Tradition ............................................................................... 49 
3.3 
The Upper Mississippian Tradition and the Oneota ............................................ 54 
3.4 
The Mississippian Period central Illinois River valley ........................................ 56 
3.5 
Eveland Phase (A.D. 1100-1175) ....................................................................... 61 
3.6 
Orendorf Phase (A.D. 1200-1250) ...................................................................... 64 
3.7 
Larson Phase (A.D. 1250-1300) ......................................................................... 67 
3.8 
Crable Phase (A.D. 1300-1425) ......................................................................... 72 
3.9 
3.10  The Bold Counselor Phase Oneota ..................................................................... 79 
3.11  Regional Abandonment ...................................................................................... 84 

4.1 
4.2 

 
CHAPTER 4  METHODOLOGICAL CONSIDERATIONS .................................................... 86 
Introduction ....................................................................................................... 86 
Data Collection Methods.................................................................................... 87 
4.2.1  Ceramic Vessel Technological Data ............................................................. 87 
4.2.2  Ceramic Vessel Stylistic Data ...................................................................... 89 
Compositional Analysis of Archaeological Ceramics ......................................... 91 
4.3.1  Compositional Analysis in Archaeology ....................................................... 92 
4.3.2  Clay: Geological, Chemical and Mineralogical Considerations..................... 95 
4.3.3  Technological Choice and Pottery Production .............................................. 97 
4.3.4  Use-Wear Effects on Sherd Chemistry ......................................................... 99 

4.3 

ix 

4.4 

4.5 
4.6 

4.3.5  Diagenesis and Sherd Chemistry .................................................................. 99 
Compositional Methods: pXRF, XRD, and LA-ICP-MS .................................. 100 
4.4.1  Portable X-Ray Fluorescence ..................................................................... 101 
4.4.2  X-Ray Diffraction ...................................................................................... 101 
4.4.3  Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry ................ 103 
Analytical Methods for Monoplex Social Networks ......................................... 104 
Definitions and Methods for Constructing and Analyzing Multilayer  
Networks ......................................................................................................... 108 
4.6.1  Multilayer Network Analysis Measures ...................................................... 110 

 
CHAPTER 5  NETWORKS OF INTERACTION THROUGH CULTURAL  

5.1 
5.2 
5.3 

TRANSMISSION ............................................................................................ 116 
Introduction ..................................................................................................... 116 
Cultural Transmission Theory, Artifact Variation, and Network Ties ............... 119 
Defining the Sample and Assessing Dependencies ........................................... 124 
5.3.1  Assessing Dependencies............................................................................. 130 
5.3.2 

Identifying Social Information Bearing Artifact Type-Attributes from  
Cultural Transmission ................................................................................ 135 

5.4  Methodology: Constructing Social Interaction Networks from Social  

Information Bearing Artifact Type-Attributes .................................................. 142 
Evaluating the Results: Statistical Interpretation of Ceramic Industry Social 
Interaction Network Models ............................................................................. 156 

5.5.1  Statistical Analysis of Pre-Migration Interaction Networks,  

1200 – 1300 A.D. ....................................................................................... 161 

5.5.2  Statistical Analysis of Post-Migration Interaction Networks,  

1300 – 1450 A.D. ....................................................................................... 174 
5.5.3  The Role of Geographic Distance ............................................................... 190 

Discussion and Visual Interpretation of Ceramic Industry Social Interaction 
Network Models .............................................................................................. 194 
5.6.1  Pre-Migration Technological Similarity Networks, 1200 – 1300 A.D. ........ 197 
5.6.2  Post-Migration Technological Similarity Networks, 1300 – 1450 A.D. ...... 207 
5.6.3  Technological Similarity Networks Across Time, 1200 – 1450 A.D. .......... 216 
Conclusion ....................................................................................................... 225 

5.5 

5.6 

5.7 

 
CHAPTER 6  CERAMIC STYLE AND NETWORKS OF SOCIAL IDENTIFICATION ...... 230 
6.1 
Introduction ..................................................................................................... 230 
6.2  Migration and Social Identification .................................................................. 232 
Oneota Migration into West-Central Illinois..................................................... 236 
6.3 
6.3.1  Plates, Ceramic Design, and Sun Symbolism in the CIRV .......................... 241 
6.4  Methodology.................................................................................................... 251 
6.5 
Results and Discussion: Social Identification in the Late Prehistoric CIRV ...... 262 
6.6 
Conclusion ....................................................................................................... 273 

 
CHAPTER 7  NETWORKS OF ECONOMIC RELATIONSHIPS: RESULTS OF THE 

CHEMICAL ANALYSES ............................................................................... 275 
Introduction ..................................................................................................... 275 

7.1 

x 

7.2 
7.3 
7.4 
7.5 

Ceramic Industry Economic Relationships ....................................................... 276 
Central Illinois River valley Geology ............................................................... 279 
The Ceramic and Clay Sample ......................................................................... 285 
Ceramic Paste and Clay Chemical Characterization Using LA-ICP-MS ........... 287 
7.5.1  Controlling for Shell Tempering ................................................................. 290 
7.5.2  Statistical Routines in the Analysis of Geochemical Data ........................... 292 
Results of the Clay Analyses ............................................................................ 304 
Results of the Ceramic Analyses ...................................................................... 309 
7.7.1  Compositional Group Identification and Assignment ................................. 311 
7.7.2  Structure within the Core compositional group ........................................... 319 
7.8 
Compositional Groups as Economic Social Networks ...................................... 330 
7.9 
Ceramic Industry Economic Network Analysis and Discussion ........................ 335 
7.10  Conclusion ....................................................................................................... 346 

7.6 
7.7 

 
CHAPTER 8  TOWARD EXPLAINING SOCIAL INTERRELATIONSHIPS THROUGH 

 

xi 

CERAMIC INDUSTRY MULTILAYER SOCIAL NETWORKS ................... 349 
Introduction ..................................................................................................... 349 
Culture Contact and Multi-dimensionality in Archaeological Social Networks . 349 
Layers of Evidence – Results of the Individual Network Layers ....................... 353 
8.3.1  Relational Interaction from Cultural Transmission ..................................... 354 
8.3.2  Categorical Identities from Ceramic Design ............................................... 357 
8.3.3  Economic Relationships as Relational Interaction ...................................... 359 
Building Late Prehistoric CIRV Ceramic Industry Multilayer Networks .......... 361 
Overlap and Influence among Layers and Communities ................................... 370 
8.5.1  Layer Interactions ...................................................................................... 370 
8.5.2  Community and Layer Influence ................................................................ 370 
Intercultural Communal Coexistence in the Late Prehistoric CIRV .................. 382 
Contributions of this Research ......................................................................... 386 
8.7.1  Contributions to Archaeology and CIRV Archaeology ............................... 388 
Future Directions ............................................................................................. 390 

8.1 
8.2 
8.3 

8.4 
8.5 

8.6 
8.7 

8.8 

 
APPENDICES ........................................................................................................................ 393 
APPENDIX A Coding Sheet ....................................................................................... 394 
 
APPENDIX B Ceramic Vessel Measurement Data Availability ................................... 404 
APPENDIX C All R Code for Statistical Analyses ...................................................... 405 
APPENDIX D LA-ICP-MS Data and Supplementary Statistical Documentation  

    for Group Assignments ........................................................................ 572 
APPENDIX E Plate Stylistic Design Group Sketches .................................................. 581 
APPENDIX F Jar and Plate Profile Sample ................................................................. 625 
APPENDIX G Mineralogical Analysis Results ............................................................ 643 
APPENDIX H Site Identification Codes and Radiocarbon Probabilities ...................... 644 

 
REFERENCES ....................................................................................................................... 652 
 

 

LIST OF TABLES 

Table 2.1 Matrix of expectations for intercultural communal coexistence strategies .................. 37 

Table 5.1 Expectations for Attributes under Global or Local Functional Control, and Serving  

as Emblemic and Assertive Markers (Eerkens and Bettinger 2008, p. 25) .............. 122 

Table 5.2 Expectations for Attributes under Social or Engineering Constraint ......................... 123 

Table 5.3 Coding Schema (See Appendix A for Full Coding Sheet) ........................................ 126 

Table 5.4 Count of plate sherds from each site for each continuous variable above n crit ......... 128 

Table 5.5 Count of burial jar sherds from each site for each continuous variable above n crit .. 129 

Table 5.6 Count of domestic jar sherds from each site for each continuous variable  

above n crit ............................................................................................................ 129 

Table 5.7 Pearson correlation coefficient for pairwise complete burial jar metric  

observations........................................................................................................... 132 

Table 5.8 Pearson correlation coefficient for pairwise complete domestic jar metric  

observations........................................................................................................... 133 

Table 5.9 Pearson correlation coefficient for pairwise complete plate metric observations....... 134 

Table 5.10 VOM, AV, and VOV values, scores, and summary data for type attributes ............ 137 

Table 5.11 Summation of networks constructed with artifact type-attribute social interaction 

markers .................................................................................................................. 147 

Table 5.12 Network Statistics for Ceramic Industry Social Interaction Network Models ......... 189 

Table 6.1 Summary of plate sample design techniques by site ................................................. 253 

Table 6.2 Counts of vessels by site and design category;  Ú  indicates pre-migration  
occupation (1200 – 1300 A.D.),  Ù indicates post-migration occupation  
(1300 – 1450 A.D.),  <> indicates occupation(s) that span(s) the pre- and post-
migration time periods ........................................................................................... 261 

Table 6.3 Central Illinois River Valley Social Identification Network Statistics ...................... 264 

Table 7.1 Distribution of pottery samples by site and vessel type ............................................ 286 

Table 7.2 Elemental summary statistics measured across 131 replicates of New Ohio  

Red clay ................................................................................................................ 289 

xii 

Table 7.3 Average chemical concentrations and standard deviations for the two clay groups 

(ppm) ..................................................................................................................... 308 

Table 7.4 Eigen values and percent variance for first 12 principal components on the  

ceramic data set ..................................................................................................... 313 

Table 7.5 Mahalanobis distance based probabilities of group membership in the core and 

outgroups for the outgroup sherds .......................................................................... 316 

Table 7.6 Mahalanobis distance based probabilities of group membership in the Core A  

group and Core B and Core C provisional groups .................................................. 321 

Table 7.7 Compositional group assignments by site ................................................................ 329 

Table 7.8 Compositional group assignments summarized by site geography and vessel class .. 329 

Table 7.9 Central Illinois River Valley Ceramic Industry Economic Network Statistics .......... 338 

Table 8.1 Matrix of expectations for intercultural communal coexistence strategies ................ 351 

Table 8.2 Network properties for individual undirected network layers ................................... 369 

Table D.1 Component loadings for the first 12 principal components, accounting for 90.4%  

of the variance in the 44 element data set ............................................................... 572 

Table D.2 Posterior classification probabilities based on jackknifed Mahalanobis for Core  

A1 and Core A2 Sub-Groups ................................................................................. 573 

Table D.3 Mean and standard deviation values for the ceramic geochemical compositional 

groups.................................................................................................................... 578 

Table G.1 X-ray Diffraction Results ........................................................................................ 643 

Table H.1 Site IAS and ISM Identification Numbers ............................................................... 644 

Table H.2 Radiocarbon assay probabilities and results ............................................................ 645 

 
 
 
 
 
 
 
 
 
 
 

xiii 

 

LIST OF FIGURES 

Figure 3.1 Lidar map of, and archaeological sites under consideration in the Late Prehistoric 

central Illinois River valley (circa 1200 – 1450 A.D.) .............................................. 48 

Figure 3.2 Probability distributions of three recalibrated dates for the Eveland site  

(Bender et al. 1975) ................................................................................................. 63 

Figure 3.3 Probability distributions of five recalibrated dates for the Orendorf site  

(Bender et al. 1975) ................................................................................................. 65 

Figure 3.4 Probability distributions of four recalibrated dates for the Larson site  

(Bender, et al. 1975) ................................................................................................ 68 

Figure 3.5 Probability distributions of one recalibrated dates for Walsh Site  

(Wilson, personal communication 2017) .................................................................. 71 

Figure 3.6 Probability distributions of four recalibrated dates for Ten Mile Creek and  

Star Bridge sites; dates include DirectAMS Codes D-AMS 020156 – D-AMS  
020159 respectively ................................................................................................. 74 

Figure 3.7 Probability distributions of four recalibrated dates for Crable and the Oneota 

occupation of the C.W. Cooper sites ........................................................................ 75 

Figure 5.1 Mean-standard deviation relationships for type-attribute variables calculated by 

material culture class with best-fit regression lines. Log base 10 values  
reported to account for effects related to different measurement scales................... 127 

Figure 5.2 QQplot of domestic jar rim angles showing deviation from normality in  

Eveland and Kingston Lake ................................................................................... 131 

Figure 5.3 Scatterplot of Burial Jar Height by Burial Jar Orifice Diameter with best-fit  

regression line and 0.95 confidence interval shading .............................................. 132 

Figure 5.4 VOM, AV, and VOV residual scores for all 15 ceramic vessel type attributes 

measurements ........................................................................................................ 138 

Figure 5.5 Ridgeline plot of domestic jar type-attributes likely constrained by social  

forces, all measurements are in mm aside from rim angle which is in degrees ........ 141 

Figure 5.6 Ridgeline plot of plate type-attributes likely constrained by social forces, all 

measurements are in cm aside from flare angle which is in degrees........................ 142 

Figure 5.7 Adjacency matrix representation of multilayer social media friendship network ..... 153 

xiv 

Figure 5.8 Flattened adjacency matrix representation of multilayer social media friendship 

network ................................................................................................................. 153 

Figure 5.9 Example of multilayer network slicing with networks embedded in  

geographical regions, showing a network of European airports rendered using 
MuxViz with each layer representing a different airline and edges representing  
flights between airports (De Domenico, Porter, et al. 2015) ................................... 154 

Figure 5.10 Network Randomization Results for Jar Pre-Migration Layer. Observed statistic 
represents red line. Histogram shows distribution of statistic based on network 
randomization of 5000 random graphs using the Erdős–Rényi random network 
modeling technique. ............................................................................................. 162 

Figure 5.11 Network Randomization Results for Plate Pre-Migration Layer. Observed statistic 

represents red line. Histogram shows distribution of statistic based on network 
randomization of 5000 random graphs using the Erdős–Rényi random network 
modeling technique. ............................................................................................. 163 

Figure 5.12 Authorities and Hubs in the Jar and Plate Pre-Migration Period Network Layers. 

Authority and Hub scores are modeled as node size.............................................. 165 

Figure 5.13 Degree distribution of Jar and Plate Pre-Migration networks. ............................... 166 

Figure 5.14 Edge betweenness community detection in the Jar and Plate Pre-Migration  

Attribute Networks ............................................................................................... 168 

Figure 5.15 Network Randomization Results for Multilayer Pre-Migration Network.  

Observed statistic represents red line. Histogram shows distribution of statistic  
based on network randomization of 5000 random graphs using the Erdős–Rényi 
random network modeling technique. ................................................................... 169 

Figure 5.16 Authorities and Hubs in the Multilayer Pre-Migration Period Network.  

Authority and Hub scores are modeled as node size.............................................. 170 

Figure 5.17 Edge betweenness community detection in the Multilayer Pre-Migration  

Network ............................................................................................................... 171 

Figure 5.18 Network Randomization Results for Post-Migration Jar Attribute Network.  

Observed statistic represents red line. Histogram shows distribution of statistic  
based on network randomization of 5000 random graphs using the Erdős–Rényi 
random network modeling technique. ................................................................... 177 

Figure 5.19 Network Randomization Results for Post-Migration Plate Attribute Network. 

Observed statistic represents red line. Histogram shows distribution of statistic  
based on network randomization of 5000 random graphs using the Erdős–Rényi 
random network modeling technique. ................................................................... 178 

xv 

Figure 5.20 Authorities and Hubs in the Jar and Plate Post-Migration Period Network  

Layers. Authority and Hub scores are modeled as node size. ................................ 180 

Figure 5.21 Edge betweenness community detection in the Jar and Plate Post-Migration  

Attribute Networks ............................................................................................... 181 

Figure 5.22 Degree Distributions of Jar and Plate Post-Migration Networks............................ 182 

Figure 5.23 Network Randomization Results for Multilayer Post-Migration Network.  

Observed statistic represents red line. Histogram shows distribution of statistic  
based on network randomization of 5000 random graphs using the Erdős–Rényi 
random network modeling technique. ................................................................... 183 

Figure 5.24 Hubs and Authorities in the Post-Migration Multilayer Attribute Network. Hub  

and Authority score modeled as node size ............................................................ 185 

Figure 5.25 Edge Betweenness Community Detection in the Multilayer Post-Migration  

Attribute Network ................................................................................................ 186 

Figure 5.26 Distributions of Randomly Sampled Linear Models for Strength of Relational 
Connection as a Function of Geographic Distance in Multilayer jar and plate  
attribute networks. Dashed red line indicates linear model for observed data ........ 191 

Figure 5.27 Distributions of Randomly Sampled Linear Models for Strength of Relational 

Connection as a Function of Geographic Distance in Jar and Plate Attribute 
Interaction Networks faceted by time phase designation. Dashed red line  
indicates linear model for observed data ............................................................... 192 

Figure 5.28 Yifan Hu multilevel network graph layout of domestic jar technological  

similarity network for the Pre-Migration Time Period (1200-1300 A.D.); edges  
are colored by weight; nodes are colored and sized by closeness centrality ........... 198 

Figure 5.29 Geographic network graph layout of domestic jar technological similarity  
network for the Pre-Migration Time Period (1200-1300 A.D.); edges are  
colored by weight; nodes are colored and sized by closeness centrality ................ 199 

Figure 5.30 Yifan Hu multilevel network graph layout of plate technological similarity  

network for the Pre-Migration Time Period (1200-1300 A.D.); edges are  
colored by weight; nodes are colored and sized by weighted degree ..................... 200 

Figure 5.31 Geographic network graph layout of plate technological similarity network for  
the Pre-Migration Time Period (1200-1300 A.D.); edges are colored by weight;  
nodes are colored and sized by closeness centrality .............................................. 201 

Figure 5.32 Yifan Hu multilevel network graph layout of domestic jar and plate  

technological similarity flattened multilayer network for the Pre-Migration  
Time Period (1200-1300 A.D.); edges are colored by weight; nodes are  
colored and sized by weighted degree................................................................... 202 

xvi 

Figure 5.33 Geographic network graph layout of domestic jar and plate technological  
similarity flattened multilayer network for the Pre-Migration Time Period 
 (1200-1300 A.D.); edges are colored by weight; nodes are colored and sized  
by weighted degree .............................................................................................. 203 

Figure 5.34 Geographic network graph layout of domestic jar (left) and plate (right) 

technological similarity sliced multilayer network for the Pre-Migration Time  
Period (1200-1300 A.D.); edges are colored by weight; nodes are colored and  
sized by closeness centrality ................................................................................. 205 

Figure 5.35 Yifan Hu multilevel network graph layout of domestic jar technological  

similarity network for the Post-Migration Time Period (1300-1450 A.D.);  
edges are colored by weight; nodes are colored and sized by weighted degree ...... 211 

Figure 5.36 Geographic network graph layout of domestic jar technological similarity  
network for the Post-Migration Time Period (1300-1450 A.D.); edges are  
colored by weight; nodes are colored and sized by closeness centrality ................ 208 

Figure 5.37 Yifan Hu multilevel network graph layout of plate technological similarity  
network for the Post-Migration Time Period (1300-1450 A.D.); edges are  
colored by weight; nodes are colored and sized by weighted degree ..................... 211 

Figure 5.38 Geographic network graph layout of domestic plate similarity network for the  
Post-Migration Time Period (1300-1450 A.D.); edges are colored by weight;  
nodes are colored and sized by weighted  degree .................................................. 212 

Figure 5.39 Yifan Hu multilevel network graph layout of domestic jar and plate  

technological similarity flattened multilayer network for the Post-Migration  
Time Period (1300-1450 A.D.); edges are colored by weight; nodes are  
colored and sized by weighted degree................................................................... 213 

Figure 5.40 Geographic network graph layout of domestic jar and plate technological  

similarity flattened multilayer network for the Post-Migration Time Period  
(1300-1450 A.D.); edges are colored by weight; nodes are colored and sized  
by weighted degree .............................................................................................. 214 

Figure 5.41 Geographic network graph layout of domestic jar (left) and plate (right) 

technological similarity sliced multilayer network for the Post-Migration Time  
Period (1300-1450 A.D.); edges are colored by weight; nodes are colored and  
sized by closeness centrality for jars (left) and weighted degree for plates  
(right) ................................................................................................................... 215 

Figure 5.42 Yifan Hu multilevel network graph layout of domestic jar technological  

similarity network flattened across Time Periods (1200 – 1450 A.D.); edges are 
colored by weight; nodes are colored and sized by weighted degree score ............ 217 

xvii 

Figure 5.43 Geographic network graph layout of domestic jar technological similarity  

network flattened across Time Periods (1200 – 1450 A.D.); edges are colored  
by weight; nodes are colored and sized by weighted degree .................................. 218 

Figure 5.44 Yifan Hu multilevel network graph layout of plate technological similarity  

network flattened across Time Periods (1200 – 1450 A.D.); edges are colored  
by weight; nodes are colored and sized by closeness centrality score .................... 219 

Figure 5.45 Geographic network graph layout of plate technological similarity network  

flattened across Time Periods (1200 – 1450 A.D.); edges are colored by weight; 
nodes are colored and sized by weighted degree ................................................... 220 

Figure 5.46 Yifan Hu multilevel network graph layout of domestic jar and plate  

technological similarity multilayer network flattened across Time Periods  
(1200 – 1450 A.D.); edges are colored by weight; nodes are colored and sized  
by weighted degree .............................................................................................. 221 

Figure 5.47 Geographic network graph layout of domestic jar and plate technological  

similarity multilayer network flattened across Time Periods (1200 –  
1450 A.D.); edges are colored by weight; nodes are colored and sized by  
weighted degree ................................................................................................... 222 

Figure 5.48 Geographic network graph layout of domestic jar (left) and plate (right) 

technological similarity sliced multilayer network flattened across Time Period 
(1200-1450 A.D.); edges are colored by weight; nodes are colored and sized by 
weighted degree ................................................................................................... 224 

Figure 6.1 Examples of plate form. Images © Andy Upton 2018, courtesy Western Illinois 

Archaeological Research Center and Dickson Mounds Museum ............................ 243 

Figure 6.2 Ridgeline density plots for plate continuous attribute measurements at Late  

Prehistoric CIRV sites ........................................................................................... 244 

Figure 6.3 Plate decoration techniques: trailed (left) and incised (right). Images © Andy  

Upton 2018, courtesy Western Illinois Archaeological Research Center ................ 246 

Figure 6.4 Trailed and punctate impression decoration. Image © Andy Upton 2018,  

courtesy Western Illinois Archaeological Research Center ..................................... 247 

Figure 6.5 Plate sherd showing sun with nested cross motif. Image © Andy Upton 2018,  

courtesy Western Illinois Archaeological Research Center ..................................... 248 

Figure 6.6 Sketch tracings of plate decoration motif emblems ................................................. 255 

Figure 6.7 Distribution of Brainerd-Robinson coefficients for simulated (green) and  

observed (blue) design category matrices ............................................................... 257 

Figure 6.8 Correlation Matrix Heat-Map of Rescaled Brainerd-Robinson Coefficients ............ 262 

xviii 

Figure 6.9 Yifan Hu multilevel network graph layout for the Pre-Migration Time Period  

(1200-1300 A.D.; left) and Post-Migration Time Period (1300-1450 A.D.; right) .. 265 

Figure 6.10 Geographic network graph layout for the Pre-Migration Time Period  

(1200-1300 A.D.) ................................................................................................. 267 

Figure 6.11 Geographic network graph layout for the Post-Migration Time Period  

(1300-1450 A.D.) ................................................................................................. 267 

Figure 6.12 Yifan Hu multilevel network graph layout flattened across time  

(1200 – 1450 A.D) ............................................................................................... 268 

Figure 6.13 Geographic network graph layout flattened across time (1200 – 1450 A.D) .......... 268 

Figure 6.14 Network randomization results for pre-migration social identification network. 
Observed statistic represents red line. Histogram shows distribution of statistic  
based on network randomization of 5000 random graphs using the Erdős–Rényi 
random network modeling technique. ................................................................... 270 

Figure 6.15 Network randomization results for post-migration social identification network. 
Observed statistic represents red line. Histogram shows distribution of statistic  
based on network randomization of 5000 random graphs using the Erdős–Rényi 
random network modeling technique. ................................................................... 270 

Figure 6.16 Histogram showing the range of design categories present at sites in different  

CIRV time periods ............................................................................................... 271 

Figure 7.1 Bedrock geology map of the CIRV showing locations of archaeological sites and  

clay samples. Adapted from (adapted from Kolata 2005) ....................................... 280 

Figure 7.2 Surficial deposits of west-central Illinois. Cross-section A-A’ shows the increased 

thickness of the glacial sediments approaching Lake Michigan. Adapted from  
(Curry, et al. 2011) ................................................................................................ 282 

Figure 7.3 Statistical workflow for the analysis of compositional data ..................................... 296 

Figure 7.4 Principal components biplot showing the distinction between the two clay  
groups identified. Ellipses represent 90% confidence intervals for group  
membership. The first two principal components account for 66.5% of the  
variance in the clay data set. .................................................................................. 305 

Figure 7.5 Bivariate plot of logged (based 10) Beryllium and Lithium showing distinctions 

between the two clay groups. Ellipses represent 90% confidence intervals for  
group membership. ................................................................................................ 306 

Figure 7.6 Bivariate plot of logged (based 10) Cesium and Nickel showing further chemical 

distinctions between the two clay groups. Ellipses represent 90% confidence  
intervals for group membership. ............................................................................ 307 

xix 

Figure 7.7 Principal components biplot showing elemental enrichment for sherds recovered  
from sites north of the Spoon/Illinois River confluence in general. Ellipses show  
90% confidence intervals. Together, PC 1 and 2 account for 49.99% of variance  
in the ceramic dataset. ............................................................................................ 312 

Figure 7.8 3D scattergram of PCs 1, 2, and 3 showing core and non-core compositional  

groups.................................................................................................................... 314 

Figure 7.9 Principal components 1 and 5 biplot showing distinctions between the Core  

group, Outgroup 1, and Outgroup 2. Ellipses demarcate 90% confidence  
intervals. ................................................................................................................ 315 

Figure 7.10 Bivariate plot of log base 10 magnesium and ytterbium concentrations of  

Outgroup 1 and 2 and Core sherds with 90% confidence ellipse boundaries ......... 318 

Figure 7.11 Principal components 1 and 2 biplot showing distinctions between the Core  
group, and core provisional groups – Core B and Core C. Ellipses demarcate  
90% confidence intervals. .................................................................................... 320 

Figure 7.12 Principal components 1 and 2 biplot showing distinctions within the Core A  

group. Ellipses demarcate 90% confidence intervals. ............................................ 323 

Figure 7.13 Bivariate plot of log base 10 magnesium and nickel concentrations of Core A1  

and Core A2 sherds with 90% confidence ellipse boundaries. ............................... 324 

Figure 7.14 Principal component 1 and 2 bivariate plot of all group, sub-group, and  

provisional group assignments with 90% confidence ellipse boundaries. .............. 326 

Figure 7.15 Principal component 1 and 2 bivariate plot of all group, sub-group, and  

provisional group assignments emphasizing component loadings with 90% 
confidence ellipse boundaries. .............................................................................. 327 

Figure 7.16 Bivariate plot of log base 10 magnesium and molybdenum concentrations of all 

group, sub-group, and provisional group assignments with 90% confidence  
ellipse boundaries. ................................................................................................ 328 

Figure 7.17 Distribution of Brainerd-Robinson coefficients for simulated (green) and  

observed (blue) compositional group membership matrices .................................. 331 

Figure 7.18 Correlation matrix heat-map of rescaled Brainerd-Robinson coefficients .............. 337 

Figure 7.19 Yifan Hu multilevel network graph layout for the Pre-Migration Time Period  

(1200-1300 A.D.; left) and Post-Migration Time Period (1300-1450 A.D.; right) . 340 

Figure 7.20 Geographic network graph layout for the Pre-Migration Time Period  

(1200-1300 A.D.) ................................................................................................. 342 

xx 

Figure 7.21 Geographic network graph layout for the Post-Migration Time Period (1300-

1450A.D.) ............................................................................................................ 342 

Figure 7.22 Yifan Hu multilevel network graph layout flattened across time  

(1200-1450 A.D.) ................................................................................................. 343 

Figure 7.23 Geographic network graph layout flattened across time (1200-1450A.D.) ............ 343 

Figure 7.24 Network randomization results for pre-migration ceramic industry economic 

network. Observed statistic represents red line. Histogram shows distribution of 
statistic based on network randomization of 5000 random graphs using the  
Erdős–Rényi random network modeling technique. .............................................. 344 

Figure 7.25 Network randomization results for post-migration ceramic industry economic 

network. Observed statistic represents red line. Histogram shows distribution of 
statistic based on network randomization of 5000 random graphs using the  
Erdős–Rényi random network modeling technique. .............................................. 345 

Figure 8.1 Pre-migration multilayer network (circa 1200 – 1300 A.D.) ................................... 364 

Figure 8.2 Post-migration multilayer network (circa 1300 - 1450 A.D.) .................................. 365 

Figure 8.3 Flattened multilayer network (circa 1200 - 1450 A.D.) ........................................... 366 

Figure 8.4 Multilevel graph layout for the pre-migration multilayer network (circa 1200 -  

1300 A.D.) ............................................................................................................. 367 

Figure 8.5 Multilevel graph layout for the post-migration multilayer network (circa 1300 -  

1450 A.D.) ............................................................................................................. 368 

Figure 8.6 Edge overlap for the pre-migration time period ...................................................... 371 

Figure 8.7 Edge overlap for the post-migration time period ..................................................... 372 

Figure 8.8 Node centrality measures for the pre-migration multilayer network ........................ 377 

Figure 8.9 Node centrality measures for the post-migration multilayer network ...................... 377 

Figure 8.10 Summary of node degree centrality and strength for the pre-migration time  

period .................................................................................................................... 379 

Figure 8.11 Summary of node degree centrality and strength for the post-migration time  

period .................................................................................................................... 379 

Figure 8.12 Site-node degree deviation for the pre-migration CIRV time period; lower  

scores indicate more even influence across layers .................................................. 381 

xxi 

Figure 8.13 Site-node degree deviation for the post-migration CIRV time period; lower  

scores indicate more even influence across layers .................................................. 381 

Figure D.1 Percent variance explained by each principal component for the sherd data set ...... 572 
 
Figure H.1 Emmons Lake radiocarbon assay probability ......................................................... 646 

Figure H.2 Kingston Lake radiocarbon assay probability ........................................................ 646 

Figure H.3 Baehr South radiocarbon assay probability ............................................................ 647 

Figure H.4 Buckeye Bend radiocarbon assay probability ......................................................... 647 

Figure H.5 Morton Village radiocarbon assay probability (1) .................................................. 648 

Figure H.6 Morton Village radiocarbon assay probability (2) .................................................. 648 

Figure H.7 Morton Village radiocarbon assay probability (3) .................................................. 649 

Figure H.8 Star Bridge radiocarbon assay probability (1) ........................................................ 649 

Figure H.9 Star Bridge radiocarbon assay probability (2) ........................................................ 650 

Figure H.10 Ten Mile Creek radiocarbon assay probability (1) ............................................... 650 

Figure H.11 Ten Mile Creek radiocarbon assay probability (2) ............................................... 651 

 

 

 

 

xxii 

CHAPTER 1 INTRODUCTION 

 
 
1.1 Brief Introduction to the Research Problem 

 

The story of human kind is, in many ways, one of social relations among groups, among 

individuals, and among things. For many thousands of years, demographic upheaval and 

migration have led to social settings in which extant social relationships are challenged, 

negotiated, or reinforced as a result of the intersection of previously separate network 

formations. This dissertation offers theoretical and methodological means to investigate social 

settings in which disparate material culture traditions coexist or intermix in time and space 

through the comparative modeling of various networks of relationships that connect individuals 

and communities. Under this model, the structure of network relationships and the structural 

positioning of actors within the network act as sensitive indicators in the potential for and 

trajectory of behavioral responses to culture contact at various scales.  

Using archaeological data from the Late Prehistoric Period in west central Illinois (circa 

1200 – 1450 A.D.), I explore how network relationships among complex and smaller-scale 

societies structured, and are restructured by, migration. The case study under consideration here 

is marked by a well-documented in-migration process of a tribal group into a chiefly 

environment, though the location of origin of the immigrants is unknown (Esarey and Conrad 

1998; Santure, et al. 1990; Steadman 1998). In this study, I draw on a body of contemporary 

social theory focused on parsing social structure across multiple types of interrelationships to 

investigate questions revolving around how both indigenous societies and migrant peoples 

approach intercultural social and economic relations. 

 

 

1 

1.2 Multicultural Social Interrelationships and Multilayer Social Network Analysis 

Explaining social interrelationships in settings characterized by coexisting material 

culture traditions has been of central and continuous concern in archaeology since its first 

articulation as a discipline (e.g. Childe 1936; Wolfe 1982); in particular, in contexts where 

differing traditions amalgamate (Frangipane 2015; Liebmann 2013; Stone 2003). Recent 

archaeological research recognizes the value of incorporating formal network analysis 

methodologies based on ‘relational’ sociology as theorized by Harrison White to address 

questions related to coexisting material culture traditions (Borck, et al. 2015; Brughmans 2013; 

Mills, Roberts Jr., et al. 2013). I employ a theoretical framework that builds on this application 

of White’s relational theory to archaeological contexts in order to address anthropologically 

significant issues related to cultural contact, social interaction, identity, and exchange. 

This study is specifically focused on examining the structuring and restructuring of social 

interrelationships following culture contact at geographic and demographic scales above the 

individual or household (i.e. at the spatially bounded community scale). Prior scholarship on 

intercultural contacts emphasizes interaction spheres, hybridization, technological transfer, or 

models of exchange as measures for constructing borders and defining societal membership, 

often based on anthropological perspectives of social identity or ethnicity (Barth 1969; Bentley 

1987; Blanton 2015; Graves 1994; Jones 1997; C. G. Sampson 1988; Shennan 1989). Identity, as 

rooted in culture or ethnicity, is a foundational variable in guiding both intra- and inter-group 

social interrelationship formation and maintenance. However, no theoretical consensus has 

emerged to the anthropological study of identity. This is particularly true in archaeological 

contexts, where taxonomic distinctions in material culture are traditionally relied upon to model 

geographic and temporal patterns related to social organization, interaction, identification, and 

2 

change. Equating patterns of material culture similarity with traditional anthropological models 

of identity presupposes the derivation of identity from an archaeological definition of a culture, 

which often leads to the projection of normative and idealist notions of culture onto past peoples 

(Shennan 1989). In this dissertation, I argue that cultural or ethnic identity and networks of social 

interrelationships recursively interplay, and that analyzing social interrelationships across 

multiple layers in separate and in aggregate provides new insights into regional scale 

understanding of social interaction and identification among people and the communities in 

which they are nested in the past and present.  

The theoretical perspective I employ in this research builds on the integration of 

anthropological archaeology and ‘relational’ sociology as theorized Harrison White (Mills, 

Roberts Jr., et al. 2013; Peeples 2011). In opposition to considering network analysis as a de-

contextualized structuralist research strategy, White argues that social networks should be 

studied in conjunction with cultural systems (Fuhse 2015; Mische 2011; White 1992). That is, 

social networks are imprinted with culture and therefore serve as a habitat of cultural forms. 

Therefore, the traditional archaeological hermeneutic to the study of culture is eschewed in favor 

of a perspective that seeks to model cultural forms through their linkages within a network. 

Network relationships reflect and build on cultural models such as kinship, gender, heterarchy, 

and hierarchy. White views interactions and categories used to construct networks as being 

driven through the inherent uncertainty in the roles of participants (White 2008a). From this 

uncertainty, White sees identities as a means to ‘gain footing’ in, or to ‘control’, social contexts 

(White 1992). These control attempts are posited to leave a trace in social space as ‘stories’, or 

information defining and relating identities to each other. White’s ‘New York School’ of 

relational sociology (Mische 2011) posits that processes of collective social identification, that 

3 

form the empirical basis of ‘stories’, take place in either relational identification or categorical 

identification.  

Relational identification is a process whereby individuals identify with larger collectives 

through networks of interpersonal interaction (Peeples 2011), whereas categorical identification 

refers to a process whereby individuals identify with collectives based on formal social units 

such as ethnic groups or genders that are defined outside of the relations among members 

(Peeples 2011). Networks consist of the traces of meaning from previous interactions based on 

categorical or relational identification, which become encapsulated in stories that relate identities 

to one another. As individuals jointly reproduce relational or categorical identities through their 

mutually patterned actions, they acquire a style (White 1993). And “styles must mate to change” 

(White 1993:163). That is, novelty in stories or identities develops only from the “creative 

combination of cultural forms at the intersection of previously separate network formations” 

(Fuhse 2015:19). White’s relational perspective on culture is geared toward empirical 

applicability wherein social networks act as informal patterns of order that emerge from stories 

that are built in response to the uncertainty of identities and attempts to control interactions, 

governed by neo-institutional rules, and jointly reproduced as styles (Fuhse 2015). Because 

White’s styles are inherently the product of singular institutional frameworks, however, I argue 

here that investigating culture as networks is enhanced when multiple networks constituting 

phenomenological realities in distinct cultural spheres are explored simultaneously in separate 

and in aggregate. Only then may style and story, when mated, be parsed to uncover the 

constituent components of cultural change. This dissertation is a formal empirical application 

and expansion of White’s theoretical conception of whether or not, and if so how, novel 

4 

interactive frameworks may form because of the intersection of previously separate network 

formations.  

From trends inherent in multiple networks of relational identification and categorical 

identification, expectations are offered that seek to characterize communal behavioral strategies 

in the negotiation of a multicultural social and economic environment following cultural contact. 

These characterizations are referred to as behavioral explanations of patterns of intercultural 

communal coexistence. Through analysis of multiple layers of social interaction and social 

identification, it is possible to examine and to explain how communities constructed social, 

economic, and other relational networks before an in-migration and capture communally based 

responses to multicultural society after cultural contact. 

 

1.3 The Case Study 

 

The focus of this dissertation is the latter portion of the Late Prehistoric Period (circa 

A.D. 1200 – 1450) of the central Illinois River valley (CIRV) in the North American Midwest. 

This region spans an approximately 80-mile expanse, as the crow flies, of the Illinois River from 

Pekin, IL southerly to Meredosia, IL. Publicized reports in newspapers, magazines, and 

professional journals in the late 19th and early 20th centuries led to the first archaeological field 

schools in North American being established by Dr. Fay-Cooper Cole of the University of 

Chicago in 1930-1932 in the Dickson Mounds vicinity near the confluence of the Illinois and 

Spoon Rivers. The cultural sequence resulting from these investigations is still, by and large, in 

use today (Cole and Deuel 1937; Harn 1978). Progressive, though at times sporadic, research 

investigations continued in the region throughout the 20th and 21st centuries (Bardolph 2014; 

Conrad 1989, 1991; Esarey and Conrad 1981, 1998; Harn 1978:235-237; Hatch 2015, 2017; G. 

5 

R. Milner, et al. 1991; Steadman 1998, 2001, 2008; Strezewski 2003; Vanderwarker and Wilson 

2016; Vanderwarker, et al. 2013; G. D. Wilson, et al. 2018; J. J. Wilson 2010). Aside from a few 

notable exceptions, research efforts in the CIRV rarely endeavor toward regional scale issues 

(Conrad 1991; Harn 1978; J. J. Wilson 2010). Nevertheless, the availability of material culture, 

and in particular ceramic artifacts, from sites across the geographic and temporal expanse of the 

Late Prehistoric period lends to the regional scale focus of this dissertation.  

 

Of central concern to the period under consideration in this study is an expansionary 

process of a distinct Upper Mississippian cultural group, the Oneota, who began pushing out of 

the western Upper Midwest and into surrounding environs beginning in the 13th and early 14th 

centuries A.D. (Brown and Sasso 2001; Hollinger 2005; Overstreet 1997). Some characterize the 

spread of the Oneota cultural tradition throughout the US Midwest and eastern Prairie Plains as 

an aggressive, rapid territorial expansion (Hollinger 2005). The Oneota expansion coincided with 

a decline in Middle Mississippian influences across the Upper Midwest region and with the onset 

of the droughty Pacific climatic episode (Gibbon 1995). While many Late Woodland populations 

in the riverine Midwest and western Great Lakes were replaced by or integrated into Oneota 

peoples during this expansion, societies in the ecologically rich CIRV, or northern Middle 

Mississippian frontier, maintained their positions in fortified temple mound centers, and outlying 

sites, and entered into a period of regional cohabitation with an intrusive Oneota population 

(Esarey and Conrad 1998). Recent archaeological inquiry in the Late Prehistoric CIRV has 

focused on the unprecedented levels of violence seen in burial and cemetery contexts both prior 

to and following the Oneota in-migration (Hatch 2015; Steadman 2008; Vanderwarker and 

Wilson 2016; G. D. Wilson 2012). Although the CIRV is remarkable for its levels of sustained 

violence, evidence indicating the communal cohabitation of these distinct but interrelated 

6 

cultural groups is apparent (Esarey and Conrad 1998). Coexisting Oneota and Mississippian 

material culture at multiple sites at the household level provides the opportunity to examine the 

various social interrelationships that were present. Instead of focusing on traditional typological 

cultural classifications, hybridity, or technological transfer, my research examines the ways in 

which models of network interrelationships between CIRV communities change concomitant 

with Oneota in-migration. In this study, I argue that multicultural society following migration or 

population movement can be fruitfully explored by dissecting networks of culture across distinct 

layers. In particular, I explore networks of categorical social identification, networks of 

economic interaction, and relational networks of cultural transmission each as evidenced in 

ceramic industry. Across these multiple network layers, community-scale interrelationships are 

modeled in separate and in aggregate to assess how immigrant and indigene behavior exposes 

approaches to intercultural social and economic relations in a Late Prehistoric period central 

Illinois River valley case study.  

 

1.4 Dissertation Organization 

Chapter 2 (“Multilayer Social Networks and Intercultural Communal Coexistence”) of 

this dissertation provides a necessary historical background to anthropological and 

archaeological perspectives on social identification and social interaction before developing and 

adapting a model rooted in a contemporary body of theory on processual social structure in 

complex systems to the study of cultural contact. This model forms the overall basis of the 

theoretical framework underlying this study.  

Chapter 3 (“Regional and Cultural Background”) introduces the Late Prehistoric central 

Illinois River valley (or CIRV) as well as the Middle Mississippian and Oneota cultural 

7 

traditions through the lens of the settlements whose interrelationships form the focus of interest 

in this dissertation.  

 

Chapter 4 (“Methodological Consideration”) presents finer grain detail on many of the 

methodologies employed in this dissertation for data collection and data analysis. While the four 

chapters that follow each address these areas, a fuller and richer discussion is provided in 

Chapter 4 in cases that would otherwise detract from the linear arguments made therein.  

 

Chapter 5 (“Networks of Interaction through Cultural Transmission”) develops and 

applies a model rooted in cultural transmission theory to identify technological artifact attributes 

constrained by social, as opposed to engineering, forces. These socially-mediated artifact 

attributes are used to model networks of relational identification through social interaction. This 

method results in a proportional scale of ceramic technological similarity that represents a proxy 

measure to model and analyze the strength and directionality of relational connections among 

communities across the study area through time.  

 

Chapter 6 (“Ceramic Design and Networks of Social Identification”) presents network 

models of social identification constructed based on patterns of proportional similarity in designs 

incised or trailed on the interior outflaring rims of ceramic plates.  

 

Chapter 7 (“Networks of Economic Relationships – Results of the Chemical Analyses”) 

presents the results of laser ablation inductively coupled plasma mass spectrometry (LA-ICP-

MS) analysis of clay samples and Mississippian and Oneota pottery. The resulting chemical 

compositional groups form the basis of models of economic interaction related to ceramic 

industry.  

 

Chapter 8 (“Toward Explaining Social Interrelationships through a Ceramic Industry 

Multilayer Network”) draws together each of the unique relational perspectives on ceramic 

8 

industry discussed in Chapters 5 - 7 into synthetic multilayer networks. Through analysis of the 

different layers in the multilayer networks, it is possible to access the influence and overlap of 

each individual network in structuring and being restructured by migration-induced culture 

contact in a Late Prehistoric west-central Illinois case study region. From these trends, patterns 

of intercultural communal coexistence are revealed. Finally, contributions of the study and future 

directions are offered.  

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

9 

CHAPTER 2 MULTILAYER SOCIAL NETWORKS AND INTERCULTURAL 

COMMUNAL COEXISTENCE  

 
 
2.1 Introduction 

Although parsimony is often stated to be desirable when constructing scientific theories, 
theoretical economy is self-defeating if it ignores the diversity and complexity of what is 
being explained (Trigger 2006, p. 498) 
 

This chapter provides a detailed overview of the theoretical framework underlying this 

 

study. The discussion is divided into three broad sections. To provide a necessary background, 

initially discussed are traditional anthropological perspectives, and their evolution, on two key 

components of culture contact in non-state societies: social interaction and social identification. 

Focus is placed on models that endeavor to explain social interrelationships and social structure 

in settings characterized by the presence of multiple, distinct social groups or where culture 

contact has otherwise occurred. I then discuss key concepts and terms derived from a 

contemporary body of theory on processual social structure in complex systems. This body of 

theory is then adapted into a model of intercultural communal coexistence, which is argued to 

offer new insights into the study of culture contact based on enhanced understanding of the 

transmutability and multi-dimensionality of social structure both preceding and postdating a 

migration process in a Late Prehistoric period central Illinois River valley case study and 

beyond. Finally, I discuss the methods and techniques used to link this body of theory with the 

archaeological data considered in this dissertation.  

 

2.2 Evolving Perspectives on Social Interaction and Identity Formation 

Archaeologists have long placed an analytical focus on identifying cultural or social 

groups, exploring group organization, and understanding how these groups interact and change 

10 

over time in prehistory. Over the last century, the theoretical perspectives and methodological 

tools to accomplish these goals have changed in dramatic fashion. Nascent archaeological studies 

of the late nineteenth and early twentieth centuries rooted their knowledge and inquiry of 

prehistoric human society in identifying archaeological cultures. Distributions of shared material 

culture were used to define discrete territories of peoples with an oft stated or unstated objective 

being the creation of an historical and pre-historical lineage tracing contemporary national or 

ethnic populations to antecedents in the distant past (Jones 1997:1-14; Peeples 2011:8-10; 

Shennan 1989). In connecting prehistory to history, the archaeological record could be linked 

with a present ethnic variant (Kossinna 1911). Culture, language, and ethnicity were therefore 

thought to be directly linkable to the past, and the archaeological record became a tool with 

which to detect the history of a politically expressed ethnic identity (i.e. the nation state) (Trigger 

2006). These efforts often resulted in furthering nationalistic political agendas or in 

delegitimizing various contemporary peoples by denying them a prehistoric past or ethnic 

identity. Thus, identity and in particular ethnicity, was a critical analytical component of early 

archaeological inquiry. While the focus of this dissertation is not ethnicity or identity per se, the 

role of ethnic identity in shaping archaeological and anthropological thought necessitates a brief 

historical overview of the use of these concepts as they relate to culture contact, migration, and 

social structure.   

The culture-historical paradigm of early archaeologists such as V. Gordon Childe is an 

out-growth of analytical focus on archaeological cultures based on patterned variation of idealist-

types in material culture (Shennan 1989). The idealist tendencies of culture-historians meant that 

they favored uniformity as opposed to variation in studying material culture, and as a result, 

many of the cultural groups they defined are not representative of the full gamut of the material 

11 

expressions of individuals and groups within those cultures. These monolithic cultural entities 

are based on normative and idealist conceptions of culture (Jones 1997). That is, as opposed to 

being discovered through a combination of deductive and inductive methods, archaeologists 

were responsible for constructing a type, rooted in ancient Greek artistic notions of the ideal, and 

therefore a cultural social entity. Cultures were thought of as homogenous entities whose 

histories unfolded in a coherent, linear narrative towards increasing complexity and resulting in 

the nations and ethnic groups that dominated European academic and political discourse (Jones 

1997). Further, cultures remained relatively static until diffusion or migration events catalyzed 

rapid change. 

Following the instability of World War I, Childe was instrumental in sparking a trend to 

divest archaeology of its role in furthering nationalistic agendas and expanding upon the 

definition of archaeological cultures. Childe placed an emphasis on people as the producers of 

material culture and society as the object of focus in archaeological investigations based on a 

concern with systematically describing distinctions and interactions among cultures based on 

functional traits (Childe 1936; Veit 1989). Childe further placed emphasis on diffusion as a 

means for the spread of techno-functional enhancement or stylistic innovation in contrast to 

migration as a means for cultural replacement or mixing (Trigger 2006). This shift in emphasis 

toward diffusion and migration made cultural continuities of ethnic identity tenuous at best, gave 

archaeologists a working tool – the archaeological culture, and a sense of theoretical purpose – 

the posing of particularistic, historical questions.  

In Eastern North America, two taxonomic system influenced by European culture-

historian archaeologists emerged and continue to form the foundation on which modern Eastern 

North American archaeology is built: the Midwestern and the Willey and Phillips Taxonomic 

12 

Systems. While archaeologists in the United States were not utilizing the archaeological record 

to promote a nationalistic agenda, by and large, the methods used for this purpose in Europe 

were borrowed and adapted to aid in describing the vastness of the American archaeological 

record. Chiefly among these tools was that of the analysis of style. Variation in artifact style 

provided culture-historical archaeologists the ability to assign groups of artifacts into distinct 

cultural units. In addition, style enabled these cultural units to be contextualized both spatially, 

and more importantly at the time, chronologically. While these new cultural units were 

constructed using European assumptions about ethnic identity, Eastern North American 

archaeologists had, for the first time, broad generalizations about the distinct peoples that 

initially populated the area that were able to apply form to both space and time.   

Preoccupation with the creation of typologies of artifacts and the development of cultural 

chronologies, however, led American archaeologists to relegate to mere speculation the 

“reconstruction of prehistoric patterns of life” (Trigger 2006:288), any attempts to understand 

cultural change beyond migration and diffusion, and the linking of ethnology and modern North 

American Indians with archaeology. The grouping of archaeological data based on idealist types 

enables the efficient assignation of spatial and temporal units. Though in lacking any functional 

correlate to these categorizations, it meant that culture-historical archaeologists were often 

unable or unwilling to extend their analyses beyond that of taxonomy. To align itself with a 

scientific endeavor, the Midwestern and Willey and Phillips Taxonomic systems allowed 

artifacts to be divorced from the people who were responsible for their creation. While this 

fundamentally delimited the scope of American archaeology at the time, it did allow for the 

production of numerous regional chronologies of spatially bounded cultural entities that are 

largely still in use today, including in this study.  

13 

The development of the New Archaeology in the 1960s heralded a shift in attention away 

from defining idealist and normative archaeological cultures to identifications of cultures as 

expressed by individuals and groups themselves. Clarke (1968), for example, argued for a 

polythetic definition of culture. Further, Binford (1962) argued that cultural variation results 

from a multitude of factors, not just culture or ethnicity, and that archaeological data must 

therefore be subjected to a process of analysis – the foundational assumption of processualism. 

However, both culture-historians and processual archaeologists “regarded the results of their 

process of definition as entities representing the cultural traditions of human groups. Both 

adopted classificatory expedients to remove the untidiness in the cross-cutting distributions 

rather than taking the more radical step of recognizing that this untidiness is, in fact, the essence 

of the situation” (Shennan 1989:13). The shift of focus in archaeology by processualists towards 

systematics and general processes resulted in a de-emphasis on studies of identity and ethnicity 

as it relates to archaeological cultures. 

At the same time processualism re-focused American archaeological attention away from 

ethnic identity, anthropological perspectives on these dimensions to the study of people in the 

past changed. Ethnicity first became a studied phenomenon in its own right when it was 

dichotomized from culture in the 1950s (Bentley 1987). Debate followed as to the nature of 

ethnicity based on two camps: primordialists and instrumentalists. Primordialists viewed 

ethnicity as a means to seek refuge from disorienting change in those aspects of individual’s 

lives that most fundamentally define who they are based on a deep psychological and emotional 

sense of shared heritage that varies little through time (Geertz 1963; Jones 1997; Peeples 

2011:10). Social groups were therefore based on relatively static concepts of discrete and well-

bounded collective identities (Wolf 1982). Distinct ethnic identities and the boundaries that 

14 

separate them exist because of structural oppositions between groups. As a result, primordialists 

espoused that assimilation or other forms of social integration can only occur when structural 

oppositions between ethnic groups are removed (Keyes 1979). On the other hand, 

instrumentalists view ethnicity as a mechanism in pursuit of shared objective interests, primarily 

economic and political. Instrumentalists such as Barth (1969), Moerman (1965), and others 

consider ethnicity as processes, or instruments, of social categorization and interaction wherein 

members create we/they distinctions that guide inter- and intra-group interaction in situational 

contexts. These relational processes of inclusion and exclusion form identity, according to 

instrumentalists. Dynamic and fluid social organizations result wherein membership is constantly 

being negotiated and reified (Barth 1969; Stone 2003). More recent research on ethnic identity 

grapples with these two extremes: ethnic identity as being simultaneously situational and the 

product of a shared heritage (Geary 1983; Jenkins 2000, 2004; Snead and Preucel 1999; Stone 

2003; D. Upton 1996).  

Many researchers studying identity and ethnicity and their relationship to material culture 

have found Bourdieu’s practice theory and the concept of habitus to be theoretically productive 

constructs that bridge the key insights of both instrumentalists and primordialists (Bentley 1987; 

Bourdieu 1977, 1990; Conkey 1990; Lightfoot, et al. 1998; Shennan 1989), especially in multi-

ethnic or culture contact contexts (Lightfoot and Martinez 1995; D. Upton 1996). In particular, 

Bourdieu’s theory of practice is argued by Bentley (1987) to bridge the situational nature of 

identity favored by instrumentalists with the enduring shared heritage of identity favored by 

primordialists. Practice theory contends that individual habitus act to guide the fluid and 

contextual nature of cultural identity wherein cultural differences are objectified vis-á-vis others 

in the context of social interaction (Jones 1997). Individuals “enact and construct their 

15 

underlying organizational principles, worldviews, and social identities in the ordering of 

everyday life” or habitual routines (Lightfoot, et al. 1998:199). However, Bourdieu’s concept of 

habitus emphasizes cultural content within a given ethnic group as opposed to interaction 

between groups. Behavioral change is rare, in that it only occurs through encountering and 

interacting with different habitus (Bentley 1987; Stone 2003). Thus, there is a contrast between 

the primordialist camp, which sees ethnicity as a conscious construct, and the use of the concept 

of habitus necessitating ethnicity to be an unconscious construct. 

Stone (2003) details theoretical advances drawn from practice theory and posits two 

competing schools of thought guiding studies of ethnicity in the late twentieth century: 

interactionist and enculturationist approaches. Proponents of the interactionist approach view 

ethnicity and group spatial boundedness as resulting from social interaction between socially 

distinct groups (Braun and Plog 1982; Emberling 1997). As the moniker implies, the general 

impetus of the interactionist approach is that groups can be most readily distinguished based on 

the differences between them vis-à-vis their interactions. For example, distributions of 

stylistically distinct artifacts between sites, within site zones, or individual households may be 

used to infer exchange relationships or boundaries between distinct social groups at various 

scales (Bardolph 2014; Cook 2007; Cook and Fargher 2007; Friberg 2018; Rowe 2016; 

Schneider 2015; Wallis, et al. 2010; Wallis, et al. 2016; Zvelebil 2006). Style is seen as an active 

means of non-verbally communicating social differences and as a marker of social boundaries 

(Hegmon, et al. 1997; C. G. Sampson 1988; Wiessner 1983, 1990; Wobst 1977). On the other 

hand, the enculturationist approach focuses on ethnic identity as a set of shared norms of habitual 

practice (Bourdieu’s habitus) resulting from processes of enculturation (Dietler and Herbich 

1998; Jones 1997; Shennan 1989; Stark, et al. 1998). Thus, shared processes of enculturation or 

16 

social learning are sought to define spatial boundedness to groups in archaeological contexts. 

Through the theoretical guidance of habitus, these processes are thought to be unconscious and 

therefore suggest common enculturative backgrounds, where divergent learning frameworks or 

contexts imply distinct ancestry or habitual routine and therefore infer social boundedness 

(Lightfoot and Martinez 1995; Lightfoot, et al. 1998; VanPool 2008).  

Although enculturationist and interactionist approaches have provided valuable insights 

to understanding social identity, both often struggle to offer nuanced perspectives in broad 

regional contexts where multiple traditions merge, blend, or otherwise amalgamate such as the 

case study region that is the focus this study. That is, enculturation approaches generally require 

a social context where multiple groups are sufficiently distinct to identify different enculturative 

backgrounds, while interactionist approaches focus on modelling the boundaries between ethnic 

or other groups (Stone 2003).  

Multiple alternative perspectives, divorced from ethnic identity, have emerged to explain 

the process of “creation through recombination” or the “combination or convergence of two or 

more existing forms to create something different” in archaeological contexts (Liebmann 

2013:27). Terms such as acculturation, syncretism, bricolage, creolization, mestizaje, and 

hybridity each carry unique definitions and characteristics to describe and explain social 

processes of cultural amalgamation. However, each term also carries the baggage of those 

definitions and respective case study applications. For example, acculturation, which parallels 

enculturationist perspectives on ethnicity, seeks to measure transitions from one cultural pattern 

to another and therefore seeks assess the progress of assimilation. Acculturation has been 

criticized for issues of uni-directionality and lack of agency. Acculturation also acts to ‘other’ 

subaltern, often non-Western groups by casting them as passive, subordinate receptors of cultural 

17 

forms supplied by more complex, colonial, or hegemonic societies who remain unchanged 

during the process of amalgamation (Liebmann 2013). The more recent term hybridity carries 

less baggage and stresses ambivalence, resistance, and agency. Hybridity emphasizes disjuncture 

and the forcing together of unlike things. Yet, like the study of social identity through ethnicity, 

hybridity and other concepts to explain social identity in multicultural archaeological contexts 

continue to represent cultures as bounded wholes, marked by a preexisting purity in social 

formations that are combined at some later time. Indeed, in archaeological contexts, the study of 

social identity and interaction as interpreted via material culture through theoretical lenses such 

as hybridity and cultural contact are fundamentally issues of taxonomy, where the underlying 

question of analysis is really at what spatial and social scales may groups be defined (Burmeister 

2000; Liebmann 2013:32; Parkinson 2006; Renfrew 1994; Rice 1998; Trubowitz 1992).  

Traditional studies of social identity therefore rely heavily on traditional perspectives on 

ethnicity, and in archaeological contexts continue to rely heavily on taxonomic correlates to the 

nature of spatial and temporal social group boundedness. Given this pervasive focus on the 

process of social or ethnic group identification, these models may not be appropriate for 

addressing questions related to behavioral relationships at broad regional and temporal scales 

that are not necessarily driven by ethnic or cultural amalgamation. However, because North 

American archaeology’s general foundations are built upon these concepts, it is difficult if not 

impossible to fully separate out current archaeological inquiry from them. Nevertheless, the 

discussion below builds on a model from an alternative perspective on social identity that is 

explicitly focused on society as a dynamic multilayered system of relational interaction and 

categorical identification. 

 

18 

2.3 Social Systems as Multilayered, Relational Networks 

Contemporary and historical social relationships have been studied by social scientists 

through quite different theoretical lenses than the anthropological perspectives on identity and 

ethnicity discussed above. While anthropological perspectives have been influential to these 

studies, very different kinds of research questions generally prompt a very different approach. 

For example, while some anthropological archaeologists may have been more concerned with 

identifying a culturally metaphorical ‘index fossil’ to denote group or population boundaries (e.g. 

Goodby 1998; Graves 1994; C. M. Milner and Stark 1999; C. G. Sampson 1988; Stark, et al. 

1998), social scientists studying social identity and social change in modern contexts have often 

been more concerned with identifying a few generalized, essential features that govern social 

reality (Azarian 2005:33-34; Mische 2011; Tilly 2001a, 2004; White 2008a). Like many 

archaeologists, however, sociologists and other social scientists working under this paradigm 

argue that these conceptual models that govern social reality should be mined empirically as 

opposed to being rooted in theoretical abstraction. Derived out of this empirical rigor was a focus 

on social networks.  

Under the relational paradigm, social ties and the networks they form among actors are 

argued to constitute the fundamental conditions of human social existence. Networks are viewed 

as process based on the continual making and un-making of ties. Society as stratification is cast 

aside as well as the notion of static social structures or static actor identities (White 1992, 

2008a). Social identification is therefore understood within this framework as operating in terms 

of two related processes known as relational identification and categorical identification. Ties 

that form relationships through social identification are therefore multiplex, or constituted by 

different sorts of connections, and individuals must contend with inherent uncertainty in 

19 

information flows through connections that may converge or diverge. Viewing social actors as 

dynamic as opposed to static and social identification along multiple processual dimensions 

necessitates an approach to the study of the culture contact that can capture a complex, realistic 

social framework. Relational and categorical identification, as complex analytical dimensions, 

have been recently argued to be critical conduits through which collective action and social 

transformation may be viewed, understood, and predicted in archaeological contexts (Borck, et 

al. 2015; Mills, Clark, et al. 2013; Mills, Roberts Jr., et al. 2013; Peeples 2018). I employ a 

theoretical framework that builds on this application of relational sociological theory to 

archaeological contexts in order to address anthropologically significant issues. To this end, a 

multilayer network approach is drawn upon to underlie the study of culture contact that is the 

focus of this dissertation.  

In this section, I present a discussion of concepts drawn from social science that ground 

the analyses that follow within a theoretical corpus. A model is presented that captures society as 

multiple relational networks to understand the structuring and restructuring of economic, 

cultural, and identity politic interactions following migration and culture contact. 

 

2.3.1  Theory in Networks  
 

Much of the theoretical component of the application of relational methodologies in 

archaeology is drawn from the works of Harrison C. White, as well as and Charles Tilly and 

students of theirs such as Mark Granovetter and Barry Wellman. Harrison White is a theoretical 

physicist turned sociologist turned anthropologist turned structural sociologist (Azarian 2005; 

Santoro 2008). I argue that it is the melding of these unique and seemingly chaotic backgrounds 

that resulted in the primary lasting impact of White on the social sciences more broadly. Namely, 

20 

the study of the social world as networks of relationships that interplay with cultural forms. The 

root ideas related to this approach were initially presented in the unpublished release of ‘Notes 

on the Constituents of Social Structure’ in 1966 and influenced a generation of social scientists 

to expand upon White’s idea to bring together notions of the network (or net) and categories (or 

cat) into a new concept, the catnet (Santoro 2008; White 1992, 2008a, 2008b, 2008c). Quite 

different from rigid social structures, catnets consider any set of individuals comprising both a 

category (cat) and a network (net). Sociologists at the time saw this as an opportunity to 

fundamentally re-think approaches to individuals and their relationship to society and societal 

structures. Problematically for anthropologists at the time, White and his protégé’s soon left 

behind the concept of culture to focus instead on the methodological nature of network analysis, 

or the mathematical analysis of social structure. Beginning in the 1990s, however, White and 

many of his students endeavored to reintroduce the role of culture into the study of networks 

(Mische 2011). The following discussion traces social network analysis as a theoretical paradigm 

through descriptions of key concepts before exploring the intertwining of social networks and 

culture.  

Social network analysis (SNA) provides a body of theory and techniques for visualizing 

and measuring relationships among social entities (Brughmans 2010; Knappett 2013). SNA “is a 

comprehensive paradigmatic way of taking social structure seriously by studying directly how 

patterns of ties allocate resources in a social system” (Wellman 1988:20). As a theoretical 

paradigm, four concepts are integral to social network analysis, and generally agreed upon by 

network analysts: 

1.  Actors and their behaviors are interdependent rather than independent, functionally 

autonomous units; 

21 

2.  Social ties, or social or relational transactions (Tilly 2002), between transmutable social 

actors or social entities are channels for the transfer of resources of various kinds; 

3.  Social structures are conceptualized as durable, lasting patterns of relations among actors; 

and 

4.  The structural position of a node has important perceptual, attitudinal, and behavioral 

implications and has significant enabling, as well as constraining, bearings on its social 

action. (Azarian 2005:35; Berkowitz 1982; Emirbayer and Goodwin 1994; Knoke and 

Kuklinski 1982; Scott 2000; Wasserman and Faust 1994; Wasserman and Galaskiewicz 

1994; Wellman 1983).  

 

The basal units of network analysis are actors, ties, and the networks they form together. 

Actors are social units. Actors may be individual human beings, informal groups, formal 

organizations, or palimpsests of individuals, groups, and scalar organizations among them. 

Actors are defined as discrete analytical units by the researcher. Actors are often referred to as 

nodes or vertices in the terminology of SNA, depending upon whether the researcher is inclined 

more toward the social or physical sciences respectively. In archaeology, actors are typically 

defined as either households or spatially discrete communities or settlements.  

Ties are formed through processes of social interaction among at least two actors. A 

succinct definition of a tie is as a quantification of a relationship (Östborn and Gerding 2014). 

However, ties are a theoretical construct with significant theoretical depth (White 1992). They 

are also defined by the analyst, but instead of scale being a primary concern as with actors, ties 

must be defined as an abstraction to wade through the total, erratic confrontations of a dyad of 

actors in all their contexts (White 1992). Ties are thus ambiguous until defined, with its basic 

parameters including timing, intensity, symmetry, and topic (Azarian 2005). Through their 

22 

ambiguous nature, ties may be applied to any relational or categorical experience and be able to 

account for diachronic changes therein. For example, ties may include familial or friendship 

relationships, exchange relationships such as gifts or physical coercion, economic transactions, 

romantic interactions, teaching-learning interactions, mentorship interactions, and so on (Nexon 

2009). Ties may represent cooperation or love as well as competition, conflict, or outright 

hostility (White and Lorrain 1971). Ties may be direct, or the result of face-to-face relations, 

such as the co-presence of individuals at conference sessions or tribal council meetings, or 

individuals engaged in a fist-fight. They may also be indirect through a third party or a physical 

communicative or non-communicative medium such as the adoption of common ideologies or 

methodologies through interaction with text, the exchange of information through a khipu record 

or a cuneiform tablet, or through the emulation of projectile points, pottery, or other artifacts. No 

physical presence of interaction is therefore required to define a tie. The ties of most concern to 

archaeologists are those with cultural implications that may be significant at multiple scalar 

levels (Mills, et al. 2015).  

Ties are also referred to as relationships, links, or edges again reflecting the inclinations 

of the researcher from social science toward more physical science orientations respectively. 

Interactions defined as ties can be ‘weighted’, for example the number of times two authors 

shared co-authorship roles on research papers. Other interactions can be ‘unweighted’, or binary, 

such as the presence or absence of a researcher at a conference symposium. Ties may be 

directed, originating with a source actor and reaching a target actor, where the relationships is 

not necessarily mutual such as advice seeking, learning, or antagonism (Knoke and Kuklinski 

1982). On the other hand, ties may be undirected and therefore do not distinguish between 

23 

senders and receivers. Undirected ties can be constructed based on marriage, alliance, or kinship 

relationships, for example.  

Ties may be ephemeral and persist only for a brief moment, such as a chance encounter 

during a sporting match or ritualistic gathering. Other ties, however, may be of sufficient depth 

or of sufficient repetition such that they become durable. As ties blend into the routine, it is 

argued that they tend to acquire understandings, practices, commitments, and cultural standings 

that are at least partially autonomous from the initial motivations and interests that led to their 

production in the first place (Nexon 2004). For example, religious or political movements cannot 

outlive the death of their founder(s) unless a transformation to routine, durable ties takes place 

among followers. In this way, a lasting network is formed.  

Networks are spatio-temporal patterns of durable ties and are a ubiquitous feature of 

social life. When ties become routine and therefore become durable, the presence or absence of 

specific actors may no longer be essential to the maintenance of the network. Social structure is 

therefore observed through the identification and mapping of the form and content of social 

networks (Nexon 2004:27). For many years after White sparked a relational revolution with 

‘Notes on the Constituents of Social Structure’, many social scientists were dismayed by network 

analyst’s focus on the methodological and mathematical formulations of networks and network 

structure. Within network analysis itself, the primary focus of analysis shifted from that of the 

individual actor and their cultural milieu to that of the entirety of network structure, prompting 

the need for new mathematical models to aid in interpretation. Cultural theorists saw network 

analysis, as a result, as positivistic and reductionist, decomposing cultural richness to 1s, 0s, and 

graph objects (Mische 2011). A paradigm shift in sociology, however, heralded change. The 

increasing popularity of cultural sociology, and the maturing of the sub-field of SNA 

24 

practitioners, during the 1990s led to a convergence of scholars studying networks, culture, and 

historical analysis. A primary figure involved in this exchange of information was again Harrison 

White.  

“In short, the New York area in the 1990s and 2000s was a rich hub of conversation that 

contributed to a reformulation of the link between networks, culture and social interaction” 

(Mische 2011:8). Out of this reformulation emerged four key tenets that returned social network 

analysis to its roots, roots where network and culture should be studied in conjunction. These 

four tenets include: 

1.  Networks are conduits for culture; 

2.  Networks shape culture (or vice versa); 

3.  Culture itself is organized into networks of cultural forms; and 

4.  Networks are composed of cultural processes of communicative interaction (Mische 

2011). 

In opposition to considering network analysis as a de-contextualized structuralist research 

strategy, White argues that social networks should be studied in conjunction with cultural 

systems (Fuhse 2015; White 1992). That is, culture and network structure are argued to interplay 

in a recursive manner as opposed to being abstractions of each other. Social networks are 

imprinted with culture and therefore serve as a habitat of cultural forms. Network relationships 

build on cultural models such as kinship, gender, heterarchy, and hierarchy. However, White 

views interactions as being driven through the inherent uncertainty in the roles of participants, 

harkening back to the classical structural-functionalism tradition in sociology of Parsons, 

Luhmann, and others. From the inherent uncertainty in the roles of participants, White sees 

identities as a means to ‘gain footing’ in, or to ‘control’, social contexts (White 1992). Control 

25 

“boils down to handling one’s relationships, with the primary aim of reducing uncertainties as far 

as possible” (Azarian 2005:66). In other words, control is a term used to describe tie 

management, in consideration of the fact that an actor is embedded at the intersection of multiple 

social networks that often lack clear definitions and conditions on how to conduct life. These 

control attempts are posited to leave a trace in social space as ‘stories’, or information defining 

and relating identities to each other. Stories invoke a subjective dimension based on an actor’s 

interpretations of a tie, thereby providing a rationale for expectations and claims related to a 

dyadic relationship. Stories report on the synchronic and diachronic nature of the relationship – 

friendship or enmity, attraction or repulsion, cooperation or competition, etc. From stories, ties, 

and networks social landscapes appear as a “huge and dense texture of interlocking and 

overlapping networks, without any clear-cut boundaries…ties of various kinds concatenate into 

numerous strings, which evolve into a complex and multi-layered texture of endless networks, 

intertwining and weaving together in such intricate ways that it is practically impossible to keep 

track of the individuality of any of them” (Azarian 2005:54).  

White made a point of contention, in regard to the web of interlocking social ties, 

between contemporary society and societies traditionally in the domain of anthropological 

research. He argued that intensifying interaction among the various spheres of modern society 

have resulted in social actors becoming a nodal point of inflection between many, often 

divergent social groups. Social actors take on a plurality of roles in these many social groups, 

which may have contrasting expectations and behavioral profiles. Constant switching is therefore 

required, a concept referred to as embeddedness (Granovetter 2001; White 1992). However, I 

argue that many such forces exist(ed) in anthropological contexts among bands, tribes, and 

chiefdoms. Multiple social groups with often diverging norms and behavioral profiles are no 

26 

doubt present in networks in non-state societies. Furthermore, social actors in pre-modern social 

settings are each uniquely situated within different social spheres that fundamentally constrain 

their ability to comprehend the social landscape beyond their individual spheres, despite any 

increases in overlap in their social networks relative to those in a contemporary setting. As a 

result, I argue that it would be no easier for an actor in a social context that is traditionally within 

the domain of anthropological inquiry to be able to predict or fathom the outcome of their actions 

just a few removes away than it is for individuals in contemporary society (contra White 1973). 

In this way I extend White’s concept of embeddedness, or individual social actors being 

embedded as a nodal inflection point within multiple, often contrasting networks, to the 

anthropological cultural world.  

White’s relational perspective on culture is geared toward empirical applicability wherein 

social networks act as informal patterns of order that emerge from stories built in response to the 

uncertainty of identities and attempts to control interactions (Fuhse 2015). Networks consist of 

the traces of meaning from previous interactions encapsulated in stories that relate identities to 

one another. For White, novelty in stories or identities develops from the creative combination of 

cultural forms at the intersection of previously separate network formations. That is, while they 

“mate to change”, such “change comes only through messes and fights, and emerges out of 

chaos” (White 1993:77-78). This is a product of both direct interaction and structural 

equivalence, or actors occupying similar positions in a network. That is, novelty occurs when 

previously separate network formations converge in both repeated directed action and in 

similarity in identities in a superposition of overlap and interpenetration around themes or topics.  

Because of the inherent embeddedness of individual actors in a multitude of networks, 

multiple networks are required to understand change in both micro- and macro-cultural and 

27 

network structure. Problematically, however, many SNA practitioners today continue to 

construct models that decompose networks of networks into static, one-dimensional models. For 

example, political scientists may model voting interactions among politicians or economists 

model trade interactions among countries in isolation from other interactive dimensions among 

actors. The following section thus returns to the concept of ties and how and why change in 

networks of social and cultural systems is best modeled along multi-dimensional, comparative 

continua, setting the stage for a novel approach to the study of social structure in anthropological 

archaeology.  

 

2.3.2  Multilayer Ties in Anthropological Archaeology 
 

More often than not, individual social ties span across multiple dimensions in a complex 

overlay. Many ties that are initially one-dimensional generate depth as new layers or dimensions 

are appended to them. Dimensions may belong to separate, or specialized, spheres of life. “Often 

having a greater strength, a many-stranded tie represents the extent to which the connected 

parties are bound to each other in different social arenas and with a multiplicity of interests” 

(Azarian 2005:50). The anthropologist Max Gluckman (1967) is regarded as the first to diagnose 

the presence of an all-embracing kind of connection between two actors, where multiple 

dimensions blur. In his study of Lozi society, Gluckman (1967) identified that village and 

kinship groupings overlap but have a distinctive character. That is, an individual Lozi actor is 

simultaneously embedded as a member in different types of groupings. Relationships extended to 

neighbors, blood-brothers, friends, political allies and foes, members of the royal family, and 

with fellow-tribesmen. “This multiple membership of diverse groups and in diverse relationships 

is an important source of quarrels and conflict; but it is equally the basis of internal cohesion in 

28 

any society” (Gluckman 1967: 20). Thus, while individual actors in modern contexts must 

contend with membership in groups that often are partially or wholly separate (Granovetter 

2001; White and Lorrain 1971), actors in non-state contexts more typically are embedded in 

networks that are somewhat or highly intersecting. As Gluckman (1967:19-20) pointed out in 

this regard, “Lozi social structure is uncomplicated when compared to our own; but it is 

complicated compared with, say, Andamanese or Bushman structure. Degree of complication 

therefore defines relatively the degree of congruence in the links between the positions of 

persons in various systems of ties which make up the total social system.” Yet, regardless of 

societal complexity, networks of networks constitute the fundamental conditions of social reality. 

Here, I argue that rather than concatenating multiple relational layers into a single, all-

encompassing multiplex tie, it is more theoretically economical to parse ties into individual 

network layers. Each type of tie may therefore span a distinct social network of its own. 

Understanding of the entire social system is only approachable through analysis of how the 

network layers influence and co-construct each other (Szell, et al. 2010). As a result, society may 

be characterized by the superpositioning of its constitutive network layers. Building on a recent 

formalism, I refer to this superpositioning as a multilayer social network (Kivelä, et al. 2014).  

The fundamental basis of a multilayer network approach is that it is implausible to 

consider a dyadic tie in isolation. The implication of this is that social relationships are 

embedded within a larger system made of similar ties, meaning that actions that occur in one 

relationship may affect, or be dependent upon, other relationships within the larger network 

system. In other words, the relationships between two focal nodes is not independent from the 

actor’s ties to other actors. This is more so true in anthropological contexts primarily because of 

the presence of fewer social categories and perhaps fewer hierarchical classes as a result of a 

29 

reduction in the scale of the social system in comparison to modern social systems. According to 

Breiger (1975:9), “it has for long been a basic assumption of anthropology that where relations 

are multiplex, that is where the relations between two persons derive from their activities in 

several institutional fields, the different types of relations impinge on and influence that actors in 

the various roles they play. Indeed, it is a basic assumption of those subscribing to the network 

approach that behavior cannot be explained in terms of any one single activity field.”  

Multilayer networks constitute a social network where different layers may represent 

different types of social relationships. For example, nuclear family ties, friendship ties, clan ties, 

activity party ties, and economic ties may all be modeled in different layers. In instances where 

the actors are identical across each layer, the network may be referred to as a multiplex network 

(Kivelä, et al. 2014). Whereas if actors are differentially represented across the layers, the 

network may be referred to as a node-disjoint multilayer network. In either case, the multi-

relational nature of these networks is thought to play an important role in the organization of 

large-scale networks (Szell, et al. 2010), and to illuminate political and social change in middle 

range and early state societies (Mills, Clark, et al. 2013; Munson and Macri 2009; Scholnick, et 

al. 2013).  

Multilayer network methodology begins analysis by exploring the structure of different 

network model layers as separate entities. Key insights are then able to be mined through the 

comparisons of network layers. There are three primary analytical dimensions able to be 

explored across the different layers. First, it is possible to examine the degree of overlap among 

layers. Overlap is a quantification of similarities across the layers, or how often the different 

layers are characterized by common connections among nodes. For example, in anthropological 

contexts, a family network layer and feasting network layer may overlap significantly whereas a 

30 

friendship network and antagonism network may overlap very little, presenting implications for 

understanding multilayer network structure as a whole. Second, it is possible to explore the 

structural positioning of actors within each network layer. Actors may be centrally located in 

information or interaction flows in certain layers and quite isolated in other layers. For example, 

a market-hub may be of central importance to an economic network layer but have little 

importance to a religious network layer. Finally, it is possible to investigate the influence each 

layer has on the structure of the full multilayer network. Influence, in this regard, considers how 

many actors and ties are present in a given network layer relative to other layers. Certain network 

layers may be considerably more influential than others. For example, a multilayer transportation 

network may have a highly influential road network layer in an in-land context or a multilayer 

economic network may have a highly influential cash transaction network layer in a pre-

information technology market economy.  

This study represents the first application of a multilayer network approach applied in 

anthropological archaeology. A multilayer network approach is argued to be particularly 

instructive in contexts where more than one archaeologically or anthropologically defined 

cultural group is present. In other words, a multilayer network approach may provide a deeper 

understanding of multi-cultural social contexts because of the focus on parsing social ties 

regardless of the taxonomic placement of actors (whether actors may be individuals, households, 

or communities). From a normative point of view, the blurring of cultural or other group 

boundaries invariably invokes the theoretical baggage inherent in concepts such as hybridity, 

acculturation, syncretism, or creolization, ultimately being cast as an issue that is fundamentally 

related to taxonomic distinctions (Liebmann 2013). Beginning with social relationships that span 

multiple networks and defining social actors based on their membership and roles in various 

31 

networks, on the other hand, provides a means of penetrating how individuals from the different 

groups may cross-cut or blur social boundaries. In turn, this theoretical underpinning may lead to 

greater insight into the individual and collective role of various networks in structuring 

multicultural relationships, reflecting and being reflective of cultural milieu, and providing 

deeper understanding of taxonomically defined groups themselves. That is, a multilayer social 

network approach applied in archaeological domains need not supplant or disregard taxonomic 

groups. Instead, multilayer networks and taxonomic cultural groups are argued to recursively 

interplay. In archaeological contexts, a multilayer network approach is ultimately reliant on 

taxonomic groups to facilitate communication of findings and to provide meaning to the 

scientific community and the public at large beyond the relational. Inherently, this is because 

archaeological multilayer social networks must be constructed from the same kinds of material 

culture that were used to construct taxonomic cultural entities. However, unlike taxonomic 

groups, networks can cross scales, recast boundaries as being both relational and spatial, and 

avoid social determinism (Knappett 2013).  

Because material culture remains and traces must be used to construct social networks, 

the scale at which actors can be defined in archaeological contexts is often delimited to 

individual households, spatially bounded household groups, sites, or site clusters. As a result, 

archaeologists often spend substantial amounts of time on the construction of ties and networks 

from often incomplete data, delimiting analytical scales to that of the regional or inter-regional 

(Sindbæk 2013). Out of this primary analytical scale has come a particular interest in 

understanding processes of collective action and social transformations (Gjesfjeld 2015; Mills, 

Clark, et al. 2013; Mizoguchi 2009). Tilly (1978, 1998a, 2002), in building on the catnet concept, 

posits that two analytical dimensions are particularly apt for studying the organization of 

32 

collective action and social transformations at broad geographic and demographic scales. Tilly 

recasts the ‘cat’ component of catnet as categorical identification and the ‘net’ component as 

relational identification. The next section discusses these uniquely relational analytical 

dimensions.  

 

2.3.3  Social Transformation through Relational and Categorical Identification 

 
Harrison White has made a powerful distillate of the most insipid wines in the 
sociological cellar – group taxonomies. There we find only two elements. There are 
categories of people who share some characteristic…A full-fledged category contains 
people all of whom recognize their common characteristic, and whom everyone else 
recognizes as having that characteristic. There are also networks of people who are linked 
to each other, directly or indirectly, by a specific kind of interpersonal bond (Tilly 
1978:62)  

 
 

If the networks present in a social system are nearly endless, how does one wade through 

such a morass to define specific network layers that might be sensitive features in explanations 

of group contact, continuity, or change? Here, I follow Peeples (2011, 2018) in turning to a 

theoretical perspective that builds on the work of historical sociologists and political scientists 

studying collective action and social movements among large groups of people – many of whom 

are related in academic genealogy to Harrison White (Diani 2007; Emirbayer and Goodwin 

1994; Fuhse 2012, 2015; Nexon 2004, 2009; Stokke and Tjomsland 1996; Tilly 1978, 2001a, 

2002, 2004; White 1992, 1993, 2008a, 2008c; White and Lorrain 1971). For collective social 

action, or the converging of large numbers of individuals toward a common outcome, to occur it 

must be organized. Organization refers to the extent of common identity and unifying structure 

among the individuals in a population (Tilly 1978). Through the catnet concept, organization can 

be thought of as operating primarily along two analytical dimensions: relational identification 

33 

and categorical identification. These concepts are discussed at length by Peeples (2011:17-38; 

2018:24-39) and as a result are only presented in abridged form here. 

 

Relational identification refers to a process through which individuals identify themselves 

and others with larger social groups based on their positions within networks of interpersonal 

interaction and are forged out of direct and indirect connections among people (Peeples 2018). 

Routine social ties in this regard may be formed through co-residence, co-activity in work 

parties, kinship obligations, or friendships, for example. Activities such as exchange or sport 

contests that are more limited in frequency may be less influential in forming relational ties, but 

are important because they connect distinct social settings that may otherwise be partially or 

wholly separate, forming ‘weak tie’ relationships (Granovetter 1973; Peeples 2018).  

 

Categorical identification, on the other hand, is a process through which individuals 

identify themselves and others with larger groups based on perceived similarities with socially 

defined categories or social roles to which one can belong (Peeples 2018). Categories are usually 

named social entities that are not built out of direct or indirect relations. As a result, symbols are 

used in order to facilitate recognition (Calhoun 1993). Formal categories might include political 

organizations, religious affiliation, genders, artisanship craft, clan or moiety, and the like. 

Categorical identities are not a simple extension of relational ties because they are defined 

without direct reference to the internal relations among individuals (Peeples 2018; Stokke and 

Tjomsland 1996). Categories may therefore be manipulated and used strategically by individuals. 

Competition, stress, or conflict may lead to increasing pronouncement of categorical identities at 

multiple scalar levels. Some categories may be resistant to change as a result of being rooted in 

acculturation, socialization, and learning (Jenkins 2000, 2004).  

34 

 

Through explicit consideration of the interplay between relations and categories, it is 

possible to understand how social transformations originate and spread (Mills, Clark, et al. 2013; 

Nexon 2009; Peeples 2011; Tilly 1978; White 2008a). Proponents of the relational/categorical 

identification distinction argue that social transformation only occurs through social movements 

resulting from sustained collective action, or when there is parity in the scale of relational and 

categorical identification among individuals across broad demographic and geographic scales. 

That is, the extent to which a group is characterized by both strong relational networks and a 

high degree of categorical homogeneity provides a means of assessing the potential for larger 

scale collective action, the formation of social movements, and the enacting of social 

transformation (Peeples 2011, 2018; Tilly 1978:62-69). Collective action may be rooted in an 

evolutionary perspective, where individuals overcome rational economic obstacles to 

cooperation through repeated relational interaction (Blanton 2010, 2011; Blanton and Fargher 

2009). However, social movements also depend on groups that share common identities that 

extend beyond any specific action or protest (Tilly 1978). In leading to social transformation, 

social movements “invoke new or altered social identities while at the same time reconfiguring 

the social, economic, and political relationships among people” (Peeples 2011:25). Such social 

transformations are one possible outcome following culture contact. 

The relational/categorical distinction to the analysis of social change presupposes the 

presence of multiple, often overlapping networks as being necessary to any understanding of 

social structure or socio-cultural systems more broadly. Because the end goal of any social 

transformation is to reconfigure multiple extant relationships, a multilayer network approach is a 

particularly apt at not only determining if a social transformation did or did not occur but also the 

particular relational dimensions that may have been motivating or delimiting factors. As a result, 

35 

defining individual networks as contributing toward either categorical identification or relational 

identification provides a firm theoretical grounding to the application of multilayer network 

analysis methodology.  

 

2.4 Intercultural Communal Coexistence – Linking Culture Contact, Multilayer Social 

Network Analysis, and Archaeological Evidence 

 

In archaeological contexts, material culture represents a physical manifestation of the 

stories from which social identity and relational interactions can be gleaned and network 

relationships can be modeled. Migration represents a critical social context in which to observe 

the creative refashioning of cultural forms resulting from the intersection of previously separate 

social networks. As a process, migrations are often guided by networks formed in a stepwise 

fashion through connections based in kinship, exchange, or other social ties (Mills, et al. 2016). 

This has led to the use of “network-mediated migration theory” by many anthropologists and 

sociologists as an alternative to the “rational choice and decision making models” used in other 

social science disciplines (Brettell 2000:107). A network approach replaces predetermined 

categories with explicitly defined ties that allow groups to be defined based on social 

relationships. Social networks are of paramount importance for navigating culture contact during 

communal migrations. Migrants must adapt to a new cultural and natural landscape where 

information and interaction with existing groups can ease or antagonize settlement. Interaction 

networks and identification networks are sensitive indicators of the negotiation of social and 

economic systems by indigenous and migrant peoples (Rockman 2003). Differential positions of 

influence within a network can be elucidated through this approach by analyzing the locations of 

individual, household, or community nodes with respect to each other. In this way, networks may 

reveal the nature of intercultural communal coexistence between cultural groups. Intercultural 

36 

communal coexistence, as used here, refers to the synchronous habitation of lineally 

asymmetrical groups in proximity. It is not deterministic of peaceful or tolerant relations. 

Following culture contact, individuals, communities, and households pursue various relational 

and identification strategies in multicultural environments (Lightfoot 1995). Due to 

archaeology’s focus on material culture remains, attempts to elucidate ideological strategies of 

multicultural coexistence are eschewed in favor of elucidating behavioral strategies of 

multicultural coexistence at the regional scale. That is, expectations are offered here that seek to 

characterize communal behavioral strategies in the negotiation of a multicultural social and 

economic environment following cultural contact. More specifically, a multicultural environment 

is argued here to manifest in four general forms based on the expectations in Table 2.1. These 

general forms of intercultural communal coexistence are drawn heavily from Peeples’ (2011, 

2018) reformulation of Tilly’s (Nexon 2004, 2009; 1978) insights regarding collective action and 

social transformation processes.  

Communal Coexistence Trend  Depth of Relational Interaction  Categorical Identities Similarity 
Pluralistic Coexistence 
Absent or Limited 
Accommodative Coexistence  Moderate to High 
Absent or Limited 
Integrative Coexistence 
Ethnogenesis 
Moderate to High 

Low 
Low 
Moderate to High 
Moderate to High 
Table 2.1 Matrix of expectations for intercultural communal coexistence strategies 

Expectations for communal social trends are based on whether or not social and 

 

economic relational interaction between communities occurs more often than not and whether 

categorical identities between communities are more similar than they are different. Depth of 

relational interaction is linked to the concept of relational identification. Because of the focus on 

eliciting behavioral strategies in the negotiation of a multicultural social environment, relational 

interaction captures networks of direct or indirect interpersonal interaction. Relational 

37 

identification is then inferred. Categorical identities similarity is linked to the concept of 

categorical identification and seeks to access the behavior of indexing extant social categories. 

Relational interaction and categorical identity similarities are assessed through an analysis of the 

positioning of a community node in individual network layers. That is, two communities would 

be considered to have absent or limited relational interaction if a proportional majority of proxy 

evidence for interaction suggests that communities are divergent as opposed to convergent. Low 

categorical identity similarity would be assessed if proxy evidence for the presence of social 

categories among two sites are proportionally more different than they are similar.  

 

Among large groups of individuals who engage in direct or indirect interaction 

infrequently or never and who maintain categorical distinctions, collective action or social 

movements are likely to be rare if not non-existent. Such social settings following culture contact 

would therefore be characterized by pluralistic communal coexistence. A modern correlate to a 

pluralistic social setting following culture contact would be a ghetto, migrant camp, enclave or 

the establishment of a commune. With an absence of either shared identification categories or 

routine pathways of interaction, individuals in these circumstances will tend to be focused on 

their own or their group’s interests, with little desire to engage in inter-cultural dialogue or 

categorical identities (Nexon 2009). An archaeological correlate to pluralistic coexistence is the 

Tiwanaku colonial expansion into the Middle Moquegua Valley sector of the Osmore drainage 

between the 7th and 11th centuries A.D. Tiwanaku occupations in the region were restricted to 

four large town sites, “suggesting insularity and separation from the valley’s indigenous 

inhabitants in the surrounding countryside. Like present-day diaspora communities, Tiwanaku 

colonists looked homeward and avoided transculturation with peoples of the local indigenous 

38 

tradition, and local peoples likewise did not adopt Tiwanaku cultural practices nor, it appears, 

live or intermarry with Tiwanaku settlers” (P. S. Goldstein 2015:9204).   

 

On the opposite end of the intercultural communal coexistence spectrum is ethnogenesis, 

or the refashioning of traditions between communities to form a durable group identity, which is 

marked by both engagement in relational interaction more often than not and a proportional 

similarity of categorical identities among cultural groups (Hill 2013). The cost of cooperation in 

these circumstances is low due to the strength of overlapping network ties. Any tendencies for 

sub-divisions to form within relational networks is also low as a result of the high degree of 

categorical commonality (Peeples 2011). Examples of ethnogenesis in communal coexistence 

following cultural contact include resettled farmers forming the Cahokia polity (Alt 2006; 

Pauketat 2003; Pauketat and Emerson 1999), the polyethnic community formed by immigrants 

from the South Sulawesi mainland and indigenous peoples on the island of Bonerate, Indonesia 

(Broch 1987), and in aggregated communities during the Linden and Pinedale phases (1200 – 

1325 A.D.) of the Silver Creek Area among the Western Pueblos (Mills 1999; Stone 2003).  

 

Intercultural settings characterized by sparse social ties but strong similarities in 

categorical identities following culture contact are referred to here as instances of integrative 

communal coexistence. While common categorical identities may lead to rapid, intercultural 

joint-action, a lack of clearly defined pathways for relational ties beyond normal daily social and 

economic routines result in challenges to sustaining collective action that act to prohibit social 

transformation or ethnogenesis. Such settings may be characterized by a downplaying of 

categorical distinctions in public settings, but a maintenance of those distinctions in private 

social settings, and a lack of routinized direct or indirect relational interaction. Symbols can be 

used in a manipulative framework by elites to encourage integrative communal coexistence 

39 

among heterogenous populations. For example, elites may use symbols to incite shared feelings 

of belonging but by otherwise maintain the status quo. Such a strategy was employed by elites in 

the Naco region and La Sierra polity of Prehispanic Southeastern Mesoamerica and likewise by 

elites during the Uruk expansion in Early Mesopotamia (Emberling 1997, 1999; Schortman and 

Urban 1992; Schortman, et al. 2001).  

 

A fourth and final manifestation of intercultural communal coexistence occurs in social 

settings following culture contact where relational transaction costs are relatively low but 

where heterogeneous or exclusive categorial identities delimit the extent of collective action or 

social movements. These settings are characterized as accommodative coexistence. Collective 

action may be limited to sub-divisions within densely relational networks that do share common 

categorical identities as opposed to spreading across a broader array of actors (Peeples 2018). 

Examples of social contexts similar in nature to accommodative coexistence include Native 

Alaskan men and Native Californian women intermarrying and living side-by-side at historic 

Fort Ross yet maintaining distinct categorical identities as seen in evidence from their habitual 

daily routines (Lightfoot, et al. 1998). Another example of accommodative coexistence is the 

reincorporation of Paleoeskimo Frobisher Bay Dorset peoples into interaction networks with 

other Dorset peoples in the eastern Arctic. Despite increasing interaction with far-flung 

interaction networks after more than 200 years of apparent isolation, Frobisher Bay Dorset 

peoples maintained a distinctive stylistic material culture, and therefore categorical, identity 

(Odess 1998). Finally, Grasshopper Pueblo witnessed an in-migration event wherein migrants 

maintained categorical distinctions as seen in architectural and pottery style despite living side-

by-side and participating in the construction of new room blocks and pit structures (Stone 2003).  

40 

 

An intercultural communal coexistence framework is therefore grounded in the analysis 

of multiple layers of network relationships. In particular, categorical and relational layers are 

argued to be critical lenses with which to model behavioral response trends to multicultural 

regional cohabitation, thereby necessitating a multilayer network analytical framework. 

Traditional attempts in this regard using concepts such as assimilation or hybridity are generally 

ill-suited to grasp the complex dynamics of multicultural social settings (Kent 2002; Rumbaut 

2015). By instead focusing on relations and categories, it is possible to both problematize the 

interplay of multiple lines of evidence as well as parse the complexity of multicultural social 

contexts. Archaeological settings in particular are uniquely suited to explore long-term trends in 

networks of social interaction and categorical identification, majority-minority power dynamics, 

and negotiations of identity politics. It is therefore possible to examine how communities 

constructed social, economic, and other relational networks before an in-migration and capture 

communally based responses to multicultural society after cultural contact.  

 

2.4.1  Material Culture Correlates to Intercultural Communal Coexistence 
 

If intercultural communal coexistence consists of behavioral response trends to 

multicultural regional cohabitation following culture contact as diagnosed through a multilayer 

network analysis of relational and categorical similarities, what specific lines of evidence are 

able to be used to identify such trends in the archaeological record? As discussed in the 

preceding section, many such trends have been identified already. Each of the anthropological or 

archaeological examples for the various communal coexistence trends discussed previously rely 

on multiple lines of evidence to identify both categorical and relational lines of evidence. Here, I 

discuss lines of evidence that may be used in a multilayer network analysis of intercultural 

41 

communal coexistence as well as introduce the specific lines of evidence used in this dissertation 

in a Late Prehistoric central Illinois River valley archaeological case study.  

A common theme in archaeological examples discussed in the previous section is using 

stylistic and technological dimensions of material culture to infer the presence of migrants or 

heterogeneous populations and therefore the occurrence of culture contact. The presence of a 

migrant population is often bolstered with osteological evidence such as analysis of cranial 

morphology, mitochondrial DNA, or dental strontium signatures. From these lines of evidence, it 

is possible to model host and migrant populations as lineally distinct. Material culture style may 

then be used to model categorical identities, and technological choices related to material culture 

may be used to model relational identification and interaction. Exchange of material culture as 

assessed via style, technological choices, or geo-chemical patterning is another tool with which 

to model relational interaction. In each of these cases, it is assumed that as different layers of 

data converge among communities, so does the likelihood that individuals from those different 

communities engaged in more frequent relational interaction and were characterized by a higher 

degree of categorical similarity.  

 

The key principals discussed in this chapter are applied in the rest of this dissertation to 

an archaeological case study across the Middle to Late Mississippian transition in an 

archaeological region known as the central Illinois River valley (or CIRV; circa 1200 – 1450 

A.D.), which is briefly summarized here. The CIRV is characterized by a suite of large, mounded 

and often palisaded towns, smaller villages, and outlying sites that are primarily dotted along the 

western bluff edge of the Illinois River valley expanse. In situ social dynamics are argued to be 

largely responsible for the Mississippianization of the region beginning circa 1050 – 1100 A.D. 

(Bardolph 2014; Bardolph and Wilson 2015; Friberg 2018; Steadman 1998; G. D. Wilson, et al. 

42 

2018). Beginning in the late 13th century, Oneota peoples began an expansionary process out of 

an upper midwest core and into the lower and midwest and central plains (Hollinger 2005; Pugh 

2010). Mississippian peoples in the CIRV, which represents the northern frontier of contiguous 

Mississippian territorial expansion, maintained their positions in fortified temple mound centers 

and outlying sites and entered into a period of regional cohabitation with an intrusive Oneota 

population. Available data from CIRV settlements exhibit varying degrees of intermixing 

between Mississippian and Oneota material culture, intermixing that has had proved to be a 

quandary to the taxonomic models that define these distinct cultural groups. Tantalizing evidence 

for cultural mixing is most readily apparent in the mixing of ceramic traits. Because of the 

availability of an array of ceramic data from sites across the geographic and temporal expanse of 

the CIRV, ceramic industry is the focus of modeling relational and categorical similarity among 

sites.  

 

In assessing intercultural communal coexistence in a Late Prehistoric CIRV case study 

region, connections indicative of three types of relationships gleaned from ceramic industry are 

considered here: i) exchange relations, overlapping resource exploitation zones, or raw material 

acquisition information sharing indicated by geochemical source groups (Gjesfjeld 2015, 2018; 

Golitko and Feinman 2014); ii) shared categorical identities as evidenced by proportions of 

stylistic decoration similarity (Borck, et al. 2015; Mills, Clark, et al. 2013; Mills, Roberts Jr., et 

al. 2013) and iii) relationships of descent or shared learning mechanisms based on relative 

technological similarity in type-attributes constrained by social, as opposed to engineering, 

forces (Eerkens and Bettinger 2008; Peeples 2011). All three network models chosen for this 

research constitute frameworks for constructing relationships between humans, wherein edges 

between sites act as statements of probability that a relationship existed. Pottery exchange, 

43 

overlapping resource exploitation areas, or raw material source location information sharing 

indicate episodes of direct or indirect economic relational interaction (Brose 1994; Brown 2004; 

Zvelebil 2006). Repeated relational interaction leads to pathways for relational identification. 

Categorical identities are mechanisms for people to index ascription to common social units, 

express solidarity, and nonverbally communicate social information (Braun 1985; Wiessner 

1990). Distinctive combinations of technological characteristics indicate shared relationships of 

learning and the expression of social information (Herbich 1987; Stark, et al. 1998).  

Because each of the different network layers utilizes a distinct theoretical bridge in 

linking archaeological evidence to either relational or categorical identity, a more thorough 

discussion of those theoretical bridges is provided in each individual chapter. A brief description 

is provided for each here, however. Relational identification through social interaction is 

assessed across three distinct analytical layers. The first two layers are assessed by using 

technological characteristics of two distinct vessel classes – domestic cooking jars and plates 

primarily used in the serving of food. By drawing on a theory of cultural transmission, it is 

possible to differentiate between variation in vessel technological attributes mainly affected by 

engineering constraints from that affected mainly by social constraints (Eerkens and Bettinger 

2008). Commonality between site assemblages in technological attributes of pottery is therefore 

argued to be indicative of either historical relations of descent or shared learning mechanisms 

(VanPool 2008). This ensures that similarities in relational social ties are not confused with 

similarities caused by engineering constraints in the execution of a given artifact attribute. The 

resulting networks of interaction through cultural transmission are discussed in Chapter 5. 

Another means of establishing relational identities is through compositional analysis. 

Proportional similarity among sites of membership in geo-chemical compositional groups may 

44 

show that potters and potter communities not only resided within a particular geographic 

location, and perhaps engaged in exchange relationships, but also shared specific information 

about how to procure and prepare their raw materials. Thus, compositional analysis provides an 

essential additional objective measure to assess not only variation in the transmission of 

information related to pottery making but also to model economic relationships of exchange. 

Network models of economic interaction are discussed in Chapter 7. Finally, categorical 

identities as assessed via stylistic designs incised or trailed on the outflaring rim of the plate 

vessel class are analyzed in Chapter 6. As primarily serving vessels, plates are often used in 

highly visible contexts. Stylistic design groups are therefore argued to be reflective of social 

roles or social groups to which individuals may index belonging because the process of 

symbolization must be used to facilitate the recognition of members compared to non-members.   

Comparing models of communal coexistence against network models of exchange, 

interaction, and identification enables economic, social, and identity politic relationships to be 

contextualized relative to one another. A multilayer perspective allows these relationships to then 

be explored in aggregate and is the topic of Chapter 8. In this way models of human behavioral 

relationships can lead to a systemic understanding of the impact of a migration process on a 

whole society by understanding individual networks and how they influence and co-construct 

each other (Szell, et al. 2010).  

On a regional level, this research contributes to an understanding of social structure 

during the Late Prehistoric period in the U.S. Eastern Woodlands. This critical period in 

American prehistory preceded the collapse and abandonment of fifteenth century chiefly polities 

in the central Illinois River valley (Esarey and Conrad 1998), the American Bottom (Cobb and 

Butler 2002, 2006), the lower Ohio valley and central Mississippi valley (Cobb 2005), and the 

45 

lower Savannah River drainage (Anderson, et al. 1995). While many analyses of societal 

collapse focus on environmental factors (Bird, et al. 2017; Weiss and Bradley 2001) this research 

offers an alternative perspective by analyzing network models of social relations prior to 

abandonment and population displacement (Borck, et al. 2015). Problematizing and integrating 

social interaction and categorical identification with larger-scale political and social change is 

fundamental for understanding how culture is created, continued, and contested by people in the 

past and the present. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

46 

CHAPTER 3 REGIONAL AND CULTURAL BACKGROUND: LATE PREHISTORY IN 

THE CENTRAL ILLINOIS RIVER VALLEY 

 
 
3.1 Introduction 

 

Exploring social relationships between communities presupposed a basic knowledge of 

those communities themselves. Since potter communities are used here as a proxy measure for 

the larger, spatially bounded settlements within which they were nested, it is necessary to 

provide a proper context and association. This chapter presents an overview of the Middle 

Mississippian and Oneota cultural traditions more generally as well as the occupation of the 

central Illinois River valley by these societies primarily through the lens of the settlements whose 

interrelationships form the focus of interest in this dissertation. The archaeological and cultural 

background of this region has been discussed from a number of vantages previously. These 

include, but are not limited to, considerations of bioarchaeology (Bengtson 2012; Hatch 2015; 

Steadman 1998, 2001, 2008; Strezewski 2003; J. J. Wilson 2010), subsistence patterns (Tubbs 

2013; Vanderwarker and Wilson 2016; Vanderwarker, et al. 2013), residence patterns (Painter 

2014), settlement patterns (Harn 1978, 1994), chronology (G. D. Wilson, et al. 2018), or in 

general taxonomic definitions and descriptions of Middle Mississippian and Oneota central 

Illinois River valley expressions (Cole and Deuel 1937; Conrad 1989, 1991; Esarey and Conrad 

1998; Santure, et al. 1990). This chapter endeavors to synthesize much of this information to 

enable a contextualized interpretation of the results of this study. All radiocarbon assay 

calibrations are presented courtesy of OxCal 4.3 (Reimer, et al. 2013).  

 

B ecause this study focuses on relational connections among communities, environmental 

factors are generally de-emphasized in the succeeding substantive analytical chapters.  

 
 

47 

3.2 Geographic Setting 

 

The archaeological region known as the central Illinois River valley (hereafter CIRV; 

Figure 3.1) encompasses a 210 km stretch of the Illinois River extending approximately from the 

modern village of Hennepin, IL southerly to the village of Meredosia, IL (Harn 1994:4-9); 

though the Late Prehistoric CIRV is centralized in an approximately 137 km stretch of the 

Illinois River from the present town of Peoria, IL southerly to the unincorporated village of 

Chambersburg, IL. This archaeologically defined region has been referred to in the past as the 

Central Illinois Valley (Conrad 1991:120), but has more recently referenced to by the moniker 

used herein. Modern topography, surficial geology, and hydrology is largely a product of  

Figure 3.1 Lidar map of, and archaeological sites under consideration in the Late Prehistoric central 

Illinois River valley (circa 1200 – 1450 A.D.) 

 

48 

 
Illinoisan and Wisconsin glaciation, which spanned in varying levels of intensity from 

approximately 250,000 to 13,600 years before present (Wiggers 1997). The CIRV is the 

southeastern part of the Galesburg Plain, which encompasses a 20,700 km2 landform including 

the central Illinois and Mississippi River valleys from the beginning of the lower Illinois River 

valley northward to the Green River drainage system (Leighton, et al. 1948). The Illinois River 

and associated tributaries in the CIRV, including the Spoon and La Moine Rivers, are 

characterized by a relatively slow current, with an expansive Illinois River floodplain 

distinguishing the physiographic region from northerly, southerly, and easterly environs. 

 

Climatic conditions in the CIR during the Late Prehistoric period were largely similar to 

the climate at the turn of the 2nd millennium A.D., indicating that a wide variety of floral and 

faunal resources were available to support human occupations (F. B. King 1990). Harn 

(1978:237-241) and Harn (1994:4-9) provide a rich description of the physiology and natural 

history of the region. The following two sections describe the Mississippian and Oneota 

archaeological traditions more broadly before returning to the central Illinois River valley case 

study in Section 3.4. 

 

3.3 The Mississippian Tradition 

 

Different, yet linked, societies bearing traits such as intensified maize horticulture and 

agriculture, fortified communities with large earthen mounds, social ranking, and a set of rituals 

and symbols concerned with fertility, ancestors, and war largely characterizes the Mississippian 

cultural development (Blitz 2010). Extending from central Illinois and Wisconsin to the Gulf 

coast and east to Florida and North Carolina and dating to approximately AD 1000-1550, the 

Mississippian phenomenon constitutes the social melding and integration of different groups 

49 

through contact, coalescence, and population movement that supported newly formed elite 

hierarchies. Archaeologically, variation in Mississippian complexity is manifest in polity scales, 

settlement tiers and the built and perceived landscape, the organization of labor, mortuary ritual 

and ideology, and tribute and feasting (Cobb 2003). Elites are thought to have attained and 

maintained their largely knowledge based authority through warfare related activities, ritual 

feasting, ceremonial smoking, and public display of goods that imbue prestige, with 

ethnographic accounts explaining a duality of conception in the political sphere of Mississippian 

society between war and peace (Dye 2013). Significant Mississippian communities are often 

marked by large earthen mounds, an open plaza around which structures were arranged, and 

likely dominated regional or local settlement hierarchies. Household arrangement around plazas 

is also featured prominently in many non-mounded, secondary communities. While smaller 

communities and individual households may have been dispersed across the landscape for 

economic reasons, members of each community are thought to have engaged in the same basic 

subsistence and household activities (Schroeder 2004). Architectural variation encompasses wall 

trench and occasionally individual post structures, smaller functionally distinct structures such as 

sweat lodges or storage facilities, and prominent mound-top structures. Migration, warfare, 

exchange, and the movement of exotic raw materials, finished artifacts, ideas and even 

subsistence items structure the succeeding discussion of Mississippian societies.  

 

An order of magnitude larger than any other Mississippian society, Cahokia represents 

not only the beginning but can also be argued to be the apogee of Mississippian society. 

Research amongst Mississippian societies often implicates Cahokia due to its early emergence, 

size, and complexity (Benson, et al. 2009; Emerson 2012; Emerson and Lewis 1991; G. R. 

Milner 1990; Pauketat 1994, 2003; Pauketat and Emerson 1991, 1997; Schroeder 2004). The 

50 

founding of Cahokia catalyzed, or was catalyzed by, large scale population movement within the 

American Bottom region and an influx of indigenous and migrant peoples to Cahokia itself. 

Large numbers of kin groups became attached to Cahokia and began a dynamic period of 

cultural negotiation wherein the greatest public works in eastern North America were constructed 

in this planned but accretional site (Alt 2006; Pauketat 2003). Outside of Cahokia proper, the 

American Bottom region witnessed the large scale abandonment of pre-Mississippian villages 

and the appearance of dispersed Mississippian farmsteads, lower level mound centers and an 

upland farming community known as the Richland Complex whose culturally pluralistic 

immigrants negotiated with Cahokians and defined Mississippianism in their own practical terms 

(Pauketat 2003). Cahokia likely dominated the American Bottom region politically and 

economically, however relatively autonomous mound centers and their respective territories 

were perhaps present throughout the Mississippian period (G. R. Milner 1990). While 

authoritative power presided at Cahokia, rich grave offerings in Mound 72 are considered by 

Brown (2006) to represent collective, ritual performance with allegorical implications wherein 

structural power disregards any notions of individual hierarchy in favor of communal celebration 

of Mississippian ideology. Symbols of prestige seem to have increased in importance at Cahokia 

over time. Kelly (1991a) explains that Cahokia emerged as a major trade hub as a result of the 

lack of high quality raw materials in the American Bottom floodplain and that population 

increases led to mechanisms wherein non-elite were able to obtain chert and salt, thereby 

circumventing elite control, playing a role in the de-emphasis of utilitarian good exchange 

overtime, and likely contributing to the increase in exchange of prestige-imbuing goods. 

Increasing interaction with southern Mississippian groups also occurred overtime at Cahokia 

according to Kelly and is seen in a strong congruence of ceramic style and in ceremonial ware. 

51 

Brown and Kelly (2000) posit Cahokia as a foundational nexus in the formative processes of the 

Southeastern Ceremonial Complex, a continuity in belief systems and iconography in the 

Mississippian Period, and a Copper-Dominated Horizon between 1250 and 1350 A.D. as seen at 

Etowah, Moundville, and Spiro. Together, this indicates the material and ideological 

interconnectedness of Mississippian societies as emanating from an incipient American Bottom 

region.  

 

Hierarchical relationships and cultural complexity were not uniform amongst 

Mississippian societies, and the nature of that variation has fundamental ramifications for 

understanding social interaction, organization, and identity formation at vertical and horizontal 

levels. Beck (2003) offers a model of Mississippian chiefly variability wherein chiefdoms form 

through hierarchically organized staple finance consolidation via either coercive expansion or 

persuasive aggregation. The directionality of power is either Constituent (lower level leaders 

toward higher) or Apical (higher level leader(s) toward lower). Power is often thought to be 

wrested at either one or two levels above the household or community in Mississippian societies, 

forming a simple or complex chiefdom with paramount chiefs presiding over complex chiefdoms 

(Blitz 1999; Earle 1989; Pauketat 1994). Chiefdoms, furthermore, are considered a highly 

unstable and dynamic form of political organization. Blitz (1999) proposes that this political 

dynamic consisted of oscillations between dispersed and concentrated regional power centers, 

where mound-affiliated political units assembled and disassembled to create polities of different 

size and complexity in a fission- fusion process. An important component of chiefdoms, or 

middle complex societies in general, is their kin-based organization. Knight (1986, 1990) argues 

that this feature of ethnographic and ethnohistoric descendants of Mississippian chiefdoms in the 

southeast resulted from an aristocratic organization likely evolving out of a uniform base of 

52 

ranked exogamous matriclan moiety systems. As such, kin relationships were a fundamental 

guiding agent to not only inter-group but also intra-group political, economic, and social 

interactions in Mississippian societies.  

 

Variation is inherent in Mississippian groups both inter- and intra-regionally. 

Mississippian mound centers vary not only in size and political economy but also in specific 

functionality. Some mound centers hosted large swaths of the population while others were 

primarily ceremonial in nature and show evidence of only limited occupation (Anderson 1991; 

Brown 1996; Conrad 1991; G. R. Milner 1986). Regardless, these mound centers played host to 

large gatherings of otherwise dispersed Mississippian peoples wherein elite and non-elite alike 

interacted and negotiated an ever changing dynamic of local Mississippian ideology (Sullivan 

and Harle 2009). One unique Mississippian site at the far northern fringes of the Mississippian 

sphere, Aztalan, may have functioned as a conduit through which both material goods and 

information were directed to elites in the American Bottom, as an outpost for 

Mississippianization, a trade hub, a successful proselytization of indigenous Woodland peoples, 

a movement/expansion of already Mississippianized Woodland peoples from Northern Illinois or 

as a hybrid resulting from Middle Mississippian and Effigy Mound peoples (L. G. Goldstein and 

Richards 1991). The case of Aztalan illustrates the importance of understanding local and 

regional contexts in investigations of the nature of any specific Mississippian center and the 

locality under its purview.  

 

While much focus has been placed on the major Mississippian centers, the bulk of the 

Mississippian population and mainstay of local Mississippianism, as an ideology, was housed in 

the peripheries in the form of small communities or farmsteads. The Mississippians who lived at 

these sites are known to have assisted through labor and goods in mound construction, 

53 

communal hunting forays, agricultural field preparation, and cultivation of community fields 

whose products fed the disadvantaged in society in addition to those of a high social standing 

(Scarry 1999). Elite influence did not penetrate into these peripheral areas evenly. In a case study 

of Mill Creek chert hoe production and exchange, Cobb (2000) shows that while elites may have 

exerted some influence on the distribution of these tools in their respective areas of purview, that 

influence did not penetrate the southwestern Illinois locus of their production. Smith (1995) 

contextualizes Mississippian household studies by explaining five pertinent levels of analysis: 

seasonality, activities, size/composition, duration and context and provides a case study at the 

single household Gypsy joint site. Finally, Pauketat (1989) offers a model of ceramic refuse 

formation processes in order to determine the duration of small habitation sites during the 

Lohmann and Stirling phases of the American Bottom region, and then uses the model to test the 

economic integration of these largely self-sufficient homesteads within a larger Cahokia centered 

settlement hierarchy.  

 

3.4 The Upper Mississippian Tradition and the Oneota 

 

The upper Mississippi watershed, or Prairie Peninsula, that encompasses parts of the 

present day states of Minnesota, Wisconsin, Iowa, Illinois, Indiana, Missouri, Kansas and 

Michigan, was once home to a suite of peoples who, by virtue of shared cultural elements such 

as shell-tempered and wet-paste decorated globular pottery, a diversified economic regime 

incorporating maize, beans and squash agriculture, and an adherence to broad symbolic 

activities, have been established by archaeologists as Upper Mississippian peoples (Fisher 1997; 

McKern 1939; Swartz 1996). More specifically, archaeologists refer to the subset of peoples 

living in the Prairie Peninsula from approximately A.D. 1000 – 1700 as the Oneota. Various 

54 

accounts have been developed that attempt to account for the emergence of these peoples from 

the materially, economically, and ideologically different Late Woodland peoples who preceded 

the Oneota occupation of the region (Benn 1995; Gibbon 1972; Griffin 1960; Theler and 

Boszhardt 2006), however, little consensus is generally agreed upon.  

 

Twenty years after W.C. McKern (1945) used his Midwestern Taxonomic System to 

define Upper Mississippian peoples based on similarities in pottery style and form, Brown 

(1965) examined the cultural development and diversity of the peoples of the Prairie Peninsula, 

suggesting an assignation of this area as an interaction zone with variations in material culture 

and subsistence practices being the result of adaptation to various ecological niches. These 

Culture-Historical and early Processual definitions are, largely, still the basis for classifications 

of archaeologically recovered materials from the Late Prehistoric period in the Prairie Peninsula 

today, with the focus on ceramic assemblages produced by the peoples of this region leading to 

the moniker ‘pottery culture’ for the Oneota in general (Berres 2001). Based largely on changes 

in ceramic decoration, Overstreet (1997) distinguishes four Oneota Horizons: Emergent (A.D. 

950 – 1150), Developmental (A.D. 1150 – 1350), Classic (A. D. 1350 – 1650), and Historic (post 

A.D. 1650). Brown and Sasso (2001) posit a basic continuity of subsistence and settlement 

patterns overtime, a distinctive shift to the ethnohistorically known lifeway pattern occurring 

around A.D. 1450, and a relative uniformity in material culture following the circa A.D. 1500 

disappearance of Mississippian culture in the eastern prairie region. In focusing specifically on 

changing architectural patterns, Hollinger (1995) hypothesizes a relationship between Oneota 

architecture and post-marital residence patterns wherein a shift from patrilocal to matrilocal 

residence occurred during the Classic Horizon and a reversion to patrilocality during the turmoil 

55 

following European contact. This shift residence patterns has been accepted by other Oneota 

scholars (Schneider 2015). 

 

Inter- and intra-group interaction patterns are fundamental components not only to the 

nature of Oneota variation but also to the appearance of the Oneota lifeway in various regions 

and localities. Emerson (1999) models a process of tribalization in northern Illinois based on 

asymmetrical interaction with chiefly groups in the region producing the rapid expansion and 

correspondingly rapid collapse of the Langford tradition. Gibbon (1995) argues against a single 

Oneota mode of exchange because exchange in tribal societies plays simultaneous social, 

political, ideological, and economic roles and shifts in sometimes subtle and sometimes dramatic 

ways with the vicissitudes of broader social and natural environments. O'Gorman (2010) outlines 

the interweaving relationship between community, identity, and dwelling based on the presence 

of longhouses in the La Crosse locality during Oneota occupation (circa A.D. 1300-1650). While 

the Oneota expression in the central Illinois River valley has gained a reputation for experiencing 

significant rates of violence and trauma (Hatch 2015; G. R. Milner, et al. 1991; Vanderwarker 

and Wilson 2016; G. D. Wilson 2012, 2013), recent examination from Oneota skeletal remains 

from Winnebago phase Wisconsin suggest that violence may have been the norm among Oneota 

peoples as opposed to anomalously intensive in Late Prehistoric west-central Illinois (Oemig 

2016).  

 

3.5 The Mississippian Period central Illinois River valley  

 

The central Illinois River valley’s position at the eastern edge of the Prairie Peninsula and 

proximity to the Mississippian cultural core in the American Bottom situated this archaeological 

region at the intersection of Plains-Prairie-Woodland lifeways and booming agricultural 

56 

complexes during the beginning of the first millennium of the common age. A host of contact 

scenarios have emerged to explain the Mississippianization process in the CIRV and the 

Midwest more broadly. These scenarios include in situ emulation based on limited direct 

engagement, proselytization by small cadres of Mississippian emissaries or missionaries, or 

whole-scale movements of Mississippian peoples from Cahokia and other American Bottom 

sites (Bardolph 2014; Conrad 1991; Delaney-Rivera 2007; Emerson and Lewis 1991; Harn 1978; 

Pauketat and Emerson 1997; Steadman 2001; Stoltman 1991, 2000). While no general consensus 

exists, there is little doubt that this process is fundamentally related to entanglements among 

polity, cultural contact, frontier, and expansion.  

 

Extant Late Woodland groups in the CIRV prior to the Mississippianization are posited to 

have comprised two contemporaneous group: Bauer Branch in the south and Maples Milles in 

the north (Esarey 2000; W. Green and Nolan 2000). Biodistance indicators suggest that it is these 

Late Woodland peoples in the CIRV that adopted a maize intensive agricultural subsistence base, 

new forms of architecture, new ceramic technology and decoration, and new socio-political-

religious beliefs and practices to form a unique expression of Middle Mississippian culture 

(Bardolph 2014; Bardolph and Wilson 2015; Conrad 1991; Steadman 1998, 2001; 

Vanderwarker, et al. 2013). This cultural expression would thrive in the region from 

approximately A.D.1100 to perhaps as late as A.D. 1450. The 210 km stretch of the CIRV 

contains the remains of at least seven fortified Mississippian temple towns and numerous smaller 

villages and farming hamlets with an hypothesized distinction between Mississippian peoples in 

the upper portion of the CIRV near the Spoon River and those inhabiting the lower portion of the 

valley near the La Moine River (Conrad 1989, 1991; Harn 1978, 1994).  

57 

 

The Spoon River Mississippian manifestation is comprised of four well defined phases: 

Eveland (1100-1150 AD); Orendorf (1150-1250 AD); Larson (1250-1300 AD); and the 

Marbletown Complex (1300-1400? AD). However, multiple culture-history models have been 

developed with these dates shifting somewhat overtime (J. J. Wilson 2010:54). The earliest 

Mississippian phase, the Eveland phase, is marked by the Mississippianization of local Late 

Woodland Maple Mills peoples, with material culture similar to the Lohmann Phase of the 

American Bottom (Bardolph 2014; Conrad 1991; Esarey 2000). The type site of the period, 

Eveland, is believed to have served “as a centralized cemetery linking numerous habitation 

sites”, and is marked by finely crafted Cahokia-style material culture alongside a minor 

admixture representative of local Maple Mills ware (Conrad 1989:102). The following phase, 

Orendorf, is marked by the appearance of the first substantial Mississippian town in the CIRV, 

the Orendorf site, which underwent repeated episodes of rebuilding and renewal (Conrad 

1989:107). Fortifications first appear during the Orendorf phase, suggesting regional strife or the 

threat of violence. Large platform mounds represent the most obvious difference between the 

Orendorf phase and the subsequent Larson phase (Conrad 1991; Harn 1994). At least two or 

three contemporary Mississippian towns existed during the Larson phase, though much of the 

population resided in dispersed hamlets and farmsteads, some of which had large council houses 

and mounds of their own. The final Spoon River Mississippian occupation in the CIRV is 

marked by regional cohabitation with Bold Counselor Oneota peoples, and is referred to as the 

Marbletown Complex or Bold Counselor phase (Conrad 1991; Esarey and Conrad 1998).  

 

The La Moine River Mississippian expression is poorly studied compared to the Spoon 

River manifestation and is not as rigidly demarcated into phases as a result (Conrad 1989, 1991; 

Harn 1978, 1994). The general developmental trajectory, however, mirrors that of the northerly 

58 

Spoon River expression and as a result it is the Spoon River phases that will be discussed in 

more detail below, subsuming a general CIRV culture-history model as presented herein. Conrad 

(1989, 1991) divides the La Moine River culture into four phases: Gillette (1050-1150 A.D.), 

Orendorf and Larson contemporary (1150-1300? A.D.), Crabtree (1300-1375 A.D.), and Crable 

(1375-1450 A.D.). Like the Spoon River variant, the earliest phase, Gillette, is marked by the 

Mississippianization of local Late Woodland peoples, known as Bauer Branch (Bardolph 2014; 

Green and Nolan 2000). The following phase is marked by overlapping but contemporary 

occupations with Orendorf and Larson phase sites to the north, known primarily from a minor 

occupation of the Lawrenz Gun Club town center and the Star Bridge site (Conrad 1991). While 

A.D. 1300 marked the appearance of the Bold Counselor Oneota in the Spoon River area, La 

Moine River Mississippian sites during the coeval Crabtree phase do not show evidence of site 

level integration until the proceeding Crable phase.  

 

The historical trajectory of Middle Mississippian populations in general in the CIRV is 

argued to be one of increasing population aggregation and conflict (G. R. Milner, et al. 1991; 

Steadman 2008; G. D. Wilson 2012). Less important than the elusive causes of the increasing 

hostilities in the region are the effects of those hostilities on the Mississippians themselves. At 

least sixteen percent of adults over the age of fifteen years at the large village site Orendorf 

suffered warfare-related trauma, including scalping, decapitation, inflicted projectile points, and 

antemortem cranial depression fractures (Steadman 2008:58). Perhaps thirty percent of adult 

individuals in the Norris Farms #36 cemetery died a violent death (G. R. Milner, et al. 1991). 

Palisades at numerous sites in the region indicate high levels of endogamous or exogenous 

threats, as does evidence of a number of burned villages and outlying farmsteads (G. D. Wilson 

2012, 2013). Given the widespread evidence for conflict in the region, many scholars have 

59 

proposed a socio-ideological system of warriors gaining prestige at all levels of the social scale 

through warfare and battle; a hypothesis bolstered by widespread evidence for ritual weaponry, 

iconographic depictions of violence, and human sacrifice seen in Middle Mississippian contexts 

in the CIRV and elsewhere (Dye 2013; Knight Jr 1986; Maschner and Reedy-Maschner 1998; G. 

D. Wilson 2012).   

 

Biodistance studies further suggest that social dynamics during the Mississippian periods 

in the region were most likely the result of in situ social and demographic processes as opposed 

to being the result of gene flow from major centers in the nearby American Bottom (Steadman 

2001). Yet, exotic material culture such as marine shell gorgets and Upper Great Lakes copper 

hairpins and pendants indicate that these populations were very much a part of the widespread 

exchange network characteristic of Mississippians in other contexts (Brown 2004; Conrad 1989, 

1991; Kelly 1991a). As a result, the Mississippian periods of the CIRV are generally 

characterized by increasing factionalism, conflict, and violence under the auspices of chiefly 

cycling and power based on in situ social processes.  

 

Sometime in the early to mid-14th century, an Oneota group from the north migrated into 

the CIRV and fundamentally changed the social dynamics of the region (Esarey and Conrad 

1998; O'Gorman and Conner 2016; Santure, et al. 1990; Steadman 1998). Known by only five 

habitation sites and one cemetery, the Bold Counselor Oneota’s immigration into the CIRV 

offers an unparalleled opportunity to study inter-group social interaction within the context of 

small scale warfare and social stress. Based on biodistance studies comparing the Oneota 

population interred at the Norris Farms #36 cemetery and CIRV Middle Mississippian burial 

assemblages, Steadman (1998) concluded that the Oneota group contributed marked variation to 

the regional gene pool. Coupled with distinct differences in ceramic decoration, architectural, 

60 

and certain lithic tool patterns, there is little doubt to the non-local origins of this unique 

expression of the Oneota lifeway.  

 

For the purposes of this dissertation, time-space systematics will be bifurcated between 

the phases prior to the in-migration of Oneota peoples into the CIRV (e.g. the Eveland, Orendorf 

and Larson phases of the Spoon River variant and the Gillete, Orendorf and Larson 

contemporary, Crabtree of the La Moine variant) and the phase following this in-migration 

process (Marbletown complex of the Spoon River variant and the Crable phase of the La Moine 

River variant). This is primarily an effort to best fit models of changing social interrelationships 

concomitant with the in-migration process and recognizes that prior efforts to classify time-space 

systematics lack “grounding in empirical data…[and are characterized by a] conflicting series of 

radiometric dates, which both Harn and Conrad have noted” (Conrad 1991; Harn 1994; J. J. 

Wilson 2010:53-54). Further, the discussion below follows the culture-history sequence of the 

Spoon River variant alone, subsuming the evidence from the La Moine River variant. This is 

partially an effort to present the culture-history of the region as a unified Mississippian sequence 

despite marked evidence for perhaps competing polities, which is characteristic of Mississippian 

society in other contexts (Blitz 1999), to situate and contextualize the results and interpretation 

sections and recognize the efforts of prior archaeological research in the region.  

 

3.6 Eveland Phase (A.D. 1100-1175) 

 

The Eveland Phase marks the beginning of strong Mississippian influence in the CIRV 

and is named after the Eveland Site (11F353), where those influences are most acute. Quite 

detailed overviews of the Eveland phase and its sister phase in the La Moine River region, the 

Gillette phase, are found in Conrad (1991:124-132) and Harn (1991). As a result, an abridged 

61 

discussion will be provided here. Eveland is marked by an arrangement of “four elaborate 

ceremonial buildings and two habitation structures located at the base of the western Illinois 

River bluff” (Bardolph and Wilson 2015:143). The ceremonial buildings have been interpreted 

as a council house or earthen lodges and are architecturally characteristic of Middle 

Mississippian norms in the American Bottom and Lower Illinois River, in stark contrast to local 

Late Woodland architectural styles (Conrad 1991). Perhaps the most striking evidence of the 

ceremonial nature of these buildings is a cross-shaped building, which is posited to perhaps have 

served as a “fire temple” (Conrad 1991:124). Ceramic vessels recovered from Eveland include 

finely crafted Ramey Incised and Powell Plain jars that date to the Stirling phase component in 

the American Bottom (Vogel 1975). While the Stirling phase saw the beginnings of massive 

public works in the form of monumental architecture and infrastructure in the American Bottom, 

there are no known Mississippian towns occupied during the Eveland phase or Gillette phase. 

However, the Cahokian fluorescence in the American Bottom likely accelerated the readiness of 

local Late Woodland peoples to acculturate to the Mississippian lifeway. The alignment of 

Eveland phase ceramics with Stirling phase material culture in the American Bottom coupled 

with recent excavations by the University of California Santa Barbara have led to a revision of 

the timeline for the Eveland phase from an initial beginning at A.D. 1050 to A.D. 1100 and an 

ending around A.D. 1200; though the occupational sequence at Eveland may be further refined 

given the large probability distributions for radiocarbon assays from the site, see Figure 3.2 

(Bardolph 2014; Bardolph and Wilson 2015; G. D. Wilson, et al. 2018). As a result of these past 

and potential future revisions, the socio-interrelationships between the Eveland site and other 

CIRV sites are considered in this dissertation, despite the general focus here on the later 

Mississippian phases in the CIRV.  

62 

 

Figure 3.2 Probability distributions of three recalibrated dates for the Eveland site (Bender et al. 1975) 

Including the Eveland site, approximately thirteen other sites have been identified by 

 

 

Harn (1991) that date to the Eveland phase. Most of these sites were small homesteads, less than 

one hectare in size, with a limited number of structures that bear no evidence of rebuilding or 

extensive occupation (Harn 1991; J. J. Wilson 2010). Much of the material culture remains from 

these sites, such as Ramey Incised and Powell Plain jars, are quite similar to their American 

Bottom analogs, but with some deviation in stylistic decoration (Harn 1994). This suggests that 

perhaps either local potters were expressing and non-verbally communicating local socio-

religious symbols onto non-local pottery designs as a means to amalgamate the known with the 

unknown, or that Cahokian potters were actively negotiating the transmission of culture by 

conforming to those local socio-religious conventions. Thin section analysis indicates that these 

vessels were made from locally available clays (Harn 1991:143). Pottery morphology in the 

region became progressively dissimilar to analogs in the American Bottom overtime, suggesting 

the increasing importance of local social dynamics and/or waning Cahokian influences overtime.   

 

Recent evidence suggests that the Eveland phase was a “context of converging but still 

very much entangled Woodland and Mississippian traditions” (Bardolph and Wilson 2015:144). 

Late Woodland peoples were selectively adopting or emulating aspects of Mississippian 

63 

traditions to the south but maintained certain Bauer Branch ceramic traditions at the Lamb site 

for example; a process that is mirrored among Maples Mills traditions at the Gillette site 

(Bardolph 2014). This indicates that the Mississippianization process during the Eveland phase 

was a selective, intentional, and measured process at different sites in the CIRV and that the local 

social dynamics took early precedence (Friberg 2018). These local preferences in material 

culture and later mortuary expressions are the basis for an interrelated but perhaps also divergent 

evolution of the Spoon and La Moine River Mississippian traditions from their humble 

beginnings (Harn 1994).  

 

3.7 Orendorf Phase (A.D. 1200-1250) 

 

The revision of the Eveland phase timeline to an A.D. 1200 end frame resulted in the 

concurrent revision of the Orendorf phase to begin at A.D. 1200, though it is possible that the 

initial development of full-fledged Mississippian culture began during the latter half of the 12th 

century A.D. based on radiocarbon assays from the Orendorf site in Figure 3.3 (Bardolph 2014; 

Esarey and Conrad 1998; G. D. Wilson, et al. 2018). The Orendorf phase is known primarily 

from the type site, the Orendorf site and its adjacent cemetery (Conrad 1991; Esarey and Conrad 

1981; Steadman 2008). Orendorf is characterized by a series of four to five distinct settlements 

that appear to have been constructed over the perhaps 100 year history of the site’s occupation 

(Esarey and Conrad 1981; J. J. Wilson 2010). Information on two of these settlements are of 

particular importance to this dissertation, Orendorf Settlements C and D. Settlement C forms the 

primary focus of the unpublished working papers organized by Esarey and Conrad (1981), which 

is chiefly responsible for information on the phase in general. A report summarizing the 

Settlement D occupation is as yet forthcoming from the Illinois State Archaeological Survey.  

64 

 

The Orendorf phase marks a number of important distinctions in the Mississippian 

history of the CIRV. First, the Orendorf site is likely the first Mississippian habitation that 

conforms to the general expectations of a classic Mississippian town. Settlement D, which is 

believed to be the earliest occupation, is marked by a distinctive plaza with nearly 100 domestic 

structures arranged around this central feature of the site (Esarey and Conrad 1981). In addition 

to the central plaza, Settlements C and D both are enclosed by extensive palisades. Coupled with 

skeletal trauma and other evidence such as burned structures with intact household assemblages, 

this suggests that the threat of attack during this phase was very real (Steadman 2008). 

Figure 3.3 Probability distributions of five recalibrated dates for the Orendorf site (Bender et al. 1975) 

 

The shift to a Mississippian lifestyle included a shift to an economic base primarily 

 

 

centered around maize agriculture, deer, fish, waterfowl, and local cultigens to a lesser extent 

(Tubbs 2013; Vanderwarker and Wilson 2016; Vanderwarker, et al. 2013). Larger populations 

were able to be supported based on this subsistence regime, with Orendorf Settlements C and D 

estimated at population figures in the 400-500 range at any given time, making them perhaps two 

to three times larger than any previous settlement in the CIRV (Esarey and Conrad 1981). Larger 

65 

populations, however, often result in increased economic stress risk factors and perhaps more 

difficulty or increased competition in climbing social ladders of Mississippian defined success 

factors. The susceptibility to drought coupled with success in war as a means for prestige 

building, coalesced into an increasingly hostile Mississippian occupation throughout the CIRV 

following the relatively peaceful Eveland phase, with some sixteen percent of adults at Orendorf 

being directly affected by interpersonal trauma such as scalping, decapitation, inflicted projectile 

points, and antemortem cranial depression factures (Steadman 2008; G. D. Wilson 2012).  

 

Ceramics in the CIRV increasingly diversified from their American Bottom counterparts 

beginning in the Orendorf and later phases, indicating a distinct cultural trajectory based 

primarily on in situ social dynamics (Conrad 1991; Harn 1994; Strezewski 2003). While 

calibrated radiometric dates (n=11; see Figure 3.3 for a subset) places the Orendorf site between 

A.D. 1149 to 1320, it is generally agreed upon by Harn (1991) and Conrad (1991) that Orendorf 

predated the later, but overlapping, Larson phase based on the inferred evolution of 

Mississippian ceramic styles and forms local to the CIRV (J. J. Wilson 2010). While Cahokia-

style Ramey and Powell Plain jars gave way to more distinctively local vessels at Orendorf, the 

scrolled and curvilinear designs that form the hallmark of the Ramey tradition often adorn the 

minority of jars that are decorated from Orendorf Settlement assemblages (Conrad 1991). Jars 

and a ceramic vessel class new to the region in the Orendorf phase, a class variously referred to 

as plates or broad-rimmed bowls, are often smoothed over and plain. However, decorations 

characterized by sun-motifs or sun-emulations also seen in other Mississippian regions does 

occur (Conrad 1991; Hilgeman 2000; Vogel 1975).  

 

Several other, perhaps rival, settlements appear to be occupied alongside Orendorf during 

the Orendorf phase. These include Kingston Lake, Emmons Village, Weaver-Betts, and Ten 

66 

Mile Creek (Conrad 1991). Recently obtained radiocarbon dates from the Ten Mile Creek site, 

however, place the occupation of this site almost entirely within the 14th century A.D., some 50 

years after the supposed end of the Orendorf phase (see Figure 3.6). Although the possibility of a 

limited earlier occupation of the site remains plausible, the primary occupation of Ten Mile 

Creek (also known as Hildemeyer), however, is likely to have post-dated the Orendorf phase. 

Regardless, the Orendorf phase certainly represents the beginnings of Mississippian fluorescence 

in the central Illinois River valley, with the introduction of classic Mississippian-style sites, 

material culture reminiscent of the American Bottom but with a distinctive local flair, and 

artifacts bearing socio-religious themes associated with the Southeastern Ceremonial complex 

including the forked-eye motif, short- and long-nosed maskettes, and distinctive beakers, among 

other examples of upper and lower Mississippian world symbolism (Brown and Kelly 2000; 

Conrad 1989; Emerson 2012; Kelly 1991a; Pauketat and Emerson 1991, 1997).  

 

3.8 Larson Phase (A.D. 1250-1300) 

 

  While both Conrad (1991, p. 141) and Harn (1994, p. 26) suggest that the inhabitants of 

Orendorf may have abandoned the site in the middle of the 13th century A.D. to found a new 

Mississippian town, Larson, in the south-central portion of the region, it is plausible based on 

overlapping radiocarbon dates and distinctive ceramic differences between these sites that they 

may have been contemporaneous for a generation or more. Nevertheless, considerable effort both 

in the field and in the lab has resulted in the assignation of the Larson phase, Larson settlement 

system, and a general definition of the Spoon River Mississippian apogee as thriving during the 

latter half of the 13th century A.D. (Harn 1978, 1994). Because of the nature of the salvage 

excavations at Orendorf in comparison to the more dispersed focus on archaeological resources 

67 

in the vicinity of the Larson site, more is known about the Larson community and the 

relationship between a central town and its supposed subsidiary sites during the Larson phase 

than during the preceding Orendorf phase, which is largely defined based on the Orendorf site 

itself (Conrad 1991). Though forty years of excavations have indeed produced a bounty of 

knowledge about the Larson phase type site, the Larson town.  

 

Figure 3.4 Probability distributions of four recalibrated dates for the Larson site (Bender, et al. 1975) 

The Larson phase saw a manifestation of Mississippian culture that mirrors the settlement 

 

 

hierarchies of other Mississippian regions in the American southeast (Blitz 1999; Cobb 2003; A. 

King 2002). As a result, Harn (1978, 1994) endeavored to apply the multi-tiered Mississippian 

“settlement system” model used to define this archaeological culture in those other regions 

(Fowler 1974; B. D. Smith 1978). This model presupposes an apical primary site supported by 

progressively smaller subsidiary settlements located in key resource exploitation zones. Harn 

(1994:16-17) envisions a four-tiered system for the Larson phase CIRV that includes the central 

Larson town, several primary villages (e.g., Myer-Dickson, FV66), intermediate settlements (e.g., 

Fouts Village, Buckeye Bend, M.S.D. 1), and subsidiary settlements (e.g., Norris Farms 1 and 

24). Each of the lower tiered settlements lies within a 25 km radius of the central town. Beyond 

68 

this Larson nucleus, Harn (1994) identifies Kingston Lake, Lawrenz Gun Club, and Walsh as 

central town present during the Larson phase (Harn also identified Hildemeyer or Ten Mile 

Creek, though recent dating by the author suggests a predominant occupation in the succeeding 

Crable phase, see Figure 3.6). Conner (2016) suggests at least two temporally and spatially 

distinct Larson phase occupations at Myer-Dickson whose proximity to the regionally important 

Dickson Mounds mortuary center, presence of a plaza, and presence of one of the largest 

buildings known in prehistoric Illinois make this a unique non-nuclear settlement habitation site.    

 

Situated atop a cornering bluff overlooking the confluence of the Spoon and Illinois 

River valleys, Larson is centrally positioned in the CIRV from both ecological and geographic 

perspectives. Larson is a stockade settlement marked by a single stage, truncated pyramidal 

platform mound measuring some 60 x 60 meters and perhaps 3-5 meters high with a ramp 

abutting a 150 sq. meter plaza, which is in turn flanked by domestic structures on three sides 

(Conrad 1991; Harn 1994). No evidence for bastions is present along the stockade. Portions of 

the site were at times burned, perhaps on more than one occasion. Relatively scant remains from 

the floors of the structures in these burned portions suggest that the site was still occupied at the 

time of burning. This is observation is buttressed by comparison to structures burned with entire 

suites of artifacts related to a variety of economic and artistic pursuits seen at Myer-Dickson and 

Orendorf Settlement D (Conrad 1991). The presence of maize in most storage/refuse pits as well 

as within the domestic structures speaks to the importance of this subsistence resource to the 

Larson population (Harn 1994). In addition to maize, large quantities of fall-ripening nuts and 

seeds as well as large mammals, migratory fowl, and other aquatic resources indicates a broad 

subsistence system focusing on maize agriculture supported by hunting, gardening, gathering, 

fishing, and perhaps limited scavenging. Harn (1994:48) views the Larson settlement system as 

69 

an “integral series of procurement subsystems whereby the seasonal cycles of the local 

population and those of their target resources intersected”. That is, primary villages, intermediate 

settlements, and subsidiary sites were positioned strategically around the central town at 

locations allowing for the maximal exploitation of the surrounding plains-prairie-woodland-

riparian-lacustrine subsistence offerings but at such distance as to prohibit over exploitation of 

any particular resource zone. An estimated 450 – 1,175 individuals may have populated the 

central Larson town at any given time with another perhaps 1,000 – 1,500 individuals spread 

across the primary villages and intermediate settlements according to Harn (1994:53).  

 

The primary point of contention in arguing for a separation between the Orendorf and 

Larson phases are the differences in ceramic assemblages from these sites. The Larson phase saw 

the emergence of the Dickson series of jars, which are differentiated primarily by cord-marked 

lower hemispheres of the globular vessels with plain or sometimes trailed/incised line-filled 

triangle motif adorned shoulders. The line-filled triangle designs, when viewed from above, 

mimic sun rays. This upper-world symbolism indicates some connection to socio-politico-

religious themes of the Southeastern ceremonial complex (Brown and Kelly 2000; Griffin 1949; 

Hally 2006; Pauketat and Emerson 1991). Larson jars are marked by increases in the height and 

width of jar rims with more rounded shoulders, increased occurrence of cord-marking, and a 

general increase in the presence of stylistic decorations when compared to the Orendorf and 

Eveland phases. However, there is considerable overlap in these trends among the phases. 

Dickson style jars are present at both Kingston Lake and Ten Mile Creek, indicating perhaps 

incipient occupations at these sites at the extreme northern extent of the CIRV (Conrad 1991).  

 

Population aggregation in the Larson site vicinity suggests spatial emphasis in the CIRV 

shifting to the central-south portion of the valley. However, the Larson phase also may be 

70 

characterized by multiple, contemporaneous Mississippian town sites, perhaps for the first time.  

Walsh, Kingston Lake, and Lawrenz Gun Club each appear to be coeval based on radiocarbon 

assays as well as ceramic forms and surface finishes, though with some stylistic variation present 

between them (Harn 1994:21-22). Conrad (1991) views the southern cadre of towns, Walsh and 

Lawrenz Gun Club, as perhaps representing a different polity developed locally to the extreme 

southern portion of the valley, which he refers to as the Crabtree phase. Jeremy Wilson of 

Indiana University Purdue University Indianapolis has recently obtained dates from both Walsh 

and Lawrenz Gun Club, placing both of these sites within the Larson phase, though Lawrenz 

Gun Club does appear to be marked by an earlier occupation as well (see Figure 3.5). Harn 

(1994:25) explains that the “difficulty in proposing a single comprehensive occupation of the 

entire study area by each or any of the phases of the Spoon River tradition is that the various 

local artifact assemblages considered representative of a particular phase disclose a great degree 

of stylistic variability. It seems that each town and related nucleus of sites retained its  

Figure 3.5 Probability distributions of one recalibrated dates for Walsh Site (Wilson, personal 

communication 2017) 

 

 

 

71 

individuality, whether intentionally for sociopolitical reasons or incidentally because no 

competing settlement systems were simultaneously functioning nearby”. Whether the 

individuality argued for in each town’s ceramic assemblage is related to contemporaneous 

polities operating in restricted areas or the evolution of ceramic technology and style based on 

the progressive founding of new towns is certainly a matter of unresolved debate.  

 

  

3.9 Crable Phase (A.D. 1300-1425) 

 

Sometime in the late 13th or early 14th century A.D., an Oneota group from the north 

migrated into the CIRV and fundamentally changed the social dynamics of the region (Esarey 

and Conrad 1998; O'Gorman and Conner 2016; Santure, et al. 1990). Some characterize this in-

migration as part of an aggressive territorial expansion of the Oneota cultural tradition leading to 

intrusion, replacement, or displacement of peoples across US Midwest and eastern Prairie Plains 

(Hollinger 2005). Oneota expansion coincided with a rapid decline in Middle Mississippian 

influences in these regions and with the onset of the droughty Pacific climatic episode (Gibbon 

1995). While many Late Woodland populations in the riverine Midwest and western Great Lakes 

were replaced by or integrated into Oneota peoples during this expansion, CIRV societies on 

northern Middle Mississippian frontier, maintained their positions in fortified temple mound 

centers, and outlying sites, and entered into a period of coexistence with an intrusive Oneota 

population. At the regional level, the sudden appearance of five Oneota components along a 27 

km stretch of the Illinois River circa A.D. 1300 and biodistance indicators in the Norris Farms 

#36 cemetery population attests to the occurrence of a migration process in the CIRV, though the 

location of origin of the Oneota immigrants is unknown (Esarey and Conrad 1998; Santure, et al. 

1990; Steadman 1998). Recent archaeological inquiry in the Late Prehistoric CIRV has focused 

72 

on the unprecedented levels of violence seen in burial and cemetery contexts both prior to and 

following the Oneota in-migration that catalyzed the Crable phase assignation (Bengtson and 

O'Gorman 2017; Emerson 1999; Hatch 2015, 2017; G. R. Milner 1999; G. R. Milner, et al. 1991; 

Steadman 2008; Vanderwarker and Wilson 2016; Vanderwarker, et al. 2013; G. D. Wilson 

2012). Conflict and warfare, as an analytical topic, has featured prominently in discussions of 

cultural and biological evolution more broadly but more especially in regard to interactions 

among and between middle complex societies such as Mississippian and Oneota peoples 

(Carneiro 1970; Dye 2013; Golitko 2010; Keeley 2014; Maschner and Reedy-Maschner 1998; G. 

R. Milner 1999). Although the CIRV is remarkable within the corpus of eastern North American 

prehistory for its evidence of levels of interpersonal violence, evidence indicating the community 

scale coexistence of these distinct but interrelated cultural groups is also apparent. This is not to 

say that warfare was not in-grained in both Mississippian and Oneota culture and society; it no 

doubt was. However, ethnographic accounts of societies likely descendent from various Oneota 

and Mississippian peoples suggest strongly that both war and peace structured both intra- and 

inter-group interactions in a perhaps cyclical nature (Dye 2013; Landes 1959). Coexisting 

Oneota and Mississippian material culture at multiple sites at the household level provides the 

opportunity to examine the various social interrelationships that were present during the Crable 

phase and to perhaps better understand the preceding Mississippian phases of the CIRV (Esarey 

and Conrad 1998). It is my contention here that extant definitions of CIRV peoples, especially 

during the Crable phase, may place too great an emphasis on conflict at the expense of 

understanding and attempting to explain more nuanced relationships between these peoples.  

 

While both Conrad (1991) and Harn (1994) have previously parsed the Crable phase into 

two separate phases (the Crabtree (A.D. 1300-1375) and Crable (A.D. 1375-1450) phases), the 

73 

most recent phase assignation is followed here (Esarey and Conrad 1998). At or immediately 

prior to the Oneota in-migration, there appears to be a consolidation of Mississippian sites and 

peoples in the Anderson Lake and La Moine River mouth areas, but with one extreme northerly 

outlier in the form of the Ten Mile Creek site. Radiocarbon assays performed as part of this 

dissertation place two previously undated sites, Ten Mile Creek (11T2) and Star Bridge 

(11Br105), definitively within the Crable phase (see figure 3.6). 

 

Figure 3.6 Probability distributions of four recalibrated dates for Ten Mile Creek and Star Bridge sites; 

dates include DirectAMS Codes D-AMS 020156 – D-AMS 020159 respectively 

Most of the evidence used to define the Crable phase is derived from the phases’ type 

 

 

site, Crable. The Crable site is located in southern Fulton County on narrow strip of bluff edge 

overlooking the Anderson Lake Conservation Area. Archaeological research at the site has been 

a mixture of amateur and pot hunting efforts dating back to at least 1879 and professional 

excavations stretching back to the early 1930s; though no known professional excavation has 

taken place at the site since the 1970s (K. Sampson 2000). The Crable site constellation consists 

of a village area, the remains of a platform mound that was bulldozed by the landowner 

following a soured land deal, a ridge of smaller mounds, and at least four cemeteries (Painter 

2014; K. Sampson 2000). Given amateur and illicit archaeological interest in entire vessels, pot 

74 

hunting in the cemetery was extensive. Unfortunately, these amateur and illicit efforts left little 

behind to aid in understanding the nature of the occupation at Crable aside from the equally 

extensive collections of artifacts from grave goods and a handful of excavation photographs (H. 

G. Smith 1951). Radiocarbon assays from the village area date to the 14th and early 15th centuries 

A.D. (see Figure 3.7).   

 

Figure 3.7 Probability distributions of four recalibrated dates for Crable and the Oneota occupation of the 

C.W. Cooper sites 

 

 

Evidence of Crable’s connection to the Mississippian Southeastern ceremonial complex 

include conch-shell masks marked with the weeping-eye motif, copper and shell pendants with 

repoussee circles and crosses, shell gorgets with incised spiders, rattlesnakes, and avian figures, 

pottery decorated with the cross-in-circle motif, and a chipped flint mace (H. G. Smith 1951). 

Crable, however, posed quite the challenge to researchers when originally described as a result of 

the mixed Oneota and Mississippian assemblage, which was deciphered to be contemporary in 

an early publication describing the site based in part on an inventory of artifacts from Glenn 

McGirr’s collection from the site (K. Sampson 2000). While the culture-historian perspective of 

early to mid-20th century archaeology typically endeavored to separate out material culture based 

on decoration and form in order to define time-space systematics, Hale Smith noted that “if one 

75 

is to obtain a valid conception of the site, the culture complex must be viewed as a cultural 

whole…where mixture occurs, it is unwise to make a marked distinction in cultural items as 

many traits are co-existent in both the Middle and Upper Mississippi phases” (H. G. Smith 

1951:32).  

 

Unclear mixing between Oneota and Mississippian peoples in the Crable phase is not 

unique to the Crable site alone. Of the five known Bold Counselor sites in the CIRV, there is a 

spectrum of inter-group social interaction patterns with their local Mississippian neighbors 

exhibited based on currently available data. From the assemblage at the C.W. Cooper (see Figure 

3.7) site that is characterized solely by Oneota ceramic decoration and vessel forms, to evidence 

of cohabitation and at least some integration of Oneota and Mississippian peoples at the 

household level at both Morton Village and the Crable site (Esarey and Conrad 1998; Santure, et 

al. 1990; H. G. Smith 1951), the Bold Counselor occupation of the CIRV during the Crable 

phase indicates that cooperative strategies must be considered alongside evidence of endemic 

hostilities in the region. For example, while the Crable site exhibits the hallmarks of a 

Mississippian regional center such as a pyramidal mound and adjacent plaza, some 15% of 

ceramic artifacts recovered from the site have decoration that has been ascribed to the Oneota 

tradition (Esarey and Conrad 1998). Further, every feature excavated at Crable thus far shows a 

minor amount of Oneota ceramic vessels alongside a predominantly Mississippian admixture 

(Painter 2014). In remarking on the presence of Oneota decoration found on an otherwise 

uniquely Mississippian vessel type, the shallow or deep rimmed plate, Smith (1951:28) “infers 

that a transference of technique has taken place, probably indicating a culture fusion from two 

separate sources.” On the other hand, that Ten Mile Creek, Star Bridge, and Lawrenz Gun Club 

each have occupation components that date unambiguously to the Crable phase and are 

76 

characterized by non-existent or an extremely minor admixture of Oneota ceramic decoration 

indicates that Mississippian chiefly societies were not uniform in their attitudes toward the 

community scale cohabitation of Oneota immigrants. That is, while Mississippian peoples lived 

alongside Oneota peoples quite unambiguously at both Crable and Morton Village (O'Gorman 

and Conner 2016; H. G. Smith 1951), there is no evidence of such community scale cohabitation 

at Star Bridge or Ten Mile Creek based on the ceramic assemblages analyzed as part of this 

dissertation. Ceramics with distinctly Oneota decoration are present at the Lawrenz Gun Club 

site, though it is presently inconclusive as to whether the site was characterized by cohabitation 

of Mississippian and Oneota peoples during the Crable phase (Lawrence Conrad 2017, personal 

communication). Bold Counselor Oneota peoples appear to have not been uniform in their 

attitude toward local Mississippian peoples either, with distinctly homogenous Oneota 

assemblages at C.W. Cooper and limited surface scatter recovered from the Otter Creek site as 

well. That is, while Oneota decoration is present on plates, a Mississippian ceramic form, at 

Morton Village and Crable, there are no known examples of plates recovered from either C.W. 

Cooper’s or Otter Creek’s Oneota occupations (Esarey and Conrad 1998; H. G. Smith 1951).  

 

These observations presuppose the contemporaneity of each of these sites, which is a 

matter of debate. However, this discussion should make it apparent that explaining patterns of 

social interaction in the Late Prehistoric CIRV through the lens of warfare as a ‘prime mover’ is 

entirely insufficient. That is, the Oneota presence alongside Mississippian peoples during the 

Crable phase provides a setting wherein nuanced evidence may support the sentiment that social 

interaction, “trade and exchange are as likely to breed conflict as cooperation and understanding” 

(Emerson 1999:38). That is, material remains from the Crable phase suggest a duality of social 

structure between cooperation and conflict, with a high likelihood that social institutions were 

77 

enacted to at times prioritize war and at times counterbalance war with peace, and that conflict 

was likely pursued between sites or communities ascribing to the same supra-group to a greater 

or lesser frequency as conflict being pursued between sites or communities ascribing to different 

supra-groups or polities (Landes 1959). The proximity of Mississippian chiefly societies to 

Oneota tribal peoples at times resulted in population aggregation, increasing centralized 

leadership, escalated levels of violence, and increased territorial boundedness (Emerson 1999). 

Yet, at other times, and perhaps in response to that escalation in violence, Oneota and 

Mississippian peoples endeavored to overcome their differences and engage in direct interaction 

based on economic, social, political, and perhaps religious impetuses, leading to the 

hybridization of ceramic vessel forms and decoration, perhaps intermarriage, and certainly 

household scale cohabitation. It is argued here that this duality should play a more prominent 

role in discussions of social dynamics in the CIRV in the Crable and preceding phases as 

opposed to a focus on warfare alone.  

 

As part of their designation of the Bold Counselor taxonomic phase, Esarey and Conrad 

(1998:53-54) remark that: 

Group continuity in the form of retained and progressively evolving traditional cultural 
elements is apparently maintained through this local sequence. Bold Counselor phase [or 
Crable phase] is simply the addition of an extraneous cultural unit that interacts with the 
contemporary local inhabitants differentially on a site by site basis. 
 
We have seen that the Crable and household ceramic assemblages include Bold Counselor 
and Late Mississippian vessels. It would not be difficult to imagine that vessels would be 
exchanged in a cohabitation setting. Yet at Crable, not only were both household 
assemblages mixed, but the fill of every pit feature and every house basin yet examined has 
contained both Bold Counselor and Late Mississippian pottery. 
 
It may be that for the Crable site, the minority Bold Counselor population was integrated not 
as a political unit, but as marriage partners, individual refugees, or captives. The subtle 
implications of these various scenarios are brought out when it is seen that, at other sites with 
Bold Counselor and Late Mississippian cohabitation, the relative proportion of each group 
present is highly varied…Even more than usual, interpretation rests heavily on chronology.  

78 

 
These potential interaction scenarios between Mississippian and Oneota peoples at Crable are 

thus numerous and unclear based on present evidence. Painter (2014:96-105) outlines and further 

discusses these scenarios as raised by Esarey and Conrad, but ultimately finds a lack of strong 

evidence to support one hypothesized scenario over the others. The most intriguing aspect of the 

occupation of Crable is that Oneota peoples were able to produce numerous artifacts at the site 

that are quite unambiguously characteristic of Oneota peoples in other contexts. These include 

pottery with wet paste trailed designs typical of Oneota peoples, ‘snub’ edge scrapers, grooved 

maul, tanged shell spoon, and certain copper implements (H. G. Smith 1951:33-34). Without 

extensive professional excavation data, and perhaps even despite it should it become available at 

a future date, the nature of the Crable occupation by Bold Counselor and Late Mississippian 

peoples may never be clear.  

 

Chronological precision alone at a scale refined enough to provide disambiguation 

between site occupations during the Crable phase is as yet untenable. In lieu of advancements in 

dating technology and continued professional excavation at Crable and other Late Mississippian 

and Bold Counselor phase sites, this dissertation seeks to further examine the nature of social, 

economic, and identity politic interactions between the taxonomically distinct, but socially 

interrelated, Mississippian and Oneota peoples that lived side by side during the Late Prehistoric 

CIRV.  

 

3.10  The Bold Counselor Phase Oneota 

  

While the Bold Counselor Oneota have been discussed in detail in the preceding Crable 

phase section, some treatment of Bold Counselor peoples is warranted. While Esarey and Conrad 

(1998) defined a Bold Counselor phase as a taxonomic entity, given the entanglements between 

79 

Late Mississippians and Oneota peoples in the CIRV this discussion will focus on the Bold 

Counselor phase as a cultural expression of the Oneota archaeological tradition. The origins of 

Bold Counselor Oneota peoples is unknown prior to their emergence in the 14th century A.D. 

CIRV. Similar to other Oneota expressions, Bold Counselor phase peoples have been interpreted 

as tribal-scale sedentary villagers who practiced a mixed subsistence strategy including the 

cultivation of crops such as maize, hunting, fishing, and gathering of an array of locally available 

floral and faunal resources (Henning 1995; G. R. Milner, et al. 1991; Overstreet 1997). Ceramic 

stylistic similarities have been noted between Bold Counselor phase sites in the CIRV and 

Oneota sites in the Red Wing and Apple River areas (Conrad and Esarey 1983; Emerson and 

Brown 1992; Hollinger 2005; Santure, et al. 1990:154). Bold Counselor phase ceramics have 

been recovered from the Wever Terrace Village of Iowa, the Lima Lake locality, the Kingston 

locality, the Sponemann site in the American Bottom, and perhaps the McKinney Oneota village 

(Benn 1998; Henning 1995; Hollinger 2005; Jackson 1992; Nolan and Conrad 1993). Bold 

Counselor phase ceramic assemblages consist predominantly of jars and bowls with a minor 

admixture of deep-rimmed plates. Domestic jars are globular vessels characterized by high, 

everted rims (or long lip lengths), shoulder decorations consisting of horizontal or zig-zag lines 

with punctate borders and “stab and drag” vertical decorations trailed onto wet paste (Esarey and 

Conrad 1998). The most common jar should decoration motif consists of three to five trailed 

horizontal lines bordered by punctates above vertical stab and drag trailing. Bowls are common 

and typically plain, though many borrow the Crable deep-rimmed plate design, utilizing the plate 

flare to trail chevron and zig-zag lines with zoned or bordering punctates, even occasionally 

borrowing stylistic norms seen on incised Mississippian plates (Vogel 1975). Aside from 

80 

ceramic style and technology, it is the unique relationship Bold Counselor phase peoples shared 

with Mississippian peoples that distinguishes them from other Oneota groups.  

 

A plethora of speculative scenarios have been proposed to account for the presence of 

Bold Counselor phase peoples in the CIRV. These include motivations of conflict between 

Mississippian peoples in the CIRV and another Upper Mississippian group, the Langford 

tradition of the Apple River region (Emerson 1999); a product of intrusion or alliance building 

between Oneota and CIRV Mississippian peoples (G. D. Wilson 2012); as one of a series of 

repeated southerly migrations of northern groups that would continue into the proto-Historic 

period Illinois (H. G. Smith 1951); an intrusion at the front of a cultural expansion of Oneota 

groups (Henning 2005; J. J. Wilson 2010); or that “Bold Counselor phase Oneota may have 

originated among the earlier Oneota of the Apple River region and may have moved into the 

Central Illinois River valley at the invitation of the local Spoon River Mississippians [and] may 

have formed an alliance…against a third group” (Hollinger 2005, p. 160). It seems unlikely that 

‘smoking gun’ evidence will ever be found to accurately identify the location of origin of Bold 

Counselor phase Oneota peoples. However, the most plausible speculative scenario for their 

presence in the CIRV is one of Oneota cultural expansion motivated in part by a waning 

Mississippian hegemonic frontier, climatic conditions that saw increases in drought and 

difficulty in maintaining horticultural/incipient agricultural productivity in northerly latitudes, 

and perhaps Oneota socio-economic reorganization that favored densely occupied communities 

adjacent to habitats most favorable for maize horticulture/incipient agriculture (Gibbon 1972; 

O'Gorman 2010; Overstreet 1997). 

 

Available data from CIRV settlements (Figure 3.1) exhibit varying degrees of 

intermixing between Mississippian and Oneota material culture. From the Oneota assemblage at 

81 

C.W. Cooper that “shows almost no evidence of any influence or actual presence by the Late 

Mississippians” (Esarey and Conrad 1998:41) and the ‘purely’ Late Mississippian assemblages 

at the fortified Ten Mile Creek and Star Bridge Mississippian mound centers (Conrad 1991), to 

evidence “probably indicating a cultural fusion from two separate sources” at the Crable mound 

center (H. G. Smith 1951:28), no discernible pattern emerges as to the nature of cultural 

interrelationships in the Late Prehistoric CIRV. Tantalizing evidence for cultural mixing between 

Oneota and Mississippian peoples is most readily apparent in the mixing of ceramic traits. For 

example, the use of deep-rimmed plates by Oneota peoples is apparent at several sites in the 

CIRV, but virtually absent in Oneota contexts outside this region. In fact, the presence of Crable 

plates at Oneota sites outside the CIRV is a common indicator for the potentiality of a Bold 

Counselor phase presence (Benn 1998; Henning 1995). At the Crable Mississippian mound 

center itself, some 14% of vessels from a sample of pit features were ascribed to Oneota, leading 

Esarey and Conrad (1998:46) to suggest that “the most likely explanation for these assemblages 

is that Bold Counselor people were present (in one social context or another) as a minority 

admixture to Crable’s overwhelmingly Mississippian-derived population. Furthermore, this 

admixture seems to represent social integration at the household level.” The Morton Village site 

appears to indicate the inverse: an Oneota village with an admixture of Late Mississippian people 

(O'Gorman and Conner 2016). Trends in technological distinctions suggest possible interaction-

based transmission processes from Oneota and perhaps other Upper Mississippian peoples as 

possibly being influential in type-attribute trends seen on distinctly Mississippian ceramics. 

Specifically, domestic jar rim heights (or lip lengths) and plate flare angles are known 

qualitatively to increase overtime in the CIRV (Harn 1978). Analyzing these trends 

quantitatively reveals that sites with an Oneota presence, which are also the most recent pre-

82 

Columbian sites in the region, show the highest values for these metrics, while earlier 

Mississippian sites show the lowest values. Perhaps interaction based transmission processes 

from Oneota and other Upper Mississippian peoples were influential in the morphological 

changes demonstrated in these type-attributes (A. J. Upton 2016).  

 

Aside from Bold Counselor habitation sites, the Norris Farms #36 cemetery provides key 

data about these peoples themselves. The Norris Farms #36 cemetery represents the largest 

Oneota burial sample presently available, with some 264 burials assigned to the Bold Counselor 

phase (Santure, et al. 1990; Tubbs 2013). The cemetery is a modest “D”-shaped mound situated 

on a bluff edge overlooking the Illinois River valley and is immediately adjacent to the Morton 

Village habitation site. As is typical of Oneota mortuary treatment elsewhere, the majority of 

burials were single individuals, extended, and elliptical in shape (Foley-Winkler 2011; Kreisa 

1993; O'Gorman 1996). Fully one-third of adult burials in the Norris Farms #36 cemetery died a 

violent death, though this seemingly high rate of trauma may not be unique to the Bold 

Counselor phase (G. R. Milner 1999; G. R. Milner, et al. 1991; Santure, et al. 1990), as Oneota 

in Wisconsin appear to be characterized by similar rates of violence (Oemig 2016). Many 

individuals were likely interred in open graves, with evidence suggesting that some of which 

were covered by a pole roof prior to being filled (Santure, et al. 1990:72). Non-celestial 

orientation of the graves is apparent. From a comparative mortuary perspective (Bengtson 2012; 

L. G. Goldstein 1981, 2006), both similarities and differences exist between Norris Farms #36 

and nearly Mississippian mortuary sites that may be related to ethnic identity. Differences such 

as the covered graves, artifact styles, and non-celestial orientation of the graves suggest a 

distinctly Oneota ethnic identity at Morton Village (Tubbs 2013). However, similarities such as a 

preponderance of single-internment burials, occasional instances of post-internment additions, a 

83 

wide range of burial furniture with primarily utilitarian objects accompany male internments, and 

a positive linear relationship between age and burial furniture density suggest some degree of 

permeability of ethnic identity among Bold Counselor peoples in the CIRV (L. G. Goldstein 

2000; Santure, et al. 1990; Tubbs 2013). 

 

3.11  Regional Abandonment 

 

After an approximately 250 year history of occupation by Late Prehistoric peoples, the 

central Illinois River valley witnessed complete regional abandonment circa 1425 – 1450 A.D. 

(Esarey and Conrad 1998; Santure, et al. 1990). In fact, there were no substantial occupations 

until the late 17th century A.D. when Illiniwek from northern Ohio took refuge in the region 

while fleeing from Iroquoian aggression further to the east (Ethridge 2009a; Hollinger 2005). 

Regional abandonment was not unique to the CIRV during the mid-15th century A.D.: the 

American Bottom, the lower Ohio Valley, interior western Kentucky, lower Savannah River 

Valley, and Upper Susquehanna drainage all witnessed wholesale depopulation and 

abandonment (Cobb and Butler 2002). Explanations of abandonment often incorporate 

deteriorating or changing climate as a primary contributing factor, however social stresses and 

the responses of social leaders to climatic conditions were no doubt critical factors as well. 

Hollinger (2005:162) posits a scattering of Bold Counselor peoples to the Lima Lake locality and 

other portions of the Mississippi Alluvial Plains region where they would have been absorbed by 

local Oneota groups; and likewise posits a merging of Mississippian peoples in the CIRV with 

Angel phase Mississippians to perhaps form the Caborn-Welborn phase of Mississippian peoples 

at the mouth of the Wabash River.  

84 

 

Regardless of the outcome, the CIRV represents a significant contribution to 

understanding social structure during the Late Prehistoric period in the U.S. Eastern Woodlands. 

This regional case study will be the backdrop for exploring long-term trends in networks of 

social interaction and categorical identification, majority-minority power dynamics, and 

negotiations of identity politics. In particular, this regional and cultural backdrop will be the 

focus of an examination of how communities of ceramic artisans constructed social and 

economic relations before and after an intrusive migration process to better understand the ways 

humans navigate cultural contact and multicultural community scale interrelationships.  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

85 

CHAPTER 4 METHODOLOGICAL CONSIDERATIONS 

 
 
4.1 Introduction 

An essential component to any scientific endeavor is a series of systematic and 

reproducible protocols for the collection and analysis of data. Collecting data from 

archaeological contexts poses a number of challenges toward this end. For example, random 

sampling is often impractical due to limitations on data availability and the expense and time 

horizons required for excavation or survey. Furthermore, archaeological artifacts or features 

available in museum or private collections are often fragmentary and incomplete. From an 

analytical perspective, new methodologies have burgeoned at an unprecedented rate in the latter 

half of the 20th and early 21st centuries. These issues therefore require some treatment regarding 

the methodologies employed in this dissertation for data collection and data analysis in 

particular. In this chapter, I provide such treatment. 

Unlike many anthropological archaeological dissertations which separate theory, 

methodology, analysis, results, and interpretations into separate chapters, the four chapters that 

follow this contain each of these pieces as a bounded whole, much like an academic journal 

article. In order not to detract from the linear arguments made in Chapters 5 – 8, this chapter 

incorporates a rich discussion of many methodological considerations including descriptions of 

statistical measures for social network analysis, data collection routines, and intricacies related to 

the collection of mineralogical and geochemical data from sediments and archaeological 

ceramics. This chapter therefore ‘fills in the gap’ in those cases where it was not deemed 

essential to provide an extended treatment of methodology or analytical protocol in the chapter 

itself. 

 

86 

4.2 Data Collection Methods  

Discussed here the methodologies for data collection used in Chapters 5 and 6 at greater 

length. Specifically, this discussion considers how continuous type-attributes were measured and 

how stylistic decorations were identified and categorized. In this way, it is hoped that this study 

may be seen as systematic in approach and the methodologies reproducible inasmuch as possible 

in other archaeological contexts.  

 
4.2.1  Ceramic Vessel Technological Data 

In Chapter 5, I introduce a model adapted from cultural transmission theory designed to 

differentiate between artifact attributes that are likely constrained by social forces from those 

constrained by engineering forces. To apply this model, continuous artifact attribute 

measurements were taken from three distinct vessel classes: domestic jars, burial jars, and plates. 

Specific guidelines for each of the continuous artifact attributes are provided in the coding sheet 

in Appendix A. I provide additional detail here as to how each measurement was systematically 

collected.  

Analog calipers were used to measure eight type attributes on jars, seven type attributes 

on plates, and four type attributes on burial jars. Because these vessels were made by hand in a 

non-standardized production context, it was necessary to take multiple measurements on each 

vessel. For each continuous attribute measurement, the maximal observation that was not an 

outlier was recorded. An outlier was assessed as being greater than or equal to twice that of any 

other measurement.  

Domestic jars are characterized by a globular shape with an everted rim (see Appendix F 

for jar profile samples). As a result, it was possible to assess up to eight attribute measurements 

on a continuous scale for each sherd. Jar orifice diameter was measured using an orifice diameter 

87 

chart. Because of the everted rim, the orifice diameter measures the greatest extent of vessel 

opening (i.e. as opposed to the restricted opening below the everted rim). In cases where an 

insufficient amount of the jar rim was present to discern an accurate diameter, no measurement 

was recorded. Jar lip thickness refers to the extruded edge or margin of the orifice of the vessel 

and measures the distance from the interior of the everted rim lip to its exterior. Measurements 

for domestic jar shoulder thickness were taken above where the vessel wall angle is 90˚ 

perpendicular to the vessel opening. In other words, the shoulder is maximal measurement 

observed between the point of everted rim attachment and where the vessel wall angle is 

perpendicular to the vessel opening plane. Domestic jar wall thickness was measures within a cm 

of the equator of the globular jar (or where the vessel wall angle is 90˚ perpendicular to the 

vessel opening plane, and as a result was often not present. Jar rim height measures the area 

between the lip and neck of the vessel. Finally, domestic jar rim angle was measured using a 

protractor where a measurement of 90˚ equates to a completely vertical rim, a measurement less 

than 90˚ equates to an in-slanting rim, and a measurement of 360˚ equates to a completely 

unrestricted vessel opening. A flat plane such as the underside of a desk was used to determine 

the opening plane of the jar prior to recording the rim angle measurement.  

Burial jars are typically intact due to the great care taken in the positioning and 

entombing of them alongside deceased individuals. As a result, measurements were constrained 

to four features. Of the four, three were measured following the same criteria as for domestic jars 

and include orifice diameter, lip thickness, and rim height. The fourth attribute measures burial 

jar height, or the vertical distance between the base of the vessel and its opening plane.  

Plates are used to primarily serve food and are characterized by an outflaring rim 

attached to a globular body (see Appendix F for plate profile samples). This enables seven 

88 

measurements to be observed. Plate diameter refers to the circumference of the opening plane of 

the plate, or where the plate touches a surface when flipped upside-down, and was assessed using 

a rim diameter chart. The plate flare is used to refer to the outflaring rim and was assessed in 

length, or the distance from the opening of the globular plate well to the plate lip, as well as in 

angle. Plate flare angle measures the degree of eversion of the outflaring rim above the globular 

well of the plate. Plate lip thickness measures the margin of the plate rim prior to any tapering. 

Plate thickness below lip measures the attachment point of the flare to the well or the maximal 

thickness of the outflaring rim, whichever was found to be thicker.  

Both domestic jars and serving plates were often adorned with stylistic decoration. These 

decorations were either incised into a dry paste or trailed into a malleably damp paste. In either 

case, incising thickness or trailing thickness measure the maximal observed thickness of these 

decorative elements.  

A host of other features were collected for domestic jars, burial jars, and plates that were 

not included in any analysis presented in this dissertation. These features are described in the 

Coding Sheet in Appendix A and will be made available in a tDAR archive at the following 

static link: https://core.tdar.org/project/447475  

 
4.2.2  Ceramic Vessel Stylistic Data 

Chapter 6 explores networks of social identification based on proportional similarities 

among sites in decoration grouping categories derived from stylistic decoration present on plates. 

A linear sequence was used to arrive at decoration grouping category assignments. The author 

alone is solely responsible for category assignments in order to avoid inter-observer 

inconsistencies. The first step in this process was the identification of wholly unique design 

features, which encompass both design techniques and decoration motifs. A design technique 

89 

refers to the technique used to decorate the vessel – whether incised, trailed, or trail-impressed. A 

decoration motif, on the other hand, refers to the specific shape and form of elements comprising 

the decoration. It was necessary to make such a distinction because of the different 

methodological processes required to apply decorations in these ways. Incised decorations 

necessitate a dry paste while trailed or trail-impressed decorations necessitate a wet paste. All 

plates were assessed for the combination of these features and a unique type number was 

assigned. For example, an identical decoration motif applied using distinct design techniques 

would be assigned different unique type numbers. These unique types are described in Appendix 

A. It is often difficult to determine if a design was unique based on a narrative description of a 

unique type decoration and as a result high-resolution photographs of each sherd were taken and 

repeatedly referenced during this process. Unique decoration type-categories totaled 94 across 

the 429 vessels with designs present.  

Since the goal of Chapter 6 was to explore social identities through symbolic 

communication, the next step in the linear sequence of category assignments was to group the 

unique types into decoration grouping categories based on perceived similarities in decoration 

motifs alone (i.e. disregarding design technique). This emphasized symbolism alone as opposed 

to technique. To accomplish this in a systematic way, photographs of plates were traced, in order 

of unique decoration motif type, using an old computer monitor that was setup flat on a desk. 

Tracing the actual designs, as opposed to appealing to the artistic intent of the decoration and 

embellishing any imperfections, enables focus to be placed on overall presentation and execution 

of the motifs present and aided in identification of other similar designs as a result. In each case, 

photographs of all plates with decorations that were previously categorized as belonging to the 

unique type were referenced during the sketching process and the most emblematic was chosen 

90 

for sketching. Photographs of each plate lacking a decoration grouping category assignment were 

then meticulously inspected to determine whether or not they might also share the symbolism 

present in the decoration grouping category in question. This process was iterated until all 

decorated plates were assigned to a decoration grouping category, determined to be wholly 

unique, or indeterminate in category assignment. It was often necessary to assign plates to a 

decoration category based on incomplete or partial decoration motifs present. In these cases, 

license was not taken beyond what was present on the plate. In other words, no assumptions were 

made about what other motifs might be present based on the co-presence of two motifs on other 

plates. Instead, decoration motif categories were assigned often based on potentially incomplete 

motifs. Nevertheless, because the potentially incomplete motifs were deemed similar in the 

actual motifs present, the decoration motif categories assigned should be considered fairly 

robust. This process resulted in 29 decoration grouping categories used in Chapter 6. Sketch 

tracings are provided in Appendix E. Photographs may be requested from the author for research 

or teaching purposes.  

 
 
4.3 Compositional Analysis of Archaeological Ceramics 

Following the development of effective methodology in the elemental, mineralogical, and 

compositional characterization from the mid-20th century to the present, identifying shared 

source information for artifacts has become a well-established and common research tool in 

archaeological studies (Glascock 2016; Neff 1993). Compositional analysis in archaeology 

explores human behavior through chemical fingerprints obtained from archaeological materials. 

Information from those chemical fingerprints is used to discern the location of raw material 

sources, identify production sites, investigate production or manufacturing technology, or trace 

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the movement or circulation of artifacts between different regions or production locales. The 

basic assumption underlying this methodology is that compositional variability in archaeological 

artifacts will arise from the geological forces responsible for the production of the raw materials 

used to create the artifacts, often in conjunction with technological choices made by the 

manufacturer. Studying human behavior from this evidence is a complex endeavor, especially 

when considering ceramic artifacts given the heterogeneous nature of clay and the multitude of 

factors that may influence the final measured composition of a pottery vessel (Neff 2003).  

The following discussion provides an overview of central concepts related to the 

compositional analysis of ceramic artifacts in particular as they relate to the compositional 

analyses presented in Chapter 7. The objective is to provide a discussion of many of the issues 

inherent in compositional analysis techniques more broadly and their application to 

anthropological archaeological research contexts more specifically.  

 

4.3.1  Compositional Analysis in Archaeology 

At the most basic level, compositional analysis in archaeology is a means to identify 

groups of similar objects. The most commonly addressed research goal built on group 

identification is the movement of objects in the past (Golitko 2010; Speakman, et al. 2007). 

Analyzing the movement of objects is theoretically grounded in the concept of the “provenience 

postulate”, which proposes “that there exists differences in chemical composition between 

different natural sources that exceed, in some recognizable way, the differences observed within 

a given source” (Weigand, et al. 1977:24). Because each source location is produced as a result 

of context-specific geological forces, the provenience postulate applies in unique ways to 

different classes of raw materials. Sourcing ceramic artifacts in particular requires a variety of 

92 

unique considerations compared to other inorganic materials. For example, while virtually every 

obsidian flow on earth is chemically distinct (Glascock 2002), raw clay resources are often 

multitudinous throughout the landscape and found in often large and diverse outcrops that are 

formed and transported through an array of geological forces that may lead to a blending of clay 

particles (Eerkens, et al. 2002; Gjesfjeld 2014). Nevertheless, the ubiquity of clay resources and 

ceramic artifacts in prehistoric contexts lends to the advantageous nature of compositional 

analysis to answer a host of behavioral questions despite these and other challenges. For 

example, while obsidian or glass artifacts can often only answer questions related to long-

distance exchange as a result of the vast distances between production or outcrop locales, pottery 

sourcing studies can often provide more informative results when examining exchange 

relationships at intra-regional or inter-regional scales (Dussubieux and Oliver 2016; Falabella, et 

al. 2013; Fowles, et al. 2007; Pearce and Moutsiou 2014; Zvelebil 2006). This is particularly 

relevant in the case of archaeological cultures such as the Oneota, which are often only able to be 

differentiated internally based on distinctions in ceramic artifacts and are therefore often 

recognized as a ‘pottery culture’ (Henning 1998; Hollinger 2005; Overstreet 1997).  

A number of methods exist for the chemical or compositional measurement of ceramics. 

The earliest such method used in archaeology was neutron activation analysis (NAA), following 

the suggestion of renowned physicist J. Robert Oppenheimer (Harbottle 1976; Sayre, et al. 

1957). Since then, many other analytical techniques from the physical sciences have been 

applied to archaeological studies for the purposes of compositional analysis. These include X-ray 

fluorescence (XRF), portable XRF (pXRF), particle-induced X-ray emission (PIXE), Scanning 

Electron Microscopy with Energy Dispersive Spectra/Wavelength Dispersive Spectra (SEM-

EDS/EDX), electron probe microanalysis (EPMA), inductively coupled plasma-mass 

93 

spectrometry (ICP-MS), and laser ablation ICP-MS (LA-ICP-MS) (Glascock 2016; Golitko 

2010:216). For many years, instrumental neutron activation analysis (INAA) was the method of 

choice for archaeological composition analysis due to the presence of numerous first and second 

generation dedicated research reactors at national laboratories, museums, and major universities 

(Glascock 2002; Neff 1993, 2003). Though LA-ICP-MS has increased ‘market share’ relative to 

INAA in recent years largely due to the waning of available research reactors for INAA and due 

to the lower detection limits, higher range of elements able to be characterized, and rapid ability 

to analyze many samples by LA-ICP-MS (Dussubieux and Oliver 2016; Glascock 2016). 

Neff and colleagues (Golitko 2010:216-217; Neff 2002:202) detail five hypotheses that 

should be considered when analyzing the chemical composition of pottery: 

1) 

Chemical patterning is a reflection of differences in elemental concentrations 

present in the source clay(s) and is therefore a function of local geological 

variability, 

2) 

The composition as measured principally reflects technological choices made by 

potters in paste preparation, such as the mixing of clays or additions of aplastic, 

thereby modifying the compositional signature of the elemental fingerprints of the 

clay resources used, 

3) 

The use-life of the ceramic objects has modified the chemical patterning of the 

paste as a result of the leaching of organic or inorganic compounds into the 

ceramic matrix, 

4) 

The raw clay chemical composition is altered as a result of diagenesis, or post-

depositional changes to the chemical profile of the ceramic objects, 

94 

5) 

Some combination of the four factors above has resulted in the chemical 

composition readings. 

Controlling for the five factors above requires knowledge about local geological 

variability regarding raw clay resources, knowledge about cultural practices related to vessel 

production such as clay preparation and tempering additions, knowledge about the chemical 

profiles of any tempering additions, potential effects caused by the use-life of the ceramic vessels 

under consideration, and knowledge about soil chemistry in the location(s) where the ceramic 

vessels were recovered. The following sections provide a brief discussion of these factors, 

particularly as they relate to shell-tempered ceramics from the Late Prehistoric period of the 

central Illinois River valley.  

 

4.3.2  Clay: Geological, Chemical and Mineralogical Considerations 

Clays are complex materials from a variety of perspectives, but it is precisely this 

complexity which lends to their value as an adaptable raw material in many applications both in 

pre-modern and industrial contexts. At the most basic level, clays may be defined as a very fine-

grained earthy material that, when moistened, becomes plastic or malleable (Rice 2005). Clays 

result from the weathering of silicate rocks, which are formed via igneous, metamorphic or 

sedimentary forces, and clays reflect the original compositional profile of the specific rocks 

which weathered to form them following the removal of large particles (sands), oxides, and 

mobile cations (Golitko 2010; Keller 1964). Primary, or residual, clays are those that form in the 

same location as their geological parent source. Hydrological, aeolian, glacial, erosional, or other 

forces may transport clays (or their initial parent source material) to a different location. These 

are referred to as secondary, transported, or sedimentary clays and are most often the product of 

95 

marine, riverine, or lacustrine forces. This often leads to a higher organic content present in 

secondary clays but also a finer-grained and well-sorted substrate. In addition to their 

depositional nature, clays may be described in terms of their granular, chemical, or mineralogical 

properties. The following discussion will briefly touch on these descriptive lenses. 

Particle-size is an oft-used quantitative measure used in defining clays. Granulometry, or 

the measurement of the distribution of particle sizes, has been applied to distinguish between the 

individual mineral grains of sediments based on their diameter. The International Organization 

for Standardization (ISO) 14688-1:2002 establishes a scale of soil sediment particle diameter 

sizes where clays are the smallest in size at less than 2 µm (or 0.002 mm). While this standard is 

used by geologists and soil scientists, different scales for the definition of clays based on particle 

size are often considered by sedimentologists, colloid chemists, or geotechnical engineers. 

Nevertheless, it is the remarkably small particle size of clay minerals that enables the highly 

desirable characteristic of plasticity.  

Clays are composed of a number of different kinds of minerals, each falling within the 

less than 2 µm size range, but no consensus exists to impose order on or classify the minerals 

into discrete categories (Rice 2005). While mineralogists and soil scientists continue to examine 

and detangle the evolving nature of clay mineralogy, often as a lens to access the principles of 

mineralogical evolution more broadly (Hazen, et al. 2013), it is known that the multitudinous 

minute minerals that compose clay are arranged in a crystalline structure which results in certain 

chemical properties (Golitko 2010:218; Rice 2005:31-53; Velde and Druc 1999:35-38). Clay 

minerals are composed of flat sheets of aluminum and silica atoms that may be arranged in 

different layer combinations, or more rarely as lath or chain structures. Alumina and silica are 

the two chemical elements most resistive to the weathering forces that result in clay. As part of 

96 

the form of the crystalline structure, the aluminum and silica cations are strongly bound in two 

dimensions but weakly bound in a third direction. Within the lattice structure of layered silica 

and alumina, these bonding arrangements result from the interplay of dominant cations and the 

anions (most often oxygen) to which they become linked (though it should be noted that other 

major cations such as calcium, magnesium, sodium, titanium, iron, and potassium may link 

together layers). Clay plasticity arises from the ‘sliding’ of various sheets of silica-aluminum-

oxygen across one another along hydroxol bonds. When heated, hydrogen ions bond with 

oxygen anions to form water and are driven off as vapor. This leaves behind the silica-aluminum 

layers, which fuse together from the artificial metamorphic reaction. Once these layers are fused, 

clay takes on the solid and water impervious properties sought after in use as serving, storing, or 

artistic objects. If sufficient heat is applied during this process, the internal crystalline structure is 

destroyed. The very high refractoriness (or ability to maintain chemical and physical robustness 

when exposed to temperatures above 1,000 ˚F) enables fired clay to serve as a cooking vessel.  

 

4.3.3  Technological Choice and Pottery Production 

Technological choices and pottery production techniques may alter baseline clay 

compositions primarily through the addition of tempers and the mixing of different clay 

resources. When considering pottery for compositional analysis, the most significant 

confounding factor is the presence of non-plastic materials embedded in the ceramic paste 

matrix. As a result of these inclusions, bulk compositional profiles of ceramic artifacts reflect not 

only the geochemistry of the clay resource(s) used, but also any other ingredients used in pottery 

manufacture (such as tempering) or inorganic material inclusions that were not removed from the 

raw clay material (such as small pebbles) in addition to changes that result from use and 

97 

diagenesis (or the absorption of chemicals from the soil in which the sherds were deposited) 

(Gjesfjeld 2014; Stoltman, et al. 2005). The influence of added tempering on compositional 

readings and paste behavior in particular has been a source of debate (Boulanger and Glascock 

2015; Neff 2008; Peacock, et al. 2007; Stoner and Glascock 2012; Tite, et al. 2001; A. J. Upton, 

et al. 2015). However, given the often elementally restricted profiles of materials used in 

tempering (e.g., volcanic ash, mollusk shell, limestone) it has been demonstrated that tempering 

is likely to only modestly influence the identification of chemical source groups unless it is 

present in remarkably high (>80%) proportions relative to clay in the paste matrix (Eerkens, et 

al. 2002; Neff 2002; Neff, et al. 1989). Mathematical corrections and/or the removal of 

tempering-abundant elements from analyses are common strategies employed to control for the 

presence of tempering in compositional studies of ceramics (Cogswell, et al. 2015; Peacock, et 

al. 2007).  

Because the LA-ICP-MS technique used in this dissertation allows the researcher to 

sample specific locations on a pottery vessel, as opposed to a bulk sampling technique such as 

INAA that analyzes the entire sherd, the effect of tempering on vessel chemical composition are 

often able to be controlled for, but highly tempered pastes often require alternate means of 

dealing with the impacts of temper on chemical compositions. A mathematical method to control 

for the presence of shell tempering in vessels used in this dissertation was used and is discussed 

in detail in Chapter 7.  

Clay mixing, or the use of bits of discarded pottery as temper – known as grog, can be a 

more impactful issue, particularly for studies aiming to determine potential geologic resource 

exploitation areas as opposed to production locales of pottery. That is, the mixing of clays may 

obfuscate the final chemical composition of a vessel such that neither constituent clay may be 

98 

differentiated. However, since most studies of ceramic provenance are primarily interested in the 

circulation of ceramic vessels out of a production locale, as opposed to a geological source area, 

these factors are generally of minor hindrance.  

 

4.3.4  Use-Wear Effects on Sherd Chemistry 

Ceramic vessels are highly versatile tools, and with that versatility comes the potential for 

use-wear effects on sherd chemistry. Since the primary uses of ceramic vessels in prehistoric 

eastern North American involve organic materials and because elements present in organic 

materials are not typically measured in provenience studies, however, use-wear effects are 

generally negligible for impacting chemical concentrations (Golitko 2010). Examples of use-

wear effects that might result in a significant impact to sherd chemistry include the storing of 

metal coins or other metal objects.  

 

4.3.5  Diagenesis and Sherd Chemistry 

Perhaps the most impactful factor effecting sherd chemistry is that of post-burial 

alteration. A number of factors impact the role of taphonomy in changing sherd chemistry, such 

as the temperature to which a vessel was fired, the mineralogical and chemical composition of 

the sherd in question, and the burial environment of the vessel. These effects are thoroughly 

discussed by Golitko (2010:224-226). For the case of Native American pottery produced in 

eastern North America, the simple leaching of mobile elements is the most probably form of 

diagenetic alteration. This is due to the fact that Late Prehistoric pottery was open or pit fired to a 

maximum of some 700 °C due to constraints imposed by mollusc shell tempering and a lack of 

evidence for forced-air firing methods (A. J. Upton, et al. 2015).  

99 

4.4 Compositional Methods: pXRF, XRD, and LA-ICP-MS 

In order to look holistically at the chemical composition of ceramics in this dissertation, 

three different methods were used to explore chemical and mineralogical characterizations. The 

bulk of analysis was performed using LA-ICP-MS, which is discussed at length in Chapter 7. 

However, two other methods were employed toward different ends. First, due to the catastrophic 

burning of a number of sites incorporated in the analysis, some sherds were re-fired to significant 

temperatures (G. D. Wilson 2013). As a result, it was hypothesized that the chemical 

composition of those vessels may have been impacted. In order to test for potential changes due 

to re-firing, x-ray diffraction was employed. X-ray diffraction assesses the crystalline structure, 

or mineralogical makeup, of ceramic vessels and was used to determine whether or not sherds 

from sites that were incinerated have distinct mineralogical profiles from sherds recovered from 

sites that were not burned. X-ray diffraction methods and results are presented below and the raw 

data is provided in Appendix G.  

A recent technology, portable x-ray fluorescence (pXRF), allows for quite rapid and quite 

inexpensive characterization of a subset of chemical concentrations compared to LA-ICP-MS. 

However, pXRF is entirely non-destructive, highly portable, and much more affordable than LA-

ICP-MS. While the data produced by LA-ICP-MS and pXRF differ in many important ways, 

funding was obtained to collect pXRF data from a subset of vessels to determine if analytical 

results might be comparable to those obtained from LA-ICP-MS analysis of the same vessels. 

Work in this regard is on-going and as a result no pXRF analytical results are provided in this 

dissertation. However, the raw data will be curated alongside raw LA-ICP-MS data in a tDAR 

archive at the following static link https://core.tdar.org/project/447475 

 

100 

4.4.1  Portable X-Ray Fluorescence 

Portable X-Ray Fluorescence (pXRF) spectrometry, performed at Michigan State 

University, was used to analyze the elemental composition of a sub-sample of 30 ceramic 

artifacts with an objective to enhance understanding of the raw material prehistoric populations 

selected for ceramic production. The first group of artifacts were selected from a previously 

analyzed sample from Morton Village (11F2) while the second group was derived from Crable 

(11F249). Random proveniences were selected to reflect the compositional diversity that may be 

present within each site. The goal of this effort was to provide raw count data that may 

potentially be used to determine the range of compositional variation detectable through the use 

of handheld spectrometry.  

Analysis was performed using a Bruker Tracer SD-III with a 10 mm2 X-Flash SDD, 

peltier cooled, detector with a typical resolution of 145 eV at 100,000 cps. An x-ray tube Rh 

target was used with a max voltage of 40 kV. pXRF settings were set to 300 second timed assays 

at 40 kV 30 µA using a green filter (12 mil AI = 1 mil Ti + 6 mil Cu). Data were collected and 

analyzed using the S1PXRF and ARTAX software.  

Results of pXRF analysis are available via a permanent web link provided in Appendix 

B.  

 
 
4.4.2  X-Ray Diffraction 

X-Ray diffraction analysis was performed on all collected material at the Advanced 

Materials Characterization Center at the University of Cincinnati College of Engineering and 

Applied Science. Samples include 9 sherds, 9 outcrop localities, and 4 core samples. 

Diffractograms were collected on a Phillips X-Pert diffractometer operating with Cu-Kα 

101 

radiation at 45Kv and 40Ma. The samples were prepared for both bulk mineralogical 

quantification and clay speciation in order to acquire the full mineralogical dataset. Bulk mineral 

analysis was scanned from 5-70⁰ 2θ, with a step size of 0.02⁰ scanning at 0.5 seconds/step. Clay 
analysis was scanned from 5-32⁰ 2θ, with a step size of 0.02⁰ scanning at 0.5 seconds/step. A 1⁰ 
divergence slit, 2⁰ anti-scatter slit, and a programmable receiving slit set to 2mm were used for 

all analyses. 

Bulk samples were crushed in a mortar and pestle to a fine powder and top-loaded into an 

aluminum holder for analysis. Clay preparation follows the pipette procedure of Moore and 

Reynolds (1997) in order to separate the clays from solution. Bulk samples were placed into 

distilled water and repeatedly agitated until a visible suspension was sustained. The <2µ fraction 

was isolated from gravity sedimentation, and a small amount was pipetted onto a glass slide and 

allowed to dry for 24 hours. The clay slides were scanned as air-dried isolates, and then 

glycolated to expand any swelling clays present in the samples. For glycolation, samples were 

placed in a dessication bowl over ethylene glycol and cooked at 60 °C for approximately 12 

hours. Individual samples remained in the glycol bowl at room temperature until ready for 

analysis.  

Quantification of bulk samples was performed using the reference intensity ratio method 

(RIR), a comparative method that scales peaks to an internal spike. Since quartz is abundant in 

most natural rock and soil samples, it provides an effective natural internal spike to reference 

other peaks to. The method follows the equation, 

, where A is the area under 

the 100% peak of the identified phase, RIR is the reference intensity ratio obtained from the 

ICDD PDF-4+ database, and x is each phase included in the quantification. This provides a 

weight percentage for each mineral phase identified in the sample. Clay quantification was done 

102 

using the same equation, but RIRs were calculated using NEWMOD modeling software (see 

website below for citation). The quantification of all mineral phases is assumed to be semi-

quantitative, with a general margin of error of approximately ±5% for the bulk minerals and 

±10% for the clay species. 

Bulk mineralogical analysis of the sherds reveals a silicate-rich mineralogy, with 

abundant quartz (32-74%), feldspar (5-20%), and total clay (29-60%) in all samples. Calcite was 

present in sample 766 (9%) and 844 (30%), most likely due to carbonate filler used in the 

production of the pottery. The sherd clay mineralogy is comprised entirely of illite with no 

evidence of swelling clays present. This is a result of the high temperature firing causing the 

destruction of swelling smectite and kaolinite, and the subsequent enhancement of the 

dehydrated 10Å illite phase. The bulk mineralogy of samples collected from outcrop and core are 

very similar to the sherds. The silicates include quartz (25-64%), feldspars (3-19%), and total 

clay (25-68%). Sample 38 is the notable exception and is composed almost entirely of calcite 

(85%). Some minor dolomite is found in several samples, as well as lesser amounts of calcite. 

The clay mineralogy is more diverse than the sherds, which includes mostly illite and kaolinite, 

with one sample (KMM-01) containing 20% mixed layer swelling illite/smectite. The observed 

bulk mineralogy is to be expected from glacial till outwash sediments, and also explains the 

abundance of clay sized particles. The anomalously high dolomite and calcite outcrop material 

could be a result of carbonate enrichment from bedrock pore fluids interacting with surficial 

deposits. 

 
4.4.3  Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry 

See Chapter 7, section 7.5, for a detailed description of LA-ICP-MS as used in this 

dissertation.  

103 

 
 
4.5 Analytical Methods for Monoplex Social Networks 

Chapters 5 – 8 each incorporate the analysis of monoplex, or single-layer, social 

networks that model a single type of tie. Numerous measures exist for the statistical analysis of 

monoplex network graph properties. Monoplex network measures used in this study focus 

broadly on those that describe network structure. These include degree distribution, centrality 

(with a particular emphasis on closeness centrality), centralization, edge weights, network 

diameter, network density, average clustering coefficient, and average path length (or distance). 

A general discussion of each of these measures is presented here. However, no mathematical 

formulae will be provided for graph measure application as all measures were implemented 

using the igraph package (Kolaczyk and Csárdi 2014), which contains detailed documentation 

and references regarding their implementation.  

Social networks are mathematically formulated as graph objects, which consist of a set of 

nodes (or vertices) and a set of edges (or links) that connect them. The number of nodes in a 

network, in this case spatially bounded archaeological communities, is referred to as network 

order. The number of edges in a network is referred to as network size. The degree of a node 

captures the number of edges that are connected to, or incident to, that node. In the case of 

directed networks, where edges are characterized by directionality, in-degree refers to the 

number of edges pointing in toward a node and out-degree refers to the number of edges 

emanating from a particular node out toward another node. When aggregated and rescaled, the 

degrees of individual nodes are studied by looking at the distribution of their frequencies, a 

concept referred to as degree distribution. In graph objects where edges carry a weight, such as 

the flow of goods in a shipping trade network or the number of passengers on individual flights 

104 

in an air transportation network, degree is the sum of a node’s edges. By extension, the weighted 

degree distribution considers the frequency of various weighted degrees and is referred to as 

strength. A related measure, density, considers the frequency of realized edges relative to the 

potential maximal number of edges possible given a set of nodes.  

Often, questions arise as to the flow of information in a graph object. One way to 

examine information flow is through understanding of the paths within a network. A common 

notion in this regard is to determine the distance between any two nodes, or the shortest path 

between them. Distance is often referred to as geodesic distance or simply geodesic. The average 

path length considers how many nodes must information travel through, on average, to reach a 

target destination node. The diameter of a graph is the value of the longest distance among nodes 

within it. Diameter captures the notion of how many nodes must information travel from the two 

most distance nodes in a graph.  

Social relationships are often reciprocal, and it is common for friends of friends to also be 

friends for example. The notion of whether or not two individuals who are friends with the same 

person are also friends corresponds to the concept of network transitivity. Transitivity is often 

referred to as the global clustering coefficient, which considers the proportion of transitive triads 

in a graph – or where two nodes who share a relationship with a third node also share a 

relationship. This may also be considered the proportion of triadic closure. Thus, transitivity 

considers a specific case of clustering – the proportion of three nodes all sharing a relationship 

together in a graph – and as a result care must be taken such that one does not confuse the global 

clustering coefficient based on triadic transitivity to be confused with statistical clustering 

measures applied to non-graph data. Graph transitivity is therefore a global measure in that it 

considers all triads within a graph object.  

105 

A local clustering coefficient is also used in network analysis. The local clustering 

coefficient extends beyond the concept of triadic transitivity and instead considers whether all 

nodes in a node’s neighborhood, or all nodes connected to a single node, are in turn completely 

connected to each other (Watts and Strogatz 1998). The average of each node’s local clustering 

coefficient is therefore able to assess the average completeness of node neighborhoods. Thus, the 

local clustering coefficient is again distinct from statistical clustering methods applied to non-

graph data.  

A common research aim in social network analysis is to determine the role of individual 

nodes in the network. For example, the unique role of the Medici family in various networks is 

hypothesized to be of importance to the family’s rise to power, prestige, and great wealth in the 

early Florentine Renaissance (Padgett and Ansell 1993). The ‘importance’ of individual nodes is 

captured in measures of node centrality, of which there are many (Scott 2000; Scott and 

Carrington 2016; Wasserman and Faust 1994). Because the research questions in this study are 

generally restricted to identifying changes in overall network structure, as opposed to an analysis 

of the role(s) that specific site-nodes may have played in the Late Prehistoric period central 

Illinois River valley, centrality measures are downplayed in favor of a set of centralization 

measures, which extend the concepts inherent in individual centrality measures to that of the 

graph object as a whole. In other words, centralization describes the extent to which information 

flow (as captured in corresponding measures of centrality) is organized around particular focal 

points. Centralization therefore assesses the likelihood that a single actor, or sub-group of actors, 

plays an outsized role in the network.  

As degree centrality considers the degree (as defined above) of individual nodes, degree 

centralization considers the variation in individual node degrees divided by the maximum degree 

106 

that is possible in a network of the same size (Scott 2000). A high degree centralization score 

therefore indicates that all nodes are primarily connected to one central node, while a low degree 

centralization score indicates the inverse – nodes connections are more evenly distributed. 

Another measure of centralization is rooted in the concept of betweenness. Betweenness 

centrality describes the extent to which a node is located between other pairs of nodes and is 

rooted in the idea that node ‘importance’ relates to where a node is located with respect to the 

paths between nodes in a network (Kolaczyk and Csárdi 2014). Betweenness centralization 

considers the extent to which all nodes are equally connected through one central node. In a 

graph with high betweenness centralization, the only way for information to travel from one 

node to another is through one central node. Betweenness centralization differs from degree 

centralization in that betweenness is rooted in analysis of paths while degree is rooted in the 

analysis of node connectivity.  

Related to measures of degree and betweenness is that of closeness. In cases where it may 

not be as relevant to have many relationships, nor to be between many nodes, it is possible to 

assess whether or not a node is still ‘close’ to the middle of information flows. Closeness 

centrality is related to the average shortest path length and describes the extent to which an 

individual node is close, on average, to other nodes (Wasserman and Faust 1994). Extending this 

concept to that of a graph as a whole, closeness centralization describes the extent to which all 

nodes are able to reach a central node in only one step. That is, a high closeness centralization 

score would indicate that one central node is only one step away from, or ‘close’, all other nodes. 

While a low centralization score would indicate that no one node is only one step away from all 

other nodes.  

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A somewhat more complex notion of centrality is that of eigenvector centrality, which 

defines a node as central based on its relationships to other central nodes. This definition is 

therefore recursive. A high eigenvector centralization score may therefore indicate that a network 

is composed of a sub-group of highly interconnected nodes and a sub-group of nodes that are 

weakly integrated into the highly interconnected sub-group, much like a core and periphery 

might be modeled.  

Because graph centralization measures are standardized between 0 and 1, their 

interpretation is often straightforward. For most other network statistical measures, however, it is 

often difficult to discern whether a score is unusually high or low. Statistical hypothesis testing 

may be used in these cases to hold certain network features constant while simulating different 

network formulations. This approach is taken here using the Erdős-Rényi graph randomization 

technique (Erdős and Rényi 1959). Erdős-Rényi graph models place equal probability on all 

graphs of a given order and size. That is, a collection of graphs are considered based on the 

provided order and size and a probability is assigned to each, where the total number of distinct 

node pairs are considered (Kolaczyk and Csárdi 2014). An extension provided by Gilbert (1959) 

enables the random graph concept to be extended to graphs of a fixed order but where each pair 

of distinct nodes are independently assigned based on a given probability. 

 
 
4.6 Definitions and Methods for Constructing and Analyzing Multilayer Networks 

In order to quantify and analyze each of the distinct ceramic industry social networks as a 

cohesive whole, it is necessary to construct a formal multilayer network. In this section, I briefly 

discuss the methods used to perceive and construct multilayer networks following De Domenico 

et al. (2013), Kivelä et al. (2014), Boccaletti et al. (2014), and Dickison et al. (2016) as well as 

108 

methods for multilayer network analysis using two different analytical platforms: MuxViz and 

multinet (De Domenico, Porter, et al. 2015; Magnani 2017).  

Single-layer networks, or graphs, are considered a tuple G = (V,E), where V is the set of 

nodes (or vertices) and E Í V x V is the set of edges (or links) that connect pairs of nodes. Nodes 

connected by an edge are said to be adjacent to one another. A multilayer network has a set of 

nodes, V, similar to a normal network graph, but is also comprised of a set of individual layers 

that are each composed of their own nodes. As a result, a multilayer network is defined as a 

quadruplet M = (VM, EM, V, L). Each distinct layer is composed of a node set VM and edge set 

EM. Elementary layers may be a specific interaction type or a time stamp, and a layer (L) consists 

of the combination of both a specific interaction type and a time stamp. A multilayer network 

may be node-aligned when all layers contain all of the nodes, or layer-disjoint if each node exists 

in at most one layer.  

A multilayer adjacency tensor is a data object used to store and manipulate both 

multilayer and multiplex networks (De Domenico, Solé-Ribalta, Cozzo, et al. 2013:3). A 

multiplex network is a specific type of multilayer network in which the only possible types of 

connections across different layers are ones in which a given node is connected to its counterpart 

nodes in the other layers (De Domenico, Solé-Ribalta, Cozzo, et al. 2013). Great care must be 

taken when performing multilayer network analysis in cases where nodes are not identical across 

the layers because the tensorial approach requires any missing nodes to be present on each layer 

but without edges (or empty) on layers where the node is otherwise absent. This can result in 

misleading network statistics such as mean degree or clustering coefficients (Cozzo, et al. 2013; 

De Domenico, Solé-Ribalta, Cozzo, et al. 2013; Kivelä, et al. 2014).   

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Because of the multilayer adjacency tensorial approach, tabular (or rectangular) data 

structures alone are unable to be used to store multilayer network. There are thus two general 

approaches used to format multilayer networks. I refer to these as either a split file approach or a 

complex file approach. A split file approach is used by MuxViz (De Domenico, Porter, et al. 

2015) and requires a master configuration text file that specifies the locations of separate text 

files that contain node and edge information. Node information is contained in a layout file, 

specifying a distinct number for each node and any other ancillary information. Edge information 

is contained within a distinct file for each layer and is formatted as an edge list. A complex file 

approach, such as that used in multinet (Dickison, et al. 2016; Magnani 2017), combines node, 

edge, and layer information into a single, complexly formatted file.  

 
4.6.1  Multilayer Network Analysis Measures 

This section details the specific multilayer network analysis metrics used in this research. 

There are two overarching trends that these metrics are designed to assess – influence and 

overlap in multilayer networks. Within a multilayer network, influence and overlap may be 

applied to the actors across the network layers, the edges that connect actors across the layers, or 

some combination of these features. Metrics falling under the concept of influence seek to 

ascertain the impact of individual network layer properties on structuring the entire multilayer 

network. While metrics falling under the concept of overlap seek to assess the different network 

layer properties relative to one another. In these ways, both overlaps and influences in multilayer 

network analysis are specifically designed to compare the different layers to one another in order 

to arrive at a richer interpretation of the full multilayer network and to aid in causal inference.  

 Multilayer network analysis was carried out in two distinct platforms – MuxViz 2.0 and 

multinet 1.1.5 (De Domenico, Porter, et al. 2015; Dickison, et al. 2016; Magnani 2017), both 

110 

using the R statistical programming language. All R code for the multinet analysis is provided in 

Appendix C. No code is provided for the analyses performed using MuxViz, as it is a graphical 

user interface driven program. However, as it is open source, all code for the analytical measures 

is freely accessible.  

The concept of graph centrality is applied throughout the individual layer analyses 

(Chapter 5 – 7) but must be extended to account for the presence of multiple network layers in a 

multilayer network. Node centrality was analyzed using MuxViz 2.0 for the multilayer network 

and a number of different centrality measures are considered in Chapter 8. Node centrality 

measures are designed to identify the most important nodes in a graph (Scott 2000; Wasserman 

and Faust 1994). However, the concept of importance can take many forms. In the multilayer 

network analysis presented in Chapter 8, three kinds of centrality are analyzed: degree, 

eigenvector, and strength.  

Perhaps the most straightforward centrality measures are that of degree centrality and 

strength, which are simply the sum of all edges that a given node is characterized by or the sum 

of all edge weights that a given node is characterized by respectively (Opsahl, et al. 2010). In the 

parlance of network analysis, this is the sum of edges or edge weights incident to a node. 

Extending degree centrality and strength to multilayer networks is quite simple – one sums the 

number of edges or edge weights incident to a given node across each of the different layers, 

which can include edges that span across different layers in a multiplex network. Thus, degree 

centrality and strength quantify the number of edges or depth of edge relationships a node has 

across the different layers, which can have far-reaching consequences for the role that each node 

plays in full multilayer network.  

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Somewhat less straightforward, eigenvector centrality characterizes nodes based on their 

connectiveness to other well-connected nodes. The basic idea is that important actors are likely 

well-connected and as a result are more likely to be connected to other well-connected nodes. A 

given node therefore has high eigenvector centrality if its neighbors also have high eigenvector 

centrality, and the recursive nature of this notion results in a vector of centralities that satisfies an 

eigenvalue problem (De Domenico, Solé-Ribalta, Omodei, et al. 2013). Using the rank-4 

multilayer adjacency tensor formulation of multilayer networks, it is naïve to simply aggregate 

all network layers and then compute eigenvector centrality or to compute eigenvector centrality 

across the layers individually and aggregating the results (De Domenico, Solé-Ribalta, Cozzo, et 

al. 2013). By simply aggregating the layers, information across the layers is intermixed with 

uncontrollable effects. While calculating individual layer eigenvector centralities would require 

that a heuristic aggregation metric (say mean or median of individual layer eigenvector 

centralities) be applied, which disregards the solution of unique eigenvalues problems that each 

individual layer metric is designed to answer. Instead, an eigentensor is used to encode the 

centrality of each node in each layer in due consideration of the whole interconnected network 

structure (De Domenico, Solé-Ribalta, Omodei, et al. 2013).  

A metric from multinet, degree deviation, is used to provide additional meaning and 

insight to the calculation of a given node’s degree by recasting degree centrality as discussed 

above. Degree deviation is defined as the standard deviation of the degree of an actor on the 

input layers. Much like degree centrality, degree deviation does not consider the weight of an 

edge, only its presence or absence. An actor with the same degree on all layers will have a 

deviation of 0, while an actor with many neighbors on one layer and just a few on another layer 

will have a high degree deviation, which indicates an uneven usage of the layers (or layers with 

112 

different densities) (Dickison, et al. 2016; Magnani 2017). Thus, degree deviation is a measure 

that quantifies the inter-layer overlap of individual nodes and can therefore aid in interpretations 

about the role that individual nodes play across the different layers of the network and in the full 

multilayer network as a cohesive whole.  

Related to both degree centrality and degree deviation is another metric from multinet 

that assesses information about the multiplexity of actors in a network – connective redundancy. 

One may ask, to what extent does an actors’ relationships on one layer hold true on other layers 

in a multilayer network? Connective redundancy answers this question by assessing each actors’ 

neighborhood (or the total number of actors incident to a given actor on specified layers) and 

degree (or the total number of edges incident to a given node on those same specified layers). 

The formal equation is one minus neighborhood divided by degree (Magnani 2017). Thus, high 

connective redundancy occurs when the actors are connected to the same neighbors on multiple 

layers (Dickison, et al. 2016).  

Additional methods for the comparative analysis of edges across different network layers 

is that of mean global edge overlapping and layer edge overlapping from MuxViz. The mean 

global edge overlap measures the fraction of edges which are common to all layers and can be 

applied to either unweighted or weighted multilayer networks (De Domenico, Porter, et al. 

2015). This acts as a measure of comparative similarity between all layers but may also be 

applied on a layer by layer basis to measure similarity of any two given layers in the case of 

layer edge overlapping. A method is also able to be applied that hierarchically clusters layers to 

determine which layers are most similar in terms of the edges present within them. Edge 

overlapping is valuable for weighted networks because the weight of each edge is factored into 

the inter-layer comparison.  

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As individual networks are constructed as edge lists and converted into adjacency 

matrices in MuxViz, it is also possible to explore each of the matrices and their aggregate as 

heatmaps. This is referred to as a matrix explorer in MuxViz and is an easy way to gain intuition 

about how the different network layers are similar and different with respect to the presence of 

actors and edges. Aggregating the individual network layers together through a process of layer 

flattening (or forming new edge weights between each actor-actor combination by summing all 

edges across all layers), also provides insight as to the structure of the full multilayer network. It 

is also possible to apply clustering to both the multilayer adjacency matrices and aggregate 

adjacency matrix to identify structurally similar actors or groups of actors.  

The final multilayer measures utilized in Chapter 8 are a class of layer comparisons from 

multinet. These measures compare each pair of layers based on common statistical measures of 

overlap, distribution dissimilarity, or correlation (Dickison, et al. 2016; Magnani 2017). In the 

analyses presented in Chapter 8, two measures of overlap in particular are used: Jaccard edge 

overlap and Simple Matching overlap. Jaccard edge overlap follows the Jaccard index, which is 

defined as the intersection divided by the union of layer edges. Simple Matching acts just as one 

would expect based on its name and assesses whether or not an edge between a pair of nodes 

present in one layer is also present in another layer, providing a return value of the percentage of 

such matching edges. Unlike the edge overlapping measure from MuxViz, edge weight is 

disregarded in the multinet implementations of both Jaccard and Simple Matching overlap. The 

Jaccard edge overlap and Simple Matching coefficients therefore quantify the interaction 

between two network layers by measuring the tendency that links are simultaneously present in 

both networks. Whereas the Jaccard coefficient considers the presence of a link as a function of 

114 

all links present, the Simple Matching coefficient simply quantifies the degree to which there are 

overlapping links.  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

115 

CHAPTER 5 NETWORKS OF INTERACTION THROUGH CULTURAL 

TRANSMISSION  

 
 
5.1 Introduction 

Explaining similarity, variation, and change in material culture is a critical and long-

standing research objective for archaeologists. It is particularly important and challenging in 

contexts where differing material culture traditions merge, blend, or otherwise amalgamate 

(Frangipane 2015; Liebmann 2013; Stone 2003). Culture historians initially used assemblage 

similarities as a proxy measure for historical relatedness and artifact typologies as a means of 

telling time to discern how sequences varied from place to place and over time (Eerkens and 

Lipo 2005:240). These cultural sequences and boundaries largely persist as the foundation of 

American archaeological inquiry today (Lyman, et al. 1997). More recent trends in the 

measurement of artifact assemblage attributes focus on interpreting variation among and between 

individuals and communities as opposed to between archaeological cultures (Goodby 1998; 

Rowe 2016). A key interpretive outcome of these studies is to evaluate networks of relational 

connections among individuals and larger social groups. Problematically, many technological 

characterization studies make a priori assumptions about which artifact attributes contribute to 

relational or social connections (Dietler and Herbich 1998; Stark, et al. 1998). For example, 

ethnoarchaeological surveys suggest that low visibility attributes act as indicators of shared 

contexts of learning (Carr 1995b; Clark 2001; Peeples 2011:173), or that high visibly attributes 

express emblemic information (Eerkens and Bettinger 2008:22). I argue here that while the study 

of material culture type-attributes is a productive avenue for discerning relational interaction 

between communities of artisans (Herbich 1987; VanPool 2008), the forces acting on the 

execution of a given artifact attribute must be problematized as opposed to assumed. That is, to 

116 

interpret attribute-based technological similarity as evidence of face-to-face interaction through 

shared learning mechanisms or historical relationships of descent (Peeples 2011), similarities 

affected by social processes must be differentiated from those affected by physical or 

engineering forces constraining the execution of a given artifact attribute. 

 

This research presented below draws from an established evolutionary approach to 

quantitatively explore which attributes are more likely to be constrained by social or engineering 

forces before modelling social relationships via network analysis techniques. In particular, I 

describe and adapt a model developed by Eerkens and Bettinger (2008). The model is explicitly 

concerned with differentiating between variation in artifact traits mainly affected by physical, or 

engineering, constraints and variation mainly affected by social constraints. Eerkens and 

Bettinger (2008) refer to physical or engineering constraints based on raw material type or other 

factors as ‘function,’ and social constraints as ‘markers,’ which operate in many ways similar to 

‘style’ as defined by Wiessner (1983, 1984, 1990). The Eerkens and Bettinger model is applied 

here as a means to determine which type-attributes across three ceramic vessel classes behave 

more or less in accord with predictions for empirical patterning in artifacts to diagnose the 

operation of different transmission processes. These type-attributes constrained by social 

processes will then be used to construct networks of relational interaction vis-à-vis cultural 

transmission. This method results in a proportional scale of ceramic technological similarity that 

represents a proxy measure to model the strength and directionality of relational connections 

among communities across the study area through time. The resulting interaction networks are 

examined on their own terms here before being used in Chapter 8 as one component of a model 

focused on interpreting the nature of communal coexistence in multicultural social environments 

using archaeological data across the Middle to Late Mississippian transition in the Late 

117 

Prehistoric central Illinois River valley (ca. A.D. 1200-1450; CIRV). While the presence of 

Oneota peoples following a circa 1300 A.D. migration into west-central Illinois has been 

demonstrated, the nature of intercultural relationships with indigenous Middle Mississippian 

peoples is unclear. It is argued that these networks provide insight into patterns of frequent 

interaction or homologous relationships between communities of ceramic artisans to better 

understand both indigenous and migrant community-based behavioral responses to multicultural 

regional and communal coexistence. In particular, four general questions are considered: 

1)  Are changes in the structure of interaction network patterns inherent across time, and 

how might the circa 1300 A.D. in-migration of an exogenous Oneota group be related 

to those changes?  

2)  Do interaction patterns support an hypothesized taxonomic distinction of Mississippian 

into La Moine and Spoon River cultural variants (Conrad 1989, 1991)? 

3)  It has been postulated that the onset of the Mississippian period circa 1200 A.D. was 

paralleled by the emergence of chronic, internecine violence and warfare (G. R. Milner 

1999; G. R. Milner, et al. 1991). The threat of warfare is argued to have transformed 

both settlement and subsistence practices such that, among other things, “families 

coalesced into large communities behind defensive walls…limiting foraging and 

fishing trips” and “women became increasingly sequestered behind village walls” 

(Vanderwarker and Wilson 2016:98-100). Given that ethnographic accounts indicate 

that when pottery manufacture is done by hand, it is typically done by women (Rice 

2005), it is possible to test whether sufficient variation in pottery attributes characterize 

different communities such that it can be reasonably assumed that potters were 

118 

geographically circumscribed in the cultural transmission of artifact attribute social 

information primarily as a result the threat of violence and warfare?  

4)  Given that the plate vessel class is absent or extremely rare in Oneota contexts outside 

the CIRV (Esarey and Conrad 1998), do imitations/emulations of serving plates by 

Oneota peoples inject sufficient variation to suggest that the adoption of this vessel 

class was made at a distance, or are the imitations/emulations technologically similar 

enough for there to be a higher likelihood that direct cultural transmission of ceramic 

technology between Mississippian and Oneota potters occurred? 

Network models of interaction through cultural transmission provide robust answers to these 

questions and shed new light on archaeological understanding of the Late Prehistoric period 

CIRV more broadly.  

 

5.2 Cultural Transmission Theory, Artifact Variation, and Network Ties 

Cultural transmission theory offers a means to link “artifact variation to different ways in 

which cultural information is transmitted through space and time” (Eerkens and Bettinger 

2008:22). The basic premise underlying this study is the supposition that different processes 

guiding the transmission of cultural traits will result in distinct patterns in measures of artifact 

variation (Eerkens and Lipo 2007; Lipo 2001). That is, artifacts or attributes should pattern 

differently if they were used to mark group identity (also referred to as “emblemic markers” 

(sensu Wiessner 1983), individual identity (also referred to as “assertive markers” (sensu 

Wiessner 1983)), or were constrained by engineering principles depending on whether they are 

context dependent. This model is designed to allow for the quantitative testing of otherwise 

qualitative assumptions about the nature of artifact attribute variation.  

119 

This model is applicable to any attribute measured on a continuous scale and involves the 

analysis of measurements of central tendency and dispersion. Attribute means and standard 

deviations are obtained for each site-based assemblage. From the mean and standard deviation, 

the coefficient of variation (CV) can be derived. The CV is a standardized measure that shows 

the extent of variability in relation to the mean of the sample or population. CVs are “appropriate 

to the study of variation in [archaeological] collections because it corrects for a near-universal 

scalar relationship between mean and standard deviation that prevents comparison between 

variables with different means using standard deviation alone” (Eerkens, et al. 2013:1135). Since 

statistical populations are rarely available in archaeological contexts, an unbiased estimator is 

used here for normally distributed data to calculate the coefficient of variation based on 

moderately sized samples. These metrics are used to derive three measures designed to “capture 

different aspects of the strength of the forces that produced variation” in the given attribute 

(Eerkens and Bettinger 2008:22).  

The first metric, “variation of the mean” (VOM) is obtained by calculating the coefficient 

of variation of sample means, or the standard deviation of sample means divided by their 

average. VOM indicates whether a given attribute is under global or local control; local control 

refers to assemblage-specific control (Eerkens and Bettinger 2008:23). Low VOM suggests 

global control in that design constraints on an attribute are arguably severe enough for local 

contexts to be inconsequential – the mean of the attribute will be roughly the same from 

assemblage to assemblage. High VOM results from substantial variability in the mean of an 

attribute from assemblage to assemblage, and infers that variability in local control matters, 

resulting from local social forces or context specific engineering constraints.  

120 

The second metric, “average variation” (AV) indicates the strength of global or local 

control. AV is obtained by calculating the average of the assemblage coefficients of variation 

and records the average amount of variation around the mean disregarding the location of the 

mean. Low AV suggests strong control in that variation around the mean is generally small (less 

latitude is taken when executing the artifact attribute). High AV infers weak global control 

because variation around the mean is generally large (more latitude is taken when executing the 

artifact attribute). That is, AV assesses the degree of type-attribute variation within the 

assemblages and is suited to assess whether control is driven primarily by individuals (high AV) 

or by the group (low AV).  

The third and final metric, “variation of variation” (VOV) “indicates the degree to which 

an attribute is homogenous with respect to strength of control and, by implication, kind of 

control” (Eerkens and Bettinger 2008:23). VOV is obtained by calculating the coefficient of 

variation of assemblage coefficients of variation. VOV assess between-assemblage differences in 

attribute variability. Low VOV suggests global homogeneity in strength and kind of control 

because variation around the mean is roughly the same from site to site. Whereas high VOV 

indicates global heterogeneity in strength and kind of control because of substantial local 

variation around the mean from assemblage to assemblage.  

In order to remove scalar effects, the final VOM, AV, and VOV scores are obtained by 

standardizing their raw values (rescaling to produce attribute distributions with a mean of 0.0 and 

standard deviation of 1.0).  

From these three metrics, functional (or selective) and social (or selectively neutral) 

dimensions of artifact variation can be explored in due consideration of demographic context. 

Eerkens and Bettinger (2008:25) summarize expectations for attributes under different forces 

121 

based on the three metrics in Table 5.1. At the most general level, the model differentiates 

between global functional control, which is characterized by relatively low VOM, and local or 

site-specific control, which is characterized by relative high VOM. Further, the signature of 

emblemic and assertive markers should be high VOV, with low AV indicating emblemic 

markers and high AV indicating assertive markers within a high VOV attribute. Though I must 

emphasize the acknowledgement by Eerkens and Bettinger (2008, p. 26) that while many 

complex factors contribute to artifact variability, much of the objective of their model is to 

simplify those complexities “in the sense that many can be regarded as local functional 

constraints”.  

 
Table 5.1 Expectations for Attributes under Global or Local Functional Control, and Serving as Emblemic 

and Assertive Markers (Eerkens and Bettinger 2008, p. 25) 

 

The concerns of the current analysis are not to characterize specific social forces as 

 

assertive or emblemic style nor to parse the nature of attribute function. Rather, the focus here is 

to identify artifact type-attributes that are free to vary from site to site, which is argued to 

indicate that social forces are more likely to be a contributing factor to that variation. As a result, 

interpretive guidelines for the current analysis are presented in Table 5.2. 

 

The guiding assumption behind each of the expectations in Table 5.2 is that moderate to 

significant variation in type-attribute measurements between site assemblages is more likely to 

122 

be related to social forces guiding the execution of a given type-attribute rather than engineering 

constraints. Because evolutionary forces tend to favor social transmission (as opposed to 

individual learning and experimentation) for complex technologies where the cost of 

experimentation is high (Eerkens and Lipo 2007:259-260), such as in the case of cooking 

vessels, variation in a given attribute from assemblage to assemblage is therefore more likely to 

Force 

Social Constraint 
(local control) 
 
Engineering 
Constraint (global 
control) 

VOM 

Undefined 
 

AV 

Undefined 
 

VOV 

Moderate - High 
 

Low – Intermediate 

Low – Intermediate 

Low 

Table 5.2 Expectations for Attributes under Social or Engineering Constraint 

 

 

result from the expression of assertive style or community-specific social information. Spencer 

(1993) argues that frequent and unpredictable warfare may further contribute to the favorability 

of social learning to acquire information, which is argued to be rampant in the case study region 

(G. R. Milner, et al. 1991; Steadman 2008; Vanderwarker and Wilson 2016; G. D. Wilson 2012, 

2013), though not ubiquitous (Hatch 2015, 2017). Confounding factors including context-

specific constraints such as raw material availability, however, may impact in these local 

dependencies.  

In a separate article, (Bettinger and Eerkens 2008) argue that variation “should decrease 

as cultural/technical complexity and population density cause transmission systems to shift 

emphasis from” models of cultural transmission favoring experimentation such as guided 

variation to models that are variation reducing such as direct bias and frequency dependent 

(Boyd and Richerson 1985, 1987; McElreath, et al. 1993). That is, the expectations in Table 5.2 

do not preconceive a specific content, context, or mode of cultural transmission (Eerkens and 

123 

Lipo 2007). Instead, these expectations are predicated upon the argument that complexity and 

risk tolerance are inversely related in the production of material culture type-attributes. As a 

result, moderate to high variation in an attribute associated with a technologically complex 

artifact class, such as shell tempered ceramics (Feathers 2006), suggests that social forces are 

more likely to have resulted in that observed variation. In sum, as proportional similarities based 

on pairwise comparisons of type-attributes between two assemblages increases, so does the 

probability that social interaction resulting from shared learning mechanisms or homologous 

relationships between those sites increases. Network ties, representing statements of probability 

that a relationship existed between two communities, will be modeled on only the type-attributes 

where moderate to high variation is observed across all communities relative to the amount of 

variation observed across all type-attributes. Thus, social information as opposed to engineering 

factors that delimit the range of variation in a given artifact attribute will contribute to the 

network ties.  

 

5.3 Defining the Sample and Assessing Dependencies 

The model is operationalized here on a database of measurements from over 1,300 

ceramic vessels belonging to three major types represented in twenty-two different central 

Illinois River valley (CIRV) site assemblages for the Late Prehistoric period of A.D. 1200-1450. 

All data, aside from three assemblages, were recorded by the author to minimize measurement 

error between individual observers. It is important to note that there is significant variability in 

the amount of data that was able to be recorded from each archaeological site. The sampling of 

sites chosen does not reflect a probabilistic survey. Further, the amount of excavation or other 

data collection from each site varies significantly. Some sites were completely excavated, while 

124 

others only saw minimal sub-surface sampling. As a result, the procedure outlined below, and 

the interpretations that follow, should be considered foundational as opposed to definitive in the 

analysis of the nature of relationships between Late Prehistoric CIRV sites.  

The ceramic vessel types under consideration – likely serving plates, domestic jars, and 

burial jars – were chosen to explore whether different spheres of society (e.g., public, private, 

and ritual respectively) were more utilized to exhibit the loading of social information in 

comparison to others. The term plate is used here to refer to a class of ceramics referred to in 

other contexts as “broad-rimmed bowls” or “deep-rimmed plates” to emphasize their likely 

function as serving vessels primarily used in more public social contexts (Esarey and Conrad 

1998; Hilgeman 2000; K. E. Smith, et al. 2004; Vogel 1975). While, domestic jars and plates are 

characterized by complex and multifaceted use-lives (Appadurai 1986), the public-private-ritual 

distinction is a generalization made to capture the primary social locus of vessel use. Table 5.3 

lists all of the variables recorded along with the type of variable and the range of levels or 

measurements used in assessing each variable. Appendix A contains the Coding Sheet, which 

describes the specific guidelines and procedures used to systematically code or measure each 

attribute. Factor and ordinal data were collected alongside continuous attribute measurements in 

order to aid in potential future analyses and are not examined as part of this dissertation aside 

from the analysis of style based on decoration, which is discussed in Chapter 6.  

Domestic jars were measured for eight type attributes across seventeen sites. Plates were 

measured for seven type attributes across sixteen sites. The largely intact nature of burial jars 

constrained measurements to four type attributes across six sites. Attempts to characterize the 

site-wide diversity of ceramics were made in sample selection. That is, samples were chosen 

from different site-contexts and from multiple repositories. A total of nineteen type-attributes are  

 

125 

 

 
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Table 5.3 Coding Schema (See Appendix A for Full Coding Sheet) 

Variable Type 
Factor 
Factor 
Factor 
Factor 
Factor 
Factor 
Factor 
Factor 
Factor 
Ordinal 
Ordinal 
Factor 
Factor 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Factor 
Continuous 
Continuous 
Continuous 
Factor 
Factor 
Factor 
Factor 
Factor  
Factor 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Continuous 
Factor 
Factor 
Factor 
Factor 

Levels | Measurement 
1 – 1,308 
1 – 25 
1 – 5 
1 – 4 
1 – 8 
1 – 3  
1 – 20 
0 – 3 
1 – 4 
1 – 7 
1 – 3 
1 – 2 
1 – 3 
cm 
cm 
mm 
mm 
mm 
mm 
degrees  
0 – 6 
mm  
mm  
mm  
-1 – 8 
-1 – 79 
-1 – 7 
-1 – 4 
0 – 5 
0 – 9 
cm  
mm  
mm  
mm  
mm  
mm  
mm  
mm  
mm  
0 – 3 
0 – 95 
-1 – 29 
0 – 9 

Variable 

Unique Sherd I.D. Number 
Site 
Institutional Holding 
Provenience Sphere 
Specific Provenience 
Sherd Type General 
Traditional Taxonomic Type 
Residue 
Tempering Agent 
Tempering Max Grain Size 
Percent Temper Occurrence 
Lip Decoration 
Handle Decoration 
Orifice Diameter*^ 
Height^ 
Max Lip Thickness*^ 
Max Shoulder Thickness* 
Max Wall Thickness* 
Rim Height*^ 
Rim Angle*  
Primary Design Technique 
Max Cord-marking Thickness* 
Max Incising Thickness 
Max Trailing Thickness* 
Shape of Elements 
Shoulder Decoration 
BR Design Group 
Shoulder Type 
Slip/Paint 
Lip Shape 
Max Diameter# 
Height 
Depth 
Flare Length# 
Flare Angle# 
Max Rim Thickness# 
Max Thickness Below Lip# 
Max Incising Thickness# 
Max Trailing Thickness# 
Primary Design Technique 
Decoration 
BR Deign Group 
Lip Shape 

126 

reported here. These data sets represent over 1,300 unique ceramic vessels or vessel fragments 

and over 5,500 individual type-attribute measurements. All values reported are the maximum 

value of the attribute present on the vessel or sherd.  

A primary statistical problem associated with investigating central tendency and 

dispersion in continuous attributes is sample size. Put another way, how many ceramic vessels 

are needed to meaningfully represent a population such that social relationships between  

communities may be modeled? A crucial decision for the model is therefore the selection of a 

critical sample size, which will act as a threshold at which site-specific samples may be included 

for study. Following Eerkens and Bettinger (2008:28), visual inspection and correlation of means 

and standard deviation across all variables were used to assess the critical sample size. Firstly,  

 

Figure 5.1 Mean-standard deviation relationships for type-attribute variables calculated by material 

culture class with best-fit regression lines. Log base 10 values reported to account for effects related to 

 
the correlation between the mean and standard deviation of attributes across each ceramic vessel 

different measurement scales 

type was assessed to be quite high (r = 0.822; see Figure 5.1 for correlations across each vessel 

127 

type). This indicates that the standard deviation of any given variable can be reasonably 

predicted based on its mean alone. Given the similarity in correlation between mean and standard 

deviation in the current data to the projectile point data used in Eerkens and Bettinger’s (2008) 

study, the critical sample size of six (6) or greater is used. This n crit is one less than that used by 

Eerkens and Bettinger and takes into account the need to maximize the number assemblages used 

in the analysis while also minimizing errors in estimating individual sample means and standard 

deviations. While several other established methods for determining critical sample size using 

observed mean, standard deviation, and sample size exist, these methods act to exclude values 

with high sample standard deviations. Using these methods would bias the current evaluation  

Site Name 

Diameter  Flare 
Length 

Lip 

Thickness 

Thickness 

Below 
Flare 
24 
36 
 
26 
16 
 
13 
44 
8 
35 
8 
 
37 
13 
15 
 

275 

Flare 
Angle  Incising  Trailing 
20 
32 
 
15 
6 
 
 
27 
 
25 
 
 
25 
26 
8 
11 
195 

8 
60 
16 
34 
15 
11 
13 
74 
13 
29 
12 
10 
34 
18 
22 
 

369 

10 
13 
 
 
 
 
 
 
 
10 
 
 
 
11 
 
 

44 

31 
74 
20 
36 
21 
11 
14 
73 
13 
47 
10 
9 
42 
33 
25 
16 
475 
 

128 

Orendorf Settlement C 
Crable 
Walsh 
Lawrenz Gun Club 
Emmons 
Baehr South 
Myer-Dickson 
Star Bridge 
Ten Mile Creek 
Kingston Lake 
Buckeye Bend 
Fouts Village 
Larson 
Morton Village 
Houston-Shryock 
Orendorf Settlement D 

Total 

18 
45 
6 
22 
11 
8 
10 
49 
7 
36 
6 
 
34 
32 
8 
16 
308 

25 
59 
7 
27 
16 
 
10 
43 
7 
42 
6 
 
40 
23 
15 
15 
335 

 

 

Table 5.4 Count of plate sherds from each site for each continuous variable above n crit 

 

Orendorf 
Settlement C 
Crable 
Walsh 
Lawrenz Gun 
Club 
C.W. Cooper 
Emmons 
Baehr South 
Myer-Dickson 
Star Bridge 
Ten Mile Creek 
Eveland 
Kingston Lake 
Buckeye Bend 
Fouts Village 
Larson 
Morton Village 
Houston-
Shryock 
Orendorf 
Settlement D 
Total 

 

 

 

Site 

Crable 
Ester Berry 
Houston-Shryock 
Vandeventer 
Norris Farms #36 
Total 

Orifice 
Diameter  Height 
28 
12 
30 
47 
29 
146 

31 
15 
30 
47 
30 
153 

Lip 

Thickness 

Rim 
Height 

32 
16 
31 
47 
30 
156 

32 
16 
31 
47 
30 
156 

Table 5.5 Count of burial jar sherds from each site for each continuous variable above n crit 

Site 

Orifice 
Diameter 

Lip 

Thickness 

Shoulder 
Thickness 

Wall 

Thickness 

Rim 
Height 

Rim 
Angle 

CM 

Thickness 

Trailing 
Thickness 

43 
44 
 
30 
23 
16 
 
14 
38 
34 
23 
39 
7 
7 
37 
39 
10 
47 
451 

47 
60 
10 
49 
28 
25 
6 
19 
51 
41 
33 
46 
8 
9 
42 
46 
13 
46 
579 

47 
60 
10 
51 
32 
26 
6 
19 
51 
41 
32 
48 
8 
9 
42 
48 
13 
45 
588 

20 
29 
 
15 
18 
 
 
6 
9 
14 
10 
14 
 
 
25 
33 
 
 

193 

47 
59 
10 
50 
29 
25 
6 
19 
51 
42 
33 
47 
8 
8 
42 
46 
13 
44 
579 

46 
55 
7 
38 
30 
21 
 
16 
40 
37 
29 
44 
7 
7 
37 
42 
12 
37 
505 

10 
49 
10 
48 
 
18 
6 
8 
44 
36 
 
24 
 
8 
37 
16 
9 
 

35 
13 
 
 

29 
7 
 
 
 
 
15 
20 
 
 
6 
32 
 
 

328 

157 

Table 5.6 Count of domestic jar sherds from each site for each continuous variable above n crit 

because the values that are free to vary from assemblage to assemblage are actively being sought 

out by the routine used in the current study. Using this fixed sample size allows all samples 

above the critical sample size to be included regardless of observed variation. 

129 

Due to the fragmentary nature of most archaeological ceramics, not all of the twenty-two 

site assemblages contained every attribute in sufficient quantity to be considered by the study (n 

crit = 6). Tables 5.4, 5.5, and 5.6 display the total number of vessels observed from each site and 

a breakdown of the number of vessels included for each continuous attribute. Indeed, only two 

sites considered in this analysis, Crable and Morton Village and its associated Norris Farms #36 

cemetery, contain sufficient quantities of vessels from each vessel class to include observations 

above the critical sample size number for each variable considered in the analysis. Efforts to 

account for the presence of missing data and unequal samples sizes are further discussed below. 

 

5.3.1  Assessing Dependencies 

 
Prior to the implementation of the model, exploratory data analysis is necessary to assess 

the distributions of each artifact attribute as well as the degree of correlation between them. 

Gaussian distributions are required for the use of the unbiased CV estimator and ensure that 

assemblage samples are sufficiently random, often despite small sample sizes. Exploring 

correlations is used to assess whether or not different metric attributes are free to vary 

independent of one another. High correlation between attributes indicates that all attributes 

within a given type will behave in the same manner. Ensuring the independence of each attribute 

allows for the analysis of variation between type-attributes as opposed to simply comparing 

different vessel classes only (Eerkens and Bettinger 2008:27). Given the large number of 

distributions that were inspected (plate = 112 distributions; burial jar = 20 distributions; domestic 

jar = 144 distributions), only distributions that do not conform to expectations for normality are 

displayed here. Figure 5.2 shows deviation from normality in the distributions of rim angles on 

domestic jars from Eveland and Kingston Lake. Inspection of the data indicates that the 

130 

deviation is caused by a preponderance of jars with a vertical rim angle (recorded as 90 degrees 

from the jar opening plane) at both sites. Density plots of these two sites show bimodal 

distributions given the 90-degree preponderance. As a result, the unbiased estimator was not 

applied to these type-attributes. No other sample distribution deviated significantly from 

normality. Thus, the unbiased estimator for the coefficient of variation was applied to every 

variable aside from the domestic jar rim angle variable at Eveland and Kingston Lake, where a 

biased coefficient of variation estimator (sample standard deviation/sample mean) was used.  

 
Figure 5.2 QQplot of domestic jar rim angles showing deviation from normality in Eveland and Kingston 

Lake 

 
 

Problematically for the current analysis, burial jars show unusually strong positive linear 

relationships across the four continuous values under consideration. As shown in Table 5.7, each 

of the burial jar metrics are characterized by either moderately (r > 0.5) or strongly (r > 0.70) 

positive linear relationships to one another based on pairwise complete Pearson correlation 

computations. A particularly strong positive linear relationship exists between burial jar orifice 

131 

diameter and burial jar vessel height (r = 0.869; Figure 5.3). This finding suggests that the 

continuous burial jar type-attributes measured in this analysis are not free to vary independent of 

one another on a single vessel. As a result, any analysis of these burial jar type-attributes will 

actually consider the entire vessel itself as opposed to any singular attribute metric. This suggests 

that burial jars in the Late Prehistoric central Illinois River valley may be constructed based on a 

relatively standardized form where varying size in a single attribute results in concurrent size 

changes in every other attribute measured here.  

 

Orifice 
Diameter 

Vessel 
Height 

Lip 

Thickness 

Rim 
Height 

Orifice Diameter 

1 

Vessel Height 

Lip Thickness 

Rim Height 

0.869 

0.659 

0.664 

 

1 

0.570 

0.777 

 

 

1 

0.477 

 

 

 

1 

 

Table 5.7 Pearson correlation coefficient for pairwise complete burial jar metric observations 

 

Figure 5.3 Scatterplot of Burial Jar Height by Burial Jar Orifice Diameter with best-fit regression line and 

0.95 confidence interval shading 

 

 

132 

This lends to potentially fruitful hypothesis generation concerning the relationship between the 

size of burial jars and the social or demographic profiles of the individuals that were  

accompanied by those jars in mortuary contexts more broadly. Perhaps the size of the burial jar 

may be related to the social position of the individual in life – their age, sex, gender, or 

relationship to the potter community (Binford 1971; Brown 1995; L. G. Goldstein 2006; Saxe 

1970). Regretfully, however, because of this high level of observed correlation among burial jar 

attributes, the burial jar class is not considered in the remainder of the analysis presented herein. 

Jar and plate continuous metrics (Tables 5.8 and 5.9 respectively) are characterized by 

non-linear or weak linear relationships to one another, with one exception. A nearly moderately 

negative linear relationship exists between the plate attributes Flare Length and Trailing 

Thickness (r = - 0.453). That is, as the length of plate flares increases, the thickness of trailed  

 

Orifice 
Diameter 

Lip 

Thickness 

Shoulder 
Thickness 

Wall 

Thickness 

Rim 
Height 

Rim 
Angle 

Cord 
Marking   Trailing  

Orifice 
Diameter 

Lip 

Thickness 
Shoulder 
Thickness 

Wall 

Thickness 

1.000 

 

0.397 

1.000 

0.334 

0.215 

0.190 

0.140 

 

 

1.000 

0.399 

 

 

 

1.000 

 

 

 

 

Rim Height 

0.325 

-0.024 

0.349 

0.311 

1.000 

 

 

 

 

 

Rim Angle 

0.204 

0.055 

0.097 

0.003 

-0.113  1.000 

 

 

 

 

 

 

Cord 

Marking 

0.073 

0.093 

0.022 

-0.024 

0.146 

0.023 

1.000 

 

 

 

 

 

 

 

Trailing  

0.374 

0.154 

0.027 

0.042 

-0.139  0.190 

NA 

1.000 

Table 5.8 Pearson correlation coefficient for pairwise complete domestic jar metric observations 

decorations tends to moderately decrease. This correlation may be related to technological 

 

 

considerations such as the tool used to create the trailed decorations or perhaps to social 

133 

considerations such as plate flares acting as a canvas onto which symbol is used as non-verbal 

communication of social identification. The latter hypothesis is considered in Chapter 7. 

It is worth noting at this point in the analysis that the methods used here are exploratory, 

as opposed to explanatory, in nature. As noted by Herbich (1987), ‘micro-styles’ or distinctive 

combinations of decorative, formal and technological features may characterize different potter 

communities within a society. Variation within components of decoration, decorative aspects 

such as organization of the decorative field, aspects of form, and details of workmanship all 

contribute to these distinctions in micro-styles. However, “no single aspect will be sufficient to 

distinguish between the work of two given communities; the micro-styles are polythetic 

sets…Luo potters are clearly attuned to the combinations of variables which distinguish the work 

of their community from that of others” (Herbich 1987:196). This analysis of type-attribute  

 

Diameter 

Flare 
Length 

Rim 

Thickness 

Thickness 

Below 
Flare 

Flare 
Angle 

Incising  Trailing 

Diameter 

1.000 

 

Flare 
Length 

0.179 

1.000 

 

 

0.298 

0.187 

1.000 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rim 

Thickness 
Thickness 

Below 
Flare 
Flare 
Angle 

-0.013 

-0.026 

0.296 

1.000 

-0.127 

0.026 

0.017 

0.129 

1.000 

Incising 

0.027 

-0.229 

-0.017 

0.067 

0.085 

1.000 

Trailing 

0.233 

-0.453 

-0.065 

0.115 

0.300 

NA 

1.000 

Table 5.9 Pearson correlation coefficient for pairwise complete plate metric observations 

 

 

134 

variation based on continuous metrics should not be considered an effort to uncover the complete 

polythetic sets responsible for distinguishing potter communities. Rather, the objective here is to 

identify which continuous type-attributes may vary between communities such that it is likely 

that they were used in such a capacity either overtly and consciously or as an unconscious by-

product of cultural evolution. Additionally, there is no attempt made to calculate the statistical 

significance between any of the given attributes based on the VOM, AV, or VOV statistics.  

 

In review, the steps followed to obtain the VOM, AV, and VOV values used in this 

analysis include: 1) measure continuous type-attributes and calculate assemblage-specific means 

and coefficients of variation for type-attributes represented by six or more observations; 2) assess 

sample distributions and dependencies to determine if type-attributes are free to vary 

independent of one another and form normal distributions; 3) compute raw VOM, AV, and VOV 

statistical measurements for each type-attribute; and 4) standardize the raw values. The 

standardized VOM, AV, and VOV values are then compared against the expectations in 

provided in Table 5.2.  

 

5.3.2 

 
 

Identifying Social Information Bearing Artifact Type-Attributes from Cultural 
Transmission 

Because the model assumes that each statistical metric is free to vary independent of each 

other, it is first necessary to assess the coefficient of determination, or the square of the 

correlation between each metric. The interactions between AV and VOM (r2 = 0.006) and 

between VOV and AV (r2 = 0.032) are quite minor, which indicates that these variables are fully 

independent of each other. That is, as the average variation around sample means increases (as 

AV increases), there is no associated tendency for the mean of an attribute itself to vary more (or 

less) from sample to sample (a stepwise increase or decrease in VOM), nor is there an associated 

135 

tendency for the magnitude of variability around the mean to vary more (or less) from sample to 

sample (a stepwise increase or decrease in VOV) (Eerkens and Bettinger 2008:30).  

 

A somewhat higher positive correlation is present between VOM and VOV (r2 = 0.205). 

That is, as domestic jar and plate attributes tend to vary widely in mean from site to site (as 

VOM increases), there is a tendency for the magnitude of variability around the means of those 

attributes to slightly increase (increasing VOV). The inverse is also true in a general sense – as 

domestic jar and plate attributes tend to have the same mean from site to site (as VOM 

decreases), there is a tendency for the magnitude of variability around the means of those 

attributes to vary somewhat less from site to site. Put another way, for attributes that are free to 

vary in mean from site to site, inter-assemblage differences in not only the location of the mean 

but also the range of variability around the mean become more apparent. Domestic jars and 

plates in the Late Prehistoric central Illinois River valley appear to be less constrained by global 

control in determining these specific attributes. This finding supports the hypothesis that certain 

type attributes on these vessels are constrained by social forces, or local afunctional control, as 

opposed to engineering constraint and therefore may contribute to the polythetic sets of micro-

styles that characterize different potter communities. Attributes that tend to have similar means 

from site to site (low VOM) tend to have low between-assemblage differences in the magnitude 

of attribute variability relative to the mean (low VOV). This suggests that these attributes are 

more likely to be constrained by moderate or strong global function across the geographic and 

temporal expanse of the Late Prehistoric central Illinois River valley. In kind, attributes that tend 

to vary widely in mean from site to site (high VOM) tend to have high between-assemblage 

differences in the magnitude of attribute variability relative to the mean (high VOV). This 

suggests that attributes with means that are free to vary from site to site are likely to be loci for 

136 

the loading of social information or are driven by context specific engineering constraints such as 

local clay characteristics.  

The critical statistical observation for the purposes of this analysis is the variation of 

variation (VOV). The slightly positive correlation between VOV and VOM supports the 

underlying assumption that modelling social interaction based on artifact attributes is fruitful. 

However, that the coefficient of determination between VOM and VOV, as a measure of the 

goodness of fit of a linear relationship, is only somewhat moderately positive is therefore only 

indicative of a weak positive linear relationship between the metrics.  

Attribute 

Orifice Diameter 
Lip Thickness 
Shoulder 
Thickness 
Wall Thickness 
Rim Height 
Rim Angle 
Cord-marking 
Thickness 
Trailing Thickness 

Vessel 
Type 
Jar 
Jar 
Jar 
Jar 
Jar 
Jar 
Jar 
Jar 
Plate  Diameter 
Plate 
Plate  Rim Thickness 
Plate 
Plate 
Plate 
Plate 

Thickness Below 
Flare 
Flare Angle 
Incising Thickness 
Trailing Thickness 

Flare Length 

# of 
Sites 
16 
18 
18 
11 
18 
18 
14 
8 
15 
15 
16 
13 
11 
15 
4 

 
 
 

AV 

High 
High 
Low 
High 
High 
Low 

Vessels  VOM  VOM 
#of 
Score 
451 
0.079  Low 
0.377  Low 
579 
0.235  Low 
588 
193 
0.579 
0.766 
579 
-1.252  Low 
505 
328 
0.724  Low 
1.428 
157 
-1.432 
308 
335 
0.319  High 
-1.769 
475 
-1.450 
275 
195 
1.116  Low 
-0.056  High 
369 
44 
0.335  High 

Low 
Low 
High 

 
 

 
 

 
 

 
 

 
 
 

VOV 

AV 
Score 
-0.712 
-0.674 
-0.716 
-0.362  Medium 
0.221  Medium 
-0.980  Medium 
-1.069 
-0.331  Medium 
-0.160  Medium 
1.213 
-0.015 
0.611 
-0.857 
High 
1.608  Medium 
2.223 
High 

 
 
 

 

VOV 
Score 
-0.773 
-0.480 
-1.323 
0.329 
0.488 
0.651 
-0.276 
0.519 
0.107 
-0.402 
-1.088 
-1.633 
1.842 
0.382 
1.656 

 

 

 

Table 5.10 VOM, AV, and VOV values, scores, and summary data for type attributes 

Turning to the standardized values (or rescaled values that form distributions with a mean 

of 0.0 and standard deviation or 1.0) of VOM, AV, and VOV themselves Table 5.10 presents the 

values, metric scores, and associated site and sherd data for each of the 15 type-attribute 

combinations. Values for each of the statistics were identified by ordering the VOM, AV, and 

137 

VOV residual scores separately and visually inspecting their distributions and associated 

probabilities for discontinuities suggestive of natural divisions from all attributes within a given  

Low 

Medium 

High 

Medium 

High 

High 

Medium 

Low 

Low 

 

 

 

Figure 5.4 VOM, AV, and VOV residual scores for all 15 ceramic vessel type attributes measurements 

 

138 

statistic. These cutoffs are reported in Figure 5.4. A clear natural division between outlying low 

 

scores and medium scores is apparent in the ordered distribution of VOM (< -1.0, n = 4), a subtle 

division is present between medium scores and high scores (> 0.40, n = 5), with medium scores 

in between (< -1.0 to > 0.40, n = 6). The ordered distribution of AV scores also shows relatively 

clear break for outlying high scores (> 0.7, n = 3), a slight break for low scores (< -0.6, n = 6), 

with medium scores falling in between (< -0.6 to > 0.7, n = 6). VOV showed a very clear break 

for outlying high scores (> 0.75, n = 2), a slighter break for low scores (< 0.0, n = 7), with 

medium scores falling in between (< 0.0 to > 0.75, n = 6). Given that VOV is the primary 

statistic of interest for this analysis, High and Medium values are reported in Table 5.10, while 

High and Low value assignments are reported for VOM and AV. 

Returning to the expectations summarized in Table 5.2, I argue here that eight of the 

fifteen type-attributes with medium or high VOV are likely to be social information bearing as 

opposed to be constrained by engineering forces. VOV is designed as a statistic to highlight 

variation expressed in individual assemblages. In exploring individual assemblage CV values for 

the eight socially influenced variables, two general patterns are present that lead to the medium 

or high VOV values. The first pattern is that of tightly constrained CV distributions with one or 

two high outlying assemblage values pushing the spread of the CV values beyond the norm 

witnessed among other vessel attributes. Plate flare angle, diameter, trailing thickness, and 

incising thickness are characterized by the trend of tight distribution with one or two high 

outliers. The second pattern is that of CV distributions with very high interquartile ranges and 

outlying values on the upper and lower ends, which characterizes jar trailing thickness, rim 

angle, rim height, and wall thickness. That these trends are dichotomized by vessel class speaks 

to the differences in function and perhaps production techniques between them.  

139 

Figures 5.5 and 5.6 display ridgeline plots of the distributions of the eight type-attributes 

constrained by social forces for jars and plates respectively. These ridgeline plots visualize the 

variation in attribute distributions and show which sites are driving variation as well as 

significant distinctions between the pre- and post-migration time periods. For example, Eveland 

domestic jars have very short rim heights and are much more likely to have vertical (90 degree) 

rim angles, two characteristics in contrast to most other assemblages. Additionally, positive skew 

appears to be driving the variation between assemblages in plate incising, suggesting that 

incising thick lines into a dry paste on plates was likely controlled by social forces such as the 

selection and transmission of incising tool norms or non-verbal communication of perhaps 

assertive style.  

It is argued here that as proportional similarity in type-attributes with medium or high 

VOV values increases, so does the likelihood that that similarity is related to shared learning 

mechanisms or historical relationships between groups. Moreover, it is argued that shared 

learning mechanisms or historical relationships between sites is a key indicator of increased 

social interaction between them. 

This analysis shows that the following variables in the Late Prehistoric central Illinois 

River valley are likely to be markers suggesting the degree of social interaction between potter 

communities: plate trailing thickness, flare angle, diameter, and incising thickness; and domestic 

jar rim angle, wall thickness, rim height, and trailing thickness.  

 

140 

Figure 5.5 Ridgeline plot of domestic jar type-attributes likely constrained by social forces, all 

measurements are in mm aside from rim angle which is in degrees 

 

 

 

141 

 
Figure 5.6 Ridgeline plot of plate type-attributes likely constrained by social forces, all measurements are 

 

in cm aside from flare angle which is in degrees 

5.4 Methodology: Constructing Social Interaction Networks from Social Information 

Bearing Artifact Type-Attributes  

 

 

 
 

The theoretical basis for the use of social network analysis is discussed in detail in 

Chapter 2. As a result, only a brief overview will be outlined here. A network constitutes a 

142 

graphical representation of a set of actors (“nodes”) and the relationships or connections 

(“edges” or “links”) between them (Borgatti, et al. 2009; Brughmans 2013; Collar, et al. 2015; 

Golitko and Feinman 2014; Peeples, et al. 2016; Scott 2000; Wasserman and Faust 1994). Nodes 

may represent actors at almost any scale, from neurons in the brain up to individual human or 

non-human actors, communities, cities, or even entire nations. Edges may be assigned between 

nodes based on nearly any conceivable index of similarity or contact, such as the presence of two 

individuals at a conference session, marriage relationships, website links, the volume of 

international trade relationships, or flights between airports. The directionality of edges may be 

considered. Edges may be undirected, such as the representation of familial ties, or they may be 

directed, such as individualistic notions of friendship within a high school clique. Furthermore, 

the intensity of the edge may be characterized. Edges may carry a weight, such as the volume of 

trade in a particular commodity between nation states or the amount of traffic flowing along 

connections in a transportation model. Alternatively, edges may be unweighted, such as a 

network of a nation states’ power grid connections, social circles from social media platforms, or 

models of hyperlinks shared between websites.  

Renewed interest in network analysis methods in archaeology has led to a number of 

applications in a host of geographic and temporal contexts including exchange relationships 

based on procurement and distribution of obsidian across pre-Hispanic Mesoamerica (Golitko 

and Feinman 2014), hierarchization and state formation based on prestige good exchange and 

monumental architecture in Japan (Mizoguchi 2009), regionalization of Clovis hunter-gatherers 

based on lithic distributions in late Pleistocene North America (B. Buchanan, et al. 2016), 

regional shifts in economy and society based on ceramic cultural markers in the mid-Holocene 

Sudan (Garcea and Hildebrand 2009), and ceramic and lithic evidence for collective action and 

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social transformation in the United States Southwest (Borck, et al. 2015; Mills, et al. 2016; Mills, 

Clark, et al. 2013; Peeples and Roberts Jr. 2013).  

 

As opposed to placing explanatory emphasis on culture, community, society, or agents 

themselves, archaeological applications of social network analysis instead focus on the 

relationships between these entities. In addition, network analysis does not place a priori 

definition on analytical constructs such as spatial structures, social organization, or economic 

systems in order to interpret network structure. As a result, network approaches can 

simultaneously incorporate multiple scales of analysis into global analytical constructs (Golitko 

and Feinman 2014). While applications of network analysis methodologies, in archaeology and 

other disciplines, typically focus on constructing a single global analytical graph, the approach 

taken here instead advocates for parsing graphs into different analytical dimensions, or layers, to 

discern how they may converge or diverge when explored independent of one another and in 

aggregate. As a result, edges may be structurally different from one another, such as a co-

authorship network separated by layers of professors and students or economic links between 

nation states separated by layers of different commodities such as foodstuffs or manufactured 

goods. This is particularly instructive in archaeology given that archaeologists “cannot directly 

observe or quantify either edges or vertices of human relations in the past, they must deduce, or 

derive, both from the observable attributes of the residual evidence available to them” (Terrell 

2013:22). For example, traditional models of social identification, organized conflict, exchange, 

and social organization may not be evident in singular network structures identified 

archaeologically (Brughmans 2010; Phillips and Gjesfjeld 2013). As a result, new models may 

need to be generated within the archaeological community that place greater emphasis not only 

on the role of network relationships, but also on the roles that the particular material culture 

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class(es) and traditional model(s) being tested may play in these and other processes. Multiple 

relations, or multilayer, network methodology seeks to parse the overlap and influence of 

different social and economic relationship layers on individual nodes and the combined network 

as a whole (Mucha, et al. 2010; Preiser-Kapeller 2011; Scholnick, et al. 2013). Multilayer 

network methodology begins analysis by exploring the structure of different network model 

layers as separate entities. It then progresses to explore i) how the different layers overlap among 

one another (or share common connections); ii) how nodes are positioned within each network 

layer; and iii) what influence each layer has on the structure of the total network (or how many 

connections a given network layer contributes to the multilayer network as a whole) (Kivelä, et 

al. 2014; Szell, et al. 2010). As a result, different models of social behavior and the 

corresponding material classes used to construct distinct network layers can be investigated 

separately and together in order to provide insight on their individual and collective role in 

structuring the interrelationships between nodes under analysis. This chapter focuses on the 

strength or degree of relationships of social interaction based on the cultural transmission of 

ceramic technological information. Economic relationships of exchange or shared raw material 

source information are discussed in Chapter 7 and social identification relationships based on 

shared categorical identities are discussed in Chapter 6. From these three distinct networks, a 

ceramic industry multilayer network is constructed in Chapter 8 toward explaining social 

interrelationships in multicultural social environments following migration, as in the Late 

Prehistoric central Illinois River valley case study region. 

 

The approach taken here considers proportional similarities in material culture as a proxy 

measure for the strength, or degree, of connectedness between past communities. Other 

researchers have demonstrated the utility of this approach in a variety of contexts (Gjesfjeld 

145 

2014; Golitko and Feinman 2014; Mills, Roberts Jr., et al. 2013; Shaw, et al. 2016). Nodes 

represent different potter communities and are presumed to be representative of spatially discrete 

pre-Columbian settlements populated by Ancestors of Native American peoples. Edges represent 

probabilistic relationships between those communities and the larger settlements within which 

they are nested. The weight of an edge represents the probabilistic strength or degree of that 

relationship. Edges are directed, meaning that they consider the degree of a relationship from one 

node directed toward another. Given that many of the Late pre-Columbian central Illinois River 

valley site assemblages considered here were recovered via surface survey, illicit excavation, or 

other non-professional archaeological excavation techniques where internal provenience of 

vessels is lacking, analyzing intra-community scale variability is not currently possible based on 

available data. Thus, the scalar focus of this investigation is explicitly regional. Analysis at the 

household or site sector scale may be an area of potential research at some sites in the future, 

however (see Chapter 5).  

 

In order to model social interaction between sites using the eight artifact type-attributes 

that have been found to be more likely to bear social information, it is necessary to develop a 

procedure to assess relative technological similarity across each of these attributes 

simultaneously respective to each material culture class. A total of four ‘monoplex’ or single-

layer networks and five multilayer networks are constructed: two from each vessel class during 

each time period under consideration, one multilayer network for each time period, one 

multilayer network for each vessel class across time periods, and one multilayer network for both 

vessel classes across time (Table 5.11). The methods developed for this study are based in part 

on techniques for measuring technological similarity in archaeological ceramics borrowed from 

quantitative morphology and genetics by Peeples (2011:185). All analyses were performed using 

146 

the R statistical package with network graphs generated using open-source software including 

the R statistical language and environment; Gephi, an open source graph visualization platform; 

and the vector graphics editor Inkscape.  

Type of Network 

Vessel Class(es) 

Time-Period 

Calendar Date 

Monoplex 
Monoplex 
Monoplex 
Monoplex 
Multilayer 
Multilayer 
Multilayer 
Multilayer 
Multilayer 

Domestic Jar 
Plate 
Domestic Jar 
Plate 
Jar and Plate 
Jar and Plate 
Jar 
Plate 
Jar and Plate 

Pre-Migration 
Pre-Migration 
Post-Migration 
Post-Migration 
Pre-Migration 
Post-Migration 
Across Time 
Across Time 
Across Time 

1200 – 1300 A.D. 
1200 – 1300 A.D. 
1300 – 1450 A.D. 
1300 – 1450 A.D. 
1200 – 1300 A.D. 
1300 – 1450 A.D. 
1200 – 1450 A.D. 
1200 – 1450 A.D. 
1200 – 1450 A.D. 

 
Table 5.11 Summation of networks constructed with artifact type-attribute social interaction markers 
 
 

The analysis performed can be summarized in six general steps. 1) First, the social 

information bearing type-attributes are converted into a symmetrical matrix of pairwise distances 

between sherds. 2) Next, the distance matrix is converted into a symmetrical similarity matrix 

between sherds. 3) The similarity matrix is then converted into a directed, weighted edge list of 

individual sherd to sherd similarities. 4) Proportional pairwise similarity is then calculated 

between each site based on individual sherd to sherd similarity scores. 5) The resulting 

proportional similarity list is then normalized by site for scores between 0 and 1, or a list of 

weighted, directed similarity between each site using a threshold value of > 0.5, to allow for the 

production of each of the individual ceramic industry social interaction networks listed in Table 

5.11. 6) Finally, domestic jar and plate networks are flattened and sliced into five multilayer 

networks that consider the roles of each vessel class and time period(s) under consideration. 

Each of these steps is applied to both material culture classes under consideration here (domestic 

147 

continuous type-attribute, Gower’s coefficient is defined as: 

"#$%="(#,$)(*)=	1−|	/0*−	/1*	|
2*

 

jars and serving plates) separately and described in detail below. All R code is provided in 

Appendix C for these operations.  

 

(1) & (2) The first step in this analytical procedure is the construction of a symmetrical 

matrix of relative distances of every sherd against every other sherd of the same vessel class in 

the sample for the type-attributes discerned to be likely bearing of social information. That is, 

each domestic jar attribute is compared to every other domestic jar attribute and each plate 

attribute is compared to every other plate attribute to assess the dissimilarity between them. In 

this way, social interaction may be modelled for each vessel class independently based on 

individual attributes. Gower’s coefficient of similarity was selected for this analysis because it 

incorporates cases with missing data handily and computes a distance score between 0, 

indicating complete dissimilarity, and 1, indicating perfect similarity (Gower 1971). For each 

where (2*) denotes the absolute range of the values for the kth variable. When all variables are 

Equation 5.1 Gower’s coefficient 

 

quantitative, as in the case here, the Gower coefficient is a range-normalized Euclidean 

coefficient, which is quite similar to the Brainerd-Robinson coefficient of similarity used in 

archaeological statistics (Brainerd 1951; Robinson 1951). Implementation of Gower’s similarity 

coefficient in the R cluster package (L. Kaufman and Rousseeuw 1990a) is focused on obtaining 

a dissimmilarity coefficient as opposed to a similarity coefficient, and is commonly used in 

clustering procedures such as those used in machine learning (Lesmeister 2015). As a result, 

statistical packages using the Gower coefficient calculate a dissimilarity score by subtracting the 

148 

similarity score from one (i.e., (1 - "#$%)). This process is reversed by subtracting the distance 
score from one (i.e., (1 - (1 - "#$%))). 

(3) Because the matrix produced from the procedures above is symmetrical and therefore 

equal to its transpose, it is easier to handle and manipulate the data in edge list format. This is 

especially true given the large number of sherd to sherd comparisons, which makes for very large 

matrices (n plate comparisons = 256,032; n jar comparisons = 354,025). Edge lists are a data 

class amenable to the production of network graphs, the others being adjacency lists and 

adjacency matrices (Kolaczyk and Csárdi 2014). Edge lists are composed of a two-column list of 

all vertext pairs connected by an edge, with ancillary columns indicating the weight of the edge, 

directionality of the edge relationships, data layer, or other information such as geospatial 

positioning, time period of the edge relationships, and the like.  

 

(4 & 5) Proportional pairwise similarity is then calculated between site assemblages for 

each material culture class separately. The coefficient developed to accomplish this is a natural 

extension of the Gower coefficient of similarity, where a proportional similarity coefficient 

(PSijk) between sites i and j is assessed by taking the sum of pairwise similarities based on the 

Gower coefficient ("#$) and dividing by the total number of pairwise comparisons between two 
site assemblages (3#$) based on the kth variable: 

45#$%=45(#,$)(*)=	∑ "01*
*301*  

To allow for network graph construction, the proportional similarity coefficient scores for each 

Equation 5.2 Proportional similarity coefficient 

 

site are then normalized between 0 and 1, and act as the weight of an edge between two sites. 

Through normalization, these weights represent the probabilistic strength of a directed 

relationship from one site to another, relative to one site’s relationships to every other site. That 

149 

is, the weights of each site’s respective relationships to every other site are normalized relative to 

each other with the strongest relationship represented by 1, the weakest relationship represented 

by 0, and relationships in between scaled proportionally. Each site thus forms their own, 

directed, ties to other sites such that the tie from actor l to k is differentiated from the tie from 

actor k to actor l. This is done for a number of reasons. First, it enables an analysis of reciprocity 

of ties. In other words, one may ask whether the tie modeled from a given site is reciprocated and 

to what degree. Furthermore, the use of directed ties enables an acknowledgement of the internal 

variation and potential obfuscation of individual potter to individual potter relationships when 

using settlements as nodes. A simple heuristic to understand directionality is the concept of 

following in the TwitterTM social network platform. User a may follow user b, but user b may or 

may not reciprocate and follow user a back. Directed networks therefore allow for the capturing 

of both agent-scale complexity in a community-scale focus and for the analysis of reciprocity in 

social interrelationships. This ensures the maximal representation of community-scale 

relationships among potters relative to each other. The weights act as statements of probability of 

the strength of relative social interaction between two sites based on the similarity of socially 

mediated artifact type-attributes. In order to model particularly strong relationships only, a 

than 0.5 are not considered when constructing network graphs. 

 

threshold value of > 0.5 is used as a cut-off value in graph construction. That is, all edges lower 

(6) Whereas the single-layer networks can be represented by a graph as a tuple (e.g. "=
(7,8) where V is a set of nodes and 8	⊆7	/	7 is the set of edges that connects pairs of nodes), 
a multilayer network constitutes a quadruplet (e.g. :=(7;,8;,7,<) where the first two 
elements in a multilayer network M yield a graph ";=(7;,8;), that has a set of global nodes 

V, and a set of layers L (Dickison, et al. 2016; Kivelä, et al. 2014). In layman’s terms, a 

150 

multilayer network is a set of actors connected through multiple types of relationships. Those 

relationships span different layers and the nodes in different layers can correspond to the same 

actor. In this chapter, the relationships between any two given spatially bounded archaeological 

sites span two layers: technological similarity in domestic cooking jars and similarity in likely 

serving plates. Because not all nodes occur within each network under consideration here (i.e. 

some sites do not have ceramic assemblages that include plates and all sites aside from one have 

occupations limited to one of the two time periods under consideration), these networks are 

considered node-colored-network representations based on layer-disjoint node sets. Further, 

because couplings between nodes are not diagonal, and therefore do not link nodes from 

different layers, the network is considered multilayer only and not multiplex. 

 

It should be noted at this point in the analysis that network graph production and 

visualization is simply an efficient means to convey information about the complex relationships 

among the Late Prehistoric central Illinois River valley settlements included in this study. The 

lack of an edge or tie, as modelled based on thresholds chosen, should not be interpreted as a 

statement that a particular kind of social relationship was absent between two settlements. 

However, by applying common threshold criteria, it does allow the most potentially meaningful 

relationships to be modelled and therefore increases the interpretability of patterns of network 

relationships. Network graphs distill an enormous amount of information, and the application of 

a common threshold allows the visualization to alert the viewer to the most pertinent or relevant 

information in each model (Weidele, et al. 2016). Furthermore, applying thresholds allows for 

the application of additional community detection algorithms otherwise not available for 

weighted networks due to the complexities of handling weights in multilayer networks (Magnani 

2017, personal communication). That is, most algorithms designed to detect communities within, 

151 

or otherwise analyze, multilayer networks are not yet capable of supporting weights, 

directionality, or other edge attributes. Only unweighted, undirected networks are generally 

supported at this time, however some exceptions are available (Edler and Rosvall 2014).  

 

Multilayer graphs are constructed in two ways for visual representation and network 

metric generalization: flattening and slicing. The first method is via flattening. Flattening is 

perhaps best illustrated with a toy example. A typical way to mathematically represent a 

multilayer network is with a set of adjacency matrices. Each matrix corresponds to a particular 

type of edge, with one row/column for each node and element (i, j) indicating actors i and j are 

connected by an edge of the corresponding type (Dickison, et al. 2016). Figure 5.7 illustrates a 

very simple representation of a multilayer network with relationships formed by friendships on 

different social media platforms. The various matrixes constitute an adjacency list of tables. To 

flatten this adjacency list of tables, it is transformed by combing all aspects i and j into a new 

aspect h. That is, a multilayer network is defined by summing all the binary friendship 

relationships between actors to emphasize the weight of a friendship across different social 

media platform layers. While the toy example shown here uses a network of binary (e.g. 

presence/absence) relationships, this process holds true for networks where the relationship is 

modeled by a weight as well. Each of the relationship layer weights are summed to create a 

flattened representation of the multilayer network. This is a method of simplification that can aid 

in the detection of cohesive subgroups using community detection algorithms, for example. 

Flattening can be problematic due to its relative simplicity, however. For example, a particularly 

dense network layer, or a layer with many edges between nodes, may reduce the ability for 

interesting patterns to be revealed in the multilayer network. That is, an excessive amount of 

edges in one layer may mask the ability of algorithms to detect meaningful. 

152 

 

 

 

 
 
 
 

 

Friendship on FacebookTM 

Bob Pat Jon Cici Jill Phil 

⎝⎜⎜⎛0 1 1 1 0 0
1 0 0 0 0 1
0 1 0 1 1 0⎠⎟⎟⎞
1 0 0 1 1 0
1 0 1 0 0 1
0 0 1 0 0 1
⎝⎜⎜⎛0 1 1 1 1 1
1 0 1 0 0 1
1 1 0 1 1 0⎠⎟⎟⎞
1 1 0 1 1 0
1 0 1 0 1 1
1 0 1 1 0 1
⎝⎜⎜⎛0 0 0 0 0 0
0 0 0 0 0 1
0 1 0 1 1 0⎠⎟⎟⎞
0 0 0 1 1 0
0 0 1 0 0 1
0 0 1 0 0 1

 

 

 

Friendship on TwitterTM 

Bob   
Pat   
Jon   
Cici   
Jill   
Phil 

Bob   
Pat   
Jon   
Cici   
Jill   
Phil 

Bob   
Pat   
Jon   
Cici   
Jill   
Phil 

Bob Pat Jon Cici Jill Phil 

Friendship on SnapchatTM 

Figure 5.7 Adjacency matrix representation of multilayer social media friendship network 

 
 

Bob Pat Jon Cici Jill Phil 

⎝⎜⎜⎛0 2 2 2 1 1
2 0 1 0 0 3
1 3 0 3 3 0⎠⎟⎟⎞
2 1 0 3 3 0
2 0 3 0 1 3
1 0 3 1 0 3

 

Bob   
Pat   
Jon   
Cici   
Jill   
Phil 

Figure 5.8 Flattened adjacency matrix representation of multilayer social media friendship network 

 
 

153 

communities or community relationships based on information from other, sparser layers. 

Furthermore, different combinations of layers may show different group configurations. If we 

only flattened the FacebookTM and SnapchatTM network layers in the example above, it would 

produce different results than the network based on all three social media platform friendship 

layers. Thus, flattening is a useful technique for simplifying the different network layers but can 

often mask potential insights as a result of the reduction of layer information.  

 

Another means of visualizing a multilayer network is through layer slicing. The idea of 

layer slicing is to visualize each layer in what is called a 2.5-dimensional representation (De 

Domenico, Nicosia, et al. 2015; De Domenico, Solé-Ribalta, Cozzo, et al. 2013). While each 

layer is made of 2-dimensional planes, in visualizing them in proximity to one another, 

preferably using the same layout, it is possible to interactively explore the multilayer structure. 

This allows for visual interpretation and appreciation of the structure of each layer and how they 

contribute to the multilayer network as a whole, but at the expense of reducing the ability to  

 

Figure 5.9 Example of multilayer network slicing with networks embedded in geographical regions, 

showing a network of European airports rendered using MuxViz with each layer representing a different 

airline and edges representing flights between airports (De Domenico, Porter, et al. 2015)  

 

 

154 

detect network structure developing over multiple layers. An example of layer slicing is shown 

in Figure 5.9. 

Layer slicing and layer flattening provide complementary means to visually interpret and 

statistically analyze multiple relations networks. Both produce sociograms, which have become 

the hallmark visualization technique of social network analysis. Other visualization methods are 

available but are not presented here. However, visualization of graph structure will be augmented 

in the succeeding sections using network measures such as degree, closeness centrality, and edge 

weight to ease visual interpretation of the role of individual nodes and network structure as a 

whole. Other methods for network graph visualization not used here include annular graphs, 

histograms of degree distributions, cognitive social structures, heatmaps, dendrograms, and 

hierarchical clustering, among others (De Domenico, Porter, et al. 2015; Dickison, et al. 2016; 

Kivelä, et al. 2014). However, contingencies related to network structure will be analyzed using 

both traditional and multilayer network statistics as well as linear models and other traditional 

statistical techniques for the analysis of relational data.  

 

Numerous statistical metrics have been developed for monoplex networks (Scott 2000; 

Wasserman and Faust 1994). In many cases, these metrics can be generalized to work with 

multilayer networks, especially if a network aggregation technique such as flattening has been 

applied to the network turning the multilayer network into a monoplex network. However, it is 

often more constructive to apply monoplex metrics to individual network layers and aggregate 

the results in order to facilitate comparison of network structure across the different layers, and 

then to further compare those individual layer results to the aggregated network as a whole. This 

is the general approach taken here: each layer will be visually presented such as to highlight 

certain structural features and monoplex network statistics will be presented and discussed before 

155 

moving on to present multilayer measures designed for implementation for networks without 

inter-layer edges.  

 

Monoplex network measures will focus on those that describe network structure, and 

include degree distribution, centrality (with a particular emphasis on closeness centrality), edge 

weights, network diameter, network density, average clustering coefficient, and average path 

length (or distance) (Brughmans 2013; Knox, et al. 2006; Kolaczyk and Csárdi 2014; Scott 

2000). These metrics will be computed for each individual network layer and for the flattened 

multilayer network.  

 

Multilayer network measures will focus on describing the relationships between network 

layers. These multilayer metrics include multilayer average degree, multilayer degree deviation, 

multilayer connective redundancy, simple matching multilayer edge comparison, Jaccard index 

multilayer edge comparison and overlapping community detection (based on the clique 

percolation method) (Afsarmanesh and Magnani 2016; Cozzo, et al. 2013; Dickison, et al. 2016; 

Kivelä, et al. 2014; Magnani 2017). These multilayer, and the prior monoplex, network metrics 

are described in Chapter 4.  

 

5.5 Evaluating the Results: Statistical Interpretation of Ceramic Industry Social 

Interaction Network Models  
 
The procedures outlined in the preceding section allow for the creation and statistical 

analysis of network graph models based on similarities between pairs of settlements, which act 

as proxy measures for the relative degree of social interaction through cultural transmission or 

homologous interrelationships between groups of potters and other groups at different spatial and 

social scales. For a given settlement to settlement comparison, a higher edge weight suggests 

more frequent interaction, stronger relational connections, and/or a higher degree of homology in 

156 

evolutionary relationships among the inhabitants of those sites. As a result, the degree of 

technological similarity may provide insight into the nature and structure of social 

interrelationships between settlements in the Late Prehistoric central Illinois River valley (CIRV) 

case study region. Patterns of social interaction and relational connections among settlements 

across the study area are visually and statistically explored via social network graphing and 

analysis techniques. Because network models are such a rich source of information beyond what 

can be presented in static visualizations, it is necessary to preface interpretations based on visual 

features with statistical analyses. In particular, this section presents a statistical analysis of the 

structural nature of pre- and post-migration interaction patterns through cultural transmission of 

ceramic attributes in the Late Prehistoric CIRV based on measurements and concepts used in 

formal social network analysis and in multilayer social network analysis (Dickison, et al. 2016; 

Scott 2000; Wasserman and Faust 1994). Given the regional scale of this analysis, interpretations 

focus on a top-down perspective to inferentially predict the dynamics of social structure in the 

CIRV. Additionally, because distance has been shown to play an important role in network 

dynamics in other archaeological contexts (Golitko and Feinman 2014; Mizoguchi 2009; Peeples 

2011), this section specifically discusses the role of geographic distance on the structure of 

network relationships in the Late Prehistoric CIRV case study region. These analyses both 

inform and are informed by the visual interpretation and discussion provided in the subsequent 

section.  

It is important to again emphasize that there is considerable variability in the amount of 

data from each site in the analyses that form the basis of the succeeding interpretations. 

Quantitative archaeological analysis is often an endeavor conducted on datasets wherein 

considerable data are missing, and this dissertation research is no exception. Given the regional 

157 

scale of this project, and the resulting reliance on extant collections, the interpretations below are 

not based on a probabilistic survey nor is there perfect comparability between any two given 

sites. Thus, the relationships modeled between sites may be negatively impacted by issues of 

sampling. Nevertheless, since the interpretations are based on comparisons between artifact 

attributes, as opposed to vessels themselves, and because the relationships modeled below 

conform to the n-critical for each attribute comparison, the interpretations should be considered 

as robustly laying the foundation for exploring the nature of site to site relationships in the Late 

Prehistoric CIRV.  

 

In examining the networks constructed here, several structural components are 

considered and evaluated across space and overtime. First, it is anticipated that changes in 

network structure overtime are related in some capacity to the in-migration of Oneota peoples 

into the CIRV circa 1300 A.D. This migration process represents the basis for the temporal 

partitioning of network graph models. One may ask whether there are changes in network 

structure across time, and how might the in-migration of an exogenous tribal group be related to 

those changes? Second, Mississippian peoples in the CIRV have been taxonomically defined as 

likely representing two distinct chiefly polities – the La Moine River and the Spoon River 

Mississippian variants (Conrad 1991). As a result, and more especially in the pre-migration 

context of the CIRV, network topological statistics such as the clustering coefficient and 

community detection algorithms are analyzed to determine how strongly settlement nodes form 

ties in dense, relatively unconnected (between group) groups and if those groups are 

geographically aligned with the hypothesized La Moine and Spoon River Mississippian variants. 

While many other factors aside from domestic jar and plate technological characteristics were 

used to differentiate between these variants, it is possible to ascertain here whether or not 

158 

ceramic technology may be a contributing or delimiting factor to the proposed taxonomic 

distinction. Thirdly, given that the serving plate ceramic vessel class is absent or extremely rare 

in Oneota contexts outside the CIRV (Esarey and Conrad 1998), particular attention is given to 

this class in the post-migration CIRV. That is, do imitations/emulations of serving plates by 

Oneota peoples inject sufficient variation to suggest that the adoption of this vessel class was 

made at a distance, or are the imitations/emulations technologically similar enough for there to 

be a higher likelihood that direct cultural transmission of ceramic technology between 

Mississippian and Oneota potters occurred? Additionally, it has been postulated that the onset of 

the Mississippian period circa 1200 A.D. was paralleled by the emergence of chronic, internecine 

violence and warfare (G. R. Milner 1999:Wilson, 2012 #1667). The threat of warfare is argued to 

have transformed both settlement and subsistence practices such that, among other things, 

“families coalesced into large communities behind defensive walls…limiting foraging and 

fishing trips” and “women became increasingly sequestered behind village walls” (Vanderwarker 

and Wilson 2016:98-100). Given that ethnographic accounts indicate that when pottery 

manufacture is done by hand, it is typically done by women (Rice 2005), it is possible to test 

whether the Mississippian CIRV is characterized by geographically circumscribed potter 

communities. That is, does sufficient variation in pottery attributes characterize different 

communities such that it can be reasonably assumed that potters were geographically 

circumscribed in the cultural transmission of artifact attribute social information primarily as a 

result the threat of violence and warfare?  

 

In addition to relying on formal methods in the statistical analysis of monoplex and 

multilayer network data, which are discussed at length in Chapter 4, interpretations are based in 

part on conditional uniform graph tests through Monte Carlo simulation. Each observed network 

159 

statistic was compared against the distribution of that statistic generated from 5,000 random 

graphs of the same order (number of nodes) and probability of an edge being given between any 

two nodes (based on the observed graph’s density) or size (number of edges) using the Erdős-

Rényi graph randomization technique (Erdős and Rényi 1959). Network randomization 

simulation enables formal hypothesis testing of whether the observed network statistics are 

unusually high or low given what might be expected if the same probability of edges (or number 

of edges) were connected to the same number of nodes as the observed network based on random 

chance alone.  

Erdős-Rényi random graph models place equal probability on all graphs of a given order 

and size. That is, a collection of graphs are considered based on the provided order and size 

(number of nodes and edges) and a probability is assigned to each, where the total number of 

distinct node pairs are considered (Kolaczyk and Csárdi 2014). As a result, each permutation of a 

network of a particular order and size is able to be drawn upon to simulate graph models 

uniformly at random. An extension provided by Gilbert (1959) enables the random graph 

concept to be extended to graphs of a fixed order but where each pair of distinct nodes are 

independently assigned based on a given probability. This is often referred to as a Bernoulli 

random graph model, but will be subsumed here under the Erdős-Rényi framework (Kolaczyk 

and Csárdi 2014). Erdős-Rényi random graph models were chosen for statistical comparison 

because they most closely resemble the topology of the networks generated using the procedure 

described above. As further described below, the networks do not appear to conform to 

properties expected of small-world or scale-free/preferential attachment models that often 

characterize large-scale networks observed in many real-world networks (Barabási and Albert 

1999; Watts and Strogatz 1998). 

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5.5.1  Statistical Analysis of Pre-Migration Interaction Networks, 1200 – 1300 A.D. 
 

Because networks are defined by their actors and the connections among them, in this 

case spatially bounded archaeological sites and the degree of similarity in socially mediated 

artifact attributes, a useful starting point in statistical network analysis is examination of these 

properties. Table 5.12 displays network summary and analytical statistics, including network 

order (number of nodes), size (number of connections or edges), and mean weighted degree (or 

average total strength of connections) for each network under consideration. In examining these 

measures for the jar and plate interaction networks for the pre-migration period, some important 

distinctions are apparent. For example, the jar attribute network includes many more edges (or 

connections) than the plate attribute network for the pre-migration period (81 edges compared to 

63 edges). While one additional site-node in the jar layer (Eveland) compared to the plate layer 

may account for the discrepancy in edges, the mean weighted degree further hints at important 

structural distinctions between the two layers. The jar attribute pre-migration network layer is 

composed of significantly stronger connections between sites on average than the plate pre-

migration layer (mean weighted degree of 5.117 compared to 3.994). Thus, in terms of simple 

summary statistics, the jar attribute layer contributes many more and many stronger connections 

in the pre-migration interaction networks that does the plate attribute layer.  

In network terminology, both layers in the pre-migration period conform to an expected 

connectedness (referred to as density), or proportionality of present ties compared to the possible 

number of ties (see Table 5.12; Figures 5.10 and 5.11), based on a Monte Carlo simulation of 

5,000 random graphs of the same number of nodes and probability of edge creation using the 

Erdős–Rényi random graph modeling technique (Erdős and Rényi, 1959). That is, pre-migration 

161 

networks conform to random expectations for density. Additionally, both the jar and plate pre-

migration networks consist of many hubs, as shown in Figure 5.12. In fact, nearly every site 

displays the behavior associated with hubs. The concept of hubs and authorities, based on the 

HITS algorithm (Kleinberg 1999), considers the importance of hub-nodes based on how many 

authorities-nodes they point to, and authority-nodes based on how many hub-nodes point to 

them. In other words, hubs advertise or distill information gathered from authority nodes. 

Because every site in the pre-migration time period has a high hub score, information is not 

hierarchically restricted nor restricted to site clusters. At a minimum, density and hub measures 

imply that the ceramic vessel attributes argued here to be socially mediated indicate shared  

 

Figure 5.10 Network Randomization Results for Jar Pre-Migration Layer. Observed statistic represents 

red line. Histogram shows distribution of statistic based on network randomization of 5000 random 

graphs using the Erdős–Rényi random network modeling technique. 

 

162 

contexts of learning and homologous relationships across sites and a capacity for site actors to 

inter-operate. That is, the interaction cost in both jar and plate attribute networks is low enough 

to suggest that on average there is a tendency for information to flow broadly and frequently 

throughout the networks in the pre-migration period (Borgatti, et al. 2009).  

 

Figure 5.11 Network Randomization Results for Plate Pre-Migration Layer. Observed statistic 

represents red line. Histogram shows distribution of statistic based on network randomization of 

5000 random graphs using the Erdős–Rényi random network modeling technique. 

On the other hand, a more interconnected domestic jar network is supported by the 

average shortest path length, or average number of nodes in between any two given nodes, which  

is just 1.182 for the domestic jar layer but a much higher 1.527 for the plate layer. In fact, none 

of the random graph models for the pre-migration jar network reported a lower average shortest 

path length than the observed network (Figure 5.10), but some 92% of 5,000 random graph 

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models based on the plate pre-migration network reported shorter average path lengths (Figure 

5.11). The unusually low average shortest path length for the jars suggests widespread and 

efficient transmission about socio-cultural information embedded in jar attributes, while the 

unusually high average shortest path length for the plates indicates the inverse – less efficient or 

restricted transmission about cultural information related to plate attributes. An alternative, and 

perhaps more plausible, interpretation of the high average shortest path length for the plate pre-

migration network is that plate attributes were more a product of adaptation to the local social 

environment whereas socially mediated jar attributes appear to have been perhaps more globally 

adapted. The diameter, or longest shortest path, which is just two for the jar layer but three for 

the plate layer further substantiates the difference in network topology between the layers in the 

pre-migration CIRV. These observations suggest that the jar attributes not constrained by 

engineering forces may have contributed more to signaling global social relationships among 

potter communities in the pre-migration CIRV or were perhaps more resistant to change given 

the presumed functional importance of cooking facilitated by domestic jars. Furthermore, since 

plates emerge as a distinct vessel class only after the occupation of the Eveland site, plate 

attributes may be characterized by a greater degree of variation in general than jars as a result of 

the novelty of the vessel class, and perhaps accompanying changes in foodways, in the increased 

situational usage of a presumed serving vessel.  

A low average shortest path length, such as that observed in the jar pre-migration 

network, is often accompanied by a high transitivity (or clustering coefficient) score in real-

world networks. This combination of structural features has been identified as a ‘small-world 

network’ where most nodes are not neighbors of each other, but information easily passes 

through the network in a relatively small number of steps (Watts and Strogatz 1998). The pre-  

164 

Figure 5.5.12 Authorities and Hubs in the Jar and Plate Pre-Migration Period Network Layers. Authority 

and Hub scores are modeled as node size. 

 

 

165 

migration jar attribute network, however, is characterized by a transitivity (or clustering 

coefficient) score only moderately above what might be expected based on chance alone (65% of 

5,000 random graph simulations report a transitivity lower than the observed jar pre-migration 

layer). The pre-migration plate attribute network is neither characterized by a low average 

shortest path length nor an unusually high clustering coefficient score. As a result, both the jar 

and plate pre-migration attribute networks do not support a small-world network model for the 

pre-migration period. 

Based on the degree distributions, or frequencies of the total connectedness of nodes in 

the network, it can be affirmed that the jar and plate pre-migration attribute networks do not 

display characteristics associated with a scale-free network using a preferential attachment  

mechanism, also known as the Barabási-Albert model (Albert and Barabási 2002; Barabási and 

Albert 1999). Figure 5.13 displays the degree distributions of the jar and plate pre-migration 

Figure 5.5.13 Degree distribution of Jar and Plate Pre-Migration networks. 

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networks. Under the Barabási-Albert model preferential attachment model, the distributions 

would be highly right skewed showing that many nodes have few connections and just a few 

nodes have many connections, which is often referred to as the ‘rich get richer’ postulate of node 

creation overtime. Such a model would suggest that ‘child’ nodes would splinter off of ‘parent’ 

nodes, with few parents connected to many budding children nodes. The incongruence of the jar 

and plate networks with the Barabási-Albert model indicates that the settlements considered here 

were likely not hierarchically organized in the Late Prehistoric CIRV. 

Both pre-migration period networks lack a central actor or actor-clique with significantly 

higher degrees of connectivity than others as indicated by low degree, betweenness, closeness, 

and eigenvector centralization scores (Table 5.12). Centralization scores address inequality in 

node interconnectedness, or if one or a few nodes are more central to the network than others in 

certain ways (Scott 2000:Wasserman, 1994 #329). The low centralization scores observed in the 

pre-migration networks indicate that node importance is relatively evenly distributed across the 

entire network. However, certain sites do appear to be more authoritative, in terms of their 

connections to other sites, based on the HITS algorithm (Kleinberg 1999). In other words, some 

sites are significantly more connected than others, suggesting that these sites were likely loci of 

information, regional events, or producers of exogamous offspring to other sites that would 

account for the many strong connections to these sites in terms of social interaction through 

cultural transmission. The Larson site in particular plays an authoritative role in both the jar and 

plate pre-migration networks, as do Lawrenz Gun Club, Buckeye Bend, Myer-Dickson, Kingston 

Lake, and Walsh to a lesser extent (Figure 5.12). However, the combination of low centralization 

scores, the presence of multiple authorities, and the ubiquity of hubs in the pre-migration period 

indicates that no one site-actor dominated regional interaction or information flow as might be 

167 

expected in a hierarchical regional settlement system as seen in other Mississippian contexts 

such as the American Bottom (Fowler 1974), at least at the unrefined scale of the entire pre-

migration period (~1200 – 1300 A.D.) considered in this analysis.  

In attempting to identify communities, or modules that form dense connections among 

themselves and sparser connections to nodes outside the module, a diverging trend is apparent 

between the jar and plate pre-migration attribute networks. A particularly instructive community 

structure detection technique for the weighted and directed networks considered here is edge 

betweenness, which maps a value to each edge (or link) in the network based on how many 

shortest paths traverse through it (Kolaczyk and Csárdi 2014; Newman and Girvan 2004). Edges 

that connect separate modules, or individual communities within a network, have high edge 

betweenness values. By gradually removing these edges with high betweenness values, a 

hierarchical map is created similar to a network dendrogram. Clusters can therefore be identified 

in the same way that clusters might be identified via hierarchical clustering techniques, for  

Figure 5.5.14 Edge betweenness community detection in the Jar and Plate Pre-Migration Attribute 

Networks 

 

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example. Figure 5.14 shows that no meaningful community structure is able to be identified 

based on edge betweenness in the pre-migration jar attribute network whereas three distinct 

modules are identified in the pre-migration plate attribute network. This finding aligns with 

interpretations from other network statistics indicating important structural differences between 

the layers where jar attributes reflect a global pattern of interaction and information flow and 

plate attributes are more so the product of localized or nuanced social interaction through cultural 

transmission.  

The multilayer network combining both jar and plate networks in the pre-migration 

period is characterized by a significantly increased mean weighted degree of 7.917 as a result of  

 

Figure 5.15 Network Randomization Results for Multilayer Pre-Migration Network. Observed statistic 
represents red line. Histogram shows distribution of statistic based on network randomization of 5000 

random graphs using the Erdős–Rényi random network modeling technique. 

 

169 

the concatenation of the two layers together. Both density and transitivity (or mean clustering 

coefficient) also increase in the flattened multilayer pre-migration attribute network in 

comparison to that of the individual jar or plate layers. Though none of these figures are 

significant relative to network randomizations for the pre-migration multilayer network as shown 

in Figure 5.15. However, despite the high average shortest path length in the pre-migration plate 

layer, the multilayer network follows the very low average shortest path of the domestic jar pre-

migration layer, with a low score of 1.215, or 1.215 steps in between any two given nodes in the 

network on average. No doubt, the higher edge weights in the jar layer contribute to this trend. 

The increased number of edges and stronger edge weights in the pre-migration jar attribute 

network also obfuscate the nuances of authorities across the jar and plate attribute layers. In 

general, trends of authority in the pre-migration jar attribute layer supersede those in the plate 

layer when modeled as a singular multilayer network (Figure 5.16). This trend holds true in  

Figure 5.5.16 Authorities and Hubs in the Multilayer Pre-Migration Period Network. Authority and Hub 

scores are modeled as node size. 

 

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community detection, where no community structures are able to be identified in the multilayer 

network as in the jar pre-migration layer (Figure 5.17). The ability to identify that 1) increased 

jar edge weights obfuscate the much higher average shortest path length of the plate layer in the 

pre-migration period, and 2) the nuanced nature of authorities and community structures across 

the jar and plate networks further substantiates the value of the multilayer network analysis 

methodology. 

 

In examining the multilayer network for the pre-migration period using formal techniques 

from multilayer social network analysis, Eveland shows the highest degree deviation, or standard 

deviation of an actor’s degree over the different layers. Degree deviation shows which actors are 

unevenly represented on different layers (Dickison, et al. 2016). All other sites are characterized 

by low degree deviations indicating that their presence in the jar and plate network layers is 

Figure 5.17 Edge betweenness community detection in the Multilayer Pre-Migration Network 

 

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comparable aside from Walsh and Orendorf C, which also have high degree deviations indicating 

an uneven presence in the jar and plate layers. Perhaps this is an indication that Walsh and 

Orendorf C were both occupied early in the occupational sequence of the pre-migration CIRV 

during the initial introduction of the plate vessel class.  

 

With an average connective redundancy of 0.375, the jar and plate networks are 

characterized by a fairly high degree of multiplexity. Average connective redundancy between 

the pre-migration layers is a measure that considers how often actors are connected to the same 

neighbors across multiple layers (Dickison, et al. 2016). However connective redundancy does 

not consider the weight of an edge, only its presence or absence across layers as weight and 

directionality have yet to be implemented in many multilayer network analysis algorithms 

(Matteo Magnani personal communication, 2017).  

 

Despite the many structural differences discussed above, the jar and plate pre-migration 

attribute network layers do share much in common. A simple matching coefficient considering 

common edges across the multiple layers shows that they share nearly 87% of edges in common 

when directionality and weight are not factored into the comparison. A more nuanced 

comparison using the Jaccard measure of similarity, which is computed as the amount of 

common edges between the layers divided by the union of all edges for pairs of layers (Dickison, 

et al. 2016), shows that the jar and plate attribute networks in the pre-migration period are 67% 

similar. Again, this metric is only able to consider deprecated edges by disregarding weight and 

directionality.  

 

In summary, when considering formal statistical measures for the analysis of monoplex 

and multilayer social networks, the jar and plate attribute networks in the pre-migration period 

are largely similar but with some very important distinctions. The most instructive measures 

172 

evidencing the distinctions between the layers are the average shortest path, HITS algorithm, and 

edge betweenness community detection. In general, these metrics indicate that the interactions 

through cultural transmission based on the sharing of jar attribute information represent 

connectivity among sites at a regional scale, whereas the sharing of plate attribute information 

represents connectivity at a more localized or nuanced scale. These scalar differences suggest 

distinctions in the production and likely situational usage of these vessel types in the pre-

migration period and speaks to the complexity of modeling social interrelationships between 

archaeological sites using artifactual data. Numerous authorities are modeled in the jar attribute 

network layer, but the Larson site plays a particularly authoritative role in this layer. Perhaps the 

emergence of the Dickson series of plain, cord-marked, or trailed jars at Larson, representing a 

fundamentally CIRV innovation to the production of Mississippian domestic jars, in addition to 

the central location of Larson geographically and its proximity to the Dickson Mounds mortuary 

ceremonial center are responsible for this authoritative distinction (Harn 1971, 1980, 1991, 1994; 

Strezewski 2003; J. J. Wilson 2010).  

 

Pre-migration CIRV interaction networks can overall be described as distributed, or 

lacking any central actor or actor-cliques, and highly cohesive, or generally lacking any 

structural evidence for distinct communities, modules, or cliques within the individual or 

multilayer networks, save those identified in the plate pre-migration attribute network layer. 

These interpretations, which are further discussed and expanded upon in the discussion in 

Section 6.6.1, indicate that social networks of interaction through cultural transmission of 

socially mediated jar and plate attributes in the pre-migration period do not support an 

hypothesized cultural distinction of CIRV Mississippian peoples into a La Moine and Spoon 

River variants (Conrad 1991), nor do they provide support for a model of delimited mobility as a 

173 

result of the threat of warfare (Vanderwarker and Wilson 2016). Were there to be intensive 

cultural distinctions between Mississippian peoples in different portions of the CIRV, it would be 

expected that those distinctions would be reflected in separate communities, cliques, or modules 

forming sub-networks of interaction through information sharing, imitation, and cultural 

transmission of ceramic artifact attributes. While some distinctions do exist in the plate vessel 

class, they do not follow a geographic divide based on the Spoon and La Moine River Valleys. 

Furthermore, were there to have been a marked curtailment in mobility patterns due to chronic or 

structural violence patterns, it would be expected again that interaction through information 

sharing, imitation, and cultural transmission of ceramic artifact attributes would be bifurcated 

along alliance lines or otherwise restricted to site or site-cluster scale patterns. Because these 

patterns of bifurcation or community structure do not exist across the network layers, it is 

established here that patterns of violence seen in skeletal data, the presence of fortifications, and 

ritual weaponry (Steadman 2008; Vanderwarker and Wilson 2016; G. D. Wilson 2012, 2013) did 

not inhibit interaction patterns in the Mississippian CIRV in a structural way. Rather, and 

perhaps despite the high levels of inter-personal violence, Mississippian peoples appear to have 

sustained widespread social interaction in the sharing and cultural transmission of information 

related to jar and plate ceramic industry.  

 

5.5.2  Statistical Analysis of Post-Migration Interaction Networks, 1300 – 1450 A.D. 
 

Sometime in the late thirteenth or early fourteenth century, an expansionary process of 

Oneota peoples began out of an upper Midwest and eastern Prairie Plains core territory (Gibbon 

2002; Henning 1998). Some characterize the Oneota expansionary process as aggressive and 

warlike (Hollinger 2005). While many Late Woodland populations in the riverine Midwest and 

174 

western Great Lakes were replaced by or integrated into Oneota peoples during this expansion, 

Mississippian peoples in the central Illinois River valley, or northern Middle Mississippian 

frontier, maintained their positions in fortified temple mound centers, and outlying sites, and 

entered into a period of regional multicultural coexistence (Esarey and Conrad 1998; O'Gorman 

and Conner 2016; Painter 2014).  

The post-migration period Late Prehistoric CIRV is comprised of many fewer sites than 

were occupied during preceding phases in the region, suggesting that a consolidation process, 

population upheaval, or other demographic change seen in Mississippian contexts in other 

regions was likely also being grappled with in the CIRV based on local conditions (Benson, et al. 

2009; Blitz 2010; Cobb 2005; Cobb and Butler 2002). That is, compared to the 11 or 12 town 

and village sites modeled in the pre-migration period attribute network layers, only some 7 or 8 

sites are able to be examined following the circa 1300 A.D. Oneota in-migration, depending on 

the layer. As in the pre-migration period, the different artifact attribute network layers are node-

disjoint as a result of one additional site in the jar layer compared to the plate layer. That is, the 

C.W. Cooper Oneota habitation site lacks any presence of the plate vessel class and as such was 

not able to be modeled in the post-migration plate layer. Thus, analysis of the post-migration 

period factors in the reduced network sizes as potentially confounding network statistics given 

the very small number of nodes.  

Despite a decrease in the number of nodes in the post-migration network, the mean 

weighted degree in the plate attribute network layer actually increases compared to the pre-

migration period (from 3.994 to 4.406). However, the mean weighted degree for the jar attribute 

network layer falls precipitously in the post-migration period (from 5.117 to 3.962). 

Furthermore, the diameter (or longest shortest path in the network) in the plate attribute network 

175 

drops from 3 to 2 while the diameter in the jar attribute network layer increases dramatically 

from 2 to 4 in the post-migration period. More striking is the mean path length, which is only 

1.048 for the plate layer, indicating that actors need only move between 1.048 sites on average to 

reach a destination node. These simple summary statistics imply significant structural changes in 

networks of interaction through cultural transmission occurring alongside Oneota in-migration 

into the region.  

The significance of the shift in structure of both jar and plate attribute networks is 

apparent when examining the results of Monte Carlo network randomizations using the Erdős–

Rényi random network modeling technique (Figures 5.18 – 5.19). In particular, the average 

shortest path length for the jar attribute network shifts from being lower than any value measured 

in network randomizations for the pre-migration jar attribute network to being higher than some 

94.9% of average shortest path lengths in the 5,000 randomized networks for the post-migration 

jar attribute network based on the Erdős–Rényi random network modeling technique. 

Furthermore, the average shortest path in the plate attribute network shifts from being higher 

than some 92.4% of randomly generated networks of the same order and size as the plate 

attribute pre-migration network layer, to being higher than only 42.7% of randomly generated 

networks based on the plate attribute post-migration network. In other words, the scalar pattern at 

which the different vessel classes were used in forming strong relational connections changed 

from the pre-migration period to the post-migration period in the Late Prehistoric CIRV. 

Whereas the jar attribute network formed strong relational connections among sites at a regional 

scale in the pre-migration, relational connections in the jar attribute network altered to form 

strong relational connections only at a reduced or nuanced scale in the post-migration period. 

The infusion of Oneota domestic jar technological choices undoubtedly contributed to this scalar 

176 

shift in relational connections. However, while the infusion of distinctly Oneota designs on jars 

is readily apparent, the infusion of distinct technological choices in jar manufacture by Oneota 

peoples is less obvious without using formal quantitative methods such as those used in this 

dissertation. What’s more, that Oneota peoples maintained not only distinctive stylistic but also 

technological choices in the manufacture of domestic jars speaks to the cultural maintenance of 

an importance facet of domestic life – cooking technology. Perhaps there was broad appeal to an 

Oneota heritage and the formation of bonding ties in the domestic sphere of life by Oneota 

potters (Crowe 2007).  

On the other hand, interactions with local Mississippian peoples did result in the adoption  

Figure 5.5.18 Network Randomization Results for Post-Migration Jar Attribute Network. Observed 

statistic represents red line. Histogram shows distribution of statistic based on network randomization of 

5000 random graphs using the Erdős–Rényi random network modeling technique. 

 

177 

of a unique vessel form by Oneota peoples, the plate – a vessel ostensibly used primarily as a 

food serving tool. While not all Oneota immigrants in the CIRV adopted the plate into their 

ceramic repertoire, as no plates have yet been recovered from the Oneota occupation at C.W. 

Cooper (Esarey and Conrad 1998), examination of the post-migration plate attribute network 

suggests an impetus for cultural integration or mediation by Oneota peoples in actively choosing 

to utilize the plate vessel class. The post-migration plate attribute network shows a high mean 

weighted degree, low average shortest path length, low diameter, higher density and low 

centralization scores comparable only to the pre-migration jar attribute network (Table 5.12). In  

Figure 5.5.19 Network Randomization Results for Post-Migration Plate Attribute Network. Observed 
statistic represents red line. Histogram shows distribution of statistic based on network randomization of 

5000 random graphs using the Erdős–Rényi random network modeling technique. 

 
 

178 

other words, the scale at which strong connections were formed increased dramatically from the 

pre-migration to post-migration periods in plate attribute networks at the same time that the scale 

at which strong connections were formed in the jar attribute networks decreased dramatically.  

No site with an Oneota presence – Crable, Morton Village, C.W. Cooper – is 

characterized as an authority when analyzing the post-migration period jar attribute network 

using the HITS algorithm (Kleinberg 1999) (Figure 5.20). This indicates that, in terms of jar 

attributes, sites with an Oneota presence retained pluralistic distinctions from their Mississippian 

peers, perhaps straining the formation and maintenance of regional relational connections given 

that jars were previously a source of widespread relational interaction through cultural 

transmission. However, because the sites with an Oneota presence do act as hubs in the post-

migration period jar attribute network, mediation was perhaps pursued but not reciprocated or 

there was a concerted effort by post-migration Mississippian sites to distinguish their own 

domestic jar technological communities of practice from Oneota immigrant jar technology (D. 

Upton 1996; VanPool 2008). In other words, the post-migration jar attribute network suggests 

that inter-cultural pluralism in the domestic sphere of life likely characterized the Late 

Prehistoric Period Crable and Crabtree phases of the CIRV.  

 

While pluralism may have been present in the domestic sphere of life based on the 

domestic jar network, the public sphere of life appears to have been in part an arena of inter-

cultural accommodation, integration, or other mediation between Oneota and Mississippian 

peoples as modeled by the post-migration plate attribute interaction network. Because every site 

in the plate attribute network post-migration time period has a high hub score, information 

regarding plate manufacture was decidedly not hierarchically restricted nor restricted to site 

clusters. This implies that the plate attributes argued here to be socially mediated indicate shared 

179 

contexts of learning and homologous relationships across sites occupied during the post-

migration period and a capacity for site actors to inter-operate – at least in the public sphere of 

life that a presumed serving vessel would primarily function within. That is, the interaction cost 

in plate attribute networks is low enough to suggest that on average there is a tendency for  

Figure 5.20 Authorities and Hubs in the Jar and Plate Post-Migration Period Network Layers. Authority 

and Hub scores are modeled as node size. 

 

 

180 

information to flow broadly and frequently throughout the plate attribute network in the post-

migration period (Borgatti, et al. 2009).  

 

This duality in the scale of relational connection formation between the artifact classes is 

best illustrated in community structure detection using edge betweenness (Figure 5.21). Whereas 

the pre-migration plate attribute network is characterized by a single, region-wide community, 

three distinct communities are detected in the post-migration plate attribute network. Of the three 

distinct communities, one is comprised of sites with an Oneota presence in addition to the 

Lawrenz Gun Club site – a site marked by a modest and unclear Oneota presence. A separate 

community structure is detected that comprises three Mississippian sites with no evidence of a 

multicultural occupations between Oneota and Mississippian peoples. Finally, Baehr South, a 

modest Mississippian village site appears to straddle these distinct communities and as a result 

forms a community unto itself. Thus, according to community structure, regional scale cultural  

 

 
Figure 5.5.21 Edge betweenness community detection in the Jar and Plate Post-Migration Attribute 

Networks 

181 

pluralism was largely maintained by Oneota and Mississippian peoples in the domestic or private 

sphere of life with some public deemphasis of inter-cultural differences. The multi-cultural 

occupations at Crable and Morton Village, however, do show that limited domestic scale inter-

cultural mediation did occur. This pattern of nuanced multi-cultural public-private distinction has 

precedent in other archaeological contexts (Stone 2003). 

 

Similar to the pre-migration period attribute networks, neither the jar nor plate attribute 

networks in the post-migration period exhibit characteristics associated with small world or scale 

free preferential attachment network models. Figure 5.22 shows that both post-migration 

networks are characterized by degree distributions with quite high values at the low end of the 

distribution (e.g. degrees of 6+) and a lack of extensive kurtosis that would suggest a log-log  

Figure 5.5.22 Degree Distributions of Jar and Plate Post-Migration Networks 

 
power law distribution typical of scale-free preferential attachment models (Barabási and Albert 

  

1999). Furthermore, low centralization scores (Table 5.12) reported for the post-migration 

182 

attribute networks indicate a lack of hierarchization in information flow, another characteristic 

element of preferential attachment. While both the jar and plate post-migration networks have 

very high mean clustering coefficient scores, the clustering comprises the entire networks as 

opposed to distinct cliques that are otherwise weakly integrated with the larger network. 

Therefore, these networks continue to exhibit a unique pattern separate from the kinds of graphs 

models that are oft used in explaining modern social interaction patterns (Albert and Barabási 

2002; Barabási and Albert 1999; Wasserman and Faust 1994; Watts and Strogatz 1998). 

 

In concatenating the post-migration jar and plate attribute networks into a single 

multilayer network it is apparent that the more influential network based on edge weights, in this  

 

Figure 5.23 Network Randomization Results for Multilayer Post-Migration Network. Observed statistic 
represents red line. Histogram shows distribution of statistic based on network randomization of 5000 

random graphs using the Erdős–Rényi random network modeling technique. 

 
case the plate network, takes precendence in summary network statistics. That is, the diameter, 

 

average shortest path length, degree, centralization scores, and average clustering coefficient 

183 

score more closely follows that of the plate attribute network layer than the jar attribute network 

layer in the post-migration period. However, network randomizations of the post-migration 

multilayer attribute network show that none of the four network summary statistics are unusually 

high or low compared to 5,000 random graphs of the same order and size (or probability of edge 

creation) using the Erdős–Rényi random network modeling technique. Significantly, the 

increased average shortest path length in the aggregated multilayer attribute network does 

indicate that interaction through cultural transmission decreased in frequency or scale following 

the in-migration of Oneota peoples into the Late Prehistoric CIRV, suggesting perhaps heighted 

inter-regional tensions or an increase in regional hostility that may have cross-cut cultural lines. 

Hub and authority analysis of the post-migration multilayer attribute network indicates that 

nearly every site operates as a strong hub based on connections to authority nodes. The sole 

exception is the C.W. Cooper Oneota habitation site, which is connected reciprocally only to 

other sites with an Oneota presence. As in the hub and authority analysis of individual attribute 

network layers for the post-migration period, none of the three sites with an Oneota presence are 

modeled as operating as authorities. This perhaps indicates an unwillingness on the part of the 

local Mississippian population to engage with these sites as frequently as with each other or 

wherein interaction through cultural transmission was otherwise limited to specific spheres of 

daily life. On the other hand, since no distinct communities are able to be modeled via edge 

betweenness in the multilayer post-migration attribute network (Figure 5.25) both positive and 

negative inter-cultural interactions between Mississippian and Oneota peoples are likely to have 

occurred in some context beyond the sites with unequivocal evidence for household scale inter-

cultural interaction – Morton Village and Crable (Bengtson and O'Gorman 2017; Conrad and 

Esarey 1983; Esarey and Conrad 1998; O'Gorman and Conner 2016; Painter 2014; K. Sampson 

184 

2000; Santure, et al. 1990; H. G. Smith 1951).

  

Figure 5.5.24 Hubs and Authorities in the Post-Migration Multilayer Attribute Network. Hub and 

Authority score modeled as node size 

 

Turning to formal multilayer network analysis measures for the post-migration period, all 

sites share identical degree deviation scores (or deviation across the network layers) aside from 

the C.W. Cooper site, which lacks any plates, and therefore has a very high degree deviation 

score. This indicates remarkable consistency across the layers in the presence of edges 

(Dickison, et al. 2016). However, this measure lacks the nuance of weight and directionality and 

simply indicates that each site has roughly the same number of neighbors on each layer aside 

from C.W. Cooper in the post-migration period when weight and directionality of edges are 

ignored. 

 

With an average connectivity redundancy of 0.402, the post-migration multilayer 

attribute network is characterized by a slightly higher degree of multiplexity than the pre-

migration period. Connective redundancy provides a more nuanced look at the co-presence of 

edges among the same node across different network layers. This higher score indicates slightly 

increased consistency in connections among nodes across different layers in the post-migration 

185 

period compared to the pre-migration period. A likely driving force behind the higher connective 

redundancy score is the high density (or total number of edges observed out of the total possible 

number of edges) for each of the post-migration attribute network layers. 

 

Despite the many structural difference discussed above, the jar and plate post-migration 

attribute network layers do share much in common with each other. A simple matching 

coefficient across the multiple layers shows that the two networks share over 95% of edge-node 

connections in common when directionality and weight are not factored into the comparison for 

the post-migration period. A more nuanced comparison using the Jaccard measure of similarity, 

which is computed as the amount of common edges between the layers divided by the union of 

all edges for pairs of layers, indicates that the jar and plate attribute networks in the post-

migration period are 74% similar. Again, this metric is only able to consider deprecated edges by 

disregarding weight and directionality. That these two measures of layer comparison are so high  

Figure 5.5.25 Edge Betweenness Community Detection in the Multilayer Post-Migration 

Attribute Network 

 

186 

is an indication that there is overall more consistency in connections among sites in the post-

migration period CIRV compared to the pre-migration period. Fewer sites and overall more 

dense networks likely contribute to this trend in the post-migration period. 

 

To summarize, important structural changes occur in networks of interaction through 

cultural transmission across the Middle to Late Mississippian transition in the Late Prehistoric 

CIRV. In particular, the post-migration plates attribute network exhibits a pattern of creating 

regional scale relational connections whereas jar attribute network in the post-migration period 

saw the infusion of significant variation from the Oneota in-migration and altered to only form 

strong connections at a reduced or nuanced scale relative to the pre-migration period. In general, 

post-migration period interaction networks are characterized by attempts at inter-cultural 

mediation in the public sphere but with retention of cultural differences in the private, or 

domestic, sphere of life. Oneota immigrants into the CIRV actively chose to incorporate a new 

vessel class into their ceramic inventory, and likely accompanying foodway patterns, but retained 

distinct stylistic and technological features in cooking jars. The tensions inherent in a public de-

emphasis but private retention of inter-cultural differences no doubt contributed in some way to 

the pattern of increasing violence and aggression in the post-migration period (G. R. Milner, et 

al. 1991; Stone 2003). Though such patterns of violence were certainly nothing new to Oneota 

peoples (Hollinger 2005; Oemig 2016). Sites with an Oneota presence in particular appear to be 

weakly integrated into post-migration interaction networks. However, since two of these sites are 

marked by a significant presence of Mississippian peoples and one shows no evidence of inter-

cultural interaction at the site level, divergence among both indigenous and migrant peoples 

characterizes interactions patterns in the post-migration period Late Prehistoric CIRV. Yet, 

187 

interact these peoples did, as shown in the very dense networks of interaction through cultural 

transmission for the post-migration period.  

 

The post-migration period CIRV can overall be described as distributed, or lacking a 

central actor or actor-cliques, and cohesive but with evidence for structurally distinct 

communities in at least one interpretive layer – jar attribute networks of interaction through 

cultural transmission. Post-migration attribute networks continue to lack support for an 

hypothesized cultural distinction between Mississippian peoples into Spoon and La Moine River 

variants. Distinct community structures along geographic lines among Mississippian sites in 

these areas are not able to be modeled. Delimited mobility along cultural lines, however, is 

supported in at least one network layer – the post-migration jar attribute network – in addition to 

the geographic layout of immigrant Oneota or multi-cultural sites in a restricted portion of the 

region. Nevertheless, an active and concerted attempt at inter-cultural mediation or 

accommodation was made by Mississippian and Oneota peoples in the transference of plate 

technological characteristics and likely accompanying foodway patterns. These interpretations 

are further expanded upon in Section 6.6.2 when considering analysis of sociograms for the post-

migration period. However, because geographic distance can play a foundational role in 

interaction patterns, the following section discusses the impact of geographic distance on 

networks of interaction through cultural transmission in the Late Prehistoric CIRV.  

 

188 

 

 

  
Summary Statistics 
  Nodes 
  Edges 
  Mean Weighted Degree 
Network Size Measures 
  Diameter 
  Mean Path Length 
Network Topology Measures 
Network Density 
Mean Clustering Coefficient 
Degree Centralization 
Betweenness Centralization 
Closeness Centralization 
Eigenvector Centralization 

 
 

Plate Attributes 

Pre-
Migration 

Post-
Migration 

  
Flattened 
Across 
Time 
 

 

 

 

 

 

11 
63 
3.994 

3 
1.527 

57.3% 
62.6% 
0.250 
0.133 
0.063 
0.320 

7 
40 
4.406 

2 
1.048 

 

 

16 
101 
4.578 

4 
1.708 

95.20% 
95.20% 
0.111 
0.104 
0.013 
0.105 

42.10% 
70.80% 
0.476 
0.179 
0.259 
0.507 

Jar Attributes 

Pre-
Migration 

Post-
Migration 

  
Flattened 
Across 
Time 

Multilayer - Jar and Plate 

Pre-
Migration 

Post-
Migration 

Flattened 
Across 
Time 

  

  

  

 

 

 

8 
42 
3.962 

4 
1.375 

 

 

 

18 
121 
6.722 

4 
1.733 

  

  

  

75.00% 
75.00% 
0.163 
0.303 
0.266 
0.192 

39.50% 
68.40% 
0.359 
0.058 
0.171 
0.464 

12 
81 
5.117 

2 
1.182 

61.4% 
69.0% 
0.223 
0.086 
0.026 
0.266 

12 
95 
7.917 

2 
1.215 

72.0% 
76.8% 
0.207 
0.299 
0.034 
0.217 

 

 

 

8 
50 
7.817 

2 
1.107 

 

 

 

18 
143 
9.17 

3 
1.564 

89.30% 
89.30% 
0.163 
0.146 
0.073 
0.151 

46.70% 
77.60% 
0.408 
0.199 
0.216 
0.446 

Table 5.12 Network Statistics for Ceramic Industry Social Interaction Network Models 

189 

5.5.3  The Role of Geographic Distance  
 

A potentially confounding variable to the formation of strong ties of social interaction 

through cultural transmission between settlements is that of the physical distance between them. 

In evaluating the role of distance in the strength of relational connections, linear regression 

models are fit to network model data to investigate whether closer physical proximity is 

associated with a higher degree of relational interaction among sites. That is, do sites that are 

closer together share stronger relational connections than sites that are far apart on average, and 

as such is geographic distance a primary factor in delimiting patterns of social interaction?  

Figure 5.26 displays a scatter plot and linear models of the strength of relational 

connections in multilayer jar and plate attribute networks flattened across time as a function of 

distance in kilometers. Across each network, 100 random samples of 50 each are drawn from the 

population to inform heuristic understanding of the sampling distribution on the slope 

coefficient. A moderately negative linear relationship between the degree of relational interaction 

among sites and geographic distance characterizes these multilayer interaction networks. 

However, there is a high degree of residual variation and heteroscedasticity in the strength of 

relational connections variable. That is, a subtle distance-decay effect is seen in interaction 

networks where the strength of relational connections somewhat decreases on average across the 

entire temporal expanse of the Late Prehistoric CIRV. This is a natural, though not statistically 

significant, finding considering that sites within a day’s walk or canoe ride from each other are 

much more likely to sustain strong relational interaction patterns through cultural transmission. 

However, following Simpson’s Paradox (Simpson 1951), this trend is significantly more 

nuanced and even reversed when models are fit to individual network layers as opposed to the 

entire regional sequence in the Late Prehistoric CIRV.  

190 

Figure 5.5.26 Distributions of Randomly Sampled Linear Models for Strength of Relational Connection 

as a Function of Geographic Distance in Multilayer jar and plate attribute networks. Dashed red line 

indicates linear model for observed data 

As shown in Figure 5.27, structural differences exist in artifact attribute networks when 

 

the strength of relational connection among sites is modeled as a function of geographic distance 

across the individual vessel-class layers. During the pre-migration period Eveland, Orendorf and 

Larson Phases, the previously discussed trend of jar artifact attribute networks operating at a 

regionally inclusive scale is bolstered based on the failure to reject the null hypothesis that 

distance shows no linear relationship to the strength of relational connection. On the other hand, 

the plate attribute interaction network for the pre-migration period shows a strong negative 

191 

 

Figure 5.27 Distributions of Randomly Sampled Linear Models for Strength of Relational Connection as 
a Function of Geographic Distance in Jar and Plate Attribute Interaction Networks faceted by time phase 

designation. Dashed red line indicates linear model for observed data 

 
linear relationship between strength of relational connection and geographic distance. The role of 

geographic distance on the strength of relational connection for plate attribute pre-migration 

interaction networks is statistically significant at an alpha of 0.06 (p-value = 0.05796) and shows 

a Pearson’s correlation coefficient of r = -0.24. As a result, in the pre-migration context, 

information regarding plates was less apt to be shared at a regional scale among Mississippian 

peoples. In other words, strong relational connections were formed among more localized 

192 

communities of practice on average when considering the transmission of information related to 

plate attributes in the pre-migration CIRV. At the same time, geographic distance plays no 

discernible role in the strength of relational connections based on linear models from jar 

attributes in the pre-migration period.  

 

This trend reverses in the post-migration period, where the infusion of technological 

variation from Oneota immigrant-potters likely impacted the scale at which information spread 

among communities regarding jar attributes. As shown in Figure 5.27, a strong negative linear 

relationship exists between the degree of relational connection and geographic distance in the 

post-migration jar attribute interaction network. This trend is significant at an alpha of 0.01 (p-

value = 0.0032) and shows a Pearson’s correlation coefficient of r = -0.45. Geographic distance, 

therefore, plays a significant role in structuring relational connections in the post-migration jar 

attribute interaction network. At the same time, the null hypothesis cannot be rejected for the 

plate post-migration attribute network. In other words, no discernible linear relationship exists 

between the strength of relational connections among sites and the geographic distance between 

them as modeled in the plate attribute interaction network for the post-migration period. This 

further lends support for the presence of a public-private distinction in structuring interaction 

patterns in the post-migration CIRV.  

 

Linear models show that geographic distance influences artifact attribute interaction 

networks in nuanced ways in the Late Prehistoric CIRV. During Mississippian phases, jar 

attributes break with expectations and show no influence from geographic distance on the 

strength of relational connections among sites. This finding indicates a willingness on the part of 

Mississippian potters to share information regarding the production of domestic jars at a regional 

scale. However, the plate attribute network indicates that networks of interaction among 

193 

Mississippian peoples prior to Oneota in-migration in the CIRV were not entirely fluid. 

Geographic distance was shown to negatively impact the strength of relational connections 

among Mississippian peoples, suggesting that information regarding plate production was 

transmitted in nuanced ways across the geographic expanse of the Mississippian CIRV.  

 

Following the in-migration of Bold Counselor Phase Oneota peoples, this trend shifted – 

Oneota jar technology was maintained to a large degree and as a result impacted the scale at 

which information was shared regarding domestic jar technology. Jar technology became 

increasingly the product of the local social environment and precipitously drops in similarity 

across geographic distance. However, plate technology was shared broadly across the post-

migration CIRV as geographic distance has been shown to play no role in the cultural 

transmission of information related to plate production through networks of interaction.  

 

During both the pre- and post-migration contexts in the CIRV, one vessel class operated 

at a regional level while the other has been shown to be the product of interaction at a more 

nuanced scale. This interpretation portends the complexity networks of interaction during the 

Late Prehistoric Period in the central Illinois River valley – different forces in society likely 

operated to promote high levels of interaction and others likely operated to curtail such 

interactions to a more localized scale.   

 

5.6 Discussion and Visual Interpretation of Ceramic Industry Social Interaction Network 

Models  
  

Given that the primary interest here is the flow of information between communities of 

practice that may not follow the most efficient delivery process, as a proxy measure of the degree 

of social interaction or homologous relationships between sites, two node level statistics are 

emphasized in visualizing networks as sociogram: weighted degree and closeness centrality. 

194 

Weighted degree is equal to the sum of all edge weights connected to a given node and is 

indicative of the relative similarity of a particular node’s ceramic vessel technological 

characteristics when considering every other node. A high weighted degree indicates that the 

ceramic assemblage from a given node is more similar to other nodes’ assemblages based on the 

attributes considered, and therefore suggests that perhaps the node was more influential in being 

a locus of ceramic manufacturing technology or has more shared ancestry (homology) with other 

nodes. A low weighted degree does not necessarily indicate that a particular node is less 

important, populous, or influential, but rather it indicates that a particular node’s ceramic 

assemblage is less similar to other nodes based on the vessel attributes under consideration.  

Closeness centrality considers how near all other individual nodes are in a network to a 

given site-node in question. Closeness centrality is defined as the normalized average distance 

(or number of steps between each node based on existing links) between the node and every 

other node in the network and is therefore more pertinent to graphs constructed from one 

particular ceramic vessel class and time period. A high closeness centrality score indicates that a 

particular site may be more directly accessible to other potter communities or may be a locus 

from which innovation (information) appears and spreads, while a low closeness centrality score 

indicates that the site is either isolated, inaccessible, or embedded in a cluster that is separate, 

from the rest of the network in terms of ceramic technology. These metrics, as well as others 

presented in this section, are more fully described and defined in Chapter 4.  

 

A final note about how the networks are presented below is that of network topology. 

Network topology is the arrangement and interrelationships of the constituent parts (i.e. nodes, 

edges) of a computer network and is used here in a metaphorical sense (Scott 2000; Wasserman 

and Faust 1994). Network topology can be thought of in two ways: the physical topology of the 

195 

network and the logical topology of the network. Physical topology refers to the actual layout of 

the physical nodes, for example computer servers and the cables that connect them. While logical 

topology refers to the ways that the computer signals act in the network, or the way that data 

passes through the cables from one node-device to another. Graphs presented here attempt to 

account for this metaphorical duality by utilizing different layout methodologies. A geographic 

layout methodology is used to capture the metaphorical physical topology of the ceramic 

technology networks, while the Yifan Hu multilevel network graph layout is used to capture the 

metaphorical logical topology of the network (Hu 2005). As a force-directed algorithm, the 

Yifan Hu multilevel graph layout places the node-bodies in the graph by minimizing the energy 

of the system but uses a multilevel approach to allow spring and repulsion energy flows to be 

applied to local as well as community levels to find a global optimal layout combined with an 

octree technique to approximate short- and long-range forces.  

Network graphs have been developed to be as interpretable as possible, even to 

individuals without network analysis experience. This is accomplished by visualizing network 

structure in conjunction with the numerical properties that describe the network. This allows 

information about nodes, edges, and the structure of the network to be embedded within 

visualizations simultaneously. All graphs, or sociograms, presented below are both weighted and 

directed. Directionality is expressed in a clockwise fashion. That is, an edge emanating from a 

node in a clockwise direction indicates that node’s relationship directed toward another node. An 

edge emanating into a node that is counter-clockwise indicates another node’s relationships with 

the node in question. Weight of an edge is visualized in two specific ways. The first is color. A 

warm color palette is used to enable strong relationships (warmer in color) to be distinguished 

from weaker relationships (less warm in color), as modelled by the numerical weight of an edge 

196 

between two nodes. That is, the warmer or redder an edge is, the stronger the modelled 

relationship. The second is size. A warm color palette is combined with size to show either the 

strength of the node’s weighted degree or the strength of a node’s closeness centrality score. 

These metrics are used to show either the degree of similarity of one node to all other nodes 

(weighted degree) or to show the relative influence of one node relative to other nodes in their 

ability to form relationships with all other neighbor-nodes in the network in question (closeness 

centrality).  

Following multilayer network methodology, individual network layers are presented and 

discussed prior to the joint analysis of multiple layers. The value of this approach is to discern 

the topology, or structural nature, of individual network layers initially before aggregating layers 

together. For the purposes of the case study presented here, it allows the role of domestic jars and 

plates to be visualized and interpreted for each time period separately, which then provides a 

more nuanced engagement with the multidimensional chains of social relationships in the 

multilayer networks that follow.  

 

5.6.1  Pre-Migration Technological Similarity Networks, 1200 – 1300 A.D. 
 

While the occupational sequence of the Mississippian central Illinois River valley began 

sometime in the early 11th or 12th century A.D., the analyses presented here consider only the 

Mississippian occupation from A.D. 1200 – 1300 A.D. (Bardolph 2014; Conrad 1991). The first 

four sociograms presented are models of technological similarity for each vessel class separately 

before they are presented as flattened and sliced models for the Mississippian CIRV prior to 

Oneota in-migration. 

197 

A number of interpretations are immediately apparent, while others less so, when visually 

examining the domestic jar and plate technological attribute network graph models for the pre-

migration period. Both network layers conform to a structural interpretation of a distributed and 

highly interconnected Mississippian central Illinois River valley (CIRV). Both networks lack a 

central hub or hubs. In other words, in neither the jar nor plate pre-migration networks are all 

sites connected to a singular, central site or site cluster. Furthermore, distinct coalitions, or  

Figure 5.28 Yifan Hu multilevel network graph layout of domestic jar technological similarity network 
for the Pre-Migration Time Period (1200-1300 A.D.); edges are colored by weight; nodes are colored and 

 

sized by closeness centrality 

 

clusters of sites more connected to each other than sites exogenous to the cluster, are not 

apparent. This suggests a distributed structure of information flow within the networks as 

opposed to a hierarchical, coalitional, or broker-bridging model of information flow (Scott 

2000). However, both the domestic jar and plate networks appear to support a significant 

198 

presence located at the mouth of the Spoon River consistent with Harn’s Larson Settlement 

System (Harn 1978, 1994), or densely occupied central position within the geographic 

renderings. The central Larson town figures prominently in the jar network with many sites 

showing strong interactions based on the transmission of socially-mediated jar attributes with 

Larson (Figures 5.28 – 5.29). A presumed primary village within the Larson Settlement System, 

Buckeye Bend, figures prominently in the plate network (Figures 5.30 – 5.31). That a modestly 

sized site such as Buckeye Bend could figure so prominently in the plate attribute network is  

Figure 5.29 Geographic network graph layout of domestic jar technological similarity network for the 
Pre-Migration Time Period (1200-1300 A.D.); edges are colored by weight; nodes are colored and sized 

by closeness centrality 

 

 

 

surprising, and perhaps suggests that novelty in several key attributes (e.g. plate diameter and 

incising thickness) may have emerged at, and spread from, Buckeye Bend. Alternatively, the 

199 

prominent role Buckeye Bend plays in the pre-migration network may be owed to its long or 

intermittent occupation span that straddles both the pre- and post-migration time periods (see 

Chapter 3).  

The more numerous edges and stronger (i.e. warmer) edge weights on average in the 

domestic jar layer in comparison to the plate layer do indicate topological difference between the 

layers. Interestingly, while no site in the plate pre-migration layer is without at least one  

reciprocal relationship, three sites in the domestic jar layer only direct relationships outwards.  

Figure 5.30 Yifan Hu multilevel network graph layout of plate technological similarity network for the 
Pre-Migration Time Period (1200-1300 A.D.); edges are colored by weight; nodes are colored and sized 

 

by weighted degree 

 

 

That is, Fouts Village, Houston-Shryock, and Eveland only direct relationships to other 

sites as opposed to having any relationships reciprocally directed toward them in the pre-

migration domestic jar layer. This does not mean that these sites were isolated but does suggest 

that in terms of interactions with other sites through the cultural transmission of socially-

200 

mediated jar attributes, these sites were perhaps more imitative or had more homologous 

descendants from other sites as opposed to being a locus of imitation or producers of exogamous 

offspring.  

As seen in the network models laid out based on energy flows in the system, a distinct 

lack of site clustering is apparent in either the jar or plate pre-migration technological similarity 

networks. That is, neither network in the pre-migration period shows strong support for the 

presence of a clique or cliques. In order to form a clique, a group of sites would need to be more 

connected to each other than the rest of the nodes in the network. This lack of settlement  

Figure 5.31 Geographic network graph layout of plate technological similarity network for the Pre-

Migration Time Period (1200-1300 A.D.); edges are colored by weight; nodes are colored and sized by 

 
clustering in both jar and plate attribute networks contrasts with expectations related to the 

 

closeness centrality 

 

widespread appearance of evidence for inter-personal violence and conflict during the 

201 

Mississippian period. These expectations include intensive population aggregation, migration 

events, boundary formation, and alliance-based site clusters such as those observed in the pre-

Hispanic American Southwest (Fowles, et al. 2007; LeBlanc 2000). That is, despite increasing 

evidence for violence that has led to comparisons with warfare (G. R. Milner, et al. 1991; 

Steadman 2008; Vanderwarker and Wilson 2016; G. D. Wilson 2012), Mississippian potters 

appear to have been interacting, intermarrying, or otherwise engaging with individuals and their 

wares at  

 

Figure 5.32 Yifan Hu multilevel network graph layout of domestic jar and plate technological similarity 
flattened multilayer network for the Pre-Migration Time Period (1200-1300 A.D.); edges are colored by 

weight; nodes are colored and sized by weighted degree 

settlements across the geographic expanse of the CIRV frequently enough to transmit social 

 

information in the production of ceramic vessels. Perhaps this is an indication that conflicts were 

202 

seasonal or episodic as opposed to chronic in impacting mobility and interaction patterns. This 

interpretation is consistent with findings from a recent analysis of skeletal evidence at many pre-

migration Mississippian sites that indicated conflict and violence “was not ubiquitous” (Hatch 

2015:208). 

High density of connections and low clustering seen in both jar and plate attribute 

networks also suggests that an hypothesized distinction between Mississippian sites in the 

vicinity of the Spoon River from those near the La Moine River is not supported by ceramic  

 

Figure 5.33 Geographic network graph layout of domestic jar and plate technological similarity flattened 
multilayer network for the Pre-Migration Time Period (1200-1300 A.D.); edges are colored by weight; 

nodes are colored and sized by weighted degree 

 

attribute data in the Mississippian CIRV (Conrad 1991). That is, there is a marked lack of a 

strongly connected settlement cluster geographically positioned near the La Moine River that is 

203 

weakly integrated with settlements further to the north near the Spoon River. Though only a few 

southerly sites (Walsh, Lawrenz Gun Club) were able to be considered in this analysis for the 

pre-migration period as less professional archaeological excavation has occurred near the La 

Moine River in comparison to the Spoon River vicinity. 

Trends indicating a lack of support for reduced mobility and a lack of support for a 

Spoon-La Moine River Mississippian distinction based on jar and plate technological attributes is 

further substantiated in the flattened pre-migration network where both jar and plate network 

layers are combined into a single network for the pre-migration time period (Figures 5.32 - 5.33). 

That is, the multilayer network continues to exhibit a distributed and highly cohesive network 

topology similar to both individual network layers. In other words, shared contexts of learning, 

homologous interrelationships, and strong relationships based on frequent social interaction 

generally characterizes potter communities at settlements in the pre-migration CIRV as seen in 

socially mediated jar and plate ceramic attributes.  

With its central positioning both geographically at the Spoon-Illinois River confluence 

area and temporally in the pre-migration period, the Larson site does exhibit a higher degree of 

proportional similarity in socially mediated jar and plate attributes to other sites in the flattened 

multilayer network. Figure 5.33 shows many strong links from four sites to the north to Larson 

that are weakly reciprocated. These include Orendorf Settlements C and D, Houston-Shryock, 

and Kingston Lake. Perhaps information regarding ceramic attribute production or individuals 

flowed from these northerly sites to Larson.  

The Eveland site, on the other hand, is a significant outlier in that it is weakly integrated 

into the flattened multilayer pre-migration technology network. This is owed to three factors. 

The first is its occupational sequence very early in the pre-migration period (Bardolph 2014; 

204 

Conrad 1989, 1991; Harn 1991). Though more recent chronological calibrations suggest an early 

13th century A.D. occupation at the site (G. D. Wilson, et al. 2018). The second is the likely 

ceremonial, as opposed to domestic, nature at Eveland given the unique architectural patterns 

present at the site including a cross-shaped structure and extensive burial furniture including 

Mississippian prestige items accompanying Eveland Phase burials interred at Dickson Mounds 

(Conrad 1989; Harn 1991). Finally, and most importantly, plates emerge as a distinct vessel class 

in the CIRV only after the occupation of the Eveland site. Without any connections in the pre-

migration plate attribute network layer, relationships to and from the Eveland site can only be 

considered based on the presence of domestic jars. This is nevertheless instructive in that the 

connections from Eveland hint at which other sites may have been occupied during this early  

 

Figure 5.34 Geographic network graph layout of domestic jar (left) and plate (right) technological 
similarity sliced multilayer network for the Pre-Migration Time Period (1200-1300 A.D.); edges are 

colored by weight; nodes are colored and sized by closeness centrality 

  

205 

 

1200s A.D. timeframe.  

In sum, the overall topological structure of interaction patterns in the central Illinois 

River valley as gleaned from the cultural transmission of ceramic attributes prior to Oneota in-

migration can be characterized as highly interconnected and distributed. The analysis of distinct 

network layers in the pre-migration period suggests some important differences between the 

cultural transmission of information related to socially mediated jar attributes compared to plate  

attributes. In particular, information related to jar attributes is shared, or appealed to, globally 

much more so than information related to plate attributes. In terms of social signaling (Birch and 

Hart 2018; Bliege Bird and Smith 2005), it can be inferred that potters likely formed bonding ties 

to reinforce dense social relationships based on global Mississippian interaction patterns across 

the geographic expanse of the Eveland, Orendorf, and Larson phases of the Late Prehistoric 

central Illinois River valley through interactions regarding domestic jar attribute technology 

(Conrad 1991; Esarey and Conrad 1998). On the other hand, plate attributes seem to reflect 

adaptation to more localized social environments, which suggests nuanced interaction and 

foodway patterns.   

There is a marked lack of meaningful clustering in both the jar and plate network layers 

as well as in the flattened multilayer attribute network. As a result, ceramic attribute networks do 

not support curtailed or reduced interaction patterns posited based on a reduction in intra-

regional mobility due to increasing conflict and violence (Vanderwarker and Wilson 2016), nor 

do the attribute networks support an hypothesized taxonomic distinction between Spoon and La 

Moine River Mississippians in the pre-migration period (Conrad 1989, 1991). It is worth noting, 

however, that not all sites modeled in this pre-migration period were occupied simultaneously 

and thus these interpretations are both a product of spatial and temporal processes at relatively 

206 

unrefined scales and based entirely on interaction patterns gleaned from a subset of ceramic 

industry in the Late Prehistoric CIRV. Increased resolution in occupational sequences at sites in 

the Mississippian CIRV would greatly enhance the interpretability of these models of interaction 

through cultural transmission of ceramic technological attributes.  

 

5.6.2  Post-Migration Technological Similarity Networks, 1300 – 1450 A.D. 
 

In visually examining ceramic artifact attribute networks models for the post-migration 

period, it is apparent that significant changes in the structure of interaction through cultural 

transmission occurred just prior to, following, or concomitant with Oneota in-migration. In  

Figure 5.35 Yifan Hu multilevel network graph layout of domestic jar technological similarity network 
for the Post-Migration Time Period (1300-1450 A.D.); edges are colored by weight; nodes are colored 

and sized by closeness centrality 

 

particular, a significant reduction in the scale of interaction based on the sharing of information 

related to socially-mediated jar attributes and a significant expansion of interaction based on the 

sharing of information related to plate attributes characterizes the post-migration period CIRV. 

207 

This is in stark contrast to the pre-migration period where information related to socially 

mediated jar attributes was likely shared at a regional Mississippian scale and plate attribute 

information transmission more conformed to local scale social interaction processes. Prior to the 

in-migration of Oneota peoples, however, a marked aggregation process is evident among 

indigenous Mississippian peoples. Many fewer Mississippian sites were occupied during, and 

following, the circa 1300 A.D. Oneota in-migration. It can therefore be posited based on  

 

Figure 5.36 Geographic network graph layout of domestic jar technological similarity network for the 
Post-Migration Time Period (1300-1450 A.D.); edges are colored by weight; nodes are colored and sized 

by closeness centrality 

 

network models from the current analysis that Oneota immigration into the Mississippian CIRV 

may have been facilitated, or otherwise structurally guided, by two important factors. The first 

factor is the structure of Mississippian relationships and interaction patterns in the pre-migration 

208 

CIRV as seen in ceramic industry social interaction network models. While at times violent and 

warlike, Mississippian potters show fluidity and mobility in interaction based on the transmission  

of information related to ceramic industry, and likely the movement of individuals, between 

sites. The second is the apparent near abandonment of the Spoon and Illinois River confluence 

area by Mississippian peoples. Only one modest Mississippian site, Buckeye Bend, appears to 

have been occupied in the vicinity of the Spoon and Illinois confluence following the circa 1300 

A.D. in-migration of Oneota peoples. While Buckeye Bend has been characterized as an 

intermediate village in the Larson settlement system (Harn 1994), a radiocarbon assay produced 

for this research indicates an occupation at the site during the post-migration period (see chapter 

3). Perhaps the Spoon-Illinois confluence area’s ecological resources were exhausted or heavily 

strained as a result of intensive occupation and utilization over an approximately 100-year span, 

especially as related to agricultural pursuits. The Spoon-Illinois River confluence may have 

therefore been an attractive settlement region to Oneota peoples, who were arguably less reliant, 

in comparison to Mississippian peoples in general, on agricultural pursuits for their subsistence 

needs and were in the process of expanding out of an upper Midwest and eastern Prairie Plains 

core region (Blitz 2010; Hart 1990; Tubbs 2013; Tubbs and O'Gorman 2005).  

 

While distinctly Oneota material culture has been recovered from five known CIRV sites, 

only three of those sites have extant collections of ceramic artifacts of sufficient sample sizes to 

be included in this study: Crable, Morton Village, and C.W. Cooper (Esarey and Conrad 1998). 

Of these five sites, two are located just north of the Spoon-Illinois River confluence area – 

Morton Village and C.W. Cooper. Both of these sites were also previously occupied by 

Mississippian peoples during the Early Mississippian period in the CIRV (Bardolph 2014; 

Bardolph and Wilson 2015; Santure, et al. 1990; Strezewski 2003; G. D. Wilson, et al. 2018). 

209 

Although Morton Village shows a distinct household-scale multi-cultural occupation, evidence 

for site-level interaction between Oneota and Mississippian peoples is presently lacking at C.W. 

Cooper (Conrad and Esarey 1983; O'Gorman and Conner 2016). Household-scale interaction 

between Oneota and Mississippian peoples is also present at Crable, though the nature of the 

Oneota presence at this Mississippian town is unclear (Esarey and Conrad 1998; Painter 2014; K. 

Sampson 2000; H. G. Smith 1951).  

The robust relationships between the three sites with an Oneota presence as modeled in 

the post-migration jar attribute sociograms is unmistakable. In addition to being strategically 

close to one another geographically (three centrally located red nodes in Figure 5.36), these sites 

are also strategically close to one another socially according to the jar attribute post-migration 

network modeled based on information flows in the system (Figure 5.35). Thus, the global scale 

interaction patterns seen in domestic jar attributes in the Mississippian CIRV, and the likely 

accompanying bonding ties that such a global pattern would ostensibly foster (Birch and Hart 

2018; Crowe 2007), were starkly interrupted by the in-migration of Oneota peoples. 

Furthermore, Oneota potters in multi-cultural contexts such as Crable and Morton Village appear 

to have been free to exercise autonomy in the production and cultural transmission of 

technological information related to domestic jar attributes. Such autonomy would likely 

reinforce bonding ties to an Oneota heritage among the immigrant population in the production 

of wares used in cooking. At the same time, interaction relationships between Mississippian sites 

in the post-migration period domestic jar networks appear less intensive, active, or otherwise 

more constrained. Perhaps this resulted from differences in how to engage with Oneota 

immigrants. A strategy of cultural accommodation or perhaps integration of Oneota jar-

producing potters was pursued by at least one Mississippian site, Crable. However, the coeval 

210 

Ten Mile Creek, Star Bridge, Buckeye Bend, and Baehr South sites show no indication that 

multi-cultural accommodation took place. Instead cultural pluralism was pursued by peoples at 

these Mississippian sites.  

 

In the same way that a dramatic shift characterized the role of socially mediated jar 

attributes in the post-migration CIRV, plates attributes also formed distinct structural interaction 

patterns through cultural transmission following in the in-migration of Oneota peoples. While the 

domestic jar attribute network largely indicates that pluralistic tendencies with some cultural 

accommodation or integration in interaction through cultural transmission in the post-migration 

CIRV, network models based on socially mediated plate attributes suggest that attempts at  

 

 

Figure 5.37 Yifan Hu multilevel network graph layout of plate technological similarity network for the 
Post-Migration Time Period (1300-1450 A.D.); edges are colored by weight; nodes are colored and sized 

by weighted degree 

 

211 

integration between Oneota and Mississippian peoples were at times pursued. Figures 5.37 and 

5.38 show that at the sites where Oneota peoples endeavored to adopt the plate ceramic vessel 

type, a type absent or rare to Oneota in other contexts (Esarey and Conrad 1998; Overstreet 

1997), they likely did so based on direct interactions with Mississippian potters. 

The clique-like cluster of Mississippian sites without an Oneota presence as seen in 

Figure 5.37 suggests that cultural transmission of plate attributes perhaps fostered bonding ties in 

the consolidation process among Mississippian peoples, who became clustered together in many 

fewer sites and where public interactions in the form of the serving and sharing food likely took 

on increased importance in daily habitual routines or during seasonal or episodic feasting events.  

  

Figure 5.38 Geographic network graph layout of domestic plate similarity network for the Post-Migration 

Time Period (1300-1450 A.D.); edges are colored by weight; nodes are colored and sized by weighted 

degree 

 

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By adopting a vessel type that perhaps evinces bonding ties and likely played an important role 

in foodways, Oneota potters show a marked attempt to bridge extant cultural distinctions with 

indigenous Mississippian peoples. Likewise, Mississippian potters were likely engaging in direct 

interaction with Oneota potters by integrating them into the communities of practice where 

cultural transmission related to plate raw material acquisition and/or manufacture took place. 

This affirms Hale Smith’s (1951:28) notion in examining the material remains from Crable that 

“a transference of technique has taken place, probably indicating a culture fusion from two 

separate sources.” Such transference, however, seems limited only to the multi-cultural 

settlements, Crable and Morton Village, as no plates have yet been recovered from the C.W. 

Cooper Oneota habitation site nor is there evidence of Oneota material culture at the coeval Ten 

Mile Creek, Star Bridge, Buckeye Bend, and Baehr South Mississippian towns and habitation  

Figure 5.39 Yifan Hu multilevel network graph layout of domestic jar and plate technological similarity 
flattened multilayer network for the Post-Migration Time Period (1300-1450 A.D.); edges are colored by 

weight; nodes are colored and sized by weighted degree 

 

213 

sites. A very minor admixture of Oneota material culture, including pottery, has been recovered 

 

from Lawrenz Gun Club (Lawrence Conrad personal communication, 2017), though these 

materials were too fragmentary and too few to be included in this analysis.  

 

When considering the flattened and sliced multilayer socially mediated attribute networks 

in the post-migration period (Figures 5.39 - 5.41), it is further apparent that structural changes 

indeed characterize interaction patterns concomitant with and following Oneota in-migration. 

However, based on the aggregation of Mississippian peoples into many fewer sites, it is more 

plausible that Oneota in-migration simply exacerbated structural changes in interactions patterns 

that were already ongoing among indigenous Mississippian peoples as opposed to being the  

 

Figure 5.40 Geographic network graph layout of domestic jar and plate technological similarity flattened 
multilayer network for the Post-Migration Time Period (1300-1450 A.D.); edges are colored by weight; 

nodes are colored and sized by weighted degree 

 

 

214 

primary factor responsible for those changes. 

Oneota infusion of variation related to jar attribute production was likely a significant 

disruption to communities of practice and interaction patterns among indigenous Mississippian 

potters. The shift from global to local scale transmission of socially mediated jar attributes, and 

the inverse for socially mediated plate attributes, suggests that significant changes occurred in 

the transmission of cultural information related to ceramic industry writ large following Oneota 

in-migration. These changes undoubtedly impacted the interaction patterns of the communities of  

 

Figure 5.41 Geographic network graph layout of domestic jar (left) and plate (right) technological 
similarity sliced multilayer network for the Post-Migration Time Period (1300-1450 A.D.); edges are 

colored by weight; nodes are colored and sized by closeness centrality for jars (left) and weighted degree 

 
practice responsible for vessel production and use. That both Oneota and Mississippian peoples 

for plates (right) 

maintained distinct jar production techniques as seen in socially mediated attributes but did 

transmit and share information related to plate production techniques in limited contexts is 

perhaps an indication that cultural transmission patterns were restricted to certain spheres of 

215 

material culture or daily life only, while cultural pluralism between Mississippian and Oneota 

peoples was otherwise maintained. As a result, mobility to reinforce networks of interaction that 

would foster the maintenance of social ties at a regional scale was likely disrupted, an 

interpretation commensurate with evidence for increasing violence and threats to mobile work-

parties as seen in the Norris Farms #36 cemetery associated with the Morton Village site (G. R. 

Milner, et al. 1991; Santure, et al. 1990). On the other hand, the expansion of the scale of 

interaction through cultural transmission of plate attributes suggests that at least in the public 

sphere of life in some Mississippian or multi-cultural contexts, perhaps during seasonal or 

episodic ceremonies or ritual, attempts at inter-cultural mediation, integration, or accommodation 

did take place among Oneota and Mississippian potters. 

 

5.6.3  Technological Similarity Networks Across Time, 1200 – 1450 A.D. 

 
The preceding sections describe frameworks for social interaction through cultural 

transmission with different architectures based on material cultural class within time periods. 

That is, the different social rules, motivations, and purposes of interaction within the 

transmission of technological information related to socially-mediated jar and plate attributes 

influence both network topology and the resulting interpretations about the nature of interaction 

patterns based on visually examining model characteristics. A key value in using the multilayer 

network analysis approach taken here is to observe the combined effects of distinct networks – as 

aggregations of different spheres of interaction and different timeframes – wherein the resulting 

multilayer “framework may be more than only the combination of its parts” (Preiser-Kapeller 

2011:391). The multilayer networks presented here are produced by flattening, or concatenating, 

distinct network layers together. Though a simple procedure, the resulting models form new 

216 

topological patterns with which to draw insight about the broader social milieu, both temporally 

and materially, of which each individual settlement is a part. This section describes visual 

interpretations of the various multilayer network configurations across the Late Prehistoric CIRV 

in order to approach the actual complexity of human networks of social interaction through 

cultural transmission. 

Figures 5.42 and 5.44 provide the most readily visually interpretable models when 

considering the fundamental question of whether changes in patterns of interactions occurred 

following Oneota in-migration into the CIRV. In both the jar and plate networks, which are 

 

Figure 5.42 Yifan Hu multilevel network graph layout of domestic jar technological similarity network 
flattened across Time Periods (1200 – 1450 A.D.); edges are colored by weight; nodes are colored and 

sized by weighted degree score 

 

217 

connected across time through the long occupation span at Lawrenz Gun Club (Jeremy Wilson 

personal communication, 2018) and the extended or perhaps intermittent occupation at Buckeye 

Bend (see Chapter 3), distinct patterns of interactions are evident in the pre-migration CIRV 

(which is laid out in the upper portion of each multilayer sociogram model) compared to the 

post-migration CIRV (which is laid out in the lower portion of each model). Furthermore, trends 

discussed in the preceding sections are perhaps brought to bear in a more straightforward way 

based on the multilayer models presented in Figures 5.42 and 5.44. That is, the Yifan Hu 

algorithm lays out each site based on the energy flow in the system, with sites sharing strong ties 

being placed in closer proximity to each other and sites with weaker ties being placed further  

Figure 5.43 Geographic network graph layout of domestic jar technological similarity network flattened 
across Time Periods (1200 – 1450 A.D.); edges are colored by weight; nodes are colored and sized by 

weighted degree 

 

218 

apart from one another (Hu 2005). Changes in the structure of interaction based on socially 

mediated domestic jar attributes is apparent in Figure 5.42. That interaction through the 

transmission of socially mediated jar attributes likely formed bonding ties at a global scale is 

evidenced in the many strong links between sites occupied across much of the pre-migration time 

period, in particular from connections emanating out of or to the centrally located Larson town. 

Furthermore, the infusion of variation by Oneota peoples and a pattern of more localized or 

infrequent interaction through transmission of socially mediated jar attributes is seen in the 

portion of the model showing sites occupied during the post-migration period. Sites with an  

 

Figure 5.44 Yifan Hu multilevel network graph layout of plate technological similarity network flattened 
across Time Periods (1200 – 1450 A.D.); edges are colored by weight; nodes are colored and sized by 

closeness centrality score 

 

219 

Oneota presence are strongly connected to one another and form a distinct clique-like 

configuration at the bottom portion of Figure 5.42, likely as a result of the presence of trailed 

designs and very tall rims on jars that are unique to these sites in the post-migration period (see 

Figure 5.5). While Mississippian sites that lack any evidence of a multi-cultural occupation are 

generally more weakly connected to sites with an Oneota presence overall, it is important to note 

that many such connections do exist, suggesting that pluralistic tendencies were perhaps at times 

offset by some form of accommodation or other interaction through cultural transmission 

between Mississippian and Oneota jar-producing potters. 

Figure 5.45 Geographic network graph layout of plate technological similarity network flattened across 
Time Periods (1200 – 1450 A.D.); edges are colored by weight; nodes are colored and sized by weighted 

 

 

 

degree 

220 

A pattern of more localized interaction through socially-mediated plate attribute cultural 

transmission is seen in sites occupied during the pre-migration period in Figure 5.44. Unlike the  

multilayer jar attribute network, however, a distinction in topological patterns between the time 

periods is less apparent in the plate multilayer attribute network. Although, stronger connections 

overall between sites with a distinctly Mississippian presence in the post-migration CIRV does 

affirm that more global scale interaction through cultural transmission of socially mediated plate 

attributes occurred – in particular strong paths from Ten Mile Creek in the north to Star Bridge 

and to Baehr South near the La Moine River in the south. As do the ties emanating from and to 

Morton Village and Crable, which are both characterized by a multi-cultural occupation with 

household scale cohabitation between Mississippian and Oneota peoples.  

Figure 5.46 Yifan Hu multilevel network graph layout of domestic jar and plate technological similarity 
multilayer network flattened across Time Periods (1200 – 1450 A.D.); edges are colored by weight; nodes 

are colored and sized by weighted degree  

 

221 

When both time periods and both material culture classes are flattened into a single 

 

multilayer network model, as shown in Figures 5.46 – 5.47, regional scale interaction patterns 

encompassing the breadth of the Late Prehistoric CIRV are able to be considered. In many ways,  

these models coincide with known information about sites drawn from qualitative analyses of 

material cultural remains and traces beyond simply the continuous jar and plate attributes 

considered here. For example, Eveland, which has been described as a likely ceremonial site 

wherein local Bauer Branch and Maple Mills Late Woodland groups were proselytized into the  

 

Figure 5.47 Geographic network graph layout of domestic jar and plate technological similarity multilayer 

network flattened across Time Periods (1200 – 1450 A.D.); edges are colored by weight; nodes are 

colored and sized by weighted degree 

 

222 

Mississippian lifeway perhaps by missionaries or other emissaries from the Cahokia-dominated 

American Bottom region (Conrad 1989), is modeled as being quite loosely connected to other 

Mississippian sites. Furthermore, Eveland is modeled as having the strongest degree of 

interaction with other sites known to be quite early in the regional sequence of the Late 

Prehistoric CIRV such as at Orendorf Settlement C and Kingston Lake (Conrad 1991). On the 

opposite end of both the multilayer network model and the time sequence of the CIRV, is C.W. 

Cooper. Esarey and Conrad (1998) have described C.W. Cooper as an Oneota habitation site 

with no evidence of a Mississippian presence in the post-migration period. Indeed, C.W. Cooper 

is modeled as having very limited interaction with all sites aside from other sites with an Oneota 

presence – Crable and Morton Village. In fact, no other site shares a reciprocal connection to 

C.W. Cooper aside from Crable and Morton Village. Nevertheless, that the three sites with an 

Oneota presence cluster together in the multilayer model but with stark distinctions between how 

each site is connected to the broader post-migration milieu evidences the close relationships 

maintained by Oneota peoples following in-migration but perhaps diverging strategies on how to 

engage with local Mississippian peoples. If these sites were sequentially occupied as opposed to 

being coeval, the differing relationships suggest evolving strategies of multi-cultural interactions 

pursued by both Oneota and Mississippian peoples.  

Lawrenz Gun Club and Buckeye Bend, the two sites with occupational sequences that 

span both the pre- and post-migration periods, are placed much closer to the pre-migration sites 

in both the jar and plate Yifan Hu network layouts. This strongly suggests that the primary 

occupations at each site were during the pre-migration period, a notion supported by placement 

of these sites in pre-migration phases by both Conrad (1991) and Harn (1994). Because these 

sites straddle both time periods under consideration in this analysis, and because it is not known 

223 

whether these occupations were intermittent or continuous, the role they played in regional 

networks of interaction may be overemphasized. Better chronological precision for these and 

other sites would allow for testing of whether or not the experimental procedure used in this 

analysis to construct network models of social interaction through cultural transmission 

contributed to a false-positive overemphasis or if these two sites indeed played a unique role in 

brokering the pre- and post-migration social milieus of the Late Prehistoric CIRV.  

 

Figure 5.48 Geographic network graph layout of domestic jar (left) and plate (right) technological 

similarity sliced multilayer network flattened across Time Period (1200-1450 A.D.); edges are colored by 

 

weight; nodes are colored and sized by weighted degree 

When considering the multilayer network model flattened to include both material classes 

and time periods with a geographic layout (Figure 5.47), two overarching trends emerge. First, 

the two most outlying sites in the region – Ten Mile Creek to the north and Walsh to the south – 

overall tend to be weakly integrated into the regional network. Second, the four sites just to the 

north of the Spoon-Illinois confluence area – Orendorf Settlements C and D, Houston-Shryock 

224 

and Kingston Lake – show strong connections to sites in the Spoon-Illinois confluence area that 

are not reciprocated as strongly. These one-sided interactions indicate that cultural transmission 

of information or perhaps populations flowed from these sites to sites in the Spoon-Illinois 

confluence, likely attesting to the regional importance of this area in regional dynamics during 

the Mississippian pre-migration period. Mortuary ceremonialism at Dickson Mounds and the 

may help to explain this trend (Harn 1971, 1980). 

 

5.7 Conclusion 

 

  

In this chapter, I have described and employed a quantitative method for assessing regional 

scale networks of interaction through cultural transmission based on ceramic technological 

similarity. As the discussion above illustrates, the differentiating of networks into distinct layers 

and considering the ways those different layers interact with each other provides a means of 

accessing the complexity of human social networks in archaeological contexts – information that 

is often lost when relying on qualitative or taxonomic methods that consider singular lines of 

evidence. In this concluding section, I briefly review the principal results of the analytical 

procedure described above and link these results with the broader research context of this study.  

In creating and analyzing networks of interaction through cultural transmission, four main 

research questions were posed for the Late Prehistoric Period central Illinois River valley 

(CIRV) case study region: 

1)  Are changes in the structure of interaction network patterns inherent across time, and 

how might the circa 1300 A.D. in-migration of an exogenous Oneota group be related 

to those changes?  

2)  Do interaction patterns support an hypothesized taxonomic distinction of Mississippian 

into La Moine and Spoon River cultural variants (Conrad 1989, 1991)? 

225 

3)  It has been postulated that the onset of the Mississippian period circa 1200 A.D. was 

paralleled by the emergence of chronic, internecine violence and warfare (G. R. Milner 

1999). The threat of warfare is argued to have transformed both settlement and 

subsistence practices such that, among other things, “families coalesced into large 

communities behind defensive walls…limiting foraging and fishing trips” and “women 

became increasingly sequestered behind village walls” (Vanderwarker and Wilson 

2016:98-100). Given that ethnographic accounts indicate that when pottery 

manufacture is done by hand, it is typically done by women (Rice 2005), it is possible 

to test whether sufficient variation in pottery attributes characterize different 

communities such that it can be reasonably assumed that potters were geographically 

circumscribed in the cultural transmission of artifact attribute social information 

primarily as a result the threat of violence and warfare?  

4)  Given that the plate vessel class is absent or extremely rare in Oneota contexts outside 

the CIRV (Esarey and Conrad 1998), do imitations/emulations of serving plates by 

Oneota peoples inject sufficient variation to suggest that the adoption of this vessel 

class was made at a distance, or are the imitations/emulations technologically similar 

enough for there to be a higher likelihood that direct cultural transmission of ceramic 

technology between Mississippian and Oneota potters occurred? 

The statistical and visual interpretations of attribute interaction networks provide robust answers 

to each of the questions above.  

 

Significant structural changes indeed occur in networks of interaction across the Middle 

to Late Mississippian transition concomitant with the circa 1300 A.D. in-migration of Oneota 

peoples into the CIRV. In particular, the scale at which attribute interaction networks form 

226 

relational connections changes across time. In the pre-migration context, technological similarity 

in jar attributes suggests cultural transmission across a regional interaction network. At the same 

time, spatial distance acted as a major factor in influencing the degree of technological similarity 

in plate attributes, suggesting cultural transmission at a more nuanced scale of interaction. This 

trend inverses following Oneota in-migration and infusion of significant variation in jar 

technological norms by Oneota peoples, leading to networks of cultural transmission of jar 

attributes at reduced or nuanced scales of interaction largely based on spatial proximity. 

However, technological similarity in plate technology exhibits a pattern of creating regional 

scale relational connections among post-migration sites. Thus, neither the pre- nor post-

migration CIRV is characterized by parity in the scale at which networks of interaction through 

cultural transmission formed strong relational connections across the different vessel classes 

under consideration.  

 

Both the pre- and post-migration contexts of the CIRV are characterized by densely 

connected (or highly cohesive) and distributed (or lacking any primary central actor or actor-

clique) network models across each of the vessel classes. While distinct communities were found 

in the plate attribute pre-migration interaction network and the jar attribute post-migration 

interaction network, these community structures do not align in spatial proximity to the major 

river tributaries flowing into the Illinois River – the Spoon and La Moine. As a result, network 

models of interaction through cultural transmission in jar and plate attribute technology do not 

support an hypothesized taxonomic distinction of Mississippian cultures into Spoon and La 

Moine River cultural variants (Conrad 1989, 1991).  

Likewise, because the pre-migration period is characterized by densely connected and 

distributed networks of interaction through cultural transmission, a model of delimited intra-

227 

regional mobility as a result of the threat of structural violence or warfare is not supported 

(Vanderwarker and Wilson 2016). Again, distinct community structures were able to be detected 

for the pre-migration plate attribute network layer, however these distinctions are not consistent 

across the different interaction network layers in the pre-migration CIRV context and do not 

follow a geographic pattern that would indicate reduced mobility due to the threat of warfare or 

violence. No doubt, violence was ingrained into the cultural fabric of Mississippian peoples 

during the Orendorf and Larson phases (Conrad 1989, 1991; Steadman 2008; G. D. Wilson 2012, 

2013). Network models among sites occupied during these phases, however, indicate that despite 

the high levels of inter-personal violence, Mississippian peoples sustained widespread interaction 

patterns through information sharing and cultural transmission related to ceramic industry.  

 

The post-migration CIRV saw significant infusion of variation related to jar attribute 

technology by Oneota peoples. That variation interrupted the structurally regional scale relational 

interaction pattern seen in the pre-migration jar attribute interaction network. As a consequence, 

sites with an Oneota presence are weakly integrated into the post-migration jar attribute 

interaction network. On the other hand, Oneota peoples did adopt the plate vessel class at two 

multi-cultural sites, Morton Village and Crable, likely as a result of the regional scale at which 

plate technological information spread in the post-migration CIRV. This suggests that the plate 

vessel class was adopted by Oneota peoples based on direct interaction through cultural 

transmission with Mississippian potters, and likely as a means to bridge extant cultural 

distinctions in the public sphere of life where a serving plate is most likely to have been utilized.  

Since both Oneota and Mississippian peoples maintained culturally distinct jar production 

technology as seen in socially mediated attributes but did share information related to plate 

production techniques in limited contexts is an indication that cultural transmission patterns were 

228 

restricted to certain spheres of material culture or daily life only, while cultural pluralism 

between Mississippian and Oneota peoples was otherwise maintained. As a result, mobility to 

reinforce networks of interaction that would foster the maintenance of social ties at a 

regionalscale was likely disrupted. On the other hand, the expansion of the scale of interaction 

through cultural transmission of plate attributes suggests that at least in the public sphere of life 

in some Mississippian or multi-cultural contexts, perhaps during seasonal or episodic ceremonies 

or ritual, attempts at inter-cultural mediation, integration, or accommodation did occur among 

Oneota and Mississippian potters. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

229 

CHAPTER 6 CERAMIC STYLE AND NETWORKS OF SOCIAL IDENTIFICATION  

 
 
6.1 Introduction 

There is a long and storied history on the use of style to explain group formation and 

interaction processes in archaeology. Style was used by classical archaeologists such as Gerhard, 

Beazley, Furtwängler and others in the latter half of the 19th century as a replacement over an 

earlier interest in artifactual and cultural beauty in order to systematically categorize artifacts 

chronologically, determine where they were made, and try to ascertain who might have made 

them (Trigger 2006:65-66). A similar technique was used by prehistoric archaeologists on both 

sides of the Atlantic under the Culture-Historical paradigm of the early 20th century. Variation in 

artifact style provided a bridge to artifact classification and the defining of distinct 

archaeological cultures. That is, culture-historical archaeologists assigned groups of stylistically 

similar artifacts into distinct cultural units. In addition, style enabled these cultural units to be 

contextualized both spatially, and more importantly, chronologically (Childe 1936; Cole and 

Deuel 1937; McKern 1939). The specific nature of artifact stylistic differences often provided a 

means to assign a relatively brief chronology onto cultural units, and as a result, prehistoric 

archaeologists had for the first time broad generalizations about the distinct peoples who came 

before us along spatial and chronological dimensions. Both of these dimensions are necessary to 

model group identification and interaction processes in the archaeological record. 

In the latter half of the 20th century, following the shift toward a nomothetic and scientific 

New Archaeology (Binford 1962), stylistic variation was used to search for analogous traits 

which in turn would lead to analogous inference and reveal adaptive cultural systems (Flannery 

1968). Style, therefore, could lead to the uncovering of social grouping, interaction, information 

exchange, and social units in prehistoric contexts at fine grained scales heretofore thought 

230 

unknowable. Efforts in this regard are abundant (Braun 1985; Goodby 1998; Hargrave, et al. 

1991; Hegmon, et al. 1997; C. M. Milner and Stark 1999; Odess 1998; C. G. Sampson 1988; 

Schortman and Urban 1992; Schortman, et al. 2001; Stark Miriam, et al. 2000; Stark, et al. 1995, 

1998). These studies are often influenced by ethnoarchaeological research indicating an active 

use of style as a form of non-verbal communication to express social identities (Bowser 2000; 

Carr 1995a; Graves 1981, 1994; Hegmon 2000; Herbich 1987; Kramer 1985; Longacre 1991; 

Skibo, et al. 1989; Wiessner 1983, 1984, 1990; Wobst 1977).  

A recent trend in American prehistoric archaeology and beyond focuses on a particular 

aspect of style – pottery decoration – as a means to access patterns of shared categorical 

identities at various social and spatial scales (Birch and Hart 2018; Hart and Engelbrecht 2012; 

Mills, Clark, et al. 2013; Mills, et al. 2015; Mizoguchi 2009; Peeples 2011, 2018). Due to its 

highly visible and often symbolic nature, pottery decoration is posited as being an integral part of 

an active process to signal group membership and individual skill under this paradigm. 

Categories of group membership may be related to ethnicity, gender, political status, religious 

affiliation, labor or craft expertise, or other social units at both hierarchical and heterarchical 

levels. Because “categorical distinctions are not necessarily built out of direct and frequent 

interactions among people, such identities must be symbolized in order to facilitate recognition 

among members and non-members of categorical social groups” (Peeples 2011:261-262). 

Regardless of the specific social grouping, symbolic communication and social identity are 

argued to interplay recursively. Active expression of identity is therefore intricately linked to the 

process of symbolization, a process also referred to in other contexts as emblemic style 

(Wiessner 1983, 1984, 1985, 1990). Consequently, it is argued here that stylistic patterns gleaned 

from symbolic decoration on pottery vessels may reveal networks of shared categorical identities 

231 

among groups of people in archaeological contexts.  

 

This chapter presents an analysis of Mississippian and Oneota pottery that draws on 

theories of pottery style, social signaling (Birch and Hart 2018; Bliege Bird and Smith 2005; 

Hart and Engelbrecht 2012), and categorical identification (Azarian 2005; Fuhse 2012; Mills, 

Clark, et al. 2013; Mische 2011; Peeples 2011, 2018; Tilly 2004; White 1992, 2008a). In 

particular, social network analysis models are used to assess patterns of similarities in social 

identification across the middle to late Mississippian transition in the Late Prehistoric central 

Illinois River valley (ca. A.D. 1200- 1450; CIRV). The objective is to reveal the ways in which 

migration was structured by, and restructured, networks of social identification. Network models 

are constructed based on patterns of proportional similarity in designs incised or trailed on the 

interior outflaring rims of ceramic plates on either side of a circa 1300 A.D. in-migration of 

Oneota peoples into the region. Plates were used primarily as serving or presentation pieces 

(Hilgeman 2000). Plate designs are a highly visible decorative component during quotidian or 

ritualistic public gatherings. Results indicate that intra-regional mobility and shifting patterns in 

the scale of parity in networks of social identification during the Middle to Late Mississippian 

transition resulted in the formation of a spatial and social internal frontier that in many ways 

structured the in-migration of Bold Counselor Oneota peoples into the CIRV. In turn, Oneota 

peoples likely contributed to increasing diversity in common categories of social identification, 

thereby acting to disrupt and exacerbate ongoing restructuring of regional social identification 

networks.  

 

6.2 Migration and Social Identification 

232 

Explaining variability in communal interrelationships within multicultural social 

environments is a key research aim for archaeologists and anthropologists. Establishing and 

maintaining intercultural relationships is one way for migrant groups to adapt to a novel social 

environments (Burmeister 2000), or for societies to respond to severe pressure and threat from 

external (Kowalewski 2006) or internal forces (Birch 2010). Social diversity based on the 

intersection of migrant and indigenous peoples can be critical to the process of social change (Alt 

2006). However, differential patterns of interactions in multicultural contexts may be pursued by 

communities of social actors, from factionalism and conflict along culturally pluralistic lines, to 

private retention of cultural or ethnic distinctions with public de-emphasis and cultural 

accommodation, to hybridity and cross-cultural mediation or integration and ethnogenesis 

(Broch 1987; Liebmann 2013; Pugh 2010; Stone 2003). That is, a spectrum of internally 

motivated processes leads to the selective adoption of technology, social identities, and 

individuals (Frangipane 2015; Pollack, et al. 2002; Schwartz and Green 2013; Trubowitz 1992).  

Indexing common social identities represents a primary mechanism visible in 

archaeological contests that creates and sustains intercultural network relationships (Bowser 

2000). Other mechanisms include engaging in direct relational interaction through cultural 

transmission or exchange and overlapping resource exploitation areas. These processes are often 

more overt on the spatial frontiers of polities due to the waning influence of cultural cores over 

geographic distance (Rice 1998). The goal of this chapter is to explore the role of a theoretically 

justified ceramic stylistic trait, plate design motifs, in evidencing patterns of similarities in 

categorical identification and discern how those patterns might change contemporaneous with 

the in-migration of a tribal Oneota group into a chiefly Mississippian environment late in the 

prehistory of west-central Illinois.  

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Recent archaeological research recognizes the value of incorporating formal network 

analysis methodologies based on the relational sociology of Harrison White, Charles Tilly, and 

others to address questions related to coexisting material culture traditions (Azarian 2005; Borck, 

et al. 2015; Collar, et al. 2015; Fuhse 2012, 2015; Mills, et al. 2016; Mills, Clark, et al. 2013; 

Mills, et al. 2015; Mills, Roberts Jr., et al. 2013; Mische 2011; Peeples, et al. 2016; Tilly 1978, 

2001b; White 1992, 2008a; White and Godart 2007). Here, I employ a theoretical framework 

that builds on this application of relational theory to archaeological contexts in order to address 

anthropologically significant issues related to processes of social identification.  

Because relational theory is examined at length in Chapter 2, only a brief discussion is 

presented here. White argues that social networks must be studied in conjunction with cultural 

systems (Fuhse 2015; White 1992). That is, cultural and network structure are argued to interplay 

in a recursive manner as opposed to being abstractions of each other. Network relationships build 

on cultural models such as kinship, gender, heterarchy, and hierarchy. White views interactions 

as being driven through the inherent uncertainty in the roles of participants. From this 

uncertainty, White sees social identities as a means to ‘gain footing’ in, or to ‘control’, social 

contexts (White 1992). These control attempts are posited to leave a trace in social space as 

‘stories’ or information defining and relating identities to each other. Identities in this way are 

mobilized as process and often codified by symbolic representation. For White, novelty in stories 

or identities develops from the “creative combination of cultural forms at the intersection of 

previously separate network formations” (White 1993:77).  

The ‘New York School’ of relational sociology (Mische 2011), building upon the 

theoretical work of White and others (Azarian 2005), posits that processes of collective social 

identification take place in either relational identification or categorical identification. Relational 

234 

identification is a process whereby individuals identify with larger collectives based on their 

position within networks of interpersonal interaction (Peeples 2011:18-19; 2018). Strong ties in 

this regard are based on interactions rooted in kinship, communities of practice, or shared 

historical origin, and are discussed in Chapter 5. Relations forged through more limited contexts 

such as the exchange of material goods or information exchange based on shared resource 

exploitation areas are discussed in Chapter 7. Such “weak ties” generated from more limited 

contexts of interaction often play an important role in connecting social contexts that would often 

otherwise be completely separate (Granovetter 1973). The focus of this chapter is categorical 

identification, which refers to a process whereby individuals identify with larger collectives 

based on perceptions of belonging to formal social units such as ethnic groups, genders, political 

affiliations, religious affiliations, or other units at various scales (Peeples 2011:20-23; 2018). 

Categorical identification need not be coupled with direct social interaction. That is, two 

individuals may perceive belonging in the same formal social unit irrespective of familial or 

interactional relationships.  

 

Migration represents a critical social context in which to observe the creative 

refashioning of cultural forms resulting from the intersection of previously separate social 

networks. As a process, migrations are often guided by networks formed in a stepwise fashion 

through connections based in kinship, exchange, or other social ties (Mills, et al. 2016). This has 

led to the use of “network-mediated migration theory” by many anthropologists and sociologists 

as an alternative to the “rational choice and decision-making models” used in other social science 

disciplines (Brettell 2000:107; Mills, et al. 2016). A network approach replaces predetermined 

typologies with explicitly defined ties that allow groups to be described based on social 

relationships of interaction or shared categorical identity ascription.  

235 

 

Social networks are of paramount importance for communal migrations. Migrants must 

adapt to a new cultural and natural landscape where information and interaction with existing 

groups can ease or antagonize settlement. Migration is a vehicle for cultural maintenance or 

change based on the clash between public and private, adaptation and tradition, and external and 

internal cultural transfer (Anthony 1990; Burmeister 2000; Stone 2003). Identification networks 

are sensitive indicators of the negotiation of social and economic systems by indigenous and 

migrant groups (Rockman 2003). Individuals, communities, and households pursue various 

social identification strategies in multicultural environments resulting from migration. Due to 

archaeology’s focus on material culture remains, attempts to elucidate ideological strategies in 

multicultural contexts are eschewed here in favor of elucidating behavioral strategies in 

multicultural contexts at the community scale. In particular, the analysis presented here is 

focused on ascertaining the geographic and demographic scale at which categorical identities 

were expressed on serving wares and how those scales might change concomitant with the in-

migration of an exogenous group in a non-state archaeological setting.  

 

6.3 Oneota Migration into West-Central Illinois  

During the twelfth and thirteenth centuries a large-scale movement of Oneota peoples out 

of an Upper Midwest core region and into the lower and eastern Midwest was ongoing. This 

population movement has been described as an aggressive territorial expansion (Hollinger 2005). 

Oneota expansion coincided with a rapid decline in Middle Mississippian influences in these 

regions and with the onset of the droughty Pacific climatic episode (Gibbon 1995). While many 

Late Woodland populations in the riverine Midwest and western Great Lakes were replaced by 

or integrated into Oneota peoples during this expansion process, societies in the ecologically rich 

236 

central Illinois River valley (or CIRV), or northern Middle Mississippian frontier, maintained 

their positions in fortified temple mound centers and outlying sites, and entered into a period of 

regional coexistence with an intrusive Oneota population known archaeologically as the Bold 

Counselor (Esarey and Conrad 1998). The sudden appearance of characteristically Oneota 

material culture at five sites circa 1300 A.D. and biodistance indicators in the Norris Farms #36 

cemetery population attests to the occurrence of a migration process in the CIRV, though the 

specific location of origin of the Oneota immigrants is unknown (Esarey and Conrad 1998; 

Santure, et al. 1990; Steadman 1998). Recent archaeological inquiry in the Late Prehistoric 

CIRV has focused on the unprecedented levels of violence seen in burial and cemetery contexts 

both prior to and following Oneota in-migration (Hatch 2015, 2017; G. R. Milner, et al. 1991; 

Steadman 2008; Vanderwarker and Wilson 2016; G. D. Wilson 2012, 2013). Although the CIRV 

is remarkable for its levels of sustained inter-personal violence, evidence indicating the 

communal coexistence of these distinct but interrelated cultural groups is apparent. Coexisting 

Oneota and Mississippian material culture at multiple sites at the household level provides the 

opportunity to examine the various social interrelationships that were present.  

A discussion of the Mississippian CIRV is warranted in order to provide a baseline for 

network restructuring concomitant with Oneota in-migration. The archaeological region known 

as the CIRV encompasses a 210 km stretch of the Illinois River extending approximately from 

the modern village of Hennepin, IL southerly to the village of Meredosia, IL (Harn 1994:4-9); 

though the Late Prehistoric CIRV is centralized in an approximately 137 km stretch of the 

Illinois River from the present town of Peoria, IL southerly to the unincorporated village of 

Chambersburg, IL. The Mississippian phases of the CIRV have been defined largely based on 

reference to material cultural correlates in the American Bottom, a few hundred river kilometers 

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to the south along the Illinois River (Conrad 1991). During the approximately 350-year span of 

Mississippian occupation, the CIRV housed at least seven fortified Mississippian temple towns 

and numerous smaller villages and farming hamlets. Subtle trends in material culture based on 

geographic location have led to a hypothesized cultural distinction between Mississippian 

peoples in the upper portion of the CIRV near the Spoon River and those inhabiting the lower 

portion of the valley near the La Moine River (Conrad 1991; Harn 1978, 1994).  

The central Illinois River valley’s position at the eastern edge of the Prairie Peninsula and 

proximity to the Mississippian cultural core in the American Bottom situated this archaeological 

region at the intersection of Plains-Prairie-Woodland lifeways and booming agricultural 

complexes during the beginning of the first millennium of the common age. The immense 

population size and political and artifactual complexity at the American Bottom site Cahokia 

have led to models that view the site as the axis mundi for Mississippian culture in eastern North 

America (Pauketat 1994; Pauketat and Emerson 1997). However, recent research challenges the 

intensity of Cahokian influence on both demographic and cultural transformations in comparison 

to in situ processes in the CIRV (Bardolph 2014; Bardolph and Wilson 2015; Friberg 2018; 

Steadman 1998, 2001). That is, far from being passively colonized or demographically replaced 

by Mississippian peoples from the American Bottom, Late Woodland peoples local to the CIRV 

were “selectively adopting or emulating aspects of Mississippian lifeways, while maintaining 

certain [local] traditions” (Bardolph and Wilson 2015:138). Nevertheless, the 

Mississippianization process promoted increasing regional interconnectedness through cultural 

realignment among dispersed Late Woodland peoples. This resulted in profound changes to 

settlement, subsistence, architectural, ceramic, and socio-politico-religious systems in the CIRV 

and a distinct expression of the Mississippian lifeway at the northern fringe of its expansion in 

238 

the American midcontinent, save a few relatively short-lived outposts at Aztalan (L. G. Goldstein 

and Richards 1991), in the Apple River valley (Emerson 1991), and in the Trempealeau region of 

Wisconsin (W. B. Green and Rodell 1994; Pauketat, et al. 2015).  

The historical trajectory of Middle Mississippian populations in general in the CIRV is 

argued to be one of increasing population aggregation, factionalism, and conflict (Steadman 

2008; Vanderwarker and Wilson 2016; G. D. Wilson 2012, 2013; J. J. Wilson 2010). Around 

1200 A.D., Mississippian communities began to aggregate into fewer and larger settlements – a 

trend that would only intensify over time in the region. These settlements could best be described 

as nucleated towns, which were often coupled with a mound-fronted plaza surrounded by 

domestic structures and often fortifications. Some towns, such as Orendorf and Lawrenz Gun 

Club, were rebuilt numerous times over successive occupations that spanned many generations, 

while others such as Larson were perhaps only occupied for a generation or two. Numerous 

villages, intermediate settlements, hamlets, and single-family farms were occupied alongside 

towns (Conrad 1989, 1991; Esarey and Conrad 1998; Harn 1978, 1994).  

Material culture, and in particular burial goods, shows clear connections between 

Mississippian peoples in the CIRV and symbolically adorned exotic items characteristic of the 

so-called Southern Cult, or pan-Mississippian cosmological symbolism. These include but are 

not limited to shell gorgets, Ramey knives, copper pendants, engraved marine shell, flint clay 

effigy and figurine pipes, stone discoidals, and copper-coated earplugs (Brown and Kelly 2000; 

Conrad 1989, 1991; Harn 1971, 1980, 1991; Knight Jr 1986). Evidence for interpersonal 

violence in the region has been shown to increase overtime (G. R. Milner, et al. 1991; Steadman 

2008), however it was not a ubiquitous phenomenon (Hatch 2015). An analysis of ceramic 

technology in this dissertation (Chapter 5) indicates that sites across the Mississippian CIRV 

239 

were interacting extensively despite the high levels of violence, suggesting that the threat of 

violence was perhaps episodic as opposed to chronic in delimiting regional mobility. 

Paleodemographic analyses suggest that the emergence of palisaded towns was accompanied by 

a high-pressure system of elevated fertility and mortality (J. J. Wilson 2010).  

Sometime in the early to mid-14th century, an Oneota group from the north migrated into 

the CIRV and fundamentally changed the social dynamics of the region (Esarey and Conrad 

1998; O'Gorman and Conner 2016). Available data from CIRV settlements exhibit varying 

degrees of intermixing between Mississippian and Oneota material culture. Because intermixing 

occurs in simultaneous occupations, it has caused a quandary in attempts to taxonomically 

differentiate Bold Counselor Oneota from their Late Mississippian contemporaries and vice 

versa (Conrad 1991; Esarey and Conrad 1998; H. G. Smith 1951). From the Oneota assemblage 

at C.W. Cooper that is suggestive of a site-unit intrusion because it “shows almost no evidence of 

any influence or actual presence by the Late Mississippians” (Esarey and Conrad 1998:41), to 

evidence “probably indicating a cultural fusion from two separate sources” at the Crable mound 

center (H. G. Smith 1951:28), to the ‘purely’ Late Mississippian assemblages at the fortified Ten 

Mile Creek and Star Bridge towns (Conrad 1991), no discernible pattern emerges using 

traditional taxonomic methods as to the nature of cultural interrelationships in the Late 

Prehistoric CIRV. Tantalizing evidence for cultural mixing between Oneota and Mississippian 

peoples is most readily apparent in the intermingling of ceramic traits. For example, the use of 

plates by Oneota peoples is apparent at several sites in the CIRV, but virtually absent in Oneota 

contexts outside the region. At the Crable Mississippian mound center, some 14% of vessels 

from a sample of pit features were ascribed to Oneota, leading Esarey and Conrad (1998:46) to 

suggest that “the most likely explanation for these assemblages is that Bold Counselor peoples 

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were present (in one social context or another) as a minority admixture to Crable’s 

overwhelmingly Mississippian-derived population. Furthermore, this admixture seems to 

represent social integration at the household level.” The Morton Village site appears to indicate 

the inverse: an Oneota village with a minor admixture of Late Mississippian peoples (O'Gorman 

and Conner 2016).  

Given these taxonomic quandaries, an alternative perspective is warranted. In order to 

access patterns of similarities in social identification processes, a high-visibility stylistic material 

culture trait is needed. In the CIRV, stylistic traits are abundant, but the most commonly 

recovered material culture class with stylistic treatment used in high-visibility contexts is pottery 

and in particular the plate vessel class. As a result, the Late Prehistoric CIRV is an appropriate 

context, and ceramic plates are an apt material cultural class, with which to apply network-

mediated methodologies to explore community scale structuring of, and responses to, cultural 

contact.  

 
6.3.1  Plates, Ceramic Design, and Sun Symbolism in the CIRV 

Pottery assemblages in the Late Prehistoric central Illinois River valley (CIRV) consist of 

five basic vessel forms – plates, jars, bowls, bottles, and pans. Symbolic motifs are widely 

adorned on many of these vessel forms, and sub-variants of these forms, but occur in greatest 

frequencies on plates, effigy bowls, beakers (a specialized bowl form), and jars (Conrad 1991; 

Esarey and Conrad 1998; Harn 1994) . Of these vessels, the most commonly recovered across 

the geographic and temporal expanse of the CIRV with largely intact symbolic decoration motifs 

are plates. Where site level data is available, plates comprise on order of 2.5 – 10% of vessel 

assemblages and are thus not overly common across domestic contexts (Conrad 1991; Esarey 

and Conrad 1998; Harn 1994). Mississippian and Oneota plates are similar in shape and form to 

241 

circular dinner plates you might find in your kitchen cabinet or the kind you might have your 

dinner served in at a fine-dining restaurant. Based on the high frequency of often finely crafted 

decorative motifs on the interior outflaring rims of plates and the unrestricted access to their 

contents, plates likely functioned primarily as serving vessels (Hilgeman 2000; Lieto and 

O’Gorman 2014).  

As a vessel form, plates are common at Mississippian sites in the American Bottom and 

surrounding regions along the Illinois and Ohio River valleys. Plates comprise a significant 

proportion of decorated vessels at major Mississippian mound centers such as Cahokia (Griffin 

1949; Vogel 1975), Kincaid (Orr 1951), Angel (Hilgeman 2000), Common Field (M. Buchanan 

2014), and town sites in the CIRV such as Larson, Crable, Star Bridge, Lawrenz Gun Club, 

Orendorf, Walsh, and Ten Mile Creek (Conrad 1991; Esarey and Conrad 1998; Harn 1994; 

Painter 2014; K. Sampson 2000; H. G. Smith 1951), as well as at village and subsidiary sites 

such as Morton Village, Fouts Village, and Buckeye Bend among many others (Cole and Deuel 

1937; Conrad 1991; Harn 1994; Lieto and O’Gorman 2014; Santure, et al. 1990). There is a 

minor occurrence of plates found at Mississippian period sites in present-day western Kentucky, 

the Nashville Basin, and the Tennessee-Cumberland region (K. E. Smith, et al. 2004). Despite 

the widespread adoption of Mississippian cultural characteristics across the late Precolumbian 

American southeast, however, plates are generally rare in Mississippian period assemblages in 

areas south and east of present-day Tennessee.  

Plates are characterized by a complex profile that includes a flattened, outflaring rim and 

a distinctive concave well (Hilgeman 2000:36-40). The morphology of plates is chronologically 

significant across the Mississippian regions wherein these vessels have been recovered (Clay 

1976:47; Conrad 1991:148; Hilgeman 2000:42; Kelly 1984, 1991b; Orr 1951:339; K. E. Smith, 

242 

et al. 2004:50-51). In particular, plate rims increase in size overtime (e.g. Figure 6.1 C.) and  

A. 

C. 

B. 

D. 

 

Figure 6.1 Examples of plate form. Images © Andy Upton 2018, courtesy Western Illinois 

Archaeological Research Center and Dickson Mounds Museum 

become more concave toward the well (e.g. Figure 6.1 B.). As a result, plates become more 

 

bowl-like overtime. However, this is a very general trend and older plate forms (i.e. with shorter 

rims and a flatter profile) persist alongside the later, more bowl-like vessels. Figure 6.2 shows 

continuous attribute metric trends for plates in the CIRV showing these trends quantitatively. In  

243 

Site Occupational Time Period(s) 

Pre-Migration (~1200 – 1300 A.D.) 
Pre- and Post-Migration (~1200 – 1450 A.D.) 
Post-Migration (1300 – 1450 A.D.) 

Figure 6.2 Ridgeline density plots for plate continuous attribute measurements at Late Prehistoric CIRV 

sites 

 

244 

general, the flare angle of plates decreases overtime (where a 90˚ angle is vertical) and plate flare 

length increases overtime. However, there is considerable overlap between time periods. This 

has led to a myriad of ambiguous typological classifications for plates across the different 

Mississippian contexts of recovery such as ‘Wells incised, ‘O’Byam incised’, ‘Crable deep-

rimmed plate’, and ‘O’Byam incised variety Wells’. In addition, a plethora of terms are used in 

the literature to denote or sub-divide the vessel class, including ‘broad-rimmed bowls’, ‘broad-

rimmed plate’, ‘deep-rimmed plate’, ‘deep rim plate’, ‘short rim plate’, ‘standard plate’, and 

‘broad shallow bowls’, among others. For ease and consistency, I use the term ‘plate’ to refer to 

this class of vessel, despite the more bowl-like shape of the vessel class overtime. This signals 

the primary serving function of the vessel class and disambiguates the likely more utilitarian 

bowls which are characterized by rounded, as opposed to flattened, rims. Furthermore, since the 

focus of this research is to consider alternative perspectives to artifact classification, no attempt 

is made here to assign plates to a taxonomic type nor to refine any sort of typology. Instead, this 

research focuses on using proportions of similarities in decorative motifs used on the plate 

serving vessel class as a means to model changes in networks of shared categorical ascription 

concomitant with demographic change in a multicultural context.  

Plates in the CIRV are almost ubiquitously burnished or polished to a soft luster (Conrad 

1991). Decoration occurs only on the interior surface of the outflaring rim. As a result, prepared 

foodstuffs served in the well of plates would leave any decorative motifs clearly visible when 

used in a public context. Plates tend to break along the joint between the inner lip and the 

outflaring rim, often leaving a significant portion of the outflaring rim and any accompanying 

decorative motifs present (Hilgeman 2000). Decoration technique on plates in the CIRV can be 

characterized in one of two forms: incising or trailing. Incised decorations are sliced into a 

245 

leather hard or semi-dried paste and generally form a “V” shape in profile as a result of the 

cutting motion. A fine pointed or edged, sharp, and sturdy tool would be required to execute 

plate incising. Possible tools such as a lithic points, flake-tools or drills, porcupine quills, or 

other faunal implements such as an awl could perhaps be used. Much less common is the 

scratching of designs onto a dry paste with a wider tool such as a pebble or scraper resulting in 

thicker but shallower incision lines. Trailed decorations, on the other hand, are drawn into a 

malleably damp or moist paste and as a result generally form a “U” shape in profile. Tools for  

 

 

Figure 6.3 Plate decoration techniques: trailed (left) and incised (right). Images © Andy Upton 2018, 

courtesy Western Illinois Archaeological Research Center 

 

trailing designs would be characterized by a blunted tip – sticks, reeds, rounded-tip river pebbles, 

cylindrical pottery sherds, or polished faunal long bones might make good tools for this purpose. 

Quite rare are trailed lines wide enough to suggest a human finger was used as the implement 

responsible for decoration. Different tools and production sequences would therefore be required 

246 

to trail decorations rather than incise them. However, plates with trailed designs typically co-

occur as an outlying minor admixture (i.e. < 15% trailed plates) alongside an overwhelming 

majority of plates with incised designs at CIRV sites (See Table 6.1). This suggests some level of 

experimentation or perhaps assertive style (Wiessner 1990) in plate decoration by potters across 

the geographic and temporal expanse of the Mississippian CIRV. A very minor admixture of 

plates are both trailed and impressed with punctate design motifs characteristic of Oneota 

peoples, showing an incipient hybridization of Oneota decoration and a Mississippian vessel 

form (Esarey and Conrad 1998; Lieto and O’Gorman 2014). The only definitive trend regarding 

plate decoration is that plates with decorative motifs characteristic of Oneota peoples are always  

 

Figure 6.4 Trailed and punctate impression decoration. Image © Andy Upton 2018, courtesy Western 

Illinois Archaeological Research Center 

 

247 

trailed and never incised (e.g. Figure 6.4). 

Motifs present on CIRV plates almost entirely depict Upper World Symbolism and in 

particular the sun. Line-filled triangular designs use positive and negative space to form sun rays 

emanating out of the vessel well (e.g. Figure 6.1A & B, Figure 6.4). Zig-zag designs are often 

formed by the presence of multiple line-filled triangular designs on the upper and lower portions 

of the outflaring rims (e.g. Figure 6.1D). Finely incised variants of the line-filled triangular 

designs have been referred to as Wells Incised in the CIRV and American Bottom (Harn 1994; 

Vogel 1975). Fewer line-filled triangular designs are present at sites with earlier occupations in  

 

Figure 6.5 Plate sherd showing sun with nested cross motif. Image © Andy Upton 2018, courtesy 

Western Illinois Archaeological Research Center 

 
the CIRV such as Orendorf and Kingston Lake in favor of simpler curvilinear or rectilinear line-

based designs (Conrad 1991:138). On the other hand, sites with occupations extending into the 

248 

14th century A.D., such as Lawrenz Gun Club, Crable, and Star Bridge, often depict a half-risen 

sun itself using curvilinear arc lines flanked on all sides by triangles (e.g. Figure 6.1C; Figure 

6.3). Rare is a complete circular sun with nested cross motif surrounded by triangular sun-rays 

(Figure 6.5).  

In the American Bottom region, individual design motifs and entire pot symbolism of 

Ramey Incised vessels are argued “to have been an active element of elite-commoner socio-

ideological discourse” in hierarchical Mississippian society and to have relayed information 

about the Cahokian-style cosmos (Pauketat and Emerson 1991:920). Upper world symbolism 

appears on Ramey incised vessels dominated by unambiguous sun motifs. Ramey incised pottery 

spread into the CIRV during the early Mississippian period along with other facets of the 

Mississippian lifeway (Bardolph 2014; Friberg 2018; Harn 1991). However, both the form of 

execution and symbols present on Ramey incised pottery in the CIRV are distinct from 

counterparts in the American Bottom. If Ramey incised pottery does reflect cosmology as 

practiced by Cahokians and other Mississippian peoples in the American Bottom region, the 

selective adoption of decorative motifs suggests that peoples in the CIRV “did not adopt 

Mississippian religion wholesale, but rather made sense of the changing cultural climate within 

their own worldviews, renegotiating their identities and social relationships in the process, and 

bundling these spheres of interaction into the products of their daily practice” (Friberg 2018:53). 

While the Ramey incised vessel type did not persist into the Middle and Late Mississippian 

CIRV phases (1200 – 1450 A.D.) that are the focus of this research, certain Ramey incised 

design motifs do – concentric arcs, nested chevrons, and line-filled triangles unmistakably 

interpretable as sun (or fire) Upper World symbolism. In many ways, plate design motifs 

depicting Upper World symbolism can be seen as an outgrowth of Ramey incised symbolism. It 

249 

can therefore be inferred that the sun and Upper World symbolism adorning plates in the Middle 

and Late Mississippian phases of the CIRV likely reflect a complex interplay between 

cosmological and religious themes that relay social identification to a broader Mississippian 

world but within distinct, localized worldviews.  

The sun was intertwined into the cultural fabric of most, if not all, Native American 

Tribes in the southeast, midwest, and plains regions during the protohistoric period. 

Ethnographic accounts of the descendants of Mississippian peoples in the southeastern United 

States indicate a cosmos that consists of three worlds: This World, an Upper World, and an 

Under World. The Upper World epitomized perfect order and consistency, where things existed 

in a grander and purer form than in This World (Hudson 1976:122-183). The sun, as the source 

of all light, warmth, and life, was one of the principal gods and often at the center of Upper 

World ceremonialism. Among some Tribes, the sun was referred to as ‘our grandparent’ – 

terminology rooted in the same respect and affection afforded to the Ancestors (Hudson 

1976:127). Whereas among other Tribes, the leading family were known as the Suns and the 

primary chief was called the Great Sun (Lankford 2011:54-55). Such was the integration of solar 

reverence among the Natchez that Swanton (1928:206) remarked that the “Natchez state was 

thus to all intents and purposes a solar theocracy.” The sun’s gender was not fixed among Tribes 

and was sometimes male and sometimes female. For example, the “Cherokees believed that 

sacred fire, like the Sun, was an old woman. Out of respect, they fed her a portion of each meal” 

(Hudson 1976:126). The sun dance was, and is, practiced by Tribes in the plains region. 

Descriptions of the sun dance among the Arapaho, Arikara, Blackfeet, Cheyenne, Crow, Hidatsa, 

Kiowa, Mandans, Ojibway, Omaha, Sioux, and Ute indicate that the sun, as a manifestation of a 

deity, was vital in reaffirming Tribal membership and cultural identity (Spier 1921). The sun was 

250 

a central manitous, or other-than-human spirit, among the Illinois, Miami, Potawatomi, and 

Ojibwa (Thwaites 1897). Upon contact with Jesuit missionaries, the Illinois “linked their sun god 

Manitoua assouv with the Christian God…which literally meant ‘Great Spirit’” (Bilodeau 

2001:358, 362). While the role of the sun and Upper World cosmology among Mississippian and 

Oneota peoples will always be a source of debate, the near ubiquity of solar reverence among the 

likely descendants of these peoples in the southeastern, midwestern, and plains regions of the 

United States suggests that the adorning of sun symbolism on plates was likely interwoven into 

socio-politico-religious beliefs. As a result, the plate vessel class and the symbolic decorative 

motifs emblazoned upon them are theoretically justified as a good proxy for active expressions 

of categorical commonality at a region scale because they were likely produced with a concern 

for visual communication regarding social categorical identification. 

 

6.4 Methodology 

Social network analysis provides a body of theory and techniques for visualizing and 

measuring patterns of shared categorical identities between social entities (Scott 2000; Scott and 

Carrington 2016; Wasserman and Faust 1994). The application of network analysis techniques in 

archaeology is contingent upon the basic theoretical argument that similarities in material culture 

used and discarded at different sites can act as a proxy measure for the degree of social 

connectedness between them, whether direct or indirect, material or informational (Brughmans 

2013; Peeples, et al. 2016:61). The network models of social identification chosen for this 

research constitute a framework for constructing bonds of shared categorical identification 

between individuals and communities, wherein ties between sites in network models act as 

statements of probability that a relationship existed (Matthew Peeples personal communication, 

251 

2017). Expressed in stylistic decoration, categorical identities are mechanisms for people to 

index ascription to common social units, express solidarity, and nonverbally communicate social 

information related to group membership (Braun 1985; Wiessner 1990). 

While Mississippian plates have been explored from a variety of typological perspectives 

(Conrad 1991; Hilgeman 2000; Vogel 1975), this research represents the first coding scheme 

devised for Mississippian plate decoration in the CIRV. Each plate sherd was assessed for the 

presence of a design technique and decoration motif. A design technique, as used here, refers to 

the technique used to decorate the vessel – whether incised, trailed, or trail-impressed. Whereas a 

decoration motif refers to the specific shape and form of elements comprising the decoration. A 

sampling of 490 plates from 15 Late Prehistoric CIRV sites was assessed for this analysis. All 

samples were assessed solely by the author to minimize inter-observer inaccuracies in design 

technique and decoration motif characterization. Among the sample of 490 vessel observations, 

74 percent (n = 364) have incised decoration, 11 percent (n = 53) have trailed decoration, 2 

percent (n = 12) have both trailed and impressed (punctate) decorations, and 12 percent (n = 61) 

are plain with no decoration present. Plates with no decoration motif present are considered in 

the analysis because the absence of a motif may be symbolically charged given the majority of 

plates with decorations. However, plates with indeterminate or isolate decoration motifs are not 

considered. A decoration category was assigned to each unique combination of design technique 

and decoration motifs present. These unique decoration categories total 94 across the 429 vessels 

with design techniques present. Descriptions of each unique decoration motif category are 

provided in the Coding Sheet in Appendix A. Of the decorated vessels, two decorative motif 

categories are wholly unique with no duplicates. Removing these isolate motifs as well as the 

vessels with indeterminate motifs results in a sampling universe of some 411 vessels across 15  

252 

Site 

Plates 
(n) 

Plain 

Incised 

Trailed 

Trailed-
Impressed 

Time Period 

Baehr South 
Buckeye Bend 
Crable 
Emmons 
Fouts Village 
Houston-Shryock 
Kingston Lake 
Larson 

Lawrenz Gun Club 

Morton Village 
Myer-Dickson 
Orendorf C 
Star Bridge 
Ten Mile Creek 
Walsh 

Total 

11 

12 
74 
24 
11 
27 
47 
42 

42 
34 
17 
32 
81 
16 
20 
490 

- 

- 

2.7% (2) 
29.2% (7) 
9.1% (1) 
11.1% (3) 
17% (8) 
14.3% (6) 

9.5% (4) 
11.8% (4) 
11.8% (2) 
43.8% (14) 
7.4% (6) 
12.5% (2) 
10% (2) 

100% (11) 
100% (12) 

81.9% (59) 
82.4% (14) 
100% (10) 
91.7% (22) 
71.8% (28) 
94.4% (34) 

- 
- 

13.9% (10) 
17.6% (3) 

- 

8.3% (2) 
28.2% (11) 
5.6% (2) 

89.5% (34) 

10.5% (4) 

60% (18) 
86.7% (13) 
38.9% (7) 
97.3% (73) 
92.9% (13) 
88.9% (16) 

10% (3) 
13.3% (2) 
61.1% (11) 
2.7% (2) 
7.1% (1) 
11.1% (2) 

- 
- 

4.2% (3) 

- 
- 
- 
- 
- 

- 

30% (9) 

- 
- 
- 
- 
- 

Post-Migration 
Pre- and Post-
Migration 
Post-Migration 
Pre-Migration 
Pre-Migration 
Pre-Migration 
Pre-Migration 
Pre-Migration 
Pre- and Post-
Migration 
Post-Migration 
Pre-Migration 
Pre-Migration 
Post-Migration 
Post-Migration 
Pre-Migration 

61 

364 

53 

12 

 

Table 6.1 Summary of plate sample design techniques by site 

 
sites from which to model networks of social identification. The unique decoration motif 

categories were distilled into 29 decoration grouping categories based on perceived similarities 

in decoration motifs alone (i.e. disregarding design technique) in order to focus solely on 

symbolism. A vessel with decorations emblematic of the decoration grouping category was then 

sketch-traced and shared unique decoration categories noted and subsumed. The full sketches are 

provided in Appendix E. Design group counts are summarized in Table 6.2, and decoration motif 

grouping category emblems provided in Figure 6.6.  

It is important to note that there is significant variability in the amount of plate decoration 

data that was able to be recorded from each archaeological site. Given the regional scale of this 

project, and the resulting reliance on extant collections, the sampling of sites and vessels chosen 

does not reflect a probabilistic survey. Further, the amount of excavation or other data collection 

253 

from each site varies significantly. Some sites were almost completely excavated, while others 

only saw minimal sub-surface testing. Decorations themselves are also often incomplete or only 

partially present, potentially obfuscating accurate decoration motif grouping categorizations. 

Inasmuch as possible, the entire vessel was considered when decorations were assessed. 

However, complete plate vessels are quite rare. Plates were seldom used as burial furniture, 

where they might be recovered intact, aside from at the Crable site, for example (H. G. Smith 

1951). Thus, in some cases, only individual decoration motif elements might be present. In these 

cases, decoration motif categorizations were made based on perceived similarities in possibly 

incomplete decoration elements (e.g. decoration groupings 7 and 13, Figure 6.6). Furthermore, a 

regression of the number of decoration category groupings as a function of vessel sample size 

from each site indicates that a significant portion of variation in the number of design category 

groupings is explained by sample size (r = 0.85, R2 = 0.71). Thus, the patterns of shared 

categorical identification modeled between sites may be negatively impacted by the vagaries of 

sampling. The interpretations that follow should therefore be considered as foundational as 

opposed to definitive in the analysis of the nature of social identification processes among Late 

Prehistoric CIRV sites. 

Categorical social identification is explored across the 29 plate decoration motif 

groupings observed using the Brainerd-Robinson coefficient of similarity, which is commonly 

used in archaeological analysis as a means to explore relative frequencies, whether counts or 

percentages, of proportional similarity (Brainerd 1951; Robinson 1951; Shennan 1997:233-234). 

This measure is a form of city block metric that ranges from a score of 0, indicating no 

similarity, to a score of 200, indicating complete similarity in terms of the proportions of plate 

motif groupings present between two sites. For the present purposes, Brainerd-Robinson  

254 

Figure 6.6 Sketch tracings of plate decoration motif emblems 

 
 
 

255 

 

Figure 6.6 (cont.)  

 

 
coefficients were calculated using scripts written by Matthew Peeples and Gianmarco Alberti in 

 

the R statistical platform that were edited by the author (see Appendix C for the relevant code). 

These scripts calculate raw and rescaled BR coefficients as well as a Monte Carlo procedure to 

assess differences among samples that are likely the result of sampling error (DeBoer, et al. 

1996).  

The most important aspects of a particular network model are the definition of nodes and 

the types of tie used to construct relationships between the nodes. Spatially bounded 

archaeological sites represent nodes in this study. Shared categorical identities as evidenced by 

256 

proportional similarity in stylistic decoration on serving plates among sites is the type of network 

tie considered. Ties were assigned by defining a threshold similarity value for the Brainerd-

Robinson (BR) coefficient scores. The threshold value was chosen through an evaluative 

framework that considers a Monte Carlo procedure that simulates BR scores from randomly 

generated matrices based on the actual proportions of design group categories present at each 

site. That is, the matrix in Table 6.2 was column and row randomized with replacement 10,000 

times. The distribution of the BR coefficient values for the randomized matrices provides an 

estimate of the overall range and frequency of BR scores that might be expected by chance given 

the number of sites and relative counts for each design category. The random distribution and 

observed distribution of rescaled BR coefficients are shown in Figure 6.7. While neither the  

 

         Randomized BR 
             Observed BR 
             Randomized BR µ 
             Observed BR µ 
               

Figure 6.7 Distribution of Brainerd-Robinson coefficients for simulated (green) and observed (blue) 

design category matrices 

 

 

257 

simulated nor observed BR coefficient distributions are characterized by a normal distribution, 

the simulated data set does show a closer approximation and wider range of BR values overall. 

This indicates that the underlying structure of relationships among archaeological site-nodes is 

markedly different from what might be expected by chance. Ties between site-nodes are given 

for all rescaled BR coefficient scores greater than the mean BR value for the observed data set. 

This is an arbitrary value (BR > 0.4) but follows the heuristic of giving a tie between two site-

nodes when categorical identities among them are more similar than they are different based on 

the range and frequency of observed similarity scores. Further, this allows the most robust 

relationships among site-nodes to be modeled and evaluated using network graphs. Network data 

was handled in the R statistical package and exported to Gephi 0.9.2 (Bastian, et al. 2009) for 

visualization. Geographic network visualizations were rendered in Gephi and overlain on 

vectorized LiDAR maps using the open-source Inkscape program, version 0.92.2. Slight jittering 

of site geographic coordinates was applied to protect site locations. LiDAR maps are provided 

courtesy of the Illinois Geospatial Data Clearinghouse and the University of Illinois at Urbana 

Champaign. Network statistics were calculated using Gephi 0.9.2 and the R tidyverse and igraph 

package suites (Kolaczyk and Csárdi 2014; Wickham and Grolemund 2017).   

 

Network statistical measures provide insight into the nature of network topology, or 

overall structure. Network statistical measures assessed here include mean degree, or average 

number of edges among nodes in the network; mean weighted degree, or the average of the sum 

of edge weights among nodes in the network; diameter, or number of steps in the longest path 

from one node to another; mean path length, or average number of steps for each node to reach 

every other node; density, or proportion of observed ties compared to the number of possible 

ties; transitivity, which is also known as the global clustering coefficient, or proportion of 

258 

transitive triples wherein all three nodes in a triad are connected (Wasserman and Faust 1994). 

Degree, betweenness, closeness, and eigenvector centralization indices quantify the range or 

variability of individual actor indices. Centralization indices extend the concept of individual 

node centrality to the entire network. Degree centralization assesses whether or not all nodes are 

only connected to a singular central node. Betweenness centralization evaluates the extent to 

which an individual actor is located ‘between’ other actor pairs – actors in this ‘between’ space 

for many actor pairs are likely more critical information conduits. Closeness centralization 

considers how many actors are within one step, or are ‘close’, to a central node. Finally, 

eigenvector centralization gauges the degree to which central actors are connected to all other 

central actors.  

 

In addition to relying on formal methods in the statistical analysis of network data, 

interpretations are based in part on conditional uniform graph tests through Monte Carlo 

simulation. Each observed network statistic was compared against the distribution of that statistic 

generated from 5,000 random graphs of the same order (or number of nodes) and probability of 

an edge being given between any two nodes (based on the observed graph’s density) or size 

(number of edges) using the Erdős-Rényi graph randomization technique (Erdős and Rényi 

1959). Network randomization simulation enables formal hypothesis testing of whether the 

observed network statistics are unusually high or low given what might be expected if the same 

probability of edges (or number of edges) were connected to the same number of nodes as the 

observed network based on random chance alone.  

 

Erdős-Rényi graph models place equal probability on all graphs of a given order and size. 

That is, a collection of graphs are considered based on the provided order and size and a 

probability is assigned to each, where the total number of distinct node pairs are considered 

259 

(Kolaczyk and Csárdi 2014). An extension provided by Gilbert (1959) enables the random graph 

concept to be extended to graphs of a fixed order but where each pair of distinct nodes are 

independently assigned based on a given probability.  

260 

 

Design Group Category 

 
Site 
9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29 
Baehr SouthÙ 
0 
0 
Buckeye Bend<> 
1 
0 
CrableÙ 
1 
3 
EmmonsÚ 
0 
0 
Houston-ShryockÚ 
0 
0 
Kingston LakeÚ 
0 
2 
LarsonÚ 
0 
2 
Lawrenz Gun Club<> 
1 
0 
Morton VillageÙ 
2 
0 
Myer-DicksonÚ 
0 
1 
Orendorf CÚ 
0 
0 
Star BridgeÙ 
0 
1 
Ten Mile CreekÙ 
1 
0 
WalshÚ 
0 
1 
Total 
4 
Table 6.2 Counts of vessels by site and design category;  Ú  indicates pre-migration occupation (1200 – 1300 A.D.),  Ù indicates post-migration 

1  2  3  4 
0 
0  0  0  0 
0 
0  0  0  0 
1 
2  0  0  1 
1 
7  0  0  0 
1 
3  0  0  0 
1 
8  1  0  0 
2 
6  0  0  1 
2 
5  1  0  0 
0 
4  0  0  0 
0 
1  0  0  0 
0 
14  4  3  2 
1 
7  0  0  0 
1 
2  0  0  0 
2  0  0  0 
1 
62  7  3  4  126  4  8  14  12  10  24  11 

5  6  7 
3  0  2 
4  0  0 
23  2  3 
5  1  0 
9  0  0 
21  0  1 
13  0  0 
5  0  0 
4  0  0 
8  0  0 
2  0  0 
21  1  1 
4  0  0 
4  0  1 

0 
0 
0 
1 
0 
1 
2 
0 
0 
0 
1 
0 
0 
0 
5 
1 
1 
0 
0 
0 
0 
0 
0 
2 
0 
1 
0 
1 
6  10 

0 
0 
0 
0 
1 
1 
1 
0 
0 
0 
0 
0 
2 
0 
0 
0 
7 
0 
3 
0 
0 
0 
7 
1 
0 
0 
0 
3 
2  26 

0 
0 
1 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
0 
2 

 

2 
0 
1 
0 
1 
0 
0 
0 
0 
1 
0 
0 
4 
0 
1 
1 
3 
0 
0 
0 
0 
0 
0  13 
1 
0 
1 
0 
3  27 

0 
0 
0 
0 
0 
2 
0 
0 
0 
0 
0 
0 
0 
0 
2 

0 
0 
0 
0 
3 
1 
0 
1 
0 
0 
0 
0 
0 
0 
5 

0 
0 
0 
0 
8  10 
0 
0 
0 
0 
0 
0 
0 
1 
1 
3 
0 
0 
0 
0 
0 
0 
0  10 
0 
0 
0 
1 

8 
0 
1 
2 
1 
0 
2 
4 
1 
0 
0 
0 
3 
0 
0 

0 
1 
0 
1 
1 
0 
1 
0 
0 
0 
0 
1 
1 
1 
8 

0 
2 
0 
0 
0 
0 
0 
0 
0 
0 
5 
0 
1 
0 
1 
0 
1 
0 
1 
0 
0 
0 
2 
2 
0 
0 
0 
0 
4  11 

0 
0 
4 
0 
0 
0 
0 
0 
2 
0 
0 
0 
0 
0 
6 

0 
0 
0 
0 
0 
0 
0 
1 
0 
0 
0 
2 
0 
0 
3 

0 
0 
0 
0 
0 
0 
0 
0 
1 
0 
0 
1 
0 
0 
2 

0 
1 
1 
0 
0 
0 
1 
1 
1 
0 
0 
0 
0 
0 
5 

occupation (1300 – 1450 A.D.),  <> indicates occupation(s) that span(s) the pre- and post-migration time periods

261 

6.5 Results and Discussion: Social Identification in the Late Prehistoric CIRV 

A correlation matrix of all rescaled Brainerd-Robinson coefficients is shown in Figure 

6.8. As was apparent based on the histogram representation of the BR coefficients in Figure 6.7, 

there is a complete lack of coefficient values above 0.70, which corresponds to a raw BR value 

of 140. This result is in line with prior work in the region which indicates that town and village 

sites generally exhibit ceramic individuality (Conrad 1991; Harn 1994). Nevertheless, there is 

Figure 6.8 Correlation Matrix Heat-Map of Rescaled Brainerd-Robinson Coefficients 

 

 
 

262 

a strong cluster of BR coefficient values between the threshold of BR>0.40 and BR<0.68 with 

which to model networks of social categorical identification on either side of a circa A.D. 1300 

in-migration of Bold Counselor phase Oneota peoples into the Mississippian CIRV.  

 

Network visualizations are presented in Figures 6.9 – 6.14. Visualizations are presented 

in one of two ways. First is through the use of a multilevel layout algorithm that finds a global 

optimal layout while approximating short and long-range forces (Hu 2005). In other words, site-

nodes with strong similarities are laid out in closer proximity in consideration of all site-to-site 

relationships. The second layout method uses randomly jittered, or modified, geographic 

coordinates of sites in a geographic network rendering. In each visualization, site-nodes are 

colored and sized based on weighted degree, which is the sum of relationship (edge) weights. 

The edges connecting nodes are colored and sized by weight, or the strength of similarity in 

social identities. That is, edges that are darker green and larger reflect stronger similarities in 

categorical identification among sites, and darker green and larger site-nodes indicate that a 

given site is characterized by a high degree of proportional similarities in categorical 

identification on plates to many other sites.  

 

Several key changes are evident in central Illinois River valley network graphs as well as 

in their associated network statistical measures (Table 6.3). Perhaps the most significant change 

to network topology from the pre-migration to the post-migration CIRV is in transitivity, or the 

global clustering coefficient. As shown in the results of Erdős-Rényi random graph models for 

the Mississippian period (Figure 6.14), the transitivity value is significantly higher than what 

might be expected based on chance. In fact, transitivity in the pre-migration CIRV is higher than 

99.94% of random graphs constructed based on the same number of nodes and edges as the pre-

migration network. Transitivity is a measure of network cohesion and assesses the proportion of  

263 

  
Summary Statistics 
  Nodes 
  Edges 
  Mean Degree 
  Mean Weighted Degree 
Network Size Measures 
  Diameter 
  Mean Path Length 
Network Topology Measures 
Network Density 
Transitivity 
Degree Centralization 
Betweenness Centralization 
Closeness Centralization 
Eigenvector Centralization 

 

 

 

Pre-
Migration 
 

 

9 
24 
5.333 
2.922 

3 
1.389 

66.7% 
80.7% 
0.208 
0.219 
0.336 
0.277 

Post-
Migration 

Flattened 
Across 
Time 
 

 

 

7 
15 
4.286 
2.057 

2 
1.286 

71.4% 
72.2% 
0.286 
0.128 
0.519 
0.299 

14 
39 
5.571 
2.907 

4 
1.692 

42.9% 
64.6% 
0.264 
0.237 
0.299 
0.386 

Table 6.3 Central Illinois River Valley Social Identification Network Statistics 

 
node triads in which all three nodes are connected (Scott and Carrington 2016), capturing the 

 

notion that a ‘friend of a friend is a friend’ (Collar, et al. 2015). In the pre-migration CIRV, this 

notion holds true some 80.7% of the time, indicating an unusually highly interconnected network 

based on shared ascription to common social categories. This is perhaps best illustrated in Figure 

6.9, which shows one large cluster of highly interconnected sites with a single outlying site, 

Orendorf’s Settlement C. Orendorf is a multi-component site and one of the earliest occupied 

Mississippian town sites in the CIRV(Conrad 1991; Esarey and Conrad 1981). The dearth of 

edges to Orendorf Settlement C in the pre-migration network suggests that it may have been 

occupied prior to the regional scale expression of categorical identities on plates, especially 

given the preponderance of plates with no decoration present at the site (Table 6.2, Design Group 

Category 1). 

 

264 

Pre-Migration 
 

Post-Migration 

 

Figure 6.9 Yifan Hu multilevel network graph layout for the Pre-Migration Time Period (1200-1300 

A.D.; left) and Post-Migration Time Period (1300-1450 A.D.; right)  

Following Oneota in-migration, transitivity is no longer statistically significant (see 

 
 

Figure 6.15), indicating a reduction in the scale at which there is parity in ascription to 

categorical identities. That is, the strong tendency for triads of site-actors in the Mississippian 

phases who shared connections based on similarities in ascription to common social categories to 

become fully connected no longer held true in the post-migration CIRV. Thus, global scale 

ascription to categorical identities in the Mississippian CIRV gave way to ascription to 

categorical identities at a reduced social scale. This can be interpreted as a reduction in 

homophily, or the tendency of socially similar actors to interact more frequently than socially 

dissimilar actors, and an indication of greater regional variability in ascription to common social 

categories in the post-migration time period (McPherson, et al. 2001). Indeed, the range of the 

number of design categories present at sites sharply increases from the pre-migration to post-

265 

migration time periods, with the two sites that straddle both time periods showing an 

intermediary number of design categories present (Figure 6.17).  

Reduced homophily and/or greater regional variability in ascription to common social 

categories in the post-migration CIRV is further supported by a significant reduction in the mean 

weighted degree, or the average of the sum of all edge weights among nodes, from 2.922 to 

2.057. That is, the average similarity in social identification among sites in the post-migration 

CIRV reduces by 30% from the pre-migration Mississippian period. While the number of site-

nodes decreases overtime, the proportion of site-node connectedness actually increases relative 

to the number of sites present. Thus, while the post-migration CIRV can be characterized as a 

dense network with many transitive triads, the degree of similarity in social identities is on 

average significantly reduced from that of the Mississippian period.  

 

In considering the role of network relationships in structuring Oneota in-migration, 

comparing the geographic network renderings in Figures 6.10 and 6.11 provides key insight. A 

spatial aggregation process is evident in the post-migration CIRV, wherein regional emphasis in 

social identification processes shifted away from the Spoon and Illinois River confluence, to Ten 

Mile Creek in the north and Star Bridge in the south. Only one modest Mississippian site in the 

Spoon-Illinois confluence area, Buckeye Bend, remained occupied or saw a sequential 

occupation in the post-migration time period. The sudden depopulation of the Spoon-Illinois 

confluence suggests the formation of an internal frontier, or unoccupied interstice between 

settlements (Kopytoff 1987). The internal CIRV frontier was apparently attractive to Oneota 

migrants as the only other sites occupied in the area are multi-cultural sites marked by the 

cohabitation of Mississippian and Oneota peoples, such as Morton Village, as well as three 

modest Oneota habitation sites not able to be included in this analysis due to a paucity of plates  

266 

Figure 6.10 Geographic network graph layout for the Pre-Migration Time Period (1200-1300 A.D.) 
 

 

Figure 6.11 Geographic network graph layout for the Post-Migration Time Period (1300-1450 A.D.) 

 

 

267 

Pre-Migration 
ca. 1200 – 1300 A.D. 

Post-Migration  
ca. 1300 – 1450 A.D. 

Figure 6.12 Yifan Hu multilevel network graph layout flattened across time (1200 – 1450 A.D) 
 

 

Figure 6.13 Geographic network graph layout flattened across time (1200 – 1450 A.D) 

 

 

268 

present (Esarey and Conrad 1998). In other words, Oneota migrants followed the tendency of 

migrant peoples seen in other archaeological contexts, such as the American Southwest, to move 

into areas that were less densely settled (Mills, et al. 2016; Peeples and Haas Jr. 2013). Oneota 

in-migration therefore coincided with, and was likely in some way structured by, increasing 

regional diversity in social identification categories and a reduction in the scale of parity in social 

identification network relationships among Mississippian peoples in the CIRV. 

Internal frontiers offer many advantages for both migrant and indigenous peoples 

(Kopytoff 1987; Mills 2011). For example, Kopytoff (1987:14) emphasizes the unfolding of 

social processes occurring in internal frontiers due to its nature as an institutional vacuum. The 

low centralization scores, which assess the range of relations in social networks directed toward 

central nodes, attests to a lack of centralized authorities in either the pre- or post-migration time 

periods. From a relational perspective, densely connected and highly identity-conformist insular 

areas such as the Mississippian CIRV present significant challenges for the establishment of 

novel relationships with exogenous groups. Internal frontiers characterized by low population 

densities and a lack of central authority, on the other hand, offer opportunities for network-

mediated migration where migrants and host peoples initially form weak, or bridging, ties before 

forming stronger bonding ties based on a high-degree of within group cohesion (Granovetter 

1973; Mills, et al. 2016). However, unlike the model for ethnogenesis occurring out of this 

growth of immigrant-host settlement relationships proposed by Kopytoff (1987:6), the frontier 

internal to the post-migration late prehistoric CIRV was less likely a locus of integrative social 

capital and more likely a locus of cultural pluralism. The preponderance of weak ties formed by 

the multi-cultural populations at Morton Village and Crable as shown in Figures 6.9 and 6.11 

(i.e. ties not modeled or modeled as thin, light-green ties) suggests that the social diversity  

269 

 

 
 

 

Figure 6.14 Network randomization results for pre-migration social identification network. Observed 

statistic represents red line. Histogram shows distribution of statistic based on network randomization of 

5000 random graphs using the Erdős–Rényi random network modeling technique.  

 

Figure 6.15 Network randomization results for post-migration social identification network. Observed 
statistic represents red line. Histogram shows distribution of statistic based on network randomization of 

5000 random graphs using the Erdős–Rényi random network modeling technique. 

 

270 

imbued by Oneota peoples into the region perhaps exacerbated on-going trends toward regional 

non-conformity in social identities among Mississippian peoples. Furthermore, non-conformity 

in social identification is argued to be a delimiting factor in processes of collective social action, 

processes that can otherwise lead to social transformation at broad geographic and demographic 

scales (Mills, Clark, et al. 2013; Nelson, et al. 2011; Peeples 2011, 2018). As a result, any 

disruption to regional similarities in social identification by Bold Counselor phase Oneota 

peoples likely contributed to decreased cooperation and increased social stresses and conflict 

(Bengtson and O’Gorman 2017; G. R. Milner, et al. 1991; J. J. Wilson 2010).  

Figure 6.16 Histogram showing the range of design categories present at sites in different CIRV time 

 

periods 

Significant intra-regional mobility evidenced by the movement Late Mississippian 

 

 

peoples away from the Spoon-Illinois River confluence is posited here to have created a point of 

cultural inflection, wherein “new practices or beliefs may be adopted or when old ideas may be 

271 

more readily challenged” (Cobb and Butler 2006:334). As likely potters (Rice 2005), 

Mississippian women were active participants in the process of both expanding the range of 

social categories and challenging prior regional conformity in networks of social identification 

across the Middle to Late Mississippian transition. The introduction of design categories with 

distinctly Oneota characteristics, such as wet-paste trailed and punctate decorations, indicates 

some localized inclusivity among potter communities in indexing social identification. However 

only two sites, Crable and Morton Village, show marked evidence for this sort of inclusivity. A 

dearth or complete lack of characteristically Oneota decoration motifs at the other five town and 

village sites occupied in the post-migration time period indicates that cultural pluralism was 

largely pursued by Late Mississippian peoples in the CIRV. Perhaps it is these forces that 

intensified regional societal strife as there is no evidence, radiocarbon or otherwise, of any 

substantial settlement in the central Illinois River valley succeeding the post-migration time 

period until the proto-historic period (Esarey and Conrad 1998:52-53).  

 

In discussing macro-scale regional population movement during the 15th century in the 

American midcontinent, Cobb and Butler (2002:638) remark that “the diffusion of Oneota 

groups southward toward the Mississippian world appears to have been met with some violence 

(e.g., Milner et al. 1991), and Mississippian communities in the Illinois Valley and the American 

Bottom may have been rousted or integrated against their will.” By focusing on networks 

relationships of social identification, this research has shown that Mississippian communities 

were far from being passively rousted or integrated into Oneota communities. In fact, a much 

more nuanced cultural contact scenario is more in line with the empirical evidence presented 

here. Oneota peoples were indeed integrated in select inclusive Mississippian social contexts and 

appear to be integrative of Mississippian peoples in some of their own communities, but the 

272 

majority Mississippian population in the region largely maintained cultural pluralism while they 

perhaps grappled with internal flux in both social and demographic processes.  

 
6.6 Conclusion 

Movement of Oneota peoples into the Mississippian central Illinois River valley provides 

a unique window into the role of networks of social identification in structuring, and being 

restructured by, migration. In this regional, or micro-scale (Mills, et al. 2015), application of 

social network analyses in archaeology I have argued that Oneota in-migration coincided with 

increasing regional diversity in social identification categories, a reduction in the scale of parity 

in social identification network relationships, and intra-regional mobility toward consolidation 

among Mississippian peoples. Through the formation of a spatial and social internal frontier, 

these processes likely structured Oneota in-migration.  

Oneota social identification processes in-turn appear to have restructured Mississippian 

network relationships. The permeation of distinctly Oneota design motif categories into the 

region resulted in weak integration of multi-cultural Oneota and Mississippian sites into the 

larger post-migration identification network, perhaps exacerbated on-going trends toward 

regional variation and non-conformity in social identities among Mississippian peoples.  

Ultimately, the cultural contact between Mississippian and Oneota peoples is an example 

of unsuccessful longevity in a multi-cultural social environment. After only two or three 

generations, the CIRV was abandoned by Late Prehistoric peoples. However, the CIRV was not 

the only region in the midcontinent to witness regional depopulation in the fifteenth century. 

Coeval chiefly polities in the American Bottom, lower Ohio valley, and central Mississippi 

valley each collapsed and were abandoned during this tumultuous period (Cobb and Butler 

2002). While many analyses of societal collapse focus on environmental factors (Bird, et al. 

273 

2017; Weiss and Bradley 2001) this research offers an alternative perspective by showing 

changes in networks of social identification preceding abandonment and population 

displacement.  

 

Accepting the women were potters responsible for the plate decorations that form the 

basis of network models of social identification presented here, it can be concluded that women 

were active participants in the process of ascribing regional scale conformity to CIRV 

Mississippian social categories in the pre-migration period and then in asserting increasing 

variability overtime based on both a proliferation of social categories and decrease in 

proportional similarity among settlements in the post-migration CIRV. Bold Counselor phase 

women were likewise active in indexing ascription to distinctly CIRV Oneota social categories 

on a uniquely Mississippian ceramic vessel form. These results attest to the value of an 

inductively empirical relational perspective on processes of social identification in the past.   

 

 

 

 

 

 

 

 

 

 

 

274 

CHAPTER 7 NETWORKS OF ECONOMIC RELATIONSHIPS: RESULTS OF THE 

CHEMICAL ANALYSES  

 
 
7.1 Introduction  

This chapter presents the results of laser ablation inductively coupled plasma mass 

spectrometry (LA-ICP-MS) analysis of clay samples and Mississippian and Oneota pottery from 

west-central Illinois. This archaeological context, also referred to as the central Illinois River 

valley (or CIRV), is particularly apt for investigating social interactions through provenance 

studies as a result of a circa 1300 A.D. in-migration of Oneota peoples into a Mississippian 

chiefly environment and the compelling evidence for regional, and in places household, scale 

multicultural cohabitation among these peoples. Explaining social interrelationships in settings 

characterized by coexisting material culture traditions has been a critical concern in archaeology, 

particularly in settings where differing traditions merge, blend, or otherwise amalgamate 

(Frangipane 2015; Liebmann 2013; Stone 2003). By using ceramic chemical compositional data, 

this chapter assesses changes in patterns of economic interactions related to ceramic industry 

prior to and succeeding an in-migration in order to better understand behavioral response trends 

by both indigenous and migrant peoples to multi-cultural regional cohabitation. That is, it is 

argued that increasing parallels of membership in chemical compositional groups reflect 

increasing economic relationships among sites. Addressing direct or indirect economic relational 

interaction through the exchange of finished vessels, the sharing of raw source material location 

information, or involvement in similar ceramic production processes provides a complementary 

perspective to recent trends in archaeological network science that emphasize relationships 

modeled by technological or stylistic similarities in material culture (Birch and Hart 2018; 

Borck, et al. 2015; Hart and Engelbrecht 2012; Mills, Clark, et al. 2013; Mizoguchi 2009).  

275 

Results of network analysis and simulation indicate that the Mississippian CIRV was 

characterized by economic network interrelationships related to ceramic industry of an unusually 

cohesive nature, supporting an interpretation of regional scale economic interaction patterns. 

This pattern changed dramatically in concert with a circa 1300 A.D. in-migration of an Oneota 

tribal group into the region. The succeeding analysis indicates that post-migration ceramic 

industry economic network structure is characterized as highly dispersed with many fewer and 

weaker relationships, suggesting a reduction in the spatial and social scale at which economic 

relationships related to ceramic industry were pursued. Furthermore, network structure in the 

post-migration period is argued to be reflective of the presence of a social and spatial internal 

frontier, which was a possible outgrowth of buffer zone or other territorial boundary changes 

among Mississippian peoples in the CIRV and was likely impactful in structuring Oneota in-

migration. Finally, Mississippian and Oneota pottery were chemically indistinguishable, 

indicating that potters from both cultural groups in the Late Prehistoric period CIRV were 

utilizing similar or identical raw clay sources, engaging in similar paste preparation and ceramic 

production regimes, and discarding vessels in ways that did not result in diagenetic 

differentiation.   

 
 
7.2 Ceramic Industry Economic Relationships  

Addressing direct or indirect economic interaction related to ceramic industry is a vital 

third line of evidence to compare to network models that capture categorical identification and 

social interaction. Leveraging the criterion of abundance and circa 7 km radius ethnographic 

catchment zone for the procurement of raw clay materials (Arnold 1985; Bishop, et al. 1982), it 

is argued that as similarities of membership in different compositional groups converge between 

276 

archaeological communities, so does the likelihood that individuals from those communities 

engaged in more frequent direct or indirect economic interaction. As used here, economic 

network relationships related to ceramic industry are built around the concept of ‘weak ties’ 

(Granovetter 1973). In contrast to ties that are built on deep affinity such as family or marriage 

relationships, weak ties might be formed with acquaintances or strangers with a common cultural 

background. That is, weak ties are fertile grounds for connecting individuals within communities 

or segments of society that otherwise may not frequently interact, “providing contexts where 

categorical identities could have been expressed and contested” (Peeples 2018:64).  

Because quality clay resources are not ubiquitously available and seldom overtly visible 

in the densely vegetated central Illinois River valley, shared membership between two sites in 

groups identified through the geo-chemical compositional analysis of ceramic artifacts is 

therefore likely to be an indicator of economic interaction through behaviors reflective of weak 

ties. Direct economic interaction related to ceramic industry may take the form of behaviors such 

as the exchange of vessels or resource outcrop information sharing. While indirect interaction 

may occur through overlapping resource exploitation areas or shared paste preparation and 

ceramic production regimes. Each of these behaviors may have somewhat less influence in 

forming network relationships than other social interactions but, again, are important because 

they can connect distinct social milieu that might otherwise be partially or wholly separate.  

While exchange relationships often may be rooted in close personal relationships that are 

passed down through the generations, they are also often sporadic and unpredictable depending 

on the geographic scale at which goods were moved (Brose 1994; Ford 1972; Zvelebil 2006). At 

the inter-regional scale, material culture, and in particular burial goods, shows clear connections 

between Mississippian peoples in the CIRV and symbolically adorned exotic items characteristic 

277 

of the Southern Cult, or pan-Mississippian cosmological symbolism. These include but are not 

limited to shell gorgets, Ramey knives, copper pendants, engraved marine shell, flint clay effigy 

and figurine pipes, stone discoidals, and copper-coated earplugs (Brown and Kelly 2000; Conrad 

1989, 1991; Harn 1971, 1980, 1991; Knight Jr 1986). However, there is no currently robust 

evidence of intra-regional exchange during Late Prehistoric period CIRV. The intra-regional 

movement of ceramic vessels in particular is often rooted in ritual more so than routine (Fie 

2006; Wallis, et al. 2016). However, intra- and inter-regional quotidian ceramic vessel 

movement, and therefore the likely exchange of domestic goods or movement of individuals, is 

increasingly being recognized in the archaeological record (Gjesfjeld 2018; Golitko and Terrell 

2012; Niziolek 2013; Peeples 2018; Stoner and Glascock 2012; Stoner, et al. 2008).  

Exchange and other economic relationships are posited to primarily act to develop or 

reinforce social relationships between individuals or groups in non-state societies (Renfrew 

1984). From a cultural transmission perspective, economic relationships modeled based on geo-

chemical compositional groups may show that potters and potter communities not only resided 

within a particular geographic location, and perhaps engaged in exchange relationships, but also 

shared specific information about how to procure and prepare their raw materials (Neff 1993). 

This perspective expands upon stylistic and technological perspectives of pottery production 

because ethnographic accounts indicate that, in non-state and non-market contexts, while women 

are typically responsible for the production of vessels it is often men that are responsible for 

digging out and gathering raw clay (Rice 2005; Skibo and Schiffer 1995).  

Referring to these types of tie as economic in nature is not meant to reify or place a priori 

value upon ceramic vessels (Wallis 2009:48-54), but is rather meant to signify the 

transmutability of ceramic vessels themselves and emphasize an alternative perspective to how 

278 

relationships among individuals can be (re-)constructed in archaeological settings. Because 

ceramic vessel chemical compositions are the product of much more than simply the 

composition of raw materials, an approach is warranted that considers how a predominance of 

shared membership in chemical compositional groups may reflect behavioral interactions in an 

archaeological context. Here, I argue that an approach rooted in social network analysis (Scott 

2000) is an apt methodology for providing interpretive utility to the compositional analysis of 

ceramic artifacts. That is, social network analysis is well suited to extracting broader 

understanding from variation in compositional group membership among archaeological 

settlements because network analysis is explicitly concerned with modeling relationships and 

overall network structure. The following sections apply this approach with the goal of identifying 

behavioral nuances regarding the economic nature of ceramic industry prior to and following the 

circa 1300 A.D. in-migration of Oneota peoples into the central Illinois River valley.  

 

 
7.3 Central Illinois River valley Geology 

This section discusses the geological backdrop of the central Illinois River valley, 

particularly as it relates to the distribution of clay resources that may have been utilized by Late 

Prehistoric potters. Potential clay sources include clay or shale weathered from bedrock deposits, 

clay from alluvium and lacustrine deposits, and clay from modern soil profiles developed into 

the Peoria loess. Due to the overall trend in bedrock geological variation and available alluvium 

and lacustrine deposits as one moves from northeast to southwest along the Illinois River and its 

primary tributaries, it is hypothesized that chemical differences may characterize clay resources. 

As a result of the potential variability of the locations of usable clay resources accessible to 

prehistoric potters, chemical differences may therefore be reflected in archaeological ceramics.  

279 

Pertinent to the availability of clay for Late Prehistoric potters in the CIRV are bedrock 

features of Mississippian and Pennsylvanian geologic age that underlie much of the Late 

Pleistocene and Holocene aeolian loess deposits in the blufftops of the western Illinois Valley. 

Regionally, bedrock strata are flat-lying to gently sloping on the western margin of the Illinois 

Basin. These massive bedrock structural features follow a general northeast to southwest 

orientation. Pennsylvanian sediments underlie most of the study area, except for outcrops along 

valley walls where the Illinois River and the La Moine River cut through them and expose rocks 

of the older Mississippian system (see Figure 7.1) (Kolata 2005; Wanless 1957). Pennsylvanian 

rocks rest unconformably on strata belonging to the Burlington, Keokuk, Warsaw, Salem, and St. 

Louis formations of the Mississippian system with the resistant St. Louis limestone likely  

 

Figure 7.1 Bedrock geology map of the CIRV showing locations of archaeological sites and clay samples. 

(adapted from Kolata 2005) 

 

forming much of the uplands and the soft Warsaw shale the lowlands (Wanless 1957). Clayey 

shale with ironstone concretions overlies marine limestone in the uppermost layers of 

280 

Pennsylvanian cyclothems, or cyclical repetitions of beds. The shales in these cyclothems, as 

well as coals and sandstones appear to thin and disappear toward the southwest, with much of the 

thinning occurring within the Tradewater group (Horberg 1950). While the Spoon River eroded 

Pennsylvanian strata down to the Tradewater group, the more southerly La Moine River (also 

known as Crooked Creek) eroded completely through Pennsylvanian strata such that 

Mississippian strata are continuously exposed along it. Mississippian strata exposed by fluvial 

erosion from the La Moine primarily consist of limestones and thin beds of shale of the 

Valmeyer series.   

 

The uplands and lowlands were subsequently mantled with aeolian loess during the 

Pleistocene burying the bedrock surface. The mantling reaches 80 ft thick or more on the western 

blufftops of the Illinois Valley. The loess mantling consists of Late Wisconsin age till that 

extends southward to the Bloomington Moraine in eastern Peoria and Tazewell counties and 

Illinoisan till plain and morainal ridges that extend from the Bloomington Moraine westerly to 

the Mississippian River Valley (Figure 7.2) (Curry, et al. 2011). A final mantle of loess and 

Sangamon Geosol developed in till and pre-Wisconsin loess, mostly preserved only south of the 

Wisconsin till limit (Edwin Hajic, personal communication 2018).  

 

Loess would make an unlikely candidate for clay used in prehistoric pottery. As a result, 

clay would more likely be sourced from bedrock outcrops, alluvium and lacustrine deposits, or 

modern soil profiles developed in loess. This would inherently delimit the availability of 

potential clay sources to a certain extent, particularly for clay weathered from bedrock strata to 

locations along valley walls where alluvial or other forces expose otherwise deeply buried 

outcrops (Figure 7.1; Figure 7.2 A-A’).  

281 

 

The availability of alluvial and lacustrine clay deposits is largely related to fluvial action 

along the Illinois River, whose course and valley extent is largely the result of a single event (or 

events) known as the Kankakee Torrent. It is worth noting, however, that prior to the Kankakee 

Torrent late Wisconsin outwash aggraded the Illinois Valley floodplain, which remodeled 

 

 

Figure 7.2 Surficial deposits of west-central Illinois. Cross-section A-A’ shows the increased thickness of 

the glacial sediments approaching Lake Michigan. Adapted from (Curry, et al. 2011) 

 

282 

outwash terrace remnants remain but decrease in percent of valley area as one moves southerly 

down the valley (Hajic 1990). 

The Illinois River Valley is a dynamic fluvial system largely defined in the Pleistocene 

and Holocene by fluvial response to glaciation, deglaciation, and the ensuing interglacial 

conditions. Other significant factors influencing landscape evolution include climate and base 

level fluctuations in the Mississippi Valley. To a lesser extent, glacio-static and tectonic 

adjustments were likely impactful as well (Hajic 1990). A sequence of three depositional 

subsystem processes in the late Quaternary acted as controlling factors. First, is a Late Wisconsin 

Glacial Stage catastrophic flood subsystem. Glaciation in the upper Mississippi Valley resulted 

in early aggradation on the order of 20-25 m between 26,000 and 19,5000 C14 year B.P. At the 

end of this aggradation, the Mississippian River drainage diverted from its course in the modern 

Illinois Valley to its present valley, leading to a reworking and net incision of the valley train in 

the Illinois Valley as the Lake Michigan Lobe downwasted and retreated (Hajic 1990). 

Beginning circa 19,000 cal year B.P., catastrophic glacial lake outburst floods known as the 

Kankakee Torrent were catalyzed by a large influx of meltwater into proglacial lakes from a 

subglacial reservoir in the Lake Michigan Basin during the Haeger glacial phase of the Lake 

Michigan Lobe and unleashed immense volumes of melt-water into the Illinois floodplain 

(Curry, et al. 2014; Hajic 1990). Glacial dam breaches in the vicinity of Marseilles, IL circa 

15,500 C14 year B.P. (19,000 cal year BP) scoured the Illinois floodplain into bedrock, resulting 

in the 26-mile expanse of the Illinois River floodplain and cutting and exposure of the valley 

walls seen in the Late Prehistoric period and today. Thick sand, gravel, and sediment 

accumulation followed in the wake of the torrent. A lacustrine subsystem existed in the Illinois 

valley following Kankakee scouring. The Illinois River then developed a series of natural levees 

283 

at approximately the altitude of modern natural levees. These levees were the result of Holocene 

(9,800 – 9,700 C14 year B.P.) discharge from Lake Agassiz and an initial phase of lacustrine 

sedimentation that caused incision and terrace formation in the adjacent Mississippi Valley 

(Hajic 1990). Much of the remaining thick deposition lying at the bottom of the Illinois Valley 

lacustrine subsystem deposited by the Kankakee Torrent was then re-scoured by the Flag Lake 

paleochannel as early as or before 9,180 C14 year B.P. in the Emiquon and surrounding vicinities 

(Hajic 2006:71; Harn and McClure 2012). Over the next 3,000 – 6,000 years, the major 

lacustrine basins in the Illinois Floodplain were remodeled by fluvial action before conditions 

stabilized to those seen in the Late Prehistoric archaeological period (Harn and McClure 2012). 

During this period of major lacustrine basin stabilization, deep perennial lateral lakes evolved 

into emergent floodplains as a result of extensive erosion of loess off the surrounding uplands, 

which was deposited in valley lakes and alluvial fans (Hajic 1990).  

Subsequent post-Kankakee Torrent history of the Illinois River Valley is one of fine 

aggradation. This infers that little has changed regarding the bedrock valley wall outcrops since 

the Kankakee Torrent (circa 19,000 cal year BP) aside from the accumulation of colluvium at 

their base.  

The preceding discussion suggests an overarching regional trend of increasing variability 

in the location of accessible usable clay resources as one moves down the central Illinois Valley. 

In particular, shale or clay deposits of sufficient quality to produce pottery of Mississippian 

geologic age would likely only be accessible to potters in the south and central-south portions of 

the CIRV. While quality clay deposits of Pennsylvanian and Pleistocene age would be available 

across the valley, Pennsylvanian bedrock sediments and Pleistocene glacial till outwash 

sediments would be more abundant in the north and central-north portions of the valley. Thus, 

284 

subtle northeast-southwest chemical distinctions are hypothesized to characterize available clay 

resources and therefore sherd chemistry at different sites in the Late Prehistoric CIRV.  

 

7.4 The Ceramic and Clay Sample  

The present study intends to compositionally compare CIRV ceramics prior to and 

following Oneota in-migration in order to investigate potential changes in patterns of economic 

network relationships related to ceramic industry in the valley overtime. The sampling strategy 

employed four primary goals toward this end. First, I sought to examine pottery from major 

population centers and smaller outlying sites across the geographic and temporal expanse of the 

Late Prehistoric period CIRV (~1200 – 1450 A.D.). Second, inasmuch as possible I attempted to 

sample sherds from different contexts within a single site. Third, sherd samples were selected 

from two distinct vessel classes: domestic cooking jars and plates (or broad-rimmed bowls) 

(Conrad 1991; Harn 1994). And, fourth, for sites exhibiting ceramics with both Mississippian 

and Oneota characteristics at the household level, a representative sample of vessels with design 

elements characteristic of both cultural groups was analyzed (Esarey and Conrad 1998). This 

strategy allows estimation of variability between sites, within sites (where possible), between 

vessel classes primarily used in different social contexts (cooking/storing compared to 

serving/eating), and between cultural groups. A total of 34 clay samples were also analyzed in 

order to attempt to link patterns in raw material sources to patterns in sherd chemistry (Figure 

7.1). Finally, three shell tempering samples were analyzed as well to aid in correcting for the 

abundance of aplastic tempering material. In total, 620 samples were analyzed: 583 ceramic, 34 

clay, and 3 shell tempering. Table 7.1 provides summary information on the number and type of 

ceramic samples analyzed from each of the 18 sites included.  

285 

Due to the regional scale focus of this study in discerning patterns of economic 

relationships prior to and following an intrusive in-migration, it was necessary to sample 

ceramics from existing archaeological site-assemblages. Many assemblages derive from surface, 

amateur, or illicit collection activities such as the unfortunate whole-sale deep plowing of sites. 

This often precludes analysis of contextual within-site variation and the inclusion of other lines 

of evidence such as architectural patterns or other ancillary evidence as potential explanatory 

variables.  

 

 
 
 

 

 

Site 
Baehr South 
Buckeye Bend 
C.W. Cooper 
Crable 
Emmons 
Eveland 
Fouts Village 
Houston-Shryock 
Kingston Lake 
Larson 
Lawrenz Gun Club 
Morton Village 
Myer-Dickson 
Orendorf C 
Orendorf D 
Star Bridge 
Ten Mile Creek 
Walsh 
Total Ceramic Samples 

Jars  Plates  Total 
15 
20 
28 
55 
30 
30 
20 
30 
40 
40 
40 
58 
29 
30 
30 
29 
29 
30 
583 

6 
8 
28 
26 
15 
30 
9 
14 
20 
20 
19 
29 
13 
15 
21 
13 
24 
10 
320 

9 
12 
 
29 
15 
 
11 
16 
20 
20 
21 
29 
16 
15 
9 
16 
5 
20 
263 

Table 7.1 Distribution of pottery samples by site and vessel type 

 

 

286 

7.5 Ceramic Paste and Clay Chemical Characterization Using LA-ICP-MS  

Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and 

multivariate statistical techniques for the handling of compositional data have been described at 

length elsewhere and as a result are summarized here in truncated form (Baxter 2008, 2015; 

Bishop and Neff 1989; Dussubieux, et al. 2007; Glascock 2016; Neff 1993, 1994, 2012; Sharratt, 

et al. 2009; Speakman, et al. 2007). LA-ICP-MS was conducted at the Field Museum of Natural 

History Elemental Analysis Facility using an Analytik Jena (formerly Varian) quadrupole ICP-

MS (Elliot, et al. 2004) coupled to a NewWave UP213 laser ablation system (helium carrier gas, 

213 nm laser operated at 0.2 mJ and a pulse frequency of 15 Hz) (Dussubieux, et al. 2007).   

The clay samples collected during field survey were cleaned of visible organic and 

inorganic debris, dried in an oven set to 100 °C for four hours, and subsequently left to 

completely dry out over several weeks. Clay samples were then pulverized using a mortar and 

pestle, rehydrated with ultra-pure de-ionized water, and formed into discs. The clay discs were 

fired up to 600 °C using a Paragon Viking High Fire KilnTM with a Sentry 2.0 ControllerTM. 

Several studies suggest that firing temperature has no appreciable effect on chemical 

composition of clays (Sharratt, et al. 2009:799), however this method was followed to ensure 

consistency in pre-treatment of all clay samples.  

Ceramic sample preparation consisted of the production of a small sherd fragment by 

using channel locks to make a controlled break off a larger sherd (usually about 1-2 cm2). 

Ceramic samples were arranged in the ablation chamber perpendicular to the shell tempering 

present in order to avoid temper grains or other aplastic inclusions. Ablation was constrained to 

the center portion of each sherd so that analysis concentrated on pastes as opposed to slips, 

paints, or other surface contamination on the exterior or interior of the sample sherds.  

287 

Protocols established for the Field Museum’s Elemental Analysis Facility were followed 

for LA-ICP-MS analysis (Dussubieux, et al. 2007; Golitko 2010; Golitko and Terrell 2012; 

Niziolek 2013; Vaughn, et al. 2011). Clay and ceramic samples were subjected to laser ablation 

with a spot size of 150 !m. Every effort was made to avoid temper grains or other aplastic 

inclusions during ablation location selection. A blank measurement and National Institute of 

Standards and Technology (NIST) standards n610, n612, and Brick Clay (n679) were run at the 

beginning of the day and after every five or six samples to aid in concentration calculations and 

control for any drift in accuracy or precision of measurement. Error values were established 

through the analyses of New Ohio Red clay, which was subjected to the same protocols as the 

standard samples (Sharratt, et al. 2015).  

Using silica (29Si) as an internal standard to control for the time variability in ablation 

efficiency and resulting signal strength, each sample was ablated in 10 distinct locations and 

each standard ablated in 5 distinct locations. Each sample ablation measurement consists of nine 

replicates (scans of the entire elemental mass range of measured elements). The first three of the 

replicates are removed during data processing to account for any potential surface contamination 

and to allow the signal time to stabilize. The remaining replicates are averaged to produce raw 

count-per-second signal strengths for each ablation location. Concentrations were then calculated 

by subtracting blank measurement values and internal standardization of elemental signals using 

silica. The resulting signals were averaged after the deletion of extreme outlier values on an 

element-wise basis. Outlier measurements often result from the accidental targeting of temper 

and other aplastic inclusions or occasional large influxes of trace element ions into the detector 

relative to silica. Concentrations were then calculated using a linear least-squares fit regression 

288 

line derived from the silica-normalized signals for the standard reference materials (Golitko 

2010; Gratuze, et al. 2001).  

Isotopes of 60 major, minor, and trace elements were measured (7Li, 9Be, 11B, 23Na, 

24Mg, 27Al, 29Si, 31P, 35Cl, 39K, 44Ca, 45Sc, 49Ti, 51V, 53Cr, 55Mn, 57Fe, 59Co, 60Ni, 65Cu, 66Zn, 75As, 

82Se, 85Rb, 88Sr, 89Y, 90Zr, 93Nb, 95Mo, 107Ag, 111Cd, 115In, 118Sn, 121Sb, 133Cs, 137Ba, 139La, 140Ce, 

141Pr, 146Nd, 147Sm, 153Eu, 157Gd, 159Tb, 163Dy, 165Ho, 166Er, 169Tm, 172Yb, 175Lu, 178Hf, 181Ta, 

182W, 197Au, 206,207,208Pb, 209Bi, 232Th, 238U). A number of elements have been observed as being  

  
Li 
Be 
B 
P 
Cl 
Sc 
Ti 
V 
Cr 
Mn 
Fe 
Ni 
Co 
Cu 
Zn 
As 
Rb 
Sr 
Zr 
Nb 
Ag 
In 
Sn 
Sb 
Cs 

 

Average 

  
130.196  ± 
3.157  ± 
136.131  ± 
327.149  ± 
286.325  ± 
21.596  ± 
5488.957  ± 
213.309  ± 
88.854  ± 
256.581  ± 

SD  %RSD 
11% 
14.13 
10% 
0.31 
28.26 
21% 
74% 
241.26 
117% 
334.25 
4.08 
19% 
24% 
1316.82 
11% 
23.90 
8.00 
9% 
12% 
30.86 
37% 
28174.564  ±  10405.83 
11% 
8.25 
2.97 
13% 
187% 
57.26 
15% 
17.05 
4.55 
28% 
13% 
24.66 
22% 
16.43 
47.59 
32% 
16% 
3.86 
150% 
0.32 
0.03 
21% 
26% 
1.06 
105% 
1.92 
1.75 
15% 

77.784  ± 
23.067  ± 
30.542  ± 
116.666  ± 
16.550  ± 
195.345  ± 
73.393  ± 
146.909  ± 
24.565  ± 
0.213  ± 
0.132  ± 
4.162  ± 
1.828  ± 
11.352  ± 

  

  
  Ba 
  La 
  Ce 
  Pr 
  Ta 
  Au 
  Y 
  Pb 
  Bi 
  U 
  W 
  Mo 
  Nd 
  Sm 
  Eu 
  Gd 
  Tb 
  Dy 
  Ho 
  Er 
  Tm 
  Yb 
  Lu 
  Hf 
Th 

  

Average 

  

582.686  ±  73.60 
46.084  ±  14.68 
106.478  ±  29.23 
4.04 
12.119  ± 
0.34 
1.799  ± 
0.037  ± 
0.08 
9.79 
32.090  ± 
4.14 
17.892  ± 
0.676  ± 
0.52 
0.80 
3.289  ± 
0.54 
2.959  ± 
1.240  ± 
0.20 
37.954  ±  13.02 
2.60 
7.465  ± 
0.52 
1.596  ± 
6.112  ± 
2.17 
0.28 
0.993  ± 
1.35 
5.359  ± 
1.211  ± 
0.34 
0.74 
3.131  ± 
0.15 
0.515  ± 
3.218  ± 
0.80 
0.16 
0.559  ± 
2.92 
5.238  ± 
16.214  ± 
3.79 

SD  %RSD 
13% 
32% 
27% 
33% 
19% 
212% 
31% 
23% 
77% 
24% 
18% 
16% 
34% 
35% 
32% 
36% 
28% 
25% 
28% 
24% 
29% 
25% 
29% 
56% 
23% 

Table 7.2 Elemental summary statistics measured across 131 replicates of New Ohio Red clay 

289 

 
unreliably measured overtime at the EAF laboratory due to such factors as oxide interferences, 

high ionization energies, or measurements close to instrumental detection limits, and as such 

were removed from statistical analysis (35Cl, 75As, 82Se, 107Ag, 178Hf, 197Au, 209Bi). New Ohio 

Red clay standards indicate that additional elements display consistent differences across 

analyses and were also removed from statistical analysis as a result (31P, 65Cu, 121Sb). New Ohio 

Red clay was analyzed using the same protocol as the NIST standards and provides a means to 

assess error values associated with analysis and to maintain consistency between analyses. Table 

7.2 lists these approximated error values as average elemental concentration in ppm, standard 

deviation, and percent relative standard deviation. Relative standard deviations are a reflection of 

the heterogeneity inherent in clay (Neff 2003) as well as the large number of New Ohio Red clay 

standard runs (n = 131) over the course of many years of analysis (2015 – 2018). In addition, 

137Ba was shown to have markedly increased values in ceramic samples compared to clay 

samples, likely as a result of post-burial absorption of mobile cations in the presence of zeolite 

formation (Golitko 2010), and was subsequently removed from analysis. 

 

7.5.1  Controlling for Shell Tempering 

 
Both Oneota and Mississippian potters in the Late Prehistoric period CIRV almost 

exclusively used burned and crushed mollusc shell as an aplastic inclusion to improve 

performance characteristics of pottery (Conrad 1991). These benefits include improved 

workability of clay during the vessel formation process (Feathers 2006), increased strength and 

toughness (Feathers 1989), and increased thermal shock resistance of the finished vessel 

(Steponaitis 1983, 1984; Tite, et al. 2001). Shell tempering was shown to have no discernible 

‘leachate’ effect as alkali processor of maize (A. J. Upton, et al. 2015). However, improved 

290 

workability and performance characteristics provide clear advantages to the use of shell 

tempering over prior grog, sand, or limestone tempers based on increased demands of food 

processing and production among maize horticulturalists and agriculturalists.  

To understand localized geochemical patterning in mollusc shell, three samples of shell 

temper grains were subjected to LA-ICP-MS. Tempering samples derived from sherds recovered 

from three sites that span the geographic expanse of the CIRV – one sample from Kingston Lake 

in the northerly portion of the valley, one sample from Myer-Dickson in the center of the valley 

at the Spoon and Illinois River confluence area, and one sample from Lawrenz Gun Club in the 

southerly portion of the valley. Calcium comprises 96-97% of the geochemical composition of 

shell and as a result was removed from statistical analysis. For the minor and trace elements, 

only Strontium and Barium register a noticeable chemical presence in shell and as a result were 

also removed from statistical analysis. A further mathematical correction was applied to account 

for the presence of shell-temper derived calcium for ceramic samples.  

Despite my best efforts, shell tempering embedded in the ceramic matrix was frequently 

ablated during sample analysis. These sampling errors were straightforward to detect when 

examining individual ablation ICP-MS assessments, which showed high calcium and strontium 

values in particular relative to other ablation assessments. Given this differential impact of shell 

tempering on sample chemical compositions, a mathematical correction was applied to remove 

the impacts of shell tempering on compositional measurements. The mathematical correction 

used here differs from that applied by scholars working with INAA data from shell tempered 

ceramics due to the fact that LA-ICP-MS is not a bulk compositional analysis technique when 

analyzing an inherently heterogenous material such as ceramic matrix (Cogswell, et al. 2015). 

While there is a degree of error related to the spot-sampling procedure of LA-ICP-MS based on 

291 

inherent sample variability, a number of studies demonstrate that this loss of precision does not 

prohibit an adequate characterization of the clay fraction of ceramic samples and generally 

replicates the results of INAA (Cochrane and Neff 2006; Dussubieux, et al. 2007; Golitko 2010; 

Wallis and Kamenov 2013).  

In LA-ICP-MS analysis, constituent atoms are measured directly, but the use of silica as 

an internal standard results in raw measurements as ratios of elements to silica. As a result, a 

means of independently calculating silica concentrations is needed, the customary approach of 

which is to sum all element signals and assume that these account for approximately 100% of the 

sample matrix. Because all major oxides can be quantified directly aside from oxygen, oxide 

multipliers are used to account for its otherwise unmeasured contribution to the sample and the 

remaining portion is assumed to be accounted for by silica. Parts per million or oxide percentage 

concentrations for all elements are then calculated by multiplying through the resulting silica 

concentrations (Golitko 2010; Gratuze, et al. 2001). As a result, to mathematically correct for the 

differential presence of calcium, which is measured as an oxide, all other elements measured as 

an oxide percentage are summed aside from calcium for each sample. The elemental or percent 

oxide signature of every other element is then divided by this amount on a sample by sample 

basis. Thus, for samples that were not negatively impacted by erroneous ablations of shell 

tempering (i.e. low calcium concentrations), little to no correction is applied to measured 

elemental concentrations, while the inverse is true for samples highly negatively impacted by 

erroneous shell ablations.  

 

7.5.2  Statistical Routines in the Analysis of Geochemical Data  
 

292 

The statistical approach taken here mirrors an approach that has become somewhat 

standardized in the analysis of chemical compositional data in archaeology (Baxter and Buck 

2000; Bishop and Neff 1989; Glascock 1992, 2016; Harbottle 1976; Neff 1994). The following 

discussion provides an overview of these methods in general but with a particular focus on the 

analysis of ceramic artifacts. Originally developed by Sayre and colleges during the 1970s at 

Brookhaven National Laboratory, the primary goal of multivariate statistical analysis routines is 

the identification of compositionally homogenous groups among observed samples and to link 

those groups to a source location. Depending on the type of artifact, however, compositional 

groups may reflect different ‘sources’. That is, a source of origin may refer to a circumscribed 

exposure of geologic raw material or to a production locale or workshop. In other words, 

samples derived from different raw materials necessitate different provenance determination 

strategies. Here, I refer to these distinct methods as ‘natural source’ and ‘production source’ 

methodologies.  

‘Natural source’ grouping methodologies are used for non-chemically altered artifacts 

such as obsidian, gemstones, flint, basalt and the like. Raw materials from various outcrop 

locations are collected, analyzed, and used to create statistically valid compositional groups. 

Artifacts are then compared to these natural source reference groups in order to identify the most 

likely geologic source of origin for each artifact (Glascock 2016). This method follows the 

provenance postulate, which states that chemical variation between raw material source locations 

must surpass variation with a single source (Weigand, et al. 1977). On the other hand, because 

raw material processing and production systems can alter the chemical composition of artifacts 

such as pottery, glass, coins, smelted copper, or bricks, a different approach is required. 

Statistically valid compositional groups are constructed from the elemental profiles of artifacts 

293 

themselves. Different production sites are then inferred based on the criterion of abundance, 

which assumes that if a majority of samples in a statistical cluster originate from the same 

archaeological site or area, then the raw material source is likely in proximity to that site or area 

(Bishop, et al. 1982; Gjesfjeld 2014; Rice 2005). In the case of pottery, the criterion of 

abundance is often coupled with ethnographic data suggesting that a vast majority of potters 

obtain clay from sources within seven kilometers of their settlements (Arnold 1985). I refer to 

this as a ‘production source’ methodology.   

In either methodology, the end result are statistically valid “reference groups” that are 

expected to represent the limits of chemical variability associated with artifact production in a 

given location or region (Bishop, et al. 1988:318; Speakman, et al. 2008). In the present research, 

both of these approaches are followed to a certain extent, however a ‘production source’ 

methodology is primarily employed. That is, a clay survey was undertaken to provide a baseline 

for statistical patterning in raw clay materials in order to inform statistical grouping of ceramic 

artifacts.  

Geographic spatial resolution in interpretations of compositional clustering is entirely a 

function of geological variability in the study area and, for pottery, the extent to which potters 

systematically altered baseline clay chemical composition through paste preparation techniques 

or ‘recipes’. Nearly all clays are characterized by a narrow range of geochemical variability, and 

the near ubiquity of clay on the landscape often complicates the scale at which reference groups 

may be defined (Golitko 2010). Fine grained resolution is possible. For example, a study from 

Luzon in the Philippines identified both community scale as well as regional scale geochemical 

patterning, shedding light on a factionalized pottery industry enveloped in elite competition 

(Neupert 2000). In archaeological contexts that lack ethnographic insight regarding production 

294 

systems and source material locations, regional scale chemical patterning that follows such 

geographic features as river drainages, valleys, lower and higher elevations in mountainous 

regions, or islands is more often observed (Cochrane and Neff 2006; Emberling and Minc 2016; 

Golitko 2010; Lazzari, et al. 2017; Peeples 2018; Sharratt, et al. 2009; Sharratt, et al. 2015). 

Equivocal results can be observed in cases of small sample sizes and substantial geological 

complexity (Fitzpatrick, et al. 2006) 

The statistical workflow utilized for compositional analysis in archaeology is displayed in 

Figure 7.2. In particular, this workflow includes: 1) data pre-treatment that involves 

normalization or standardization of elemental values and missing data imputation, 2) 

visualization and statistical exploration of the data set to assess patterning amenable to group 

formation, 3) preliminary reference group construction, 4) statistical assessment of group 

membership probabilities and an iterative process of sample reassignment, 5) formation of core 

groups, outgroups, and attribution of unassigned samples, and 6) sub-group refinement where 

possible (Gjesfjeld 2014; Golitko 2010; Peeples 2011). A suite of statistical methods referred to 

as supervised and unsupervised learning are used in these processes. Supervised learning 

techniques are used in ‘natural source’ grouping methodologies because the raw material source 

locations are already known, providing an inherent structure to the data. With unsupervised 

learning techniques, which are used in ‘production source’ grouping methodologies, the model or 

structure of the data is not known in advanced. As such, all variables are treated as equally 

potential sources for patterned variation. Within that patterning groups are formed. For the 

present analysis on clay sediments and archaeological ceramics, unsupervised learning 

techniques are used within a production source group recognition methodology. Formal 

295 

multivariate statistical analysis was carried out in the R statistical platform, version 3.3.2, with 

some data handling in Excel. All R code is provided in Appendix C.  

 

 

Figure 7.3 Statistical workflow for the analysis of compositional data 

Beginning with retained chemical measurements, which are expressed as parts per 

million values, any missing values are first imputed using a variety of imputation methods such 

as random forest or predictive mean matching. Missing values often arise for particular elements 

when they are close to the detection limits of the analytical technique employed. For the present 

analysis using LA-ICP-MS elemental readings, these elements were removed from consideration 

and as a result no imputation was necessary. Retained chemical measurements are then converted 

to base-10 logarithms in order to account for scalar effects related to the orders of magnitude 

differences in concentrations across the different elements. Once data have been scaled 

appropriately and contain no missing values, the next step is exploratory visual analysis to search 

for potential patterning and begin forming exploratory chemical groupings. For this purpose, 

histograms, bivariate plots, compositional profile plots, and 3D scattergrams provide apt 

visualizations for inspection. Histograms might show multimodality, bivariate plots or 3D 

scattergrams might show patterning in sample densities, and compositional profile plots might 

show deviations from centroid masses. This process can be time consuming and show little in the 

way of recognizable patterning, however. For example, when analyzing biplots, there are p(p-

1)/2 possible plots to analyze, where p is the number of elements. In the present analysis, where 

296 

44 elements are retained, that equates to some 946 biplots to investigate. As a result, a statistical 

means of dimensionality reduction is necessary in order to express patterned variation along 

multivariate dimensions in a visually interpretable format in at most two or three dimensions. 

Collectively referred to as ‘ordination’ or ‘gradient analysis’, these methods order similar objects 

near each other and dissimilar objects further away. Similarity and dissimilarity in ordination 

takes into account relationships across the multiple variables observed.  

The primary ordination technique used in archaeological compositional analysis is 

principal components analysis (PCA). Because many elements have positive correlations with 

one another, PCA is an apt technique for compositional analysis in archaeology. That is, if any 

two given elements are highly correlated, they can be expressed by a single variable without a 

significant loss of information (Golitko 2010). In this way, PCA acts to reduce the number of 

variables in the data set and therefore simplify the structure of compositional data.  

In short, the goal of PCA is to transform the original multivariate data into a new 

representative dataset that explain as much of the variance as possible in the original data in a 

minimum number of variables. Orthogonal transformations convert potentially correlated 

variables into a set of linearly uncorrelated variables referred to as principal components (Baxter 

1995; Glascock 2016; Shennan 1997). Transformations proceed in such a way that the first 

principal component accounts for the largest possible variance (or variability in the data). Each 

successive principal component has the highest possible variance orthogonal (or perpendicular) 

to each preceding component. Components are calculated in this way until the number of 

components matches the original number of variables. This necessitates that there are at least as 

many observations as variables when conducting PCA, though many more observations than 

variables are necessary to obtain robust results.  

297 

In addition to providing principal components that contain maximal data set variation in a 

minimum number of variables, PCA provides a matrix of eigenvalues that express the total 

amount of original variance explained by each component and an indication of the original 

variables responsible for that variation (or component loadings that show how strongly correlated 

each original variable is to each principal component). This gives an indication of the amount of 

variance accounted for by each principal component, individually and cumulatively. Variance 

explained is often visualized using a scree plot. For most applications in archaeology, principal 

components should be retained until they reach 90% of cumulative variance explained, which is 

often along many fewer dimensions that in the original data set. PCA therefore allows for 

investigation of the chemical compositional structure in the data, in the absence of information 

known a priori.  

Simultaneous R-Q Mode Factor Analysis extends the functionality of PCA by allowing 

component loadings and sample scores to be visualized on a single biplot. By reducing the 

dimensionality of the data while maximizing the variance retained in each dimension and 

providing a sense of original variable component loadings, it is possible to visualize a significant 

amount of information that would otherwise be spread across multiple plots. Not only is it 

possible to test hypothetical group separation across multiple dimensions in a single plot, but it is 

also straightforward to determine which elements (or original variables) are most responsible for 

any observed group separate and how elements are correlated with one another. While it is 

tempting to assume that the first principal component, which expresses the largest amount of 

correlated variability in the dataset, is the most influential in contributing to group patterning, 

this is not always the case. Loadings on the second, third, fourth and so on principal components 

may in fact contribute more to patterning that is significant to anthropological, archaeological, or 

298 

geological research questions. At the same time, clear group separation may not be evident in 

principal components, even if they are well separated in multivariate space.  

With either scaled elemental data or principal components, the next step is to begin 

statistical classification of observations into separate groups. It is often instructive to use a priori 

information about sample observations to inform the validity of statistical group formation. 

Information in this regard might include archaeological site of origin, river drainage of origin, 

bedrock parent material, artifact type, artifact chronological positioning, type of temper or 

surface treatment, or a host of other potential grouping features. These features can be 

incorporated into biplot visualizations of principal components or scaled elemental data to gain 

insight into potentially statistically meaningful clustering, much in the same way that a machine 

learning engineer seeks out sensitive features for training artificial intelligence algorithms. Once 

assumptions or hypotheses are formed as to the role of individual features in group separation, 

they can be tested using statistical clustering methods. A variety of unsupervised classification 

methods are available to form initial compositional clusters, which can then be refined into 

statistically robust groups. Common classification methods include hierarchical cluster analysis, 

hierarchical divisive clustering, k-means clustering, and k-medoids clustering (Leonard Kaufman 

and Rousseeuw 1990b; Shennan 1997). Neff (2002) recommends applying multiple methods and 

treating the resulting groups as hypotheses to be evaluated using addition statistical testing. 

Groups of samples that are consistently grouped across multiple methods are most likely to stand 

up to statistical group refinement.  

Hierarchical cluster analysis (or HCA) models hierarchical relationships between samples 

based on a linkage criterion. A measurement of statistical similarity is required to provide a sense 

of the relative distance between pairs of observations and guide hierarchical classification. 

299 

Similarity measures assess the relative distance between samples across multivariate hyperspace, 

and include such metrics as Euclidean distance, squared Euclidean distance, Manhattan distance, 

Minkowski distance, Mahalanobis distance, or Brainerd-Robinson distance (Leonard Kaufman 

and Rousseeuw 1990b). A linkage criterion is then used model heterarchical and hierarchical 

relationships in the data based on algorithmic interpretations of pairwise distances between 

observations. Linkage criterion include complete-linkage clustering, average linkage clustering, 

Ward’s Method, or Ward’s Square Method (Leonard Kaufman and Rousseeuw 1990b). Average-

linkage and Ward’s Method are the most commonly employed in archaeological compositional 

analysis. Average-linkage merges the pair of samples with the highest cohesion and defines 

similarity between clusters as the average distance between all possible pairs of cases, one from 

each cluster (Baxter 2015). While Ward’s method attempts to minimize the error sum of squares 

when joining individuals or groups in the clustering process in order to ensure that groups remain 

as homogenous as possible (Shennan 1997:241-245).  

Regardless of the technique employed, the results of clustering analysis can be 

considered as an additional feature in the data set alongside any previously known information 

about the samples. The next steps in the statistical procedure is to statistically assign sample 

observations to preliminary compositional groups and refine them into statistically robust 

compositional groups. The basic idea is to analyze group members to determine if they are more 

similar to each other than they are to samples in other chemical groups. A two-step procedure is 

followed in archaeological compositional analysis to assess and refine group membership.  

Mahalanobis distance is first calculated for each sample. “Mahalanobis distance is 

effectively comparing samples to sample groupings by converting these to standard distributions 

(i.e. multivariate normal) by dividing the multivariate mean (centroid) by the multivariate 

300 

standard deviation (variance-covariance matrix)” (Golitko 2010:243-244; Harbottle 1976:57). In 

other words, Mahalanobis distance is equivalent to measuring the number of standard deviations 

and the group mean along each principal component axis (Glascock 2016). Hotelling’s T2 

statistic, which is the multivariate equivalent to a Student’s t-test, is then employed to calculate 

the probabilities of membership of each sample to every group (Shennan 1997). That is, the 

Hotelling’s T2 statistic is transformed into the related F value and compared to the F-distribution. 

Confidence intervals can then determine a given level of statistical probability that an unassigned 

sample is derived from the same underlying population as the reference group to which it is 

being compared (Bishop and Neff 1989; Golitko 2010). A jackknife procedure is employed in 

the process whereby each sample is removed from the group before being assessed for its own 

probability of group membership. While the jackknife procedure aids in avoiding bias, it does 

come with some drawbacks in that the groups being evaluated must contain at least two more 

members than the number of variables included in the dataset (Neff 2002). In the present analysis 

with 44 elements, the minimum group size for statistical evaluation using multivariate elemental 

concentration data would be 46 samples. Groups with too few samples to achieve this threshold 

for elemental data can be compared against principal component data. This is often used to 

assess the presence of subgroups within larger groups. As a general rule of thumb, “groups are 

most robust when the number of members included substantially exceeds the number of elements 

or principal components considered” (Peeples 2011:112). Multivariate probabilities using the 

jackknife procedure therefore provides a robust method for comparing a sample to potential 

chemical or principal component groups because the probabilities simultaneously take into 

account all, or most, features in a data set.  

301 

Assigning samples to core reference groups in this way is fundamentally a means of 

constructing statistically valid groupings. However, there are no set cutoffs for probability values 

that are systematically employed in archaeological compositional analysis for assigning samples 

to groups. There are, however, two heuristics that can be used when deciding upon group 

membership criteria. The first is a consideration of the probability that a sample is a member of 

the group to which is has been assigned initially. The second is a consideration that a sample is 

not a member of the group to which it has been assigned initially, or the probability of 

membership in any other group. It is best to apply both of these heuristic criteria at the same 

time. For example, applying a common threshold minimum for probability of in-group 

membership while also applying a common threshold maximum for probability of out-group 

membership. All samples that fail to meet both thresholds become unassigned. This process is 

iterated until no additional samples need to be unassigned. It is often customary to visualize the 

core group samples with unassigned samples projected in the same visualization. Should any 

unassigned samples merit inclusion in a core group, they may be incorporated and the process 

continue until group membership is sufficiently stabilized.  

An alternative heuristic in determining group membership probability using Mahalanobis 

distance and the Hotelling’s T2 statistic that is often employed is to initially treat the entire 

sample as a single group. Probabilities of group membership are assessed and any samples with 

less than a 1% probability of membership in the single group cluster are removed. This process is 

then iterated until no additional samples warrant removal. Retained samples are then considered 

to comprise a statistically robust core group with similar chemical compositions and can 

typically be related to a ceramic production system at some geographic scale. Unassigned 

302 

samples are projected against the core group to determine if any warrant inclusion in the core. 

This process iterates until group membership is stabilized.  

Unassigned samples, which often comprise 30 – 60% of samples in a production source 

grouping methodology (Neff 2002; Peeples 2011:114), can be assessed for statistical assignment 

beyond the core groups. Since non-core group sizes rarely reach the amount necessary for using 

the Hotelling’s T2 statistic on elemental data, principal component data accounting for at least 

90% of the observed variability in the elemental data are used. There are several potential 

interpretations for samples left unassigned: “they may be derived from sources not represented 

among the defined groups; they may be statistical outliers from one of the identified groups; or 

they may represent anomalous paste preparation or diagenetic effects” (Neff 2002:33).  

With core and unassigned groups defined, analysis proceeds by using the aforementioned 

statistical clustering methodologies and a priori information about samples to find additional 

structure within the core and unassigned samples.  

Another method for non-core assignment, or for the testing of core group separation, is 

canonical discriminant function analysis (or CDA). With CDA, the analyst imposes group 

patterning on the dataset. CDA assumes groups to be discrete and that all samples are members 

of those discrete groups. CDA then identifies axes of maximal separation between the groups, 

which are based on a number of linear functions (Shennan 1997:350-351). Probabilities for 

group membership can then be assessed for unassigned samples. However, group assignments 

made using CDA are less statistically rigorous than assignments made using elemental 

concentrations or principal components analysis (Bernardini 2005; Neff 2002).  

 

 

303 

7.6 Results of the Clay Analyses 

Samples of clay were gathered from deposits along the central Illinois River and its 

tributary streams and backwater lakes as well as a handful of roadcuts and small subset of core 

samples. Bulk mineralogical assessment and clay speciation using x-ray diffraction performed by 

the Advanced Materials Characterization Center at the University of Cincinnati on a subset of 

samples confirmed that the majority of samples were consistent with clay minerals (see 

Appendix G). The bulk mineralogical profile of clay samples collected from both outcrop and 

core contexts are very similar to sherd mineralogy aside from the lack of measurable swelling 

smectite and kaolinite due to the ceramic firing process. However, a number of samples were 

removed from the dataset because of high calcite content. The results presented below refer to 32 

clay samples.  

The objective for statistical analysis of clays was to provide a baseline of clay 

heterogeneity in the study region and to provide exploratory insights for the statistical analysis of 

a much larger sample of ceramic artifacts. While analysis of the compositional data from such a 

small sample size prohibits statistically robust groupings, some general trends are notable. 

General patterning suggests the presence of two clay profiles, with some evident overlap 

between them. Because clay samples were collected primarily from fluvially eroded lithographic 

profiles below aeolian Quaternary deposits, I propose that the groups result from hypothesized 

northeast-southwest chemical distinctions in available clay resources eroded from geologic 

bedrock parent materials. That is, clays from Mississippian formations would like only be 

available for extraction in the southern portion of the central Illinois River valley while 

Pennsylvanian formation and Pleistocene glacial till outwash clays would be present in higher 

concentrations in the northern portion of the central Illinois River valley (see Figure 7.1). The 

304 

Spoon and Illinois River confluence, or approximately 40°18’14.7” N latitude, was identified as 

the most notable line of demarcation between the clay compositional profiles. However, it is 

important to again emphasize that this is an exploratory hypothesis and not a statistically or 

geologically significant proposition.  

Illinois Valley 
clay north of   
Spoon/Illinois 
River 
confluence  

Illinois Valley 
clay south of 
Spoon/Illinois 
River 
confluence  

 

Figure 7.4 Principal components biplot showing the distinction between the two clay groups identified. 
Ellipses represent 90% confidence intervals for group membership. The first two principal components 

account for 66.5% of the variance in the clay data set. 

 

A biplot of principal components scores and loadings on the first two principal 

components, accounting for 66.5% of the total variance in the clay data set (Figure 7.4), shows 

the distinction between clays from north of the Spoon and Illinois River confluence and clays 

from south of the Spoon-Illinois confluence. Enrichment in most elements characterizes the 

305 

northerly clays, while southerly clays show relative depletion in most elements but a slight 

enrichment in Mo, Na, and Si relative to the northerly clays.  

 

Bivariate plots comparing individual elements better demonstrate group separation 

between the northerly and southerly clays analyzed in the central Illinois River valley. Southerly 

clays have low Be, Li, Cs, and Ni values compared to clays collected in and to the north of the 

vicinity of the Spoon-Illinois River confluence. Some overlap is present as a result of the 

demarcation of a latitudinal boundary in a dynamic fluvial environment. The positive linear  

Illinois Valley 
clay south of 
Spoon/Illinois 
River confluence  

Illinois Valley 
clay north of   
Spoon/Illinois 
River confluence  

 

Figure 7.5 Bivariate plot of logged (based 10) Beryllium and Lithium showing distinctions between the 

two clay groups. Ellipses represent 90% confidence intervals for group membership. 

 
 
relationship between Li and Be shows a general pattern of decreasing enrichment in these 

elements as one moves down valley in general from the northeast portion of the CIRV to the 

306 

southwest. A positive linear relationship also holds true for Nickel and Cesium, though with 

significant heteroscedasticity.  

 

 

 

Illinois Valley 
clay north of   
Spoon/Illinois 
River confluence  

Illinois 
Valley clay 
south of 
Spoon/Illinois 
River 
confluence  

Figure 7.6 Bivariate plot of logged (based 10) Cesium and Nickel showing further chemical distinctions 

between the two clay groups. Ellipses represent 90% confidence intervals for group membership. 

 

Calculation of statistical probabilities of group membership with such small samples 

sizes would be unreliable at best and misleading at worst. It is important to again emphasize that 

the analysis on a small sample of clay sediments is exploratory in nature and designed to provide 

insight to guide statistical analysis on a much larger sample of ceramic artifacts. Indeed, a 

general trend of decreasing enrichment in most elements as one moves from the northeast to 

southwest Illinois River valley is noted. This trend is shown visually in Figures 7.4 – 7.6 and 

numerically in Table 7.3  

307 

51040.2  ±  7488.0 

20202.9  ±  4362.4 

5.4  ±  1.5 
1.1  ±  0.3 
0.1  ±  0.0 

14125.1  ±  9630.8 
996.5  ±  365.1 

33.5  ±  9.4 
44.0  ±  9.9 
0.5  ±  0.2 

Average 
Std Dev 
68495.2  ±  9681.7 

  

67.3  ±  25.0 
2.1  ±  0.4 
72.4  ±  20.0 
18.8  ±  6.3 
99.5  ±  109.8 
5.6  ±  1.5 
5.1  ±  1.6 
3.0  ±  1.0 
1.4  ±  0.4 

Northerly Illinois Valley Clay (n = 25)  
  
Al 
B 
Be 
Ce 
Co 
Cr 
Cs 
Dy 
Er 
Eu 
Fe 
Gd 
Ho 
In 
K 
La 
Li 
Lu 
Mg 
Mn 
Mo 
Na 
Nb 
Nd 
Ni 
Pb 
Pr 
Rb 
Sc 
Si 
Sm 
Sn 
Ta 
Tb 
Th 
Ti 
Tm 
U 
V 
W 
Y 
Yb 
Zn 
Zr 

0.5  ±  0.2 
4.4  ±  2.5 
126.4  ±  24.4 
1.7  ±  0.5 
29.9  ±  7.2 
3.2  ±  1.3 
139.2  ±  27.6 
220.9  ±  201.3 

21.2  ±  6.4 
31.8  ±  8.7 
44.3  ±  10.1 
24.7  ±  6.7 
9.6  ±  2.6 
124.4  ±  19.5 
13.9  ±  2.5 

6.5  ±  1.8 
2.3  ±  0.5 
1.3  ±  0.3 
0.8  ±  0.2 
11.0  ±  4.2 

1.7  ±  0.7 

7768.3  ±  2073.5 

340711.5  ±  18112.9 

5075.4  ±  1188.7 

Southerly Illinois Valley Clay (n = 7)  
  

Average 
Std Dev 
55977.5  ±  3976.5 

  

  
 
  Al 
B 
 
 
Be 
Ce 
 
Co 
 
 
Cr 
 
Cs 
  Dy 
Er 
 
 
Eu 
 
Fe 
  Gd 
  Ho 
 
In 
  K 
La 
 
 
Li 
 
Lu 
  Mg 
  Mn 
  Mo 
  Na 
  Nb 
  Nd 
  Ni 
Pb 
 
Pr 
 
Rb 
 
 
Sc 
Si 
 
Sm 
 
Sn 
 
 
Ta 
Tb 
 
Th 
 
 
Ti 
 
Tm 
  U 
  V 
  W 
  Y 
  Yb 
 
Zn 
   Zr 

48.1  ±  24.8 
1.4  ±  0.3 
51.1  ±  9.5 
14.5  ±  1.7 
58.5  ±  14.3 
3.3  ±  0.3 
3.6  ±  1.0 
2.3  ±  0.9 
1.1  ±  0.2 

44564.0  ±  5349.1 

3.9  ±  0.9 
0.8  ±  0.2 
0.1  ±  0.0 

18794.3  ±  3789.6 

23.3  ±  4.9 
24.4  ±  4.0 
0.4  ±  0.3 

7107.1  ±  778.2 
957.5  ±  191.7 

1.4  ±  0.2 

8402.4  ±  1113.4 

16.8  ±  2.4 
21.4  ±  4.3 
30.1  ±  2.5 
24.5  ±  5.3 
6.3  ±  1.2 
97.4  ±  20.3 
10.2  ±  1.5 

362261.3  ±  7687.7 

4.5  ±  0.9 
1.5  ±  0.2 
1.0  ±  0.2 
0.6  ±  0.1 
8.0  ±  1.9 

4722.3  ±  1131.7 

0.4  ±  0.2 
3.0  ±  1.3 
89.1  ±  8.0 
1.4  ±  0.2 
22.9  ±  7.4 
2.6  ±  1.7 
99.0  ±  19.2 
361.3  ±  571.5 

Table 7.3 Average chemical concentrations and standard deviations for the two clay groups (ppm) 

308 

 
7.7 Results of the Ceramic Analyses 

Using the workflow and statistical methods discussed above, 543 ceramic samples were 

placed into a number of compositional groups and sub-groups. The ceramic sample consists of 

one primary, or core, compositional group (Core A) in addition to two outlier groups (Outgroup 

1 and Outgroup 2) and two provisional groups (Core B and Core C). Within the Core A group, 

two sub-groups are evident (Core A1 and Core A2). Among pottery samples, Core A is 

comprised of 380 samples. Within the Core A group, 133 ceramic samples were assigned to Core 

A1, 88 ceramic samples were assigned to Core A2 and 161 samples were assigned only to the 

Core A group and no sub-group. Outgroup 1 and Outgroup 2 (which are comprised of 39 and 20 

samples respectively) are likely statistical outliers of the core compositional group, and are 

therefore likely outliers of, or distinct from, the range of clay sources sampled based on ceramic 

paste compositional profiles. Core B and Core C (21 and 13 ceramic samples respectively) are 

probable statistical outliers of the Core A group. A further 68 samples (or 12.5% of the ceramic 

compositional data set) were unable to be assigned to any group based on equivocal membership 

probabilities.  

In the discussion that follows, attempts are made to relate these compositional groups to 

various production areas. It is important to emphasize that the identification of chemical 

compositional groups using elemental concentrations does not equate with the identification of 

discrete production sources. Paste preparation regimes including the mixing of clays or additions 

of aplastic materials, use-life alterations, diagenesis (or post-depositional changes to the 

chemical profile of ceramic objects), or some combination of these factors can contribute to the 

chemical profile of archaeological ceramics and therefore to the compositional groups defined 

based on elemental data (Golitko 2010; Gosselain and Livingstone Smith 2005; Neff, et al. 2003; 

309 

Peeples 2011). In addition to insights gained from analysis of the chemical composition of a 

sample of CIRV clays and an understanding of CIRV geology, this research leverages two 

general principals to define the likely geographic production areas associated with compositional 

groups. The first is the criterion of abundance (Bishop, et al. 1982), which proposes that 

ceramics will be the most common in proximity to their production source. This allows 

compositional groups to be inferentially related to a production area based on the geographic 

distribution of group members. The second is the maximal range of raw material source areas 

known to be utilized in ethnographic contexts (or a ca. 7 km radius) (Arnold 1985). Potters living 

in nearby settlements could therefore overlap in resource exploitation zones. Support for a 

geographic production area for a given compositional group is therefore strongest when multiple 

settlements within a particular geological area have high proportions of that compositional 

group.  

In general, there is support for the hypothesized down valley (or northeast – southwest) 

ceramic paste chemical distinctions in the Core A CIRV ceramic sample. That is, the Core A1 

compositional sub-group is dominated by sherds recovered from sites north of, or in proximity 

to, the Spoon/Illinois River confluence (82% or n = 109). Greater geological source material 

variation is evident in the Core A2 sub-group, which is only predominantly comprised of sherds 

recovered from sites south of the Spoon/Illinois River confluence (58% or n = 51). A number of 

sherds were unable to be assigned to either the Core A1 or Core A2 sub-groups (n = 161).  

The following section discusses the partitioning of ceramic samples into statistically robust 

compositional groups in a linear fashion. The linear sequence of compositional group 

identification and refinement is presented in its entirety in Appendix C, as the procedure was 

entirely implemented in the R statistical platform. Results were cross-referenced using the 

310 

MURRAP GAUSS routines developed by Hector Neff for accuracy. Additional support for the 

chemical compositional reference group assignments is supplied in Appendix D. In the 

succeeding section, compositional groups are used to construct networks of economic 

relationships based on overlapping resource exploitation areas, the exchange of finished vessels, 

or similar paste preparation regimes.  

 

7.7.1  Compositional Group Identification and Assignment 
 

After taking the log base 10 of all elemental concentration values, initial inspection of 

bivariate plots and exploratory R-Q mode factor analysis was carried out. A similar trend of 

elemental enrichment in clays north of the Spoon/Illinois River confluence is observed in general 

among ceramic vessels based on the location of the site of recovery on principal component 1 

(Figure 7.7). Principal component 1 is equally enriched in nearly every element. While principal 

component 2 shows a dominant contribution from molybdenum (Mo) and depletions in 

magnesium (Mg) and sodium (Na), manganese (Mn), and cobalt (Co) to a lesser extent. 

However, significant overlap between these hypothetical groups based on the geographic 

location of sherd recovery indicates that they are likely not statistically robust, an intuition 

confirmed by equivocal membership probabilities between the samples using jackknifed 

Mahalanobis distance and the Hotelling’s T2 statistic.  

Analysis proceeded using cluster analysis and other exploratory methods to identify 

potential compositional groupings. R-Q mode factor analysis resulted in 12 significant 

components. No single eigenvalue is above one, indicating that no principal components have 

high correlations with particular elements, complicating efforts to define statistically robust 

compositional groups (Table 7.4). As a result, for the remainder of the analysis, principal 

311 

components 1 through 12 (accounting for 90.4% of cumulative variance) are used to calculate 

group membership probabilities. This minimizes the sample size of the smallest potential group  

Site north of Spoon/Illinois River confluence  
Site south of Spoon/Illinois River confluence  

 

Figure 7.7 Principal components biplot showing elemental enrichment for sherds recovered from sites 

north of the Spoon/Illinois River confluence in general. Ellipses show 90% confidence intervals. 

Together, PC 1 and 2 account for 49.99% of variance in the ceramic dataset. 

 

 

for group membership probability calculations (>14) while maximizing the amount of variation 

drawn from the original dataset of 44 elements. 

Cluster analysis of the full elemental data set resulted in between two and eight optimal 

clusters depending on the method employed (see Appendix C for the relevant code). However, 

each of the statistical methods failed to produce statistically robust clusters when group 

312 

membership probabilities were assessed using Mahalanobis distances and the Hotelling’s T2 

statistic. Anywhere from 75% to 95% of samples were left unassigned to the hypothetical group 

they were assigned to by statistical clustering methods using a threshold of greater than 10% 

probability of membership in the assigned group and less than 10% probability of membership in 

any other group. That is, cluster analysis methods reliably produced equivocal group 

membership probabilities when assessed for statistically significant of group separation.  

Principal Component  Eigenvalue  % Variance 

Cumulative % Variance  

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

0.206 
0.090 
0.066 
0.044 
0.028 
0.023 
0.019 
0.016 
0.014 
0.011 
0.010 
0.009 

34.845 
15.143 
11.153 
7.438 
4.724 
3.887 
3.210 
2.715 
2.280 
1.827 
1.620 
1.526 

34.845 
49.988 
61.141 
68.579 
73.303 
77.190 
80.400 
83.115 
85.395 
87.222 
88.841 
90.367 

Table 7.4 Eigen values and percent variance for first 12 principal components on the ceramic data set 

 

 

As a result of the lack of any evident groups as defined by statistical clustering methods 

on either the full elemental data set or using principal components 1 through 12, analysis 

proceeded by initially treating the entire ceramic data set as a single compositional group and 

assessing group probabilities using jackknifed Mahalanobis distance. After each iteration, 

samples falling below a 1% membership probability cutoff were removed and the membership 

probabilities were re-calculated. Samples left unassigned were projected against the retained 

samples at each step. This process was iterated nine times until groups stabilized and resulted in 

the identification of a “core” statistical group comprised of 416 samples (76.6%) and the removal 

313 

of 127 “non-core” samples (23.4%). Figure 7.7 visualizes the retained core group and non-core 

group along the first three principal components (61.14% of cumulative variance in the ceramic 

dataset).  

Core 
Non-Core 

Figure 7.8 3D scattergram of PCs 1, 2, and 3 showing core and non-core compositional groups 

 

Unassigned “non-core” samples were inspected for meaningful group structuring using a 

 

 

combination of bivariate plots (both of logged elemental concentrations and principal 

components) as well as statistical clustering methods. Broad agreement between k-means and k-

medoids cluster analysis for the presence of two groups among the non-core sherds was 

confirmed using jackknifed Mahalanobis and Hotelling’s T2 group membership probability 

assessment. Using a somewhat different cutoff threshold of greater than 2.5% probability of 

membership in the statistical cluster and less than 10% probability of membership in any other 

group and at least four times higher likelihood of membership in the assigned group than any 

other group resulted in the placement of 59 sherds in two non-core outgroups (Figure 7.9; Table 

314 

7.5). The other 68 non-core sherds remained unassigned due to ambiguous group membership 

probabilities.  

Outgroup 1 
Outgroup 2 
Core 
Unassigned 

 

Figure 7.9 Principal components 1 and 5 biplot showing distinctions between the Core group, Outgroup 1, 

and Outgroup 2. Ellipses demarcate 90% confidence intervals.  

 
 

The identification of a core group and several outgroups indicates that the entire set of 

geochemically analyzed ceramic samples cannot be treated as a single, normally distributed 

chemical group. Given that a number of the unassigned sherds fall within the 90% confidence 

intervals of the core and outgroups on principal component bivariate plots, it is possible that they 

may be statistical outliers of one of these groups. However, equivocal membership probabilities  

 
 

315 

  
Sample # 
4 
7 
11 
12 
14 
15 
198 
207 
208 
210 
213 
217 
282 
284 
296 
297 
308 
309 
497 
532 
536 
599 
672 
674 
726 
753 
754 
787 
798 
872 
873 
874 
911 
916 
922 
1221 
1237 
1287 
1300 
56 
86 
87 
122 
131 
132 
153 
161 
167 
174 
175 
190 
200 
527 
534 
539 
875 
1066 
1190 
1192 

  
 Site 
Orendorf C 
Orendorf C 
Orendorf C 
Orendorf C 
Orendorf C 
Orendorf C 
Walsh 
Walsh 
Walsh 
Walsh 
Walsh 
Walsh 
Emmons 
Emmons 
Baehr South 
Baehr South 
Baehr South 
Baehr South 
Ten Mile Creek 
Ten Mile Creek 
Eveland 
Kingston Lake 
Lawrenz Gun Club 
Lawrenz Gun Club 
Buckeye Bend 
Fouts Village 
Fouts Village 
Larson 
Larson 
Morton Village 
Morton Village 
Morton Village 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Orendorf D 
Orendorf D 
C.W. Cooper 
Crable 
Orendorf C 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Walsh 
Walsh 
Ten Mile Creek 
Eveland 
Eveland 
Ten Mile Creek 
Crable 
Morton Village 
Morton Village 

  
Assigned Group  Core 
0.000 
0.000 
0.000 
0.000 
0.005 
0.072 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.002 
0.000 
0.001 
0.155 
0.000 
0.440 
0.003 
0.891 
0.179 
0.000 
0.144 
0.000 
0.000 
0.001 
0.002 
0.001 
0.001 
0.000 
0.000 
0.005 
0.029 
0.000 
0.006 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.052 
0.020 
0.054 
0.000 
0.000 
0.000 
0.214 
0.000 
0.000 
0.000 
0.000 

Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 1 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 
Outgroup 2 

the outgroup sherds  

316 

Table 7.5 Mahalanobis distance based probabilities of group membership in the core and outgroups for 

Membership Probability 

Outgroup 1 
96.833 
64.239 
75.526 
8.044 
73.011 
21.910 
17.853 
22.171 
56.352 
27.594 
19.716 
76.619 
81.022 
9.155 
94.941 
24.738 
75.722 
97.236 
79.610 
48.350 
28.261 
2.707 
11.242 
7.224 
20.583 
41.847 
78.897 
48.380 
31.056 
90.606 
13.973 
91.443 
53.835 
49.253 
31.838 
95.673 
34.230 
71.064 
47.899 
0.000 
0.312 
0.040 
0.002 
0.376 
0.083 
0.119 
0.013 
0.142 
0.351 
0.179 
2.032 
0.159 
0.590 
0.008 
1.965 
0.000 
0.000 
0.000 
0.000 

Outgroup 2 
0.034 
0.004 
0.017 
0.010 
0.058 
5.172 
0.000 
0.000 
0.002 
0.000 
0.001 
0.290 
0.001 
1.414 
0.037 
0.053 
0.000 
0.003 
0.009 
0.000 
0.000 
0.006 
0.023 
1.446 
0.294 
0.059 
0.612 
0.020 
0.377 
0.004 
0.003 
0.038 
0.860 
0.001 
0.009 
0.000 
0.000 
0.149 
0.010 
61.760 
44.854 
89.296 
52.612 
90.177 
38.189 
58.474 
98.434 
71.598 
89.258 
88.492 
15.133 
6.678 
24.341 
6.168 
8.336 
4.648 
9.860 
94.696 
23.712 

across the different groups as identified precludes statistically sound group assignment for the 68 

non-core unassigned sherds. 

Outgroup 1 sherds differ from Core and Outgroup 2 sherds primarily because of low 

concentrations of the heavy rare earth elements (HREEs; Eu - Lu) and light rare earth elements 

(LREEs; La - Sm). While Outgroup 2 is differentiated primarily based on enrichment in HREEs 

and LREEs as well as enrichment in molybdenum (Mo) relative to Core and Outgroup 1 sherds. 

However, Outgroup 2 sherds are more difficult to distinguish on an elemental basis (e.g. Figure 

7.9). Significant overlap exists between Outgroup 1 and 2 sherds and the Core chemical group on 

most elemental bivariate plots. Non-trivial multivariate group membership probabilities, on the 

other hand, affirm the statistical validity of the core and non-core sub-group separation (Table 

7.5).  

 

Given the broad-spectrum elemental enrichment of Outgroup 1 sherds and clays 

recovered in northerly portions of the CIRV, it would be expected that Outgroup 1 sherds would 

primarily be recovered from sites north of the Spoon/Illinois River confluence. Indeed, some 

61.5% of vessels assigned to Outgroup 1 (n = 24) were recovered from sites in proximity to or 

north of the Spoon/Illinois River confluence. No single site comprises a majority of sherds in 

Outgroup 1. However, Orendorf Settlement C and Walsh are both represented by six vessels 

each. That a number of sherds in Outgroup 1 emanated from Walsh, the most southerly site in 

the Late Prehistoric CIRV analyzed for this research, indicates that the geographic location of 

parent clay material alone may not be the sole explanation for separation of this group. Perhaps 

Outgroup 1 is demarcated by a distinct production methodology based on the mixing of clays or 

perhaps elementally enriched clays were available to potters south of the Spoon/Illinois River 

confluence. On the other hand, one cannot discount the movement of vessels given that all sites 

317 

are connected to each other by a relatively short canoe ride on the Illinois River. That some 

74.4% (n = 29) of the vessels in Outgroup 1 are jars lends credence to the supposition that 

Outgroup 1 sherds may be the product of intra-regional exchange or vessel movement between  

Outgroup 1 
Outgroup 2 
Core 
Unassigned 

 

Figure 7.10 Bivariate plot of log base 10 magnesium and ytterbium concentrations of Outgroup 1 and 2 

and Core sherds with 90% confidence ellipse boundaries 

 
sites. As domestic cooking and storage vessels with restricted access to their contents, jars are 

more likely to have been used to transport foodstuffs, seeds, or other goods between sites than a 

presumed serving vessel such as the plate that has less utility for transport of material goods. 

Given the reduced elemental concentrations in Outgroup 2 sherds and the similarly 

reduced elemental profile of southerly CIRV clays, it would be expected that a majority of 

Outgroup 2 sherds were recovered from sites south of the Spoon/Illinois River confluence. 

318 

Indeed, Outgroup 2 is dominated by sherds from Crable. Some 65% (n = 11) of Outgroup 2 

sherds are from Crable alone and the vast majority of those vessels are plates. In addition, the 

vast majority of vessels in Outgroup 2 were recovered from sites dating to the post-migration 

time period (75%). This would suggest the possible presence of a unique production system in 

addition to the use of less elementally enriched clay likely emanating from contexts south of the 

Spoon/Illinois River confluence as being primarily responsible for the compositional profile of 

Outgroup 2 vessels relative to Core or Outgroup 1 vessels.  

 

7.7.2  Structure within the Core compositional group 
 

With non-core groups identified, attention was turned to the core statistical group. Again, 

statistical cluster methods and R-Q mode factor analysis were carried out to identify potentially 

meaningful structuring with the exception that the core group was treated independently of other 

samples. This approach is warranted because the core group is demonstrably distinct from the 

non-core group and non-core sub-groups.  

As with the prior complete dataset, cluster methods failed to produce compositional 

groups that held up to statistical rigor using membership probability assessment. Thus, the core 

group was further refined by identification and removal of two core statistical outlier, or 

provisional, groups – Core B and Core C. That is, after creating hypothetical two-group 

assignments using k-means and k-medoids clustering, samples were assessed for group 

membership probabilities using a threshold of greater than 2.5% probability in the assigned 

group and less than 1% probability of membership in any other group for the first iteration. This 

acted to identify likely outliers to the core group. This process was iterated with less conservative 

membership probabilities (less than 10% membership probability in any other group and greater 

319 

than 10% within group) as groups likely to be statistical outliers of the core group were identified 

and refined. Figure 7.11 shows the separation of the Core A group and Core B and Core C  

Core B 
Core C 
Core A 

 

Figure 7.11 Principal components 1 and 2 biplot showing distinctions between the Core group, and core 

provisional groups – Core B and Core C. Ellipses demarcate 90% confidence intervals. 

provisional groups on a principal component 1 and 2 bivariate plot. Membership probabilities for 

 

the Core B and Core C groups are provided in Table 7.6. 

Core B and Core C groups are considered provisional due to their small sample sizes and 

the fact that they are probable statistical outliers to the Core A compositional group. In other 

words, as opposed to representing discrete chemical compositional distributions that may reflect 

the distribution of a given clay-source or ceramic production system, Core B and Core C are 

more likely outliers to the Core A chemical compositional distribution. Additional samples may  

320 

  

  

Sample # 

  

Membership Probability 

Core A 

Core B 

Core C 

Core Sub-Group 

Site 
Orendorf C 
Emmons 
Emmons 
Eveland 
Eveland 
Eveland 
Eveland 
Kingston Lake 
Buckeye Bend 
Buckeye Bend 
Fouts Village 
Larson 
Larson 
Larson 
Larson 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Crable 
Lawrenz Gun Club 
Myer-Dickson 
Star Bridge 
Ten Mile Creek 
Ten Mile Creek 
Ten Mile Creek 
Eveland 
Lawrenz Gun Club 
Morton Village 
Star Bridge 
Orendorf D 
Orendorf D 

48 
0.167 
268 
0.011 
272 
0.039 
533 
0.001 
540 
0.024 
541 
0.051 
543 
0.014 
585 
1.491 
741 
8.543 
743 
1.931 
760 
0.452 
770 
0.060 
771 
0.460 
777 
0.227 
795 
0.853 
858 
0.460 
860 
0.405 
863 
0.048 
870 
0.632 
1173 
0.914 
1180 
0.038 
103 
86.329 
234 
4.687 
342 
38.463 
428 
78.579 
490 
15.953 
500 
42.399 
502 
58.820 
559 
58.748 
664 
29.085 
878 
51.190 
958 
60.734 
1206 
24.504 
1236 
49.135 
Table 7.6 Mahalanobis distance based probabilities of group membership in the Core A group and Core B 

Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core B 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 
Core C 

34.973 
25.363 
12.613 
31.881 
57.217 
82.332 
66.191 
56.195 
44.750 
35.512 
11.262 
36.730 
66.461 
27.502 
29.513 
12.936 
24.510 
34.834 
40.302 
33.763 
27.812 
0.001 
0.071 
0.019 
0.008 
0.005 
0.009 
0.051 
0.007 
0.060 
0.279 
0.011 
0.009 
0.087 

0.340 
1.645 
5.743 
0.598 
9.740 
7.334 
0.829 
4.542 
5.165 
6.248 
1.567 
3.329 
7.580 
5.493 
5.013 
1.134 
4.178 
4.115 
2.105 
9.071 
3.514 
7.259 
2.539 
4.390 
0.590 
2.464 
0.463 
0.543 
3.496 
8.216 
5.128 
4.573 
2.418 
6.059 

and Core C provisional groups  

 

confirm or refute their separation into provisional groupings. Out of the original 416 core sherds, 

21 were assigned to Core B, 13 were assigned to Core C and 382 were assigned to Core A. 

Analysis proceeded by examining the Core A compositional group for potentially 

meaningful group separation, disregarding non-core groups as well as provisional groups Core B 

and Core C. No obvious clusters emerged from biplots using a priori information such as 

geographic locations of the site of recovery, vessel class, temporal occupation of sites, or based 

on the presence/absence of Oneota material culture at sites. Statistical clustering methods 

321 

including k-means, k-medoids, and hierarchical clustering were thus applied to the Core A 

group. The k-medoid (or partitioning around medoids (Leonard Kaufman and Rousseeuw 

1990b)) cluster solution for the presence of two groups was identified as the most likely 

candidate to hold up to membership probability assessment. A threshold of greater than 10% 

probability in the assigned group and less than 10% probability in any other group for initial 

iterations and greater than 3% probability in the assigned group and less than 2.5% probability of 

membership in any other group for subsequent iterations resulted in the identification of two 

quite distinct compositional groups within the Core A group. These appear to represent the 

primary statistically significant compositional groups within the entire CIRV ceramic chemical 

compositional data set. Figure 7.12 displays Core A1 and Core A2 group separation along 

principal components 1 and 2 while Figure 7.13 displays Core A sub-group separation along log 

base 10 magnesium (Mg) and nickel (Ni) parts per million concentrations. Membership 

probabilities for Core A1 and Core A2 sherds are presented in Appendix D.  

While two sub-groups were able to be identified within the Core A group, a significant 

number of vessels within Core A were unable to be assigned to either the Core A1 or Core A2 

sub-groups (42.1% or n = 161). This is not uncommon in compositional analysis studies 

(Cochrane and Neff 2006; Eerkens, et al. 2002; Fitzpatrick, et al. 2006; Golitko 2010; Hegmon, 

et al. 1997; Neff 2002, 2003; Niziolek 2013; Peeples 2011; Wallis, et al. 2010). For the present 

case, this is likely reflective of the refined geographic scale with which samples were derived (a 

single archaeological region along one major river valley spanning approximately 137 km), 

massive geologic parent features that extend across the study area, and the highly interconnected 

322 

nature of most of the communities sampled as demonstrated in other portions of this research, 

particularly during the Mississippian occupations prior to Oneota in-migration.  

Core A1  
Core A2 
Core A 

 

Figure 7.12 Principal components 1 and 2 biplot showing distinctions within the Core A group. Ellipses 

demarcate 90% confidence intervals. 

 

 

Core A1 and Core A2 follow a similar trend of group separation primarily along principal 

components 1 and 2. Core A1 is dominated by sherds emanating from sites north, or in the 

vicinity, of the Spoon/Illinois River confluence (82% or n = 109). Recall that the chemical 

profile is one of enrichment in most elements along principal component 1 and general depletion 

along principal component 2 with the exception of molybdenum (Mo) and the HREEs (see 

Figure 7.7 or 7.15). Thus, the Core A2 sub-group is primarily distinguished by depletion in most 

elements relative to the Core A1 sub-group, again affirming the overarching trend seen in the 

clay analysis of down valley elemental diminution. Core A2 shows greater variability in the 

geographic location of the site of sherd origin, with only a simple majority of sherds originating 

323 

from a site located to the south of the Spoon/Illinois River confluence (58% or n = 51). However, 

two sites alone account for some 32 of the 51 sherds in Core A2. A total of 18 sherds in Core A2 

were derived from Crable and 14 sherds in Core A2 were derived from Lawrenz Gun Club. Both 

of these sites are located well to the south of the Spoon/Illinois River confluence.  

Core A1  
Core A2 
Core A 

 

Figure 7.13 Bivariate plot of log base 10 magnesium and nickel concentrations of Core A1 and Core A2 

sherds with 90% confidence ellipse boundaries.  

 

 

In terms of individual elements, the partition in the Core A pottery sample is most readily 

viewed in a bivariate plot of magnesium (Mg) and nickel (Ni) because the distribution of these 

elements shows little overlap between the Core A1 and Core A2 sub-groups. As alkaline earth 

and transition metals respectively, it is likely that differences in these elements are the result of 

differences in clay parent materials. Leveraging the criterion of abundance (Bishop, et al. 1982), 

the preponderance of Core A2 group member sherds from northerly locales in the CIRV suggests 

324 

primarily Pennsylvanian bedrock or Pleistocene alluvium/lacustrine clay sources with a higher 

percentage of Mississippian geologic age bedrock clays perhaps being responsible for elemental 

diminution for Core A1 sherds. Figures 7.5 and 7.6 display these trends among clay materials for 

alkali, alkaline earth, and transition metals more broadly (e.g. elements Be, Li, Ce, Ni). 

However, that there is a significant number of Core A sherds that were unable to be assigned to a 

sub-group indicates the likelihood of at least some overlap in elemental distributions between 

these different source materials, even at such a broad geographic scale.  

 

All final group assignments are visualized in Figures 7.14 – 7.16 in biplots along 

principal components 1 and 2. Figure 7.14 emphasizes group separation boundaries and shows 

the outlier nature of Outgroups 1 and 2 for the entire data set and Core B and Core C for the Core 

A group. Figure 7.15 emphasizes elemental component loadings along principal component 1 

and 2. Core A1, Core B, and Outgroup 1 show general enrichment along principal component 1, 

while the inverse is true for Core A2, Core C, and Outgroup 2. Figure 7.16 displays bivariate 

separation among all groups along molybdenum (Mo) and magnesium (Mg), showing the 

inherent difficulty in using individual elemental features to account for group separation among 

most groups. Final group assignments are summarized in Tables 7.7 and 7.8 as counts by site and 

by geographic location of site and by vessel class.  

325 

Figure 7.14 Principal component 1 and 2 bivariate plot of all group, sub-group, and provisional group 

assignments with 90% confidence ellipse boundaries. 

 

 

 

 

 

 

 

 

326 

Figure 7.15 Principal component 1 and 2 bivariate plot of all group, sub-group, and provisional group 

assignments emphasizing component loadings with 90% confidence ellipse boundaries. 

 

327 

Figure 7.16 Bivariate plot of log base 10 magnesium and molybdenum concentrations of all group, sub-

group, and provisional group assignments with 90% confidence ellipse boundaries. 

 

 

 

 

 

 

 

328 

 

Site 
Baehr South (11Br47) 
Buckeye Bend (11F310) 
C.W. Cooper (11F11F15) 
Crable (11F249) 
Emmons Village (11F218) 
Eveland (11F353) 
Fouts Village 11F164) 
Houston-Shryock (11F114) 
Kingston Lake (11P11) 
Larson (11F3) 
Lawrenz Gun Club (11Cs4) 
Morton Village (11F2) 
Myer-Dickson (11F10) 
Orendorf C (11F107) 
Orendorf D (11F107) 
Star Bridge (11Br105) 
Ten Mile Creek (11T2) 
Walsh (11Br11) 
Total 

Core A  Core A1  Core A2  Core B  Core C  Outgroup 1  Outgroup 2  Unassigned 

6 
8 
14 
8 
7 
6 
5 
10 
12 
12 
5 
17 
6 
3 
10 
20 
5 
7 
161 

1 
6 
11 
8 
12 
9 
11 
12 
5 
16 
1 
12 
6 
6 
12 
2 
3 
- 
133 

3 
2 
1 
18 
6 
5 
1 
4 
8 
1 
14 
4 
2 
1 
4 
5 
4 
5 
88 

- 
2 
- 
- 
2 
4 
1 
- 
1 
4 
- 
6 
- 
1 
- 
- 
- 
- 
21 

- 
- 
- 
1 
- 
1 
- 
- 
- 
- 
2 
1 
1 
- 
2 
2 
3 
- 
13 

4 
1 
1 
1 
2 
1 
2 
3 
1 
2 
2 
3 
- 
6 
2 
- 
2 
6 
39 

- 
- 
- 
11 
- 
2 
- 
- 
- 
- 
- 
2 
- 
1 
- 
- 
2 
2 
20 

1 
1 
1 
8 
1 
2 
- 
1 
- 
5 
3 
13 
- 
12 
- 
- 
10 
10 
68 

Table 7.7 Compositional group assignments by site 
 

Geography*  Vessel Class  Core A  Core A1  Core A2  Core B  Core C  Outgroup 1  Outgroup 2  Unassigned 
North 
North 
South 
South 

Jar 
Plate 
Jar 
Plate 

28 
17 
12 
11 

19 
18 
26 
25 

14 
5 
2 
- 

63 
45 
19 
34 

64 
45 
9 
15 

6 
2 
4 
1 

22 
2 
7 
8 

3 
4 
4 
9 

Table 7.8 Compositional group assignments summarized by site geography and vessel class 
* North indicates in vicinity, or north, of Spoon/Illinois River confluence at approximately 40.297141N latitu

329 

7.8 Compositional Groups as Economic Social Networks  

Using the Brainerd-Robinson coefficient of similarity, it is possible to create networks of  

economic relationships related to ceramic industry through community-based membership in 

compositional groups. The Brainerd-Robinson coefficient of similarity assesses how similar any 

two given sites are based on parallels in the number of individual sherd assignments from those 

sites in different compositional groups. The resulting similarity scores can be modeled as social 

networks, which are in turn able to be quantitatively analyzed to reveal insights related to 

network structure and any changes overtime therein. While this method provides a means to 

model relational economic interactions as gleaned from ceramic artifacts, it must be 

acknowledged that these models are highly oversimplified and generalized based on a 

fragmented archaeological record amidst a highly complex geologic backdrop. Furthermore, 

since compositional groups are a product of both cultural practice regarding raw material source 

selection and vessel circulation as well as geological constraints on source material variation, it 

must be acknowledged that the resulting network relationships are a product of both cultural and 

geological forces, neither of which may be controlled for in a rigorous way. In other words, 

relationships as modeled should be viewed, with some skepticism, as a foundational approach 

using a novel methodology to the analysis of geo-chemical compositional data. Additional 

sampling, greater geological contextual detail, or comparisons to other Mississippian or Oneota 

contexts may lend credence to or challenge the results presented herein.  

For the purposes of this analysis, six of the eight defined compositional group accounting 

for 314 ceramic vessels from 18 sites were considered. Because of equivocal group membership 

probabilities in two or more groups, unassigned samples and samples assigned only to the Core 

A compositional group were not considered (see Table 7.8). A regression of the number of 

330 

compositional groups a site is present in as a function of sample size from that site indicates a 

statistically significant positive relationship at an alpha of 0.01 (p = 0.007) but with a limited 

explanation of variation in group membership as explained by sample size (R2 = 0.37). This 

suggests a potential correlation between the number of compositional groups and sample size but 

with a significant amount of unexplained variability. Economic relationships modeled using the 

BR coefficient of similarity may therefore be negatively impacted by the vagaries of sampling.  

Economic relational ties were assigned between sites by defining a threshold similarity value for 

Brainerd-Robinson (BR) coefficient scores. The threshold value was chosen through an  

 

         Randomized BR 
             Observed BR 
             Randomized BR µ 
             Observed BR µ 
               

Figure 7.17 Distribution of Brainerd-Robinson coefficients for simulated (green) and observed (blue) 

compositional group membership matrices 

 

 

331 

evaluative framework that considers a Monte Carlo procedure that simulates BR scores from 

randomly generated matrices based on the actual proportions of membership in compositional 

groups present at each site. That is, the six-column matrix in Table 7.8 (e.g. Core A1 – Outgroup 

2) was column and row randomized with replacement 10,000 times. The distribution of BR 

coefficient values for the randomized matrices provides an estimate of the overall range and 

frequency of BR scores that might be expected by chance given the number of sites and relative 

counts for each design category. The random distribution and observed distribution of rescaled 

BR coefficients are shown in Figure 7.17. The simulated and observed BR coefficients share 

similar distributions that both approximate normality. Put another way, the underlying structure 

of economic relationships among archaeological site-nodes is not markedly different from what 

might be expected by chance alone. This is likely a reflection of the limited number of 

compositional groups with which to model economic relationships and the fact that many 

samples were unable to be assigned to a compositional group due to equivocal membership 

probabilities. However, observed BR coefficients are nuanced in ways that suggest a deviation 

from random chance. Observed BR coefficients lack scores at the very high and low ends of the 

distribution, or greater or less than two standard deviations from the mean. Furthermore, 

significant peaks and valleys at various positions along the histogram presented in Figure 7.17 

and a reduced central tendency among observed BR coefficients shows further separation 

between observed and simulated BR coefficient distributions. Ties between site-nodes are 

therefore given for all rescaled BR coefficient values greater than the mean BR value for the 

observed data set. This is an arbitrary value (BR > 0.55) but follows the heuristic used across this 

research of giving a tie between two site-nodes when economic, or other, relationships related to 

332 

ceramic industry among them are more similar than they are different in due consideration of the 

range and frequency of observed similarity scores.  

Network data was handled in the R statistical package and exported to Gephi 0.9.2 

(Bastian, et al. 2009) for visualization. Geographic network visualizations were rendered in 

Gephi and overlain on vectorized LiDAR maps using the open-source Inkscape program, version 

0.92.2. Slight jittering of site geographic coordinates was applied to protect site locations. 

LiDAR maps are provided courtesy of the Illinois Geospatial Data Clearinghouse and the 

University of Illinois at Urbana Champaign. Network statistics were calculated using Gephi 0.9.2 

and the R tidyverse and igraph package suites (Kolaczyk and Csárdi 2014; Wickham and 

Grolemund 2017). 

 

Network statistical measures provide insight into the nature of network topology, or 

overall structure of the networks. Statistical measures assessed here include mean degree, or 

average number of edges among nodes in the network; mean weighted degree, or the average of 

the sum of edge weights among nodes in the network; diameter, or number of steps in the longest 

path from one node to another; mean path length, or average number of steps for each node to 

reach every other node; density, or proportion of observed ties compared to the number of 

possible ties; transitivity, which is also known as the global clustering coefficient, or proportion 

of transitive triples wherein all three nodes in a triad are connected (Wasserman and Faust 1994). 

Degree, betweenness, closeness, and eigenvector centralization indices quantify the range or 

variability of individual actor indices. Centralization indices extend the concept of individual 

node centrality to the entire network. Degree centralization assesses whether or not all nodes are 

only connected to a singular central node. Betweenness centralization evaluates the extent to 

which an individual actor is located ‘between’ other actor pairs – actors in this ‘between’ space 

333 

for many actor pairs are likely more critical information conduits. Closeness centralization 

considers how many actors are within one step, or are ‘close’, to a central node. Finally, 

eigenvector centralization gauges the degree to which central actors are connected to all other 

central actors.  

 

In addition to relying on formal methods in the statistical analysis of network data, 

interpretations are based in part on conditional uniform graph tests through Monte Carlo 

simulation. Each observed network statistic was compared against the distribution of that statistic 

generated from 5,000 random graphs of the same order (or number of nodes) and probability of 

an edge being given between any two nodes (based on the observed graph’s density) or size 

(number of edges) using the Erdős-Rényi graph randomization technique (Erdős and Rényi 

1959). Network randomization simulation enables formal hypothesis testing of whether the 

observed network statistics are unusually high or low given what might be expected if the same 

probability of edges (or number of edges) were connected to the same number of nodes as the 

observed network based on random chance alone.  

 

Erdős-Rényi graph models place equal probability on all graphs of a given order and size. 

That is, a collection of graphs are considered based on the provided order and size and a 

probability is assigned to each, where the total number of distinct node pairs are considered 

(Kolaczyk and Csárdi 2014). An extension provided by Gilbert (1959) enables the random graph 

concept to be extended to graphs of a fixed order but where each pair of distinct nodes are 

independently assigned based on a given probability.  

 

It is important to again emphasize that modeling membership in geochemical 

compositional groups as social networks of economic interaction related to ceramic industry 

subsumes both cultural and geological phenomenon. That is, glacial forces acting on surficial 

334 

features and the complex geology of bedrock features results in a lack of discrete patches or 

zones of geochemical distinctiveness that otherwise might lend itself to the identification of 

cultural choices made by potter communities in the central Illinois River valley archaeological 

region. Instead, a pattern of northeast-southwest trending geochemical continuum was shown to 

best describe the valley based on the sample of sediments and archaeological ceramics analyzed 

here. Geochemical compositional groups therefore rely on subtle differences in geochemical 

concentrations, resulting in boundaries between compositional groups that are a more a product 

of arbitrary statistical features as opposed to reflecting discrete geological source variation in 

clay resources. This is not uncommon in archaeometry studies (Garraty 2006; Glowacki 2006). 

Because compositional groups were recognized that had clear geographic trends in the specimens 

that comprised each group, however, it can be reasonably assumed that most pottery vessels from 

a given site were locally manufactured, lending to a theoretical approach of modeling networks 

of economic interaction related to ceramic industry.  

 

7.9 Ceramic Industry Economic Network Analysis and Discussion  

A general temporal trend is evident in economic relationships related to ceramic industry 

in CIRV in network graphs (Figures 7.19 – 7.23) as well as in their associated network statistical 

measures (Table 7.9; Figures 7.24 – 7.25). In short, ceramic industry economic relationships shift 

from being characterized as highly interconnected to highly dispersed across the pre-migration to 

post-migration transition. During both pre- and post-migration periods, there is a high tendency 

for sites to group together into triadic clusters. However, while these clusters show remarkable 

overlap in the cohesive pre-migration time period, clustering overlap becomes severely reduced 

following Oneota in-migration. In other words, the scale of parity in economic relationships 

335 

related to ceramic industry as modeled via membership in ceramic compositional groups is 

greatly reduced from the pre-migration to post-migration time periods. The likely driving force 

behind this change is a regional de-centralization away from the Spoon/Illinois River confluence 

and consolidation into fewer settlements at the northerly and southerly geographic extremes of 

the study region. This finding provides further support for the hypothesis proposed in Chapter 6 

for the formation of a social and spatial internal frontier, or unoccupied interstice between 

settlements (Kopytoff 1987), among Mississippian communities that likely contributed to, or 

acted to structure, Oneota in-migration. The following discussion considers the context of the 

formation of an internal frontier from a perspective rooted in the analysis of economic networks 

related to ceramic industry wherein it is argued that increasing parallels of membership in 

chemical compositional groups gleaned from ceramic artifacts reflect increasing economic 

relationships among sites. That is, ceramic industry compositional groups are used as a proxy 

measure to assess behavioral economic interaction prior to and succeeding culture contact.  

A correlation matrix of all rescaled Brainerd-Robinson (BR) coefficients is shown in 

Figure 7.18. There is a lack of scaled BR coefficient values above 0.91 or below 0.13. Economic 

network relationship values overall show a higher degree of variation among CIRV sites than 

those seen in categorical identification networks (see Chapter 6), but a lower degree of variation 

in models of social interaction through cultural transmission (see Chapter 5). Economic 

relationships derived from ceramic industry are modeled in network graphs only for sites that 

were occupied within the same general time period, either the Mississippian CIRV prior to 

Oneota in-migration (circa 1200 – 1300 A.D.) or following Oneota in-migration (circa 1300 –  

336 

Figure 7.18 Correlation matrix heat-map of rescaled Brainerd-Robinson coefficients 

 
1450 A.D.) and with a BR coefficient value greater than threshold value of 0.55. Because of 

extended or intermittent occupations that span across the circa 1300 A.D. Oneota in-migration 

point, Lawrenz Gun Club and Buckeye Bend are modeled in both the pre- and post-migration 

 

periods. 

Network visualizations are presented, in Figures 7.19 –7.23, in one of two ways. First is 

through the use of a multilevel layout algorithm that finds a global optimal layout while 

337 

approximating short and long-range forces (Hu 2005). In other words, site-nodes with strong 

similarities in compositional group membership are laid out in closer proximity when all site-to-

site relationships are considered. The second layout method uses randomly jittered, or modified, 

geographic coordinates of sites in a geographic network rendering. In each visualization, site-

nodes are colored and sized based on weighted degree, which is the sum of relationship (edge) 

weights. The edges connecting nodes are colored and sized by weight, or the depth of ceramic 

industry economic relationship. That is, edges that are darker blue and larger reflect a higher 

degree of economic relationships among sites, and darker blue and larger site-nodes indicate that 

a given site is characterized by a high degree of proportional similarities in compositional group 

membership to many other sites.  

Pre-
Migration 

Post-
Migration 

  
Summary Statistics 
  Nodes 
  Edges 
  Mean Degree 
  Mean Weighted Degree 
Network Size Measures 
  Diameter 
  Mean Path Length 
Network Topology Measures 
Network Density 
Mean Clustering Coefficient 
Degree Centralization 
Betweenness Centralization 
Closeness Centralization 
Eigenvector Centralization 

 

 

 

 

 

 

11 
42 
7.636 
5.576 

3 
1.291 

76.4% 
90.2% 
0.136 
0.184 
0.242 
0.179 

Flattened 
Across 
Time 
 

8 
10 
2.5 
1.655 

4 
2.071 

 

 

35.70% 
69.00% 
0.214 
0.612 
0.492 
0.48 

17 
52 
6.118 
4.387 

4 
2.066 

38.20% 
74.30% 
0.305 
0.27 
0.363 
0.502 

 

 

Table 7.9 Central Illinois River Valley Ceramic Industry Economic Network Statistics 

338 

Regressions showed no meaningful statistical relationship in the degree of economic 

interaction related to ceramic industry as a function of geographic distance between sites (pre-

migration: p = 0.69, R2 = 0.004; post-migration: p = 0.55, R2 = 0.046). This is a somewhat 

surprising finding given that it would be expected that sites closer in proximity to one another 

would likely share similar resource catchment zones or engage in more frequent exchange 

relationships. That distance is not a delimiting factor in the strength of economic relationships 

among sites attests to the relatively high degree of ceramic compositional group diversity present 

at each site (Table 7.7), where an average of four compositional sub-groups, outgroups, or 

provisional groups are represented.  

With two notable exceptions, the pre-migration time period CIRV is characterized as 

highly densely interconnected, cohesive, distributed, and with a statistically significant number 

of transitive triads, suggesting economic interaction related to ceramic industry at a broadly 

regional scale. Transitivity is a graph level measure of network cohesion. Also known as the 

global clustering coefficient, transitivity assesses the proportion of node triads in which all three 

nodes are connected (Scott and Carrington 2016), capturing the notion of whether or not a ‘friend 

of a friend is a friend’ (Collar, et al. 2015). In the pre-migration CIRV, this notion holds true 

some 76.4% of the time. Fully 100% of networks simulated based on the pre-migration economic 

network using the Erdős-Rényi graph randomization technique showed lower transitivity values, 

indicating a very highly interconnected network (see Figure 7.24). The average clustering 

coefficient (which is an aggregate of a node level statistic that assesses how complete the 

neighborhood of a network is) for the pre-migration period is 90.2%. Taken together, these 

network statistical measures portend a decidedly cohesive network structure for the pre-

migration period. The cohesion of the pre-migration ceramic industry economic network is 

339 

Pre-Migration 
 

Post-Migration 

 

Figure 7.19 Yifan Hu multilevel network graph layout for the Pre-Migration Time Period (1200-1300 

A.D.; left) and Post-Migration Time Period (1300-1450 A.D.; right) 

 
illustrated in Figure 7.19, which shows one large cluster of highly interconnected sites with a 

single outlier – Lawrenz Gun Club. The dearth of edges to Lawrenz Gun Club is most readily 

explained by its unique geographic location along the Sangamon River within the southerly 

portion of the Illinois River floodplain as opposed to along the western bluff-tops above the 

floodplain. The second notable exception to pre-migration regional scale economic interaction is 

Walsh, the most southerly CIRV site included in this research. No ceramic industry economic 

relationship modeled with Walsh in the pre-migration period was characterized above the scaled 

BR threshold value of 0.55. However, Walsh did show meaningful relationships with southerly 

CIRV sites occupied in the post-migration period such as Baehr South and Crable (Figure 7.18), 

attesting to the regional foci in the pre-migration time period around the Spoon/Illinois River 

confluence and expansive occupational scale in the subsequent post-migration period (Figures 

340 

7.20 and 7.21 show the comparison). Low centralization scores across the pre-migration period 

(Table 7.9) indicate a distributed network structure where no single site or site cluster held a 

proportionally influential position relative to other sites when considering ceramic industry 

economic interaction.  

 

Following Oneota in-migration, transitivity remained high but is no longer statistically 

significant (Figure 7.25). Coupled with significant reductions in network density, average 

degree, and average weighted degree and significant increases in the mean path length and 

network diameter, there is support for a contraction in the scale at which there is parity in 

economic relationships among sites from the pre-migration to post-migration time periods. Put 

another way, the post-migration period is characterized by many fewer relationships that are not 

only weaker on average but the network as a whole is also less efficient at transporting economic 

information related to ceramic industry, or vessels themselves, through it. Perhaps most 

significant is that while three fewer sites were occupied during the post-migration period in 

network models, network density is less than half of that seen in the post-migration period 

(76.4% to 35.7% density). Many fewer economic relationships related to ceramic industry were 

therefore pursued during the post-migration period. The relationships that were pursued were 

most often reciprocated, however. High average clustering coefficients indicate that the tendency 

for triads of site-actors to become fully economically interconnected seen in the pre-migration 

time period largely extends to the post-migration period. Yet, there is a stark shift from economic 

interaction at a global scale to a significantly reduced social scale. Therefore, a divergence is 

seen in exchange relationships, raw material catchment zones, and/or ceramic paste preparation 

methodologies in the CIRV following Oneota in-migration. This is best illustrated in Figure 7.22, 

which presents the entire ceramic industry economic network flattened across time periods and  

341 

 

 

Figure 7.20 Geographic network graph layout for the Pre-Migration Time Period (1200-1300 A.D.) 

 

Figure 7.21 Geographic network graph layout for the Post-Migration Time Period (1300-1450A.D.) 

 

342 

Pre-Migration 
ca. 1200 – 1300 A.D. 

Post-Migration  
ca. 1300 – 1450 A.D. 

Figure 7.22 Yifan Hu multilevel network graph layout flattened across time (1200-1450 A.D.) 

 

 

Figure 7.23 Geographic network graph layout flattened across time (1200-1450A.D.) 

 

343 

shows a tight-knit and strongly interconnected pre-migration network juxtaposed next to a 

splintered and dispersed post-migration period network. The three sites occupied in the 

Spoon/Illinois River confluence area in the post-migration period do show triadic transitive 

closure, and this is a significant finding because two of the three sites (Morton Village and C.W. 

Cooper) have a marked presence of Oneota material culture, suggesting that Oneota and 

Mississippian peoples not only used similar clay resources but also prepared ceramic paste in 

ways that led to similar geo-chemical profiles. For these sites, economic relationships are 

modeled primarily based on a significant presence in compositional sub-group Core A1. Finally, 

betweenness and closeness centralization scores increase significantly from the pre-migration to 

post-migration time periods, indicating a less distributed and likely more consolidated network 

structure (Table 7.9).  

 
 

 

Figure 7.24 Network randomization results for pre-migration ceramic industry economic network. 
Observed statistic represents red line. Histogram shows distribution of statistic based on network 
randomization of 5000 random graphs using the Erdős–Rényi random network modeling technique. 

 

344 

 

 
 
 

 
Figure 7.25 Network randomization results for post-migration ceramic industry economic network. 
Observed statistic represents red line. Histogram shows distribution of statistic based on network 
randomization of 5000 random graphs using the Erdős–Rényi random network modeling technique.  

That such an evident shift is seen from highly cohesive to highly dispersed ceramic 

industry economic relationships suggests changes in the territorial component of Mississippian 

societies from the pre-migration to post-migration CIRV. Interacting communities in tribal and 

chiefly societies exist within recognized territory, in which local resources are often claimed by 

segments of society (Pugh 2010). Economic networks in the pre-migration period suggest that, in 

terms of its relation to ceramic industry, resource and exchange relationships were recognized at 

a broadly regional scale. This infers that a regional territory was likely recognized across the 

CIRV in the pre-migration period, but in particular in the Spoon/Illinois River confluence area of 

core Mississippian settlement. Efficient organization of territory and resource management can 

drive solidarity and downplay in-group social friction, reinforcing existing socio-politico-

economic power structures (Kowalewski 2006). Dispersal away from the Spoon/Illinois River 

345 

confluence and concomitant fracturing of economic network relationships related to ceramic 

industry indicates that part of the process of the emergence of an internal frontier in the post-

migration CIRV was a divergence in economic interests and territorial social boundaries. Thus, 

perhaps the post-migration CIRV internal frontier burgeoned out of the establishment of buffer 

zones, which in turn could possibly be related to increasing conflict and violence (Fowles, et al. 

2007; G. R. Milner, et al. 1991; G. D. Wilson 2012). However, the economic interconnectedness 

of Ten Mile Creek, the most northerly site in the post-migration CIRV, with sites such as Morton 

Village, Crable, and Star Bridge implies that models of antagonism should be nuanced. This is 

especially true given the complex relationship between war and peace and inter- and intra-group 

interactions seen in ethnographic contexts among the Santee Dakota and Ojibwa (Landes 1959, 

1968), the Lakota (Walker 1982), and in the Mississippian ‘shatter zone’ following contact 

(Ethridge 2009b) for example.  

 
 
7.10  Conclusion 

The in-migration of Oneota peoples into the Mississippian central Illinois River valley 

provides a unique social context with which to demonstrate the role of networks of economic 

relationships as indicators of how both indigenous societies and migrant peoples approach 

intercultural social and economic relationships. Here, it was argued that increasing similarities of 

membership in chemical compositional groups among sites is a reflection of increasing economic 

interactions resulting from the exchange of finished vessels, overlapping resource exploitation 

areas, or shared paste preparation and ceramic production and refuse regimes. To that end, a 

number of findings were addressed.  

346 

First, ceramic vessels with distinctly Oneota stylistic decoration were unable to be geo-

chemically differentiated from their Mississippian counterparts. As a result, it can be assumed 

that Mississippian and Oneota potters were utilizing similar or identical raw clay sources, 

engaging in similar paste preparation and production regimes, and discarding vessels in ways 

that did not result in diagenetic differentiation. Thus, while stylistic and morphological variation 

is evident among Oneota and Mississippian peoples in the Late Prehistoric CIRV, there is no 

support for variation in aspects of ceramic industry deemed here as primarily economic in nature.  

Second, it has been argued that an observed shift in economic interaction patterns 

occurred concomitant with Oneota in-migration. Network analysis and simulation indicates that 

the Mississippian period showed unusually high cohesion in economic relationships related to 

ceramic industry compared to what might be expected by random chance, evidence supporting 

regional scale economic interaction patterns. The post-migration period of multi-cultural 

habitation, on the other hand, is characterized by a highly dispersed network structure where 

economic interaction was likely engaged in at a significantly reduced social and spatial scale. 

This was inferred to be reflective of intra-group divergences in economic interests and territorial 

boundaries related to the formation of an internal frontier. The presence of an internal frontier as 

a possible outgrowth of buffer zones is likely to have been impactful in structuring Oneota in-

migration into the region.  

The economic perspective to ceramic industry taken here provides an expansive view to 

the study of archaeological ceramics in that it considers aspects beyond style, form, and function. 

Coupled with relational methodologies, a focus on economic interactions such as vessel 

circulation or exchange, shared resource exploitation zones, and similar ceramic paste 

preparation methodologies highlights the transmutability of ceramic vessels in a way that cross-

347 

cuts gendered divisions of labor and enables often under-emphasized aspects of the ceramic 

chaîne opératoire to provide insight into archaeological case studies of behavioral entanglement 

in multi-cultural social settings.  

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

348 

CHAPTER 8 TOWARD EXPLAINING SOCIAL INTERRELATIONSHIPS THROUGH 

CERAMIC INDUSTRY MULTILAYER SOCIAL NETWORKS  

 
 
8.1 Introduction 

This dissertation has employed an empirically focused approach to the construction and 

analysis of social networks in an archaeological case study region. Thus far, each analysis was 

concerned with a specific type of tie related to ceramic industry and how relations constructed 

from that type of tie may contribute to explanations of behavioral response trends to culture 

contact. Because social identities and relationships in human social systems are nuanced in 

multi-dimensional ways, this concluding chapter draws together each of the unique relational 

perspectives on ceramic industry discussed heretofore into a synthetic multilayer network. In this 

way, it is possible to access the influence and overlap of each individual network in structuring 

and being restructured by migration-induced culture contact in a Late Prehistoric west-central 

Illinois case study region. From these trends, I argue that patterns of intercultural communal 

coexistence may be revealed. I conclude by discussing the contributions of this study more 

broadly, caveats and assumptions built into the study, and future prospects for the use of the 

theoretical model used here in other archaeological contexts and beyond.  

 
 
8.2 Culture Contact and Multi-dimensionality in Archaeological Social Networks 

At the outset of this dissertation, I argued that social networks are conduits for culture. I 

also argued that networks shape culture (and vice versa), and that culture itself is organized into 

networks of cultural forms (Azarian 2005; Mische 2011; White 1992, 1993, 2008a, 2008b; White 

and Godart 2007). Network ties were argued to emerge out of the general chaos and uncertainty 

among identities. Social networks are informal and temporary patterns of the order that emerge 

349 

from such uncertainty and are composed of stories that link identities (White 1992:65). Stories 

and identities constitute the phenomenological reality of a network. Individual social actors are 

embedded between many, often divergent socio-cultural groups that each span a distinct 

network. Because of the plurality of roles across the multitudes of distinct networks, which are 

often divergent from one another, I further argued that an entire social system may only be 

approached when multiple relational layers are interconnected and parsed. Building on a recent 

formalism, I refer to the resulting models as multilayer networks. Using this framework, I argued 

that it is possible to access and explain behavioral response trends following culture contact 

under the rubric of intercultural communal coexistence. Here, I briefly recapitulate the 

theoretical and methodological underpinnings of multilayer networks and intercultural 

communal coexistence.  

 While social network analysis has surged in popularity in recent decades, it is 

increasingly being recognized that reducing a social system to a network in which actors are 

connected by a single type of relationship is often a rudimentary approximation of reality 

(Kivelä, et al. 2014). Social interactions, for example, seldom develop on a single conduit. 

Furthermore, pairs of actors can be bound by more than one relationship. Anthropologists and 

sociologists identified the need to represent social systems through multiple social networks that 

consider different types of relationships among the same set of individuals many decades ago 

(e.g. Breiger 1975; Gluckman 1967). It is only through recent breakthroughs in complex systems 

research, however, that has led to a mathematical formulation of multilayer networks that truly 

enables this type of analysis (Boccaletti, et al. 2014; De Domenico, Solé-Ribalta, Cozzo, et al. 

2013; Dickison, et al. 2016; Kivelä, et al. 2014). Network science has shown that “the structure 

of the interactions among the constituents of the system plays a fundamental role in shaping the 

350 

emergence of complex behaviors, much more important than the role played by the specific 

properties of the single units of the system” (Battiston, et al. 2017:401-402). Methodologically, 

adjacency matrices used in monoplex (or single-layer) network analysis are incapable of coping 

with the challenges posed by networks that span multiple relational layers. Rather than reducing 

multiple types of tie into a single, all-encompassing tie known as a multiplex tie (Gluckman 

1967), however, the mathematical formulation of multilayer networks considers network 

structure as consisting of multiple layers of connectivity using a tensorial approach (De 

Domenico, Solé-Ribalta, Cozzo, et al. 2013). This results in models that capture richer and fuller 

relationships between nodes and better represent the topology and dynamics of real-world social 

systems.  

An apt application of multilayer network analysis is understanding behavioral response 

trends, or the creative refashioning of cultural forms, to culture contact following human 

migration (see also Danchev and Porter 2018; Vacca, et al. 2018). In Chapter 2, I argued that 

these trends may be understood as reflecting strategies of intercultural communal coexistence, or 

the synchronous habitation of lineally asymmetrical groups in proximity. A theoretical model of 

intercultural communal coexistence, which is not deterministic of peaceful or tolerant relations, 

proposes that communities may pursue four generalized behavioral strategies in multicultural 

environments based on evidence gleaned from relational and social identities: pluralistic 

coexistence, accommodative coexistence, integrative coexistence, or ethnogenesis (see Table 

8.1). Multiple network layers that consider both the depth of interactions rooted in relational  

Depth of Relational Interaction  Categorical Identities Similarity 
Communal Coexistence Trend 
Pluralistic Coexistence 
Absent or Limited 
Accommodative Coexistence  Moderate to High 
Integrative Coexistence 
Absent or Limited 
Moderate to High 
Ethnogenesis 

Low 
Low 
Moderate to High 
Moderate to High 

Table 8.1 Matrix of expectations for intercultural communal coexistence strategies 

351 

 

identification and similarities in categorical identities are necessary to model intercultural 

communal coexistence. As a qualitative multilayer topological measure, intercultural communal 

coexistence characterizes trends across the layers of a multilayer network using insights 

regarding processes of collective action and social transformation (Peeples 2011, 2018; Tilly 

1978). 

 

Depth of relational interaction is evaluated through processes of relational identification, 

in which individuals identify themselves and others with larger collectives through their 

positions within networks of interpersonal interaction (Peeples 2018). Relational interaction was 

examined in this study through analysis of technological type-attributes on domestic cooking jars 

and serving plates as well as through analysis of ceramic geochemical compositional 

characterizations focused on identifying patterns of economic interaction through vessel 

exchange, overlapping resource exploitation areas, or shared paste preparation and ceramic 

production regimes.  

 

Similarity in categorical identities is assessed through processes of categorical 

identification, in which individuals identify themselves and others as members in larger social 

units through similarities in socially defined roles or groups to which one can belong. 

Categorical identification relies on symbols or other forms of non-verbal communication in order 

to facilitate recognition among members and non-members of categorical social groups (Peeples 

2018). Categorical identification was examined in this study through analysis of stylistic 

decoration on plates, which are vessels primarily used as serving or presentation pieces often in 

highly public and highly visible contexts.   

352 

 

Taken together, parity in relational and categorical identities is argued elsewhere to 

portend social transformations (Peeples 2018). That is, social settings characterized by a 

moderate to high degree of identities and a moderate to high depth of relational identities at a 

macro-scale are argued to be primed for collective social action and social transformations 

(Nexon 2009). As opposed to focusing on collective social action, the emphasis in this research 

are characterizations of behavioral responses to culture contact. Thus, instead of identifying the 

potential for collective social action to occur, relational and categorical identification are used 

here as sensitive indicators of intercultural communal coexistence trends. The trends outlined in 

Table 8.1 are assessed qualitatively based on quantitative network ties. That is, no attempt is 

made to define a function that may analyze network layers and provide an assessment of 

categorical and relational identities as they relate to intercultural communal coexistence trends. 

Instead, a host of structural and topological characteristics of individual network layers are 

considered in relation to each other in order to arrive at a value indicating the depth of relational 

interaction or an assessment of categorical identities similarity in a given social context.  

 

8.3 Layers of Evidence – Results of the Individual Network Layers 

The application of network analysis methodologies in archaeology is contingent upon the 

basic theoretical argument that similarities in material culture used and discarded at different 

sites can be used as a proxy measure of the degree of social connectedness between them, 

whether direct or indirect, material or informational (Peeples, et al. 2016:61). The most 

important aspect of a particular network layer is the type of connection used to construct 

relationships between nodes. Connections indicative of three types of relationships gleaned from 

ceramic industry are considered here. All three types of tie chosen for this research constitute 

353 

frameworks for constructing relationships between humans, wherein edges between sites act as 

statements of probability that a relationship existed. A recapitulation of the results of each 

monoplex network analysis is presented here prior to a presentation and discussion of the 

complete Late Prehistoric central Illinois River valley ceramic industry multilayer network in the 

following section.  

 

8.3.1  Relational Interaction from Cultural Transmission 

The topic of Chapter 5, the first two network layers assess relational interaction by means 

of relationships of descent or shared learning mechanisms based on relative technological 

similarity in type-attributes constrained by social, as opposed to engineering, forces (Eerkens and 

Bettinger 2008; Peeples 2011). Distinctive combinations of technological characteristics signal 

shared relationships of learning and the expression of social information among individuals and 

act as a proxy measure for the communities in which they were nested (Herbich 1987; Stark, et 

al. 1998). Distinct network layers were constructed for each of two vessel classes: domestic 

cooking jars and serving plates. From a suite of continuous type-attribute measurements, a 

quantitative model was applied to identify the specific artifact type-attributes that are free to vary 

from site to site, which is argued to indicate that social forces are more likely to be a contributing 

factor to that variation. Site assemblages are then compared to each other based on pairwise 

comparison of each artifact’s socially mediated type-attributes. It was argued that as proportional 

similarities based on pairwise comparisons of type-attributes between two assemblages 

increases, so too does the probability that social interaction between those sites occurred as a 

result of shared learning mechanisms or homologous relationships. Network ties, representing 

statements of probability that a relationship rooted in relational identities existed between two 

354 

communities, were then modeled on only the type-attributes where moderate to high variation is 

observed across all communities relative to the amount of variation observed across all type-

attributes.  

Results of the jar and plate technological attribute network layers indicate that significant 

structural changes in relational interaction occur across the Middle to Late Mississippian 

transition concomitant with the circa 1300 A.D. in-migration of Oneota peoples into the CIRV. 

In particular, the scale at which attribute interaction networks form relational connections was 

shown to change across time. In the pre-migration context, technological similarity in jar 

attributes suggests cultural transmission across a regional interaction network. At the same time, 

spatial distance is argued to have acted as a major factor in influencing the degree of 

technological similarity in plate attributes, suggesting cultural transmission at a more nuanced 

scale of interaction. This trend inverses following Oneota in-migration and infusion of 

significant variation in jar technological norms by Oneota peoples, leading to networks of 

cultural transmission of jar attributes at reduced or nuanced scales of interaction largely based on 

spatial proximity. However, technological similarity in plate technology exhibits a pattern of 

creating regional scale relational connections among post-migration sites. Thus, neither the pre- 

nor post-migration CIRV is characterized by parity in the scale at which networks of interaction 

through cultural transmission formed strong relational connections across the different vessel 

classes under consideration.  

The post-migration CIRV saw a significant infusion of variation related to jar attribute 

technology by Oneota peoples. That variation interrupted the regional scale relational interaction 

pattern seen in the pre-migration jar attribute interaction network. As a consequence, sites with 

an Oneota presence are weakly integrated into the post-migration jar attribute interaction 

355 

network. On the other hand, Oneota peoples did adopt the plate vessel class at two multi-cultural 

sites, Morton Village and Crable, likely as a result of the regional scale at which plate 

technological information spread in the post-migration CIRV. This suggests that the plate vessel 

class was adopted by Oneota peoples based on direct interaction through cultural transmission 

with Mississippian potters, and likely as a means to bridge extant cultural distinctions in the 

public sphere of life where a serving plate is most likely to have been utilized.  

That both Oneota and Mississippian peoples did share information related to plate 

production techniques in limited contexts is an indication that cultural transmission patterns, and 

by extension patterns of relational interaction, were emphasized in certain spheres of material 

culture or daily life. Further, the expansion of the scale of interaction through cultural 

transmission of plate attributes suggests that in the public sphere of life in some Mississippian or 

multi-cultural contexts, attempts at inter-cultural mediation did occur among Oneota and 

Mississippian potters.  

The lack of overlap between the jar and plate network layers presents a quandary when 

qualitatively assessing the depth of relational interaction gleaned from the cultural transmission 

of ceramic technological attributes as related to table 8.1. From a relational perspective, both the 

jar and plate post-migration technological attribute layers exhibit robust network densities (see 

Table 8.2). However, different sub-groups are apparent in network vizualizations for the plate 

and jar attribute networks (e.g. Figures 5.35 and 5.37). This divergence of trends highlights an 

important issue when using material culture to model social interaction through relational 

identification – the social lives around objects often differ greatly, in particular as the social lives 

of those objects relate to the production contexts in which they are made and used (Appadurai 

1986; Herbich 1987). Culture contact, furthermore, can have unpredictable effects on changes in 

356 

the social lives of different kinds of material culture. In any case, it is apparent that potters in the 

post-migration time period CIRV formed networks, directly or indirectly, through a specific kind 

of interpersonal bond: jar and plate production methodologies. During the multi-cultural post-

migration period, networks formed through shared norms in the technological execution of plates 

spanned a regional scale, while jar attribute networks were likely formed at more nuanced spatial 

and social scales. However, because relatively dense networks were formed from both of these 

layers, it can be inferred that relational identities were likely stemmed from regional similarities 

among potters based on a common interest – producing vessels for the benefit of the community. 

As a result, under the rubric of Table 8.1, I hypothsize that the depth of relational interaction in 

the post-migration jar attribute network is moderate and in the post-migration plate attribute 

network is high, leading to an overall assessment as a moderate depth of relational interaction as 

seen in the cultural transmission of jar and plate technological attributes in the post-migration 

CIRV.  

 

8.3.2  Categorical Identities from Ceramic Design 

In Chapter 6, network layers were constructed that assess shared categorical identities as 

evidenced by proportions of stylistic decoration similarity (Borck, et al. 2015; Mills, Clark, et al. 

2013; Mills, Roberts Jr., et al. 2013). Categorical identities are mechanisms for people to index 

ascription to common social units, express solidarity, and nonverbally communicate social 

information (Braun 1985; Wiessner 1990). Due to its highly visible and often symbolic nature, 

pottery decoration is posited as being an integral part of an active process to signal group 

membership. Categories of group membership may be related to ethnicity, gender, political 

status, religious affiliation, labor or craft expertise, or other social units at both hierarchical and 

357 

heterarchical levels. Regardless of the specific social grouping, symbolic communication and 

social identity are argued to interplay recursively. Active expression of identity is therefore 

intricately linked to the process of symbolization, a process also referred to in other contexts as 

emblemic style (Wiessner 1983, 1984, 1985, 1990). Consequently, it is argued that stylistic 

patterns gleaned from symbolic decoration on pottery vessels may reveal networks of shared 

categorical identities among groups of people in archaeological contexts.  

Network models of categorical identities similarity were constructed based on patterns of 

proportional similarity in designs incised or trailed on the interior outflaring rims of ceramic 

plates. Plate are typically adorned with design motifs that would be highly visible during 

quotidian or ritualistic public gatherings. Results from analyses of the plate categorical design 

social identification network layers indicate that intra-regional mobility and shifting patterns in 

the scale of parity in networks of social identification during the Middle to Late Mississippian 

transition resulted in the formation of a spatial and social internal frontier. In many ways, this 

internal frontier likely structured networks of social identification following in-migration of Bold 

Counselor Oneota peoples into the CIRV. That is, the circa 1300 A.D. Oneota in-migration 

coincided with increasing regional diversity in social identification categories, a reduction in the 

scale of parity in social identification network relationships, and intra-regional mobility toward 

consolidation among Mississippian peoples. In turn, Oneota peoples likely contributed to 

increasing diversity in common categories of social identification through the permeation of 

distinctly Oneota design motif categories, thereby acting to disrupt and exacerbate ongoing 

restructuring of regional social identification networks and leading to weak integration of 

multicultural Oneota and Mississippian communities into the larger post-migration identification 

network.  

358 

Under the relational paradigm, social categories become entangled with stories about the 

nature and the difference of the groups involved. Social categories, in this way, constitute a lens 

that depicts in-group interaction as filled with solidarity and cross-group interaction as 

competitive (Fuhse 2015; Tilly 1998b). Increases in the diversity of social categories and the 

social and spatial fragmentation of those categories of identification in the multi-cultural post-

migration CIRV strongly suggests that overall categorical identities similarity should be assessed 

as limited using the rubric presented in Table 8.1. In other words, the distribution of identities 

across the CIRV shifted from being homogenous across the population in the pre-migration time 

period to heterogeneous across the population in the post-migration time period. Forging and 

reinforcing shared categorical interests and identities in a heterogenous distribution of identities 

is a major delimiter to collective action in such a context, even in cases of relatively dense 

relational social networks.  

 

8.3.3  Economic Relationships as Relational Interaction  

In Chapter 7, network layers assessed relational interaction through economic 

relationships related to ceramic industry through the analysis of pottery chemical composition. 

That is, increasing parallels of membership in chemical compositional groups was argued to 

reflect increasing economic relationships among communities (Gjesfjeld 2014, 2015; Golitko 

and Feinman 2014). Proportional similarities in chemical compositional groups reflect direct or 

indirect economic relational interaction through the exchange of finished vessels, the sharing of 

raw source material location information, or involvement in similar ceramic production 

processes (Brose 1994; Brown 2004; Zvelebil 2006). 

359 

Results of economic network analyses and simulation indicated that the Mississippian 

CIRV was characterized by economic network interrelationships related to ceramic industry of 

an unusually cohesive nature as opposed to what might be expected by random chance, 

supporting an interpretation of regional scale economic interaction patterns. This pattern changed 

dramatically in concert with the in-migration of an Oneota tribal group. Post-migration ceramic 

industry economic network structure was characterized as highly dispersed with many fewer and 

weaker relationships, suggesting a reduction in the spatial and social scale at which economic 

relationships related to ceramic industry were pursued. Furthermore, economic network structure 

in the post-migration period was shown to reflect the presence of a social and spatial internal 

frontier. The internal frontier was a possible outgrowth of buffer zone or other territorial 

boundary changes among Mississippian peoples in the CIRV and was argued to be likely 

impactful in structuring Oneota in-migration. Finally, Mississippian and Oneota pottery were 

shown to be chemically indistinguishable, indicating that potters from both cultural groups in the 

Late Prehistoric period CIRV were utilizing similar or identical raw clay sources, engaging in 

similar paste preparation and ceramic production regimes, and discarding vessels in ways that 

did not result in diagenetic differentiation.  

Comparing the economic interaction networks across Figures 8.4 and 8.5 to the matrix of 

intercultural communal coexistence trends in Table 8.1 indicates that the depth of relational 

interaction through economic relationships should be assessed as absent of limited at the regional 

scale in the post-migration CIRV time period. In the prior pre-migration time period, dense 

social ties reflect regionally shared common interests around the procurement, circulation, 

production, and/or disposal of ceramic artifacts. The delimiting of those ties through processes 

involved in the formation of a social and spatial internal frontier indicates that inter-personal 

360 

bonds through economic processes were re-structured to emphasize local economic processes 

related to ceramic industry.  

 
 
8.4 Building Late Prehistoric CIRV Ceramic Industry Multilayer Networks 

Multilayer networks were constructed for two separate time periods – the pre-migration, 

or Mississippian, CIRV (circa 1200 – 1300 A.D.) and for the post-migration, or Cohabitation, 

CIRV (circa 1300 – 1450 A.D.). Each of the two multilayer networks consist of four separate 

layers. Individual network layers include 1) relational interaction as assessed through similarities 

in the cultural transmission of jar type-attributes; 2) relational interaction as assessed through 

similarities in the cultural transmission of plate type-attributes; 3) categorical identification as 

assessed through proportional similarities in plate style design groups; and 4) relational 

economic interaction as assessed through parallels of membership in ceramic compositional 

reference groups. The multilayer nature of these ceramic industry network models is a 

framework to understand the structuring and restructuring of economic, cultural, and identity 

politic interactions both prior to and following a circa 1300 A.D. in-migration of Oneota peoples 

into the Mississippian central Illinois River valley.  

Multilayer network analysis was carried out using two distinct platforms – MuxViz 2.0 

and multinet 2.0.0 (De Domenico, Porter, et al. 2015; Dickison, et al. 2016; Magnani 2017), both 

using the R statistical programming language. All R code for the multinet analysis is provided in 

Appendix C. No code is provided for the analyses performed using MuxViz, as it is a graphical 

user interface driven program. However, as it is open source, all code for the analytical measures 

is freely accessible.  

361 

A detailed discussion of methods used for the construction and analysis of multilayer 

networks is provided in Chapter 4 and as such will not be reiterated here. However, it is 

necessary to note an important caveat in the formation of ceramic industry multilayer networks 

for the pre-migration and post-migration time periods of the Late Prehistoric central Illinois 

River valley. Due to the complex tensorial approach used to construct multilayer networks (via 

rank-4 tensors (De Domenico, Solé-Ribalta, Cozzo, et al. 2013)), it was necessary to convert all 

network layers to a consistent format. Because the methods used to construct the economic 

networks related to ceramic industry and the categorical identification networks related to 

ceramic style result in undirected networks, it was necessary to convert the jar and plate attribute 

networks to a similar format. That is, the jar and plate attribute network layers were converted 

from directed networks to undirected networks. In cases where two directed connections existed 

among nodes in the attribute networks, the average of the two connections was taken as the 

undirected edge weight. While this results in a significant loss of nuanced information, the 

overarching patterns in these networks remain largely intact. However, as a result of the attribute 

networks’ decomposition from directed to undirected, the multilayer networks that follow should 

be considered experimental in nature and to be used primarily as a means to provide heuristic 

insight into understandings of the individual network layers and their relationships to each other.  

While the methods used to construct individual network layers differ (see Chapters 5 – 

7), the methods used to visualize these layers in the figures below (Figures 8.1 – 8.5) were 

consistently applied across the layers. All visualizations were rendered in Gephi 0.9.2 (Bastian, 

et al. 2009), and are presented in two ways. The first method focuses on network structure in due 

consideration of the geographical positioning of site-nodes. Geographic network visualizations 

were rendered in Gephi and overlain on vectorized LiDAR maps using the open-source Inkscape 

362 

program, version 0.92.2. Slight jittering of site geographic coordinates was applied to protect site 

locations. LiDAR maps are provided courtesy of the Illinois Geospatial Data Clearinghouse and 

the University of Illinois at Urbana Champaign. The second method focuses on network structure 

disregarding the geographical location of nodes. A multilevel layout algorithm was used that 

finds a global optimal layout while approximating short and long-range forces (Hu 2005). In 

other words, site-nodes with strong relationships are laid out in closer proximity in consideration 

of all site-to-site relationships.  

Within each visualization (Figures 8.1 – 8.5), a consistent format was applied to depict 

information about the relative influence of individual nodes as well as information about the 

edge relationships as modeled. Site-nodes are colored and sized based on weighted degree, 

which is the sum of relationship (edge) weights. The edges connecting nodes are colored and 

sized by the weight of the relationship as modeled. That is, edges that are darker in color and 

larger reflect stronger similarities in categorical identification or increased depth of relational 

interaction among sites, and darker and larger site-nodes indicate that a given site-node is 

characterized by a high degree of proportional similarities in categorical identification or 

significant depth of relational interaction to many other sites. Standard monoplex network 

statistical properties are provided in Table 8.2 for each of the network layers. For definitions of 

the measures, see Chapter 4.  

 

363 

Figure 8.1 Pre-migration multilayer network (circa 1200 – 1300 A.D.) 

 

364 

Figure 8.2 Post-migration multilayer network (circa 1300 - 1450 A.D.) 

 

365 

Figure 8.3 Flattened multilayer network (circa 1200 - 1450 A.D.) 

 

366 

Figure 8.4 Multilevel graph layout for the pre-migration multilayer network (circa 1200 - 1300 A.D.) 

 

367 

Figure 8.5 Multilevel graph layout for the post-migration multilayer network (circa 1300 - 1450 A.D.) 

 

368 

 

Summary Statistics
  Nodes
  Edges
  Mean Degree
  Mean Weighted Degree
Network Size Measures
  Diameter
  Mean Path Length
Network Topology Measures
  Network Density
  Mean Clustering Coefficient
  Degree Centralization
  Betweenness Centralization
  Closeness Centralization
  Eigenvector Centralization
 

 
 
 

Jar Attribute - Relational

Plate Attributes - Relational

Plate Style - Categorical

LA-ICP-MS Economic - Relational

Pre-
Migration

Post-
Migration

Flattened 
Across 
Time

Pre-
Migration

Post-
Migration

Flattened 
Across 
Time

Pre-
Migration

Post-
Migration

Flattened 
Across 
Time

Pre-
Migration

Post-
Migration

Flattened 
Across 
Time

12
56
9.333
7.042

2
1.152

8
28
7
5.129

1
1

84.8% 100.0%
87.7% 100.0%
0.036
0.152
0.002
0.014
0.274
0.077
0.038
0.146

18
83
9.222
6.903

2
1.458

54.2%
87.9%
0.397
0.215
0.540
0.340

11
44
8
5.503

1
1.2

7
21
6
4.585

1
1

80.0% 100.0%
84.4% 100.0%
0.048
0.200
0.004
0.028
0.356
0.105
0.052
0.198

16
64
8
5.694

2
1.467

53.3%
85.7%
0.467
0.215
0.669
0.441

9
24
5.333
2.922

3
1.389

7
15
4.286
2.057

2
1.286

66.7% 71.40%
68.6% 72.20%
0.286
0.208
0.128
0.219
0.336
0.519
0.299
0.277

14
39
5.571
2.901

4
1.692

42.90%
64.60%
0.264
0.237
0.299
0.386

11
42
7.636
5.576

3
1.291

8
10
2.5
1.655

4
2.071

76.4% 35.70%
90.2% 69.00%
0.214
0.136
0.612
0.184
0.242
0.492
0.480
0.179

17
52
6.118
4.387

4
2.066

38.20%
74.30%
0.305
0.270
0.363
0.502

 

Table 8.2 Network properties for individual undirected network layers 

369 

8.5 Overlap and Influence among Layers and Communities 

In this section, I discuss the overlaps and influence among different network layers and 

among the communities within them from a quantitative perspective. Many monoplex network 

analytical measures have been extended to the analysis of multilayer networks (De Domenico, 

Porter, et al. 2015). These include analytical areas such as centrality (or node-level positioning), 

community detection, and connected components. However, there are two classes of 

measurements in particular that are unique to multilayer network analysis: overlap and influence. 

Influence in multilayer network analysis refers to the impact of a particular network layer on the 

full multilayer network. Overlap refers to the number of nodes and edges that are shared across 

different network layers. These measures may be applied to individual communities through 

inter-layer analyses of centrality, the degree to which node connectivity deviates across layers, 

and the redundancy of nodes connections across layers. In highlighting the convergence or 

divergence of individual network layers from one another, these measures emphasize a 

fundamental condition of human social reality, namely that individuals are embedded in multiple 

networks that may span very different or very similar architectures of relationships.  

 

8.5.1  Layer Interactions 

While most social network analyses tend to focus on the importance of individual nodes 

or seek to characterize network topology, the multilayer network formulation enables the 

comparative analysis of different network layers. Focus is placed here on assessing changes in 

the overlap of edges across the various Late Prehistoric CIRV ceramic industry networks. In 

particular, edge overlap assesses whether or not a node to node relationship present in one layer 

is also present in another layer (Munson and Macri 2009; Preiser-Kapeller 2011; Szell, et al. 

370 

2010). Edge overlap is measured in three ways: Jaccard similarity (or the intersection of edges 

present in both layers divided by the union of all possible edge relationships in both layers), 

Simple Matching (or whether or not an edge present in one layer is also present in another layer 

disregarding edge weight), and Edge Overlap (which is the same as Simple Matching but factors 

in edge weight). Edge overlap is a means to quantify inter-dependencies between the different 

network layers. Note, however, that no causal direction can be implied using these measures. 

Edge overlaps for the pre-migration CIRV time period are presented in Figure 8.6 and for the 

post-migration time period in Figure 8.7.  

Figure 8.6 Edge overlap for the pre-migration time period 

 

 

371 

Figure 8.7 Edge overlap for the post-migration time period 

 

 

The following interpretations are provided for each pair of layer interactions: 

Jar attributes – Plate attributes. High edge overlap is exhibited for each of the three 

different metrics for jar and plate technological attribute network layers. That this trend is 

consistent across both the pre-migration and post-migration time periods indicates that 

communities of artisans developed strong channels for relational social interaction through the 

cultural transmission of ceramic technological information in the pre-migration period and 

maintained those channels following Oneota in-migration. Thus, relative to other layers of 

interactions, the cost of interaction through shared relational identification among potter  

communities was low throughout the Late Prehistoric CIRV with regard to the exchange of 

information related to socially mediated artifact attributes of pottery vessels used for quotidian 

tasks such as cooking and serving food. This highlights the importance of teaching, learning, 

emulation, and non-verbal communication through pottery technological characteristics among 

372 

Late Prehistoric CIRV communities. It is again important to note that this interpretation is based 

on undirected networks of jar and plate technological attribute similarity, see Chapter 5 for more 

nuanced interpretations of network layers constructed using directed relationships.  

Plate attributes – Plate Style. Edge overlap across the plate technological attributes and 

plate stylistic categorical identification network layers shows the most significant numerical 

increase from the pre-migration to post-migration time periods. In other words, while categorical 

identity was less likely to influence plate technological characteristics in the pre-migration period 

(or vice versa), as the number of categorical identities present in plate stylistic designs increased 

concomitant with Oneota in-migration, so did the likelihood that sites sharing similar categorical 

identities produced plates with similar socially mediated technological attributes. This would 

suggest that while potters maintained relationships for the cultural transmission of artifact 

attributes, those relationships were more likely to be present among sub-groups that shared 

common social identities following Oneota in-migration, perhaps attesting to the increasing 

importance of exclusivity in categorical identities among Mississippian peoples in particular in 

the post-migration CIRV. 

Jar attributes – Plate Style. Edge overlap in networks of jar technological attribute and 

plate stylistic categorical identification networks follow a similar but less pronounced increase as 

in the plate technological attribute and plate style layers edge overlap. This bolsters an 

interpretation that cultural transmission of artifact attributes was more likely practiced among 

sub-groups of communities whose potters indexed shared categorical identities (or vice versa) in 

the post-migration CIRV compared to the pre-migration CIRV.  

Jar attributes – Economic interactions. Edge overlap measures between the jar attribute 

and economic interaction layers show the steepest drop from the pre-migration to post-migration 

373 

time periods (from the second highest layer edge overlap in the pre-migration to the lowest in the 

post-migration). The high edge overlap in the pre-migration period suggests that information 

about jar technological attributes flowed freely among communities who also utilized similar raw 

clay resources, had overlapping resource exploitation zones, or frequently exchanged ceramic 

vessels. The break-down in overlap among these relational channels following Oneota in-

migration is likely related to the formation of a social and spatial internal frontier discussed in 

section 8.3. Late Prehistoric communities consolidated away from the Spoon/Illinois River 

confluence area, which decreased the likelihood of overlapping resource exploitation areas and 

increased the cost of vessel exchange due to longer travel distances. Territoriality perhaps 

increased as well. Channels of interaction through relational identification were thus unequal 

across the layers in the post-migration period.  

Plate style – Economic interactions. Edge overlap in the plate stylistic categorical design 

layer and the economic interaction related to ceramic industry layer increases from being the 

lowest in the pre-migration period to being moderately high in the post-migration period. This 

indicates that overlapping resource exploitation areas, information related to raw clay resources, 

or the exchange of finished vessels was not limited to communities that indexed similar 

categorical identities using plate stylistic decoration in the Mississippian CIRV but that this trend 

changed following Oneota in-migration. This provides support for an interpretation that the post-

migration CIRV likely saw an intensification of territoriality, which was related in some way to 

sub-groups who increasingly signaled membership in social sub-groups through plate stylistic 

decoration.  

Plate attributes – Economic Interactions. Overlapping edges among the plate 

technological attribute transmission layer and the economic interaction related to ceramic 

374 

industry layer remain fairly low across the pre-migration to post-migration transition in the Late 

Prehistoric CIRV. This suggests that economic interaction related to ceramic industry did not go 

hand in hand with the cultural transmission of socially-mediated plate technological 

characteristics. In other words, communities that consistently transmitted information about 

socially mediated plate technological characteristics were not necessarily also sharing 

information related to raw clay resources, utilizing overlapping resource exploitation areas, or 

exchanging finished vessels and that this trend was consistent both prior to and following Oneota 

in-migration.  

Comparing each of the individual layers of the Late Prehistoric CIRV multilayer network 

highlights the different network model architectures along which information, individuals, and 

material culture could flow and how those channels change following culture contact. There are 

some notable trends discussed in the network layer comparisons that are worth emphasizing. In 

particular, Late Prehistoric ceramic artisans appear to have been sensitive to changes in the 

technological characteristics of both jars and plates across the pre-migration and post-migration 

time periods. This suggests low interaction costs, relative to other layers, regarding the cultural 

transmission of socially-mediated artifact attribute information through teaching and learning, 

emulation, the likely exchange of individuals across communities, and the likely gathering of 

groups together for events to facilitate such transfers of information or individuals. Another 

significant finding is that categorical identities became a more influential predictor of interaction 

through relational identification following Oneota in-migration. It is possible that this trend pre-

dated culture contact to some extent, but nevertheless a key facet of behavioral response trends to 

culture contact in the multicultural CIRV was a disruption of prior regional inclusivity in the 

indexing of social categories toward increasing exclusivity through a proliferation of social 

375 

categories. Channels of economic interaction related to ceramic industry that were largely 

tenuous in the pre-migration CIRV appear to have waned following culture contact. This 

suggests increasing territoriality and the presence of an internal frontier inhibiting otherwise 

strong channels for interaction through relational identification related to the cultural 

transmission of ceramic technological attributes in the post-migration time period. Before turning 

to a discussion of how commonalities and divergences of individual network layers may relate to 

intercultural communal coexistence trends, it is pertinent to explore the role of individual site-

actors through an analysis of community interactions across the multilayer network.  

 

8.5.2  Community and Layer Influence  

A key aim of network analysis studies is to examine the role(s) of individual nodes in a 

network. Identifying which nodes are most influential often provides a means toward interpreting 

network structure and explaining the social system as modeled (e.g. Mizoguchi 2009; Padgett 

and Ansell 1993). Using a multilayer network formulation, it is possible to explore how 

influential individual nodes are across different layers, providing a richer and fuller 

understanding of node influence on the entire social system. Toward this end, node influence is 

assessed using three measures of centrality: degree, eigenvector, and strength. Degree centrality 

and strength assess influence as a function of the overall connectedness of individual nodes. 

Whereas degree centrality only assesses the presence or absence of relationships, strength factors 

in the weight of those relationships. Eigenvector centrality characterizes nodes based on their 

connectiveness to other well-connected nodes (see Chapter 4 for an extended discussion of these 

measures). Results are presented in Figures 8.8 and 8.9.  

376 

 

 

Figure 8.8 Node centrality measures for the pre-migration multilayer network 

 

Figure 8.9 Node centrality measures for the post-migration multilayer network 

 

Based on the ceramic industry multilayer network centrality measures, Larson appears to 

be the most influential node in the pre-migration time period, while Star Bridge and Ten Mile 

Creek appear most influential in the post-migration time period. However, both time periods do 

not have high centralization scores consistent across centralization metrics (see Table 8.2) nor 

are node centrality scores highly skewed. In other words, there is little support for individual 

377 

nodes or node clusters playing outsized roles in either any individual network layer nor across 

the multilayer network for either time period. There is, however, some support for nodes playing 

more peripheral roles in interaction and identification networks. As used here, influence refers 

primarily to the extent to which individual nodes are connected to other nodes. As a result, a 

number of communities are inhibited in their influence due to a lack of presence on a given layer, 

which is the case for sites such as C.W. Cooper and Eveland where the plate vessel class has not 

been recovered (see Chapter 3). 

Some overarching trends are notable in measures of node centrality. First are the high 

centrality scores in the jar attribute layer in particular. Second are the high centrality scores in the 

plate attribute layer aside from a few notable exceptions. The influence of the economic network 

layer and the stylistic layer are both diminished from the pre-migration to post-migration period. 

However, the economic network layer appears to diminish in influence much more acutely than 

the plate stylistic layer. These trends are more apparent when summarizing all node degree 

centrality and strength measures, as presented in Figured 8.10 and 8.11.  

While the jar and plate attribute layers remain relatively consistent in influencing 

relationships for both the pre-migration and post-migration multilayer networks, the plate 

stylistic categorical design layer increases in influence at the same time that the economic 

interaction related to ceramic industry layer significantly wanes in influence. Thus, despite 

regional scale parity in ascription to common social groups as seen in proportional similarities of 

plate style groups, indexing a categorical identity was of less influence to network relationships 

relative to other channels of interaction during the pre-migration time period. In other words, 

relationships formed through the indexing of shared categorical identities often contributed the 

least to the pre-migration multilayer network for each site relative to the other  

378 

 
 

 

Figure 8.10 Summary of node degree centrality and strength for the pre-migration time period 

 

Figure 8.11 Summary of node degree centrality and strength for the post-migration time period 

 

379 

layers. This trend reversed following Oneota in-migration, where indexing categorical identity 

through stylistic designs on plates took on an increased role in community interactions. This 

attests to an active role of likely female potters in signaling membership in regional groups in the 

pre-migration time period and, increasingly, more localized groups in the post-migration time 

period. Furthermore, Mississippian sites are shown to be characterized by strong channels of 

economic interaction through ceramic industry that precipitously decrease in influence alongside 

the in-migration of Oneota peoples.  

 

In looking at the differential role of site-node influence across ceramic industry network 

layers, it is pertinent to address site-node degree deviation. Degree deviation quantitatively 

assesses variation in the influence of site-nodes across different network layers. A site-node with 

the same degree of interconnectedness across different layers will have a degree deviation of 0, 

while a site-node with many relationships on some layers and only a few on other layers will 

have a very high degree deviation, which shows an uneven usage of the layers (or layers with 

different densities) (Dickison, et al. 2016; Magnani 2017). Comparing degree deviation in 

figures 8.12 and 8.13 with centrality measures indicates that there is an inverse relationship 

between site-node degree deviation and site-node centrality across both the pre-migration and 

post-migration time periods. In other words, sites that are consistently interconnected across 

network layers are more likely to have a higher influence overall in the Late Prehistoric CIRV. 

This is an unsurprising finding but does bolster an interpretation for a lack of hegemony or 

regional hierarchy among major CIRV sites over more peripheral CIRV sites. While the most 

influential sites based on centrality measures are also larger town or ceremonial sites (e.g. 

Larson, Ten Mile Creek, Star Bridge), neither site size nor assumed site complexity alone predict 

site influence in the pre-migration and post-migration ceramic industry multilayer networks.  

380 

 

High degree deviation scores and variation in strength and eigenvector centrality indicate 

that site-nodes play different roles in different relational and categorical social networks. This  

 

Figure 8.12 Site-node degree deviation for the pre-migration CIRV time period; lower scores indicate 

more even influence across layers 

 

Figure 8.13 Site-node degree deviation for the post-migration CIRV time period; lower scores indicate 

more even influence across layers 

 

381 

 

highlights the value of a multi-measure quantitative approach to investigating community and 

layer influence in a multilayer network, and the value of a multidimensional approach more 

broadly. Additionally, the often contrasting nature of network relationships across different 

layers is highlighted. Finally, analyses of interlayer interactions and layer and community 

influence have shed light on regional scale structural changes that occurred concomitant with 

Oneota in-migration. In particular, relational network connections formed through the cultural 

transmission of socially-mediated jar and plate artifact attributes were maintained in the 

multicultural CIRV while network ties formed through economic relational interaction related to 

ceramic industry were relegated at the same time that the significance of indexing shared 

categorical identities amplified.  

 

8.6 Intercultural Communal Coexistence in the Late Prehistoric CIRV 

As the multilayer network graph visualizations and the preceding discussion summarizing 

individual network layer and community overlaps and influences shows, different types of 

interactions are characterized by distinct connectivity patterns. Exploring the inter-dependencies 

of the different network layers reveals how multiple relations shape the organization of the Late 

Prehistoric CIRV social system at different levels both prior to and succeeding circa 1300 A.D 

culture contact with Oneota immigrants. By qualitatively interpreting quantitative topological 

and statistical properties of relational network layers, it is possible to characterize regional 

behavioral response trends to intercultural communal coexistence. Here, I hypothesize that, 

based on a comparative analysis of the structure of multiple network layers of relational and 

categorical identification across the Middle to Late Mississippian transition, Oneota in-migration 

382 

into the CIRV resulted in a period of accommodative intercultural communal coexistence at the 

macro-regional scale. In social settings following culture contact characterized by 

accommodative coexistence, relational transaction costs are relatively moderate to low but 

heterogeneous or exclusive categorial identities delimit the extent of collective action or social 

movements. Collective action is therefore limited to sub-divisions within densely relational 

networks that do share common categorical identities as opposed to spreading across a broader 

array of actors (Peeples 2018). 

Significant structural changes are apparent in the depth of relational interaction and in 

categorical identification among CIRV communities coinciding with Oneota in-migration. While 

channels of relational social interaction through the cultural transmission of jar and plate 

socially-mediated technological characteristics are largely maintained, parity in the scale 

network relationships formed through economic interaction related to ceramic industry is deeply 

reduced. As a result of the imbalance in relational interaction layers, where two layers are 

characterized by moderate or high depth of relational interaction and one layer is characterized 

by low depth of relational interaction, an overall trend of moderate depth of relational interaction 

is argued here to characterize the Mississippian and Oneota multicultural occupation of the Late 

Prehistoric CIRV. 

Likewise, structural changes are apparent in categorical identities similarity paralleling 

culture contact among chiefly CIRV Mississippian peoples and exogenous Oneota peoples. The 

indexing of shared categorical identities using stylistic decorations on plates took on an increased 

role in community interactions in the post-migration relative to the pre-migration time period as 

seen in layer influence. However, analysis of network statistical properties indicates that global 

scale ascription to categorical identities in the Mississippian CIRV gave way to ascription to 

383 

categorical identities at a reduced social scale. Chapter 6 showed that the range and the number 

of design categories present at sites sharply increases from the pre-migration to post-migration 

time periods, which in part accounts for the degree of similarity in social identities on average 

being significantly reduced from that of the Mississippian period. As a result, using the rubric 

presented in Table 8.1, macro-scale categorical identities similarity in the post-migration CIRV 

time period are assessed as low.  

These structural changes to networks of relational interaction and categorical 

identification had very real implications for Mississippian and Oneota potters and the 

communities in which they were nested more broadly. However, it is important to emphasize that 

an interpretation of accommodative intercultural communal coexistence does not presuppose 

peaceful or tolerant relationships. Rather, intercultural communal coexistence is used as a means 

to infer macro-scale behavioral response trends following culture contact. The Late Prehistoric 

CIRV was marked by multicultural accommodation at the macro-regional scale despite only 

limited evidence for intra-community multicultural cohabitation, which is only thus far present at 

two out of the eight sites with occupations dating between 1300 and 1450 A.D. – Crable and 

Morton Village. That these sites were interconnected to other sites in both the jar and plate 

technological attribute network layers attests to the accommodative nature of inter-community 

relationships in the post-migration time period. The breakdown of economic relationships and 

reduction in social scale of shared categorical identities among communities, however, were 

clear inflection points in delimiting collective action or social transformations to sub-groups 

within quasi-densely relational networks that did share common categorical identities, identities 

that may have cross-cut cultural boundaries.  

384 

Behavioral response trends toward inter-community cultural accommodation highlight a 

human capacity to habituate or acclimatize to novel social environments, sometimes unwillingly 

so. For example, Chapters 6 and 7 argued for the presence of a spatial and social internal frontier 

in the Late Prehistoric CIRV. The presence of an internal frontier was likely an outgrowth of 

deteriorating economic interrelationships and diverging social identities, both of which are likely 

to have structured Oneota in-migration.  

Some degree of cultural pluralism is inherent in accommodative inter-cultural communal 

coexistence. What distinguishes accommodative and pluralistic coexistence, however, is an 

active willingness of communities to accommodate themselves to a new social setting through 

the creative refashioning of cultural forms that otherwise fit within the worldviews of each 

distinct cultural group. In the Late Prehistoric CIRV ceramic industry multilayer network, it is 

clear that Oneota and Mississippian potters developed cultural innovations in ceramic industry 

that reflect a multicultural region but that those innovations were largely rooted in social 

interaction through the cultural transmission of socially-mediated artifact attributes. Oneota 

potters adopted a unique vessel form, the plate, at two multicultural sites – Crable and Morton 

Village – but decorated their plates with uniquely Oneota stylistic patterns. This indicates 

potential broader accommodation to foodways indigenous to CIRV Mississippian communities 

by Oneota peoples but in such a way as to bridge them within their own worldviews. That both 

multicultural sites were integrated into regional relational networks of interaction attests to likely 

cultural innovations among Mississippian potters in how they made ceramic vessels of the jar 

and plate classes. As proxy evidence for the broader communal social milieu in which potters 

were nested, it can be assumed that these relational trends of the creative refashioning of cultural 

385 

forms toward accommodation best explains behavioral responses to culture contact in the Late 

Prehistoric CIRV.  

 
 
8.7 Contributions of this Research 

A significant theoretical contribution of this project involved a quantitative relational 

perspective to archaeological ceramics in the study region, as well as of culture contact more 

broadly. Studies of archaeological ceramics in the study region have traditionally focused on 

taxonomically defining vessels into mutually exclusive types. Work in this regard has resulted in 

a substantial amount of detail with which to understand the chronological and cultural 

positioning of Late Prehistoric CIRV sites. A relational perspective richly contributes to these 

studies by providing hypotheses that characterize community relationships to one another along 

certain relational and categorical dimensions, and how those relationships change overtime. That 

these hypotheses were generated from a multidimensional analysis of a single material culture 

class shows how very different perspectives and interpretations may be drawn depending on the 

artifactual evidence or theoretical underpinnings used in different models. The generalized nature 

of this theoretical model provides an accessible template for its application in archaeological 

contexts in other regions.  

This dissertation has compiled a large amount of data from ceramic artifacts recovered 

from settlements across the Late Prehistoric central Illinois River valley. These data include 

systematic technological characterizations of two classes of ceramic artifacts, a coding schema 

for categorizing stylistic decorations on plate vessels, and a chemical compositional database. 

Many of the same ceramic vessels are included in each of these different data sets. All statistical 

and network analysis programming for this project on these data was performed in the R 

386 

statistical platform. Additionally, all code is provided in Appendix C as well as in various 

GitHub repositories (https://github.com/ajupton). As R is a free and open source programming 

language, the code enables all analyses and interpretations to be reproducible by any researcher 

and therefore to be testable. After an embargo period, all data will be digitally curated alongside 

the R code and interpretations produced through this study by the Digital Archaeological Record 

(tDAR). Providing both raw data and open-source code to analyze those data in an accessible 

manner replete with comments and extended discussions of methodology will hopefully 

encourage other archaeological researchers to do the same, leading to increased collaborations on 

open-source tools for archaeologists, a greater emphasis on reproducibility in archaeological 

science, and renewed focus on archaeological data as a component of shared human heritage.  

A major methodological contribution of this dissertation stems from the vessel 

technological attribute data pre-processing steps necessary to develop networks of interaction 

through cultural transmission. A novel method was developed by adapting a model from cultural 

transmission theory that identifies which individual artifact attributes are free to vary from site to 

site, enabling attributes likely constrained by engineering principles to be differentiated from 

attributes that likely bear social information. A method is then provided for constructing and 

analyzing similarities in socially mediated artifact attribute among sites as network graph 

objects. This method is unique in that it produces weighted and directed network graphs, which 

provide significant nuance in understanding topological or structural patterns of interaction 

through cultural transmission. The method may be applied to any attribute measured on a 

continuous scale, making it generalizable to a host of other archaeological artifact or feature data. 

In developing this methodology, it was identified that burial jar technological attributes in the 

Late Prehistoric CIRV were not independent from each other. In other words, as one burial jar 

387 

attribute changes, so do all other measurable attributes change in a step-wise fashion. This may 

lead to fruitful hypothesis generation about the relationship between burial jar and the 

individual(s) it was interred alongside that are outside the scope of this study.  

Another methodological contribution of this study is using geo-chemical data within a 

relational framework. Many geo-chemical compositional analysis studies focus largely on the 

exchange or circulation of vessels themselves as explaining parallels of membership in statistical 

chemical reference groups. The use of a relational framework rooted in economic interaction 

identifies the role that the sharing of raw material source information, overlapping resource 

exploitation areas, and similar production processes play in addition to exchange in explanations 

of geo-chemical patterning.  

A component of this project was the creation of a public website, https://andyupton.net. 

The website houses hundreds of photographs of the ceramic vessels used in project analyses 

alongside blog posts that discuss the project in an accessible manner as well as an interactive tool 

for sherd continuous attribute measurement data to be explored from both a quantitative as well 

as relational perspective. This should be a trend that continues for all archaeological analyses 

funded by public sources because it increases public literacy and interest in archaeology and 

cultural heritage at multiple scales.  

 

8.7.1  Contributions to Archaeology and CIRV Archaeology 
 

This study provides the archaeological profession more broadly and archaeologists 

working in the central Illinois River valley more specifically with a number of valuable 

contributions. First, this study has shown how taxonomically defined cultural groups may be 

analyzed from a relational perspective. This provides a richer and fuller perspective on these 

388 

archaeologically defined cultures because it emphasizes social dimensions gleaned from 

artifacts, breathing life into the relationships among individuals and the unique social milieu in 

which archaeological artifacts were produced, used, and discarded. This research also shows how 

extant museum collections may be used to foster regional scale relational perspectives, thereby 

maximizing the value of museum collections and furthering arguments for long-term curation 

strategies.  

This study provides CIRV archaeologists with a regional scale understanding of social 

structure prior to and succeeding a specific migration process of Oneota peoples into the 

Mississippian CIRV. In particular, those contributions emphasize regional scale organization 

among communities in the Mississippian period and the roles of deteriorating economic 

relationships related to ceramic industry and a proliferation of categorical social identities in 

structuring Oneota in-migration into the region as well as in explaining behavioral response 

trends to culture contact. In these ways, archaeologists and other researchers examining Late 

Prehistoric CIRV peoples have been provided with a regional synthesis from a relational 

perspective in order to provide a broader context on how individual sites are structurally situated 

vis-à-vis their relationships to other sites. That is, individual CIRV communities may now be 

placed into a broader social context, and future work in the region that considers other lines of 

evidence at various scales may validate or challenge many of the interpretations provided herein. 

In concert with interaction network layers based on the cultural transmission of jar and plate 

socially mediated technological attributes, this research highlights the value of a 

multidimensional, relational perspective to the analysis of culture contact.  

A number of CIRV sites were able to be chronologically positioned using radiocarbon 

data in this project. Short-lived faunal and floral samples submitted from Morton Village (11F2), 

389 

Ten Mile Creek (11T2), Star Bridge (11Br105/11Br17), Buckeye Bend (11F310), Emmons 

Village (11F218), Kingston Lake (11P11), and Baehr South (11Br47) each returned usable 

radiocarbon dates. Importantly, the major sites of Star Bridge and Ten Mile Creek were able to 

be confidently dated to a 14th century occupation. An attempt to provide a radiocarbon date for 

Houston-Shryock (11F114) was unfortunately unsuccessful due to sample contamination. 

Calibrated probability ranges are provided for each of these dates in Appendix H.  

On a broader level, this research contributes to an understanding of social structure 

during the Late Prehistoric period in the U.S. Eastern Woodlands. This critical period in 

American prehistory preceded the collapse and abandonment of fifteenth century chiefly polities 

in the central Illinois River valley (Esarey and Conrad 1998), the American Bottom (Cobb and 

Butler 2002, 2006), the lower Ohio valley and central Mississippi valley (Cobb 2005), and the 

lower Savannah River drainage (Anderson, et al. 1995). While many analyses of societal 

collapse focus on environmental factors (Bird, et al. 2017; Weiss and Bradley 2001) this research 

offers an alternative perspective by analyzing network models of social relations prior to 

abandonment and population displacement (Borck, et al. 2015). Problematizing and integrating 

social interaction and categorical identification with larger-scale political and social change is 

fundamental for understanding how culture is created, continued, and contested by people in the 

past and the present.  

 
 
8.8 Future Directions 

As with any archaeological research endeavor, the results presented in this dissertation 

must be considered as preliminary due in large part to the limitations and the vagaries of 

sampling a representative ceramic population from many sites across a fairly large study region 

390 

encompassing some 250 years of occupations. Invariably, this research will generate as many 

questions as it addresses, if not more. However, the present study shows the potential for a 

multidimensional relational perspective to the analysis of material culture data. Additionally, this 

study shows potential for chemical studies using LA-ICP-MS on shell tempered pottery, for a 

model of cultural transmission to be applied to ceramic technological attribute data, and for 

categorical identification to be explored on plate stylistic data sets in Mississippian and Upper 

Mississippian assemblages. Each of these data strands will hopefully be used in future inter-

regional analyses across broader Mississippian and Upper Mississippian sampling universes. 

Eastern North America is primed for the emergence of big data approaches to understanding 

cultural contact and the spread of Mississippian and Upper Mississippian culture, among a host 

of other analytical avenues.  

Multilayer network anlaysis is still largely in its infancy as a mathematical formulation, 

and applications in archaeological contexts have much to offer this fledgling analytical arena. 

Material culture lends itself to studies of the kinds of relationships that can be modeled in 

network analysis because it often encapsulates information about both inter-community or inter-

regional interactions as well as information about the social identity of the artisan(s) or 

individual(s) responsible for its production. In addition, archaeology has a uniquely human 

timescale with which to apply problems longitudinally. Archaeology is therefore uniquely 

situated to explore how humans actually behaved as opposed to how they might say they 

behaved in written text or in a survey or interview – which are otherwise often the basis for 

network analysis studies.  

As with any data-driven approach, additional data would improve the interpretations 

presented in this dissertation. In this regard, this dissertation has set up testable hypotheses about 

391 

the role of relations and categories in structuring Oneota in-migration and the re-structruing of 

social relationships in the multi-cultural CIRV following culture contact. Economic interactions 

can be further explored along other analytical dimensions such as foodways and the exchange of 

other material culture classes than pottery. Targeted excavations at sites such as Crable, Ten Mile 

Creek, and Lawrenz Gun Club hold promise for testing whether or not an accommodative 

intercultural communal coexistence framework is appropriate for explaining culture contact in 

the Late Prehistoric CIRV. Additionally, a number of sites with distinctly Oneota material 

culture present were unable to be included in this dissertation due to limited artifactual evidence. 

Sleeth and Otter Creek warrant additional sub-surface testing to enrich understanding of the Bold 

Counselor Oneota and their interactions with CIRV Mississippian peoples.  

 

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 
 

392 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

APPENDICES 

393 

 
 
 
 
 
 
 
 
 
 
 
 
 

APPENDIX A 

Coding Sheet 

 
 
 
 
20 
 
21 
 
22 

23 
24 

 

 

 
 
 
 
Coding Sheet 
 
This document provides a description of all 
variables collected on ceramic artifacts. 
Included are provenance information, 
taxonomic distinctions, continuous 
measurements, and categorical values. 
Stylistic categories for jar and plate 
decorations are provided detailing 72 
distinct jar decorations and 7 jar decoration 
categories as well as 94 distinct plate 
decorations and 29 plate categories. Non-
outlier maximal values were retained for 
continuous measurements using calipers.  
 
Site Name: 
1 
2 
 
3 
4 
 
5 
 
6 

Orendorf Settlement C (#1-79) 
Crable (#80-189; 371-376;  
 
1058-1100; 1300-1308) 
Walsh (#190-220; ) 
Lawrenz Gun Club (#221-241;  
660-711; 1133-1152) 
C.W. Cooper (#242-250; 370;  
723;1279-1299) 
Emmons Village (#251-294; 764-
767; 1024-1025) 
Baehr South (#295-311) 
Myer-Dickson (#312-346; 894) 
Ester Berry (#347-362) 
Fiedler (#363-365) 

7 
8 
9 
10* 
11*  Gillette (#366-369; 377) 
12 
13 
 
14 
15 

Star Bridge (#378-486; 952-974) 
Ten Mile Creek (aka Hildemeyer)  
(#487-532; 712-722; 875) 
Eveland (#533-565) 
Kingston Lake (#567-659; 1022-
1023) 
Buckeye Bend (#724-743) 
Fouts (#744-763) 
Larson (#768-851) 

16 
17 
18 
19  Morton Village (#852-874; 876-893; 
 

1153-1166; 1167-1194) 

Houston-Shryock (#895-935;  
1101-1132) 
Orendorf Cemetery (11F414) (#936-  
951) 
Vandeventer (#975-1021; 1026-
1027) 
Norris Farms #36 (1028-1057) 
Orendorf D [courtesy Illinois State 
Archaeological Survey] (1195-1257; 
1309-1310) 
Dickson Mounds (1258-1278) 

25 
 
*Fielder and Gillette were not included in 
any analyses due to small sample sizes 
 
Institutional Holding: 

 

1 

2 

3 

4 

5 

1 

Dickson Mounds Museum, 
Lewistown, IL 
Western Illinois University, 
Macomb, IL 
Upper Mississippi Valley 
Archaeological Research 
Foundation/Western Illinois 
Archaeological Research 
Center, Macomb, IL 
(courtesy L. Conrad) 
Indiana University Purdue 
University Indianapolis 
(courtesy, J. Wilson) 
UMVARF/Illinois State 
Archaeological Survey 
(courtesy L. Conrad and T. 
Emerson, K. Emerson, A. 
Zelin) 

Domestic (e.g. feature, 
domestic structure) 
Mortuary (e.g. burial mound, 
burial furniture, associated 
with burial) 

 
Provenience Sphere:  

2 

394 

3 

Ritual (e.g. public structure, 
non-burial mound) 
Unknown 

4 

1 
2 
3 
4 
5 
6 
7 
8 
* 

 
 
Specific Provenience: 
Feature 
 
Domestic Structure 
 
 
Public Structure 
Mound 
 
Mound, with burial 
 
Occupation Area 
 
 
Surface, unknown 
Unknown 
 
 
Pilot Study Sherds 
 
Sherd Type General: 
 
 
 
 
Sherd Type Specific (Traditional Taxonomic 
Type): 
See (Conrad 1991; Conrad and Esarey 1983; 
Esarey and Conrad 1981, 1998; Harn 1971, 
1978, 1980, 1991, 1994; Harn and McClure 
2012; Santure, et al. 1990; Vogel 1975) 

Probable Cooking Jar 
Broad Rim Plate/Bowl 
Probable Burial Jar 

1 
2 
3 

1 

Mississippian Plain  
Globular 
Cahokia Cordmarked 
Powell Plain 
Ramey Incised 
Trotter Trailed  
Dickson Cordmarked 
Dickson Trailed (also   
cordmarked) 
Crable Trailed 
Lobed 
Indeterminate Jar 
Plate - Plain 

2 
3 
4 
5 
6 
7 
 
8 
9 
10 
11 
12  Wells Incised Plate 
13 
 
14 
 
15 
16  Wells Broad Trailed Plate 

Crable Deep Rimmed,  
Incised 
Crable Deep Rimmed,  
Trailed 
Plate - Indeterminate 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

0 
1 
2 
3 

1 
2 
3 
4 

17 
18 
19  
20 
 

Shell 
Grit 
Grit and Shell 
Un-tempered 

Bold Counselor Oneota Jar 
Indet. Trailed Jar 
Sepo 
Dickson Series  

 
 
 
 
 
Residue (pottery char): 
Absent 
 
 
Present, interior only 
Present, exterior only 
 
 
Present, interior and exterior 
 
Tempering Agent: 
 
 
 
 
 
Temper Maximum Grain Size Diameter: 
 
Very Fine  (0.0625-0.125 
mm) 
 
 
 
 
 
 
 
Percent Temper Occurrence:  
 
 
 
 
Jar Lip Decoration (e.g. scalloping, 
incising): 
1 
 
 
2 
 
Jar Handle Decoration (e.g. trailing): 
 
 
 
 
Jar Orifice Diameter (measured on orifice 
diameter chart): 
 
 

Fine  (0.125-0.25 mm) 
Medium  (0.25-0.5 mm) 
Coarse  (0.5-1 mm) 
Very Coarse  (1-2 mm) 
Granules (2-4 mm) 
Gravel (4+ mm) 

Present 
Absent 
No handle present 

Few (6%) 
Little (12%) 
Some (31%) 

Present 
Absent  

2 
3 
4 
5  
6 
7 

In cm 

1 

1 
2 
3 

1 
2 
3 

395 

In mm 

In mm 

Jar Height (from the bottom of the globular 
base to the top of the vessel lip – only 
measured for complete or partially complete 
vessels): 
 
 
Jar Maximum Lip Thickness (lip refers to 
the extruded edge or margin of the orifice of 
the vessel (Rice 2005): 
 
 
Jar Maximum Shoulder Thickness (shoulder 
refers to the upper part of the body of a 
restricted vessel (Rice 2005) – for domestic 
jars, the shoulder was measured below the 
everted rim-globular body attachment and 
above where the vessel wall angle is 90˚ 
perpendicular to the vessel opening): 
 
 
Jar Maximum Wall Thickness (wall refers to 
within a few cm of the equator of the 
globular jar, or where the vessel wall angle 
is 90˚ perpendicular to the vessel opening): 
 
 
Jar Rim Height (rim refers to the area 
between the lip and the neck of the vessel 
(Rice 2005)):  
 
In mm 
 
Jar Rim Angle (90˚ equates to a completely 
vertical rim, 360˚ equates to a completely 
unrestricted vessel opening): 
 
 
Jar Primary Design Technique (see Chapter 
6 for a description of incised and 
trailing/trail-impressed categorical 
distinctions): 
 
 
 
 

Plain 
Incised 
Cordmarked 
Trailed 

In degrees 

In mm 

In cm 

0 
1 
2 
3 

In mm 

In mm 

In mm 

4 
 
 
5  
6 

Trailed and Impressed  
(Includes Punctates & Stab  
and Drag) 
Trailed unidentified  
Applique 

 
 
 
 
 
 
Jar Max cordmarking Thickness (measures 
the horizontal width of cordmarking): 
 
 
Jar Max Incising Thickness (measures the 
horizontal width of incised decoration): 
 
 
Jar Max Trailing Thickness (measures the 
horizontal width of trailing decoration): 
 
 
Jar Shape of Elements (general trend of 
decoration elements): 
Missing 
 
Indeterminate 
 
 
Horizontal 
Vertical 
 
Rectilinear 
 
 
Curvilinear 
One Repeating Motif 
 
Two Repeating Motifs 
 
Three+ Repeating Motifs 
 
 
Horizontal and Vertical 
 
Jar Shoulder Decoration (each combination 
of elements received a distinct category – 
text descriptions were used in conjunction 
with high-resolution photographs during 
categorization): 
-1 
Missing 
Indeterminate 
0 
One line Horizontal Trailing 
1 
Two lines Horizontal Trailing 
2 
3 
Three lines Horizontal Trailing 
Four lines Horizontal Trailing 
4 
Five lines Horizontal Trailing 
5 
6 
Six+ lines Horizontal Trailing 
Three Concentric Chevrons 
7 

-1 
0 
1 
2 
3 
4 
5 
6 
7 
8 

396 

8 
 
9 
10 
 
11 
12 
13  
14 
15 

16 

17 
 
18 
 
 
19 
 
20 

21 
22 
 
 
23 
24 
 
 
25 
 
26  

27 

28 
 
29 

30 
31 

Inverse elongated chevrons, cutoff at 
rim  
Trotter Trailed - curvilinear motif 
Two chevrons “V” above rectilinear  
trailing 
Elongated Chevrons 
Four+ concentric chevrons 
Ramey “trailed” eye motif    
Four Concentric chevrons 
Three lines Horizontal trailing with 
punctates below and stab and drag 
below punctates* (identical to 18) 
Trailed Concentric circle cross-in-
sun motif, flanked by rectilinear 
trailing bordered by punctates 
Three lines horizontal trailing  
above stab-and-drag 
Three lines horizontal trailing  
above punctates above stab- 
 
and-drag* (need to fix same as 15) 
Two chevrons “V” above two  
lines of rectilinear trailing 
Trailed line filled triangles, triangle 
line forms rectilinear trailing 
Three Trailed arcs on shoulder 
Ramey Incised bi-shoulder vessel;  
each shoulder has a distinct Ramey  
design, see photo 
Applique forms noded arc 
Horizontal punctate above four lines  
horizontal trailing above stab and  
drag 
Code 21 Trailed arcs below    
arced punctates  
Rectilinear line of punctates above 
two lines rectilinear trailing above 
stab and drag 
Code 26 but with punctate filled 
zones above rectilinear trailing 
Two lines arced punctates above  
three trailed arcs above stab and drag 
Three trailed concentric chevrons 
with a line of punctates on one side 
of lowest chevron 
Indeterminate ladder 
Sepo Collar Decoration 

 

32 
 
 
33 
34 
35 
36 
37 
 
38 

39 
 
40 
 
 
 
 
41 
 
 
42 
 
 
43 
 
44 
 
45 
 
46 
 
 
 
 
47 

48 
 
 
 

Three lines rectilinear trailing, not  
cutoff at rim like Code 8, forms  
continuous chevron 
Overlapping Code 8 motifs 
Four lines curvilinear trailing 
Two concentric chevrons 
Two lines curvilinear trailing  
Concentric arc/curvilinear trailing  
flanked by vertical incising 
Code 20 line filled triangles/ 
rectilinear motif but incised instead 
of trailed 
Three trailed lines forming a chevron 
but lines in between are curvilinear 
Three trailed horizontal lines above a 
horizontal line of punctates above  
groups of five stab-and-drag trailing  
spaced apart roughly equal to their  
width (of five drags) 
Rectilinear line of punctates above  
three lines rectilinear trailing above  
stab and drag (code 27, three lines) 
Horizontal line of punctates above  
four lines horiz. trailing above stab  
and drag (same as 24?) 
Five lines horizontal trailing above  
stab and drag 
Two lines horizontal trailing above  
stab and drag 
Four lines horizontal trailing above  
punctates above stab and drag 
Alternating concentric chevrons  
(either V shaped or the inverse)  
flanked by two lines diagonal trailing 
with punctates either above or below 
motif (V below, inverse above) 
Alternating curvilinear trailing 
flanked by three diagonal lines with 
punctates either above or below 
trailing (same  as 46, but curvilinear 
instead of chevron motif) 
Three lines horizontal trailing above  
stab and drag with punctates   
superimposed in horizontal linear  
groups of 6-9 on lines of trailing 

397 

49 

50 
 
51 

52 

53 
 
 
 
 
54 
 
55 

56 
 
 
57 
58 

59 
 
 
60 
 

Three lines arc trailing above stab 
and drag, trailing forms arcs with 
punctates flanking two lines of 
trailing between each arc-based 
motif 
Three lines curvilinear trailing above 
stab and drag 
Punctates above four lines arc 
trailing above stab and drag, lacks 
the motif between arcs like Code 49, 
also includes punctates below 
handles 
Punctates above three lines 
rectilinear trailing above stab and 
drag, though punctates only appear 
on one side of the trailing (i.e. only 
on the right side of the “V”) 
Code 10 but only one chevron above 
rectilinear trailing. Space between  
rectilinear trailing indicates this was  
made as a motif as opposed to  
interconnected trailing  
Nested “U” shape, or U within a U;  
maybe a beaver tail or flower pedal? 
Arc line of punctates above three 
lines arc trailing above stab and drag. 
In between arc motif is a smaller and 
similar arc motif with punctates 
above three lines arc trailing. Main 
motifs are quadripartite in corners, 
smaller motifs at main directions.  
Code 44 but stab and drag occurs in 
groups of 4 eight times around the  
vessel  
Two horizontal applique nodes 
Arc of punctates above bifurcated  
arrow. Arrow consists of three 
vertical lines and three diagonal lines 
emanating from the upper/middle 
portion of the vertical lines (five total 
motifs) 
Arcs punctates above two lines arc  
trailing above stab and drag. Motif is 
quadripartite in corners 
Repeating motif of rectilinear arc of  
punctates above three diagonal lines 

 

 
 
 
 
 
 
61 
 
 
 
 
 
 
 
62 
 
63 
 
64 
 
 
 
 
 
 
 
 
65 
 
 
 
 
66 
 
67 
 
 
68 
 
 
69 
 
70 
 
71 
 

of trailing above stab and drag.  
Trailing/stab and drag are cut off  
before a typical rectilinear trailing  
would descend. Only the ascending  
portion of the trailing is present (six  
total motifs) 
Two motifs - on cardinal directions  
(including handles) are concentric  
inverse arc (“U”) trailing above an  
inverse arc of punctates. Second  
motif - on corners is a trailed spiral  
sun inside a circle of punctates. Line 
of punctates below inverse arcs is  
continuous around the vessel 
Three lines rectilinear trailing above  
stab and drag 
Two lines horizontal trailing above  
punctates above stab and drag 
Rectilinear line of punctates above  
diagonal stab and drag trailing with  
nested vertical stab and drag trailing. 
Like Code 60, but there are four lines 
of trailing and they are executed via  
stab and drag below the rectilinear  
punctates. The stab is diagonal to the 
left and diagonal to the right (see  
photo!) 
Code 61 trailed spiral sun motif  
repeating six times; second motif is  
two inverse arc “U” trailing and an  
inverse arc of punctates below  
handles 
Vertical trailing in groups of 3 eight  
times around the vessel 
Curvilinear punctates above three  
lines curvilinear trailing above stab  
and drag 
Incised inverse line filled triangle  
nested in a triangle motif repeats 7  
times. (Triangles point up) 
Two incised arcs above incised stab  
and drag motif 
Two lines curvilinear trailing above  
stab and drag 
Three lines horizontal trailing above  
punctates above stab and drag but  

398 

stab and drag only appears in groups 
of 3, 4, or 6 eight times total (similar  
to Code 40) 
Two arcs of punctates above two  
inverse “V” trailed lines above stab  
and drag 
Code 72 motif but three trailed “V”  
lines as opposed to two 
Horizontal line of punctates above  
four lines horizontal trailing above a  
line of horizontal punctates 
Code 52 but punctates only occur on 
the left side of the “V” 
Four lines horizontal trailing above  
stab and drag 
Code 27 and 41 but with four lines  
recliner trailing below punctuates  
above stab and drag 
Two lines of rectilinear punctates  
above four lines rectilinear trailing  
(likely stab and drag below, but not  
present) 
Indeterminate trailing and punctates 

 
 
 
72 
 
 
73 
 
74 
 
 
75 
 
76 
 
77 
 
 
78 
 
 
 
79 
 
Brainerd-Robinson Design Group - Jars 
(Unique Designs were re-categorized into 
design groups in order to compute Brainerd-
Robinson coefficients of agreement.) 
=(isolate, will not be 
included) 14, 21, 27, 29, 30, 
31, 33, 34, 36, 37 
=7, 8, 10, 11, 12, 19, 32, 35,  
39, 53 
=9, 13 
=17 
=18, 40, 45, 48 
=20, 38 
=41 
=42 

-1 

1 
 
2 
3 
4 
5 
6 
7 

 
 
 
 
 
 
 
 
 
Jar Shoulder Type: 
 
 
 
 
 

-1 
1 
2 
3 
4 

Missing 
Rounded (Globular) 
Sub-angular (Shallow) 
Lobed 
Bi-shoulder 

399 

0 
1 
2 
3 
 
4 
5 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

Indeterminate 
Extruded 
Flat 
Rounded 
Rolled 
Flared 
In-Curved 
Interior Beveled 
Exterior Beveled 
Out-Curved 

Eroded  
Absent  
Present, Interior Rim Only 
Present, Interior rim and  
body 
Present, Exterior 
Present, Exterior and Interior 

 
Jar Slip/Paint: (surface treatment) 
 
 
 
 
 
 
 
 
Jar Lip Shape: 
 
 
 
 
 
 
 
 
 
 
 
Plate Maximum Rim Diameter (measured 
using rim diameter chart): 
 
 
Plate Height (height refers to the bottom of 
the vessel well (or globular bowl) to the 
opening plane of the vessel rim – see image 
below): 
 
 
Plate Depth (depth refers to the bottom of 
the vessel well to the attachment between 
the well and the rim or flare): 
 
 
Plate Flare Length (flare refers to the highly 
everted outflaring rim): 
 
 
Plate Flare Angle (see image below): 
 
 
Plate Max Lip Thickness (before tapering): 
 

In degrees 

In mm 

In mm 

In mm  

In cm 

In mm 

In mm 

In mm 
 

 

In mm 
 

 
Plate Max Thickness Below Lip (or max 
thickness of the outflaring rim): 
 
 
Plate Max Incising Thickness: 
 
 
Plate Max Trailing Thickness: 
 
 
Plate Primary Design Technique: 
 
 
 
 
 
 
 
Plate Decoration (each combination received 
a distinct categorical value): 
0 
1 
2 

Plain 
Incised 
Trailed 
Trailed and Impressed  
(Includes Punctates & Stab  
and Drag) 

0 
1 
2 
3 
 
 

Indeterminate 
Plain 
Vertical line filled curvilinear 
trailing (lines below curves) 
Line filled triangles, flares out, lines  
emanate from vertical line to rim 
Repeating > (weeping eye?) 
Vertical incised lines extending from 
curvilinear trailing (lines above  
curves)  
Incised line filled triangles, flares 
out, triangles point to inside plate, 
lines follow triangle 
Repeating Curvilinear >  
Line filled triangle nested in triangle, 
points to well 
Vertical Incising 
Diagonal Incising above a horizontal 
line 
Triangle filled with horizontal lines,  
points toward well 
Triangles filled with vertical lines,  
points towards well 

3 
 
4 
5 
 
 
6 

7 
8 
 
9 
10 
 
11 
 
12 
 

13 
 
 
14 
 
 
15 
 
16 
 
17 
 
18 
19 
 
20 
 
 
21  
22 
 
23 
 
 
24 
25 
 
26 

27 

28 
 
29 

30 
 
31  
 

Code 6 Triangle on rim with vertical  
line filled triangles following bottom 
flare lip  
Sun motif with concentric curvilinear 
incising composing sun body and  
triangles composing sun rays 
Chevron incising points toward well, 
with nested arc 
Concentric chevrons pointing out  
bordered by vertical trailing 
Semi-circle filled with vertical lines  
nested within curvilinear ladder 
Vertical incising with sun ray border 
Incised concentric arcs point towards 
well 
Code 6 on rim with horizontal line  
filled curvilinear chevrons following  
bottom flare lip 
Cross hatched oblique triangle 
Code 14 sun motif with vertical  
incising between suns 
Code 14 sun motif with code 18  
vertical incising/sun ray border  
between suns 
Semi-circle filled with vertical lines 
Code 6 line filled triangles but trailed 
instead of incised 
Code 11 Horizontal Line Filled 
Triangles on rim with horizontal line 
filled triangles pointing out from 
base of rim, forms rectilinear 
chevron bordered by the line filled 
triangles 
Rectilinear chevron trailing - 
O’Byam Incised? 
Code 14 sun motif emanating from  
rim, points toward well 
Code 11 Triangle filled with 
horizontal lines, points away from 
well 
Concentric Rectilinear Chevrons,  
points towards well 
Bifurcated Concentric Chevrons,  
points toward well 

400 

32 
 
 
33 

34 
35 

36 
 
 
37 

38 

39 

 
40 
 
 
 
 
41 
 
 
42 
 
43 

44 
 
 

Line filled triangles point away from 
plate following bottom flare lip, lines 
follow triangle (inverse of Code 6)  
Code 6 Line Filled Triangles on rim 
with line filled triangles (following 
triangle) pointing out from base of 
rim, forms rectilinear chevron 
bordered by the line filled triangles 
Cross inside sun motif, whole sun  
Code 32 horizontal line filled 
triangles with sun motif pointing 
towards plate,  cutoff by triangles  
Code 34 cross inside sun motif with  
Code 18 vertical incising/sun ray  
border  between suns 
Code 9 Vertical Incising with Cross 
in Circle motif appearance in b/t 
incising 
Code 20 alternating incised line 
filled triangles on rim but with 
horizontal triangles from well lip 
extend to plate rim (i.e. NOT Code 
33), but with space b/t triangles 
Bifurcated horizontal incised line 
filled triangles flare out and point to 
inside  plate, incised line filled 
triangles point away from plate with 
lines following 
triangle - no space between triangles 
Small Code 6 diagonal line filled  
triangles on rim, with small diagonal  
line filled triangle on lip that point  
toward the plate and form sun rays  
emanating from the plate well 
Vertical incised line filled triangles  
point toward base, are bordered by  
punctates 
Curvilinear incising on rim and on  
base of rim 
Code 34 Cross in circle sun motif 
with line filled triangles in between 
suns 
Code 34 cross in circle sun, cross in  
circle is nested inside sun,  
surrounded by line filled triangles 

 

45 

46 
47 
 
48 
 
49 

50 

51 
 
 
 
 
52 
53 
 
54 
 
55 
56 
 
57 
 
58 

59 

60 
 
61  

62 
63 
 
64 
65 
 

Code 38 but with horizontal line 
filled triangles extending from rim  
Indeterminate Cross Hatching 
Curvilinear chevron bordered by  
horizontal line filled arcs 
Nested cross hatched triangle points 
towards well 
Alternating line filled triangles 
(pointing toward and away from 
well), lines follow triangles, no space 
between - Compound Triangles 
Code 14 sun motif with 
indeterminate sun flare bordered 
design between suns 
Vertical line filed triangle nested in  
two lines of rectilinear incising. Very 
reminiscent of Bold Counselor jar  
designs minus the punctates. Clearly 
incised 
Cross hatched Code 6  
Code 49 alternating triangles but  
trailed instead of incised 
Elongated and alternating incised  
oblique triangles 
Incised elongated “X” shape 
Incised line Filled squares, diagonal  
lines alternate in directionality 
Alternating code 6 triangles and code 
12 vertical line filled triangles 
Alternating incised vertical lines 
(code 9) and incised line filled arcs 
Alternating? “Arrow feather” 
diagonal incising and horizontal 
incising 
Code 14 sun motif alternating with  
code 9 vertical incising 
Code 31 bifurcated concentric 
chevrons on both exterior and 
interior rim, forms negative space 
chevron 
Code 5 but trailed instead of incised 
O’Byam Incised-like curvilinear  
trailing/incising 
Indeterminate Cross-in-circle motif 
Diagonal (as opposed to vertical)  
trailing 

401 

87 

88 
 
 
89 

90 

66 
 
 
67 
 
 
 
68 

69 
 
70  
71 
 
72 
 
73 
 
74 

75 
76 

 
77 
 
78 
 
 
79 
 
80 
 
81 

82 
 
83 

Code 14 style sun but nested within  
arcs are indeterminate line filled  
triangles and other concentric arcs 
Sun ray triangles on upper and  
lower rim forming negative space  
chevron flanked by vertical incised  
lines 
Code 33-like chevron but triangles 
are filled with concentric triangles 
(or chevrons) instead of lines 
following triangle 
O’Byam incising flanked by Code 18  
sun rays/vertical incising 
Indeterminate ladder  
Concentric chevron/triangle/“V”  
shape, points out or away from well 
Alternating arc, i.e. incomplete arc in 
between complete arcs 
Code 47 curvilinear trailing/chevron  
but with vertical line filled arcs 
Inverse of Code 26 - triangles on 
base rim follow triangle while 
exterior rim are horizontal 
Four concentric chevrons 
Opposite of Code 13 - vertical 
incised line filled triangles on 
exterior rim and 
Code 6 on interior rim pointing out 
Sun, moon?, and chevrons.  
Idiosyncratic and poorly executed 
Concentric arcs or chevrons, inverse 
of Code 19 in that they point away  
from well 
Code 40 but bottom lip triangles are  
horizontal line-filled 
Code 6 on exterior rim with Code 63 
O’Byam incising on interior rim 
Concentric arc incising, arcs are 
filled with horizontal incising near 
interior rim and nested diagonal 
incising on exterior rim 
“V” chevron points towards well,  
flanked by diagonal lines  
Horizontal incised line filled arcs, 
arcs open away from well 

 

402 

84 

Alternating trailed concentric arcs 
sun motif on exterior and interior 
rims 

85  Motif on tab - Three lines inverse arc 
 
 
 
86 

“U” shape trailing with one arc of  
punctates on the top and bottom of  
motif 
Vertical trailed lines flanked by a 
vertical line of punctates alternating 
with likely trailed arcs bordered by a 
line of punctates on interior rim. 
Much like Code 23 but punctates 
replaces triangular sun rays 
Code 23 sun and vertical incised 
motif   but the vertical lines are not 
flanked by triangular sun rays 
Code 25 (trailed Code 6) nested in a 
line of rectilinear trailing and a  
rectilinear line of punctates.  
Curvilinear incised concentric arc 
sun motif point away from base sun 
rays formed not by triangles but by 
incised lines 
Code 25 (trailed Code 6) nested in 
three lines rectilinear trailing 
bordered by punctates  
Code 33 but Code 6 style triangles  
emanate from the rim to the lip,  
creating negative space triangles  
that are not connected 
Code 19 nested arcs but trailed  
instead of incised (like Code 85 but  
no punctates below arcs) 
Alternating concentric chevrons, i.e.  
incomplete concentric chevrons  
bordered by chevrons. All point  
towards well. Main, complete,  
chevrons have punctates on outer 
border  
Like Code 27 O’Byam incising but 
trailed and two lines, more rectilinear 

91  
 
 
 
92 
 
 
93 
 
 
 
 
 
94 
 
 
Brainerd-Robinson Design Group - Plates 
(Unique Designs were re-categorized into 
design groups in order to compute Brainerd-
Robinson coefficients of agreement.) 

=(Isolate, will not be included in  
analysis)16, 17 
= plain 
=2, 5, 58, 62, 73 
=3 
=4, 7 
= 6, 25, 70 
=8 
=9, 10 
=11 
=12, 24, 57 
=13, 76 
=14, 22, 23, 28, 50, 60, 66, 87 
=15, 30, 75 
=13, 69 
=19 
=20, 26, 38, 40, 45, 74, 79, 91 
=21, 46, 48, 52 
=27, 55, 63, 94 
=29, 32, 68, 71 
=31, 61 
=33, 80 
=34, 36, 43, 44 
=39, 49, 53, 56, 81 
=41, 83, 86, 88, 90 
=47 
=51 
=54, 59, 67 
=65, 82 
=72, 78, 84, 89, 92 
=85 

Indeterminate 
Extruded 
Flat 
Rounded 
Rolled 
Flared 
In-Curved 
Interior Beveled 
Exterior Beveled 
Out-Curved 

-1 
 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
 
Plate Lip Shape: 
 
 
 
 
 
 
 
 
 
 
 
 
 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

 
 
 
 
 
 
 
  
 
 
 
 
 
 

403 

APPENDIX B  

 

Ceramic Vessel Measurement Data Availability  

 
 
All ceramic vessel technological attribute data are provided in electronic form through the 
Digital Archaeological Record (tDAR) at the following permanent link: 
 
https://core.tdar.org/project/447475  
 
After an embargo period lasting five years from the publication of this dissertation, electronic 
versions of LA-ICP-MS data presented in Chapter 7 will be available through the Field Museum 
Elemental Analysis Facility.   
 
https://www.fieldmuseum.org/science/labs/elemental-analysis-facility 
 
https://www.fieldmuseum.org/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

404 

APPENDIX C  

 

All R Code for Statistical Analyses 

 
Following an embargo period lasting six months after the publication of this dissertation, all code 
and individual data files will be presented on GitHub at the following link: 
 
https://github.com/ajupton 
 
Because GitHub is a private company whose policies may change unpredictably, all R code is 
presented in text form here. Note that the R code provided here has no warranty whatsoever and 
any kind of support is not guaranteed to be provided. You are free to do what you like with this 
code provided that you cite this dissertation document and/or any future publications out of 
which this dissertation data and methodologies are published. All stand-alone Shiny app software 
below may be freely redistributed and/or modified under the terms of the GNU General Public 
License as published by the Free Software Foundation, either version 3 of the License, or (at 
your option) any later version. See http://www.gnu.org/licenses/. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

405 

R Code from Chapter 5 
 
Routines to generate and analyze networks of interaction through cultural transmission 
from continuous artifact attribute data 
 
# Load the required libraries for analysis 
library(tidyverse) 
library(igraph) 
library(cluster) 
library(cowplot) 
library(ggridges) 
library(readxl) 
library(knitr) 
library(readr) 
library(colorRamps) 
library(RColorBrewer) 
 
# Read in data sets - domestic jars and serving plates 
jars <- read_csv("jars_cont.csv", col_types = cols(Orifice = col_double(),  
                  RimAngle = col_double())) 
 
# Read in sherd id information 
jar_unique <- read_csv("jar_unique.csv") 
 
# Set row names as the unique sherd id's 
rownames(jars) <- jar_unique$`2` 
 
# Do the same for plate data set 
plates <- read_csv("plate_cont.csv", col_types = cols(FlareAngle = col_double(),  
                    MaxDiameter = col_double())) 
plate_unique <- read_csv("plate_unique.csv") 
rownames(plates) <- plate_unique$`1` 
 
# Factorize site data for grouping 
levels(as.factor(jars$Site)) 
levels(as.factor(plates$Site)) 
 
# Function to compute the length of the data set, ignoring NAs 
my_length <- function(x){ 
          sum(!is.na(x)) 
  } 
 
# Function to compute number of vessels in total 
n_vessels <- function(x){ 
  x %>% 
    summarise_all(my_length) 
  } 
 
# Function to computer number of vessels by "Site";  
# This function can group the data by any factor or string column, "Site" is used here 
n_vessels_by_site <- function(x){ 
          x %>% group_by(Site) %>%  

406 

          summarise_all(my_length) 
  } 

Functions from Eerkens and Bettinger (2008) 
 
# Unbiased estimator of coefficient of variation 
my_cv <- function(x){ 
          (sd(x, na.rm = TRUE)/mean(x, na.rm = TRUE)) * (1 + (1/(4*length(x[!is.na(x)])))) 
  } 
 
# Standard Deviation, removing missing values by default 
my_sd <- function(x){ 
          sd(x, na.rm = TRUE) 
  } 
 
# Mean function, removing missing values by default 
my_mean <- function(x){ 
          mean(x, na.rm = TRUE) 
  } 
 
# Variation of Variation (VOV)  
# Unbiased CV of assemblage CVs 
VOV <- function(x){x %>% 
    group_by(Site) %>% 
      summarise_all(my_cv) %>% 
      summarise_all(my_cv) 
  } 
 
# Variation of the mean (VOM) 
# Unbiased CV of assemblage means 
VOM <- function(x){x %>% 
    group_by(Site) %>% 
      summarise_all(my_mean) %>% 
      summarise_all(my_cv) 
  } 
 
# Average variation (AV) 
# Mean of assemblage CVs 
AV <- function(x){x %>%  
    group_by(Site) %>% 
      summarise_all(my_cv) %>% 
      summarise_all(my_mean) 
  } 

Results of Eerkens and Bettinger (2008) analysis 
 
# Sample size determination 
# Gather sample means and standard deviations 
all_mean_sd <- bind_rows(bj_mean_sd, j_mean_sd, p_mean_sd) 
all_mean_sd_log <- all_mean_sd 
 
# Take the log base 10 of means/std in order to account for scalar effects across the  
# different measurement scales (mm, cm, degrees) 

407 

all_mean_sd_log$my_mean <- log10(all_mean_sd_log$my_mean) 
all_mean_sd_log$my_sd <- log10(all_mean_sd_log$my_sd) 
 
# Plot with regression lines 
all_mean_sd_log %>%  
  ggplot(aes(x = my_mean, y = my_sd, color = Class)) +  
  geom_point() +  
  geom_smooth(method = "lm", se = FALSE) +  
  theme_classic() +  
  xlab("Mean of Log Base 10 Measurements") +  
  ylab("Standard Deviation of Log Base 10 Measurements") 

# Calculate VOV for jars and plates, add vessel class to attribute name 
jarsVOV <- VOV(jars) 
colnames(jarsVOV) <- paste("Jar", colnames(jarsVOV), sep = "_") 
platesVOV <- VOV(plates) 
colnames(platesVOV) <- paste("Plate", colnames(platesVOV), sep = "_") 
 
# Calculate AV for jars and plates, add vessel class to attribute name 
jarsAV <- AV(jars) 
colnames(jarsAV) <- paste("Jar", colnames(jarsAV), sep = "_") 
platesAV <- AV(plates) 
colnames(platesAV) <- paste("Plate", colnames(platesAV), sep = "_") 
 
# Calculate VOM for jars and plates, add vessel class to attribute name 
jarsVOM <- VOM(jars) 
colnames(jarsVOM) <- paste("Jar", colnames(jarsVOM), sep = "_") 
platesVOM <- VOM(plates) 
colnames(platesVOM) <- paste("Plate", colnames(platesVOM), sep = "_") 
 
# Transpose scores to prepare for concatenating into a table 
VOV_scores <- t(tbl_df(c(jarsVOV[-1], platesVOV[-1]))) 
VOM_scores <- t(tbl_df(c(jarsVOM[-1], platesVOM[-1]))) 
AV_scores <- t(tbl_df(c(jarsAV[-1], platesAV[-1]))) 
 
# Bind together different score metrics and provide column names 
EB_scores <- as.data.frame(cbind(scale(VOV_scores), scale(VOM_scores), scale(AV_scores))) 
colnames(EB_scores) <- c("VOV", "VOM", "AV") 
 
# Add a column of the rownames and order the table by VOV 
EB_scores <- EB_scores %>% 
              rownames_to_column(var = "Metric") %>% 
              arrange(desc(VOV)) 
# Plot VOV  
pVOV <- EB_scores %>% 
      gather(key = EB_Metric, value = Score, VOV:AV) %>% 
      filter(EB_Metric == "VOV") %>%   
      ggplot() + geom_point(aes(x = reorder(Metric, Score), y = Score),  
                            shape = 18, size = 4) +  
      ylab("VOV") + xlab("") +  
      theme(axis.text.x = element_blank(), axis.ticks.x = element_blank(),  
            axis.text.y = element_text(family = "Times", color = "gray5"),  
            axis.title.y = element_text(family = "Times", color = "gray5"),  

408 

            legend.position = "none") + coord_cartesian(ylim = c(-2, 2)) + 
      scale_y_continuous(breaks = c(-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2)) 
 
# Plot AV 
pAV <- EB_scores %>% 
      gather(key = EB_Metric, value = Score, VOV:AV) %>% 
      filter(EB_Metric == "AV") %>%   
      ggplot() + geom_point(aes(x = reorder(Metric, Score), y = Score),  
                            shape = 18, size = 4) +  
      ylab("AV") + xlab("") +  
      theme(axis.text.x = element_blank(), axis.ticks.x = element_blank(),  
            axis.text.y = element_text(family = "Times", color = "gray5"),  
            axis.title.y = element_text(family = "Times", color = "gray5"),  
            legend.position = "none") + coord_cartesian(ylim = c(-2, 2.2)) + 
      scale_y_continuous(breaks = c(-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2))  
 
# Plot VOM 
pVOM <- EB_scores %>% 
      gather(key = EB_Metric, value = Score, VOV:AV) %>% 
      filter(EB_Metric == "VOM") %>%   
      ggplot() + geom_point(aes(x = reorder(Metric, Score), y = Score),  
                            shape = 18, size = 4) +  
      ylab("VOM") + xlab("") +  
      theme(axis.text.x = element_blank(), axis.ticks.x = element_blank(),  
            axis.text.y = element_text(family = "Times", color = "gray5"),  
            axis.title.y = element_text(family = "Times", color = "gray5"),  
            legend.position = "none") + coord_cartesian(ylim = c(-2, 2)) + 
      scale_y_continuous(breaks = c(-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2)) 
 
# plot_grid(pVOV, pVOM, pAV, align = "hv") 

Variables likely not constrained by engineering factors: 
 
Plate: 
flare angle, trailing thickness, incising thickness, and diameter 
 
Jar 
rim angle, trailing thickness, rim height, and wall thickness. 
 
Assess variable distributions at sites through ridgeline plots 
 
# Gather data for faceting. Faceting allows the graph to show each attribute's  
# distribution across the different sites 
pGathered <- gather(plates[, c(1, 2, 6, 7, 8)], Attribute, Value, MaxDiameter:MaxTrailing) 
jGathered <- gather(jars[, c(1, 5, 6, 7, 9)], Attribute, Value, MaxWall:MaxTrailing) 
 
# Read in node tables to add column to arrange by time period in ridgeline plots 
jar_node_table <- read_csv("Jar_node_table.csv") 
colnames(jar_node_table) <- c("Site", "Label", "Long", "Lat", "Time") 
plate_node_table <- read_csv("Plate_node_table.csv") 
colnames(plate_node_table) <- c("Site", "Label", "Long", "Lat", "Time") 
 

409 

# Join node table to allow for separating out sites by time in plots 
pGathered <- pGathered %>% left_join(plate_node_table[c(1, 5)]) 
pGathered$Time1 <- as.factor(pGathered$Time) # Add Time column as factor for discrete color sc
ale 
jGathered <- jGathered %>% left_join(jar_node_table[c(1, 5)]) 
jGathered$Time1 <- as.factor(jGathered$Time) 
 
# Create plate ridgeline plot 
pRidge <- pGathered %>% group_by(Site) %>% arrange(Time, Site) %>%  
            ggplot(aes(x = Value, y = reorder(Site, desc(Time)), fill = Time1)) +  
            geom_density_ridges() +  
            facet_wrap(~Attribute, scale = "free") +  
            theme(axis.text.y = element_text(size=12)) +  
            xlab("") +  
            ylab("") + ggtitle("Plate Attributes") + 
            scale_fill_brewer(palette = "Greens") +  
            theme(legend.position = "none")  
 
 
# Create plate ridgeline plot 
jRidge <- jGathered %>% group_by(Site) %>% arrange(Site, Time) %>%  
            ggplot(aes(x = Value, y = reorder(Site, desc(Time)), fill = Time1)) +  
            geom_density_ridges() +  
            facet_wrap(~Attribute, scale = "free") +  
            theme(axis.text.y = element_text(size=12)) +  
            xlab("") +  
            ylab("") + ggtitle("Jar Attributes") + 
            scale_fill_brewer(palette = "Greens") +  
            theme(legend.position = "none")  
         
 
# Show the jar ridgeline plot 
# jRidge 
 
# Show the plate ridgeline plot 
# pRidge 

Calculating proportional similarity from socially mediated artifact type-attributes 
 
# Select the socially mediated variables from jars and plates 
jar_social <- jars %>% 
                select(Site, MaxWall, RimHeight, RimAngle, MaxTrailing) 
 
plate_social <- plates %>% 
                  select(Site, MaxDiameter, FlareAngle, MaxIncising, MaxTrailing) 

Assessing similarity 
 
# Calculating Gower distance for jars 
jdaisy <- as.matrix(daisy(jar_social[-1], metric = "gower", stand = TRUE)) 
 
# Convert matrix of distances to matrix of similarities 
jdaisy_sim <- 1 - jdaisy 

410 

 
# Change from unique sherd i.d. to site name for column and row names 
rownames(jdaisy_sim) <- as.matrix(jars[1]) 
colnames(jdaisy_sim) <- as.matrix(jars[1]) 
 
# Calculating Gower distance for plates 
pdaisy <- as.matrix(daisy(plate_social[-1], metric = "gower", stand = TRUE)) 
 
# Convert matrix of distance to matrix of similarities 
pdaisy_sim <- 1 - pdaisy 
 
# Change from unique sherd i.d. to site name for column and row names  
rownames(pdaisy_sim) <- as.matrix(plates[1])  
colnames(pdaisy_sim) <- as.matrix(plates[1]) 

Turning similarity into social networks 
 
# Graph object of jars 
jg <- graph_from_adjacency_matrix(jdaisy_sim,  
                                  mode = "directed", weighted = TRUE) 
 
# Graph object of plates 
pg <- graph_from_adjacency_matrix(pdaisy_sim,  
                                  mode = "directed", weighted = TRUE) 

# Construct jar weighted edgelist 
jel <- as_edgelist(jg, names = TRUE) 
jweights <- as.numeric(E(jg)$weight) 
jwel <- tbl_df(cbind(jel, jweights)) 
colnames(jwel) <- c("Source", "Target", "weight") 
jwel$weight <- as.numeric(jwel$weight) 
 
# Construct plate weighted edgelist 
pel <- as_edgelist(pg, names = TRUE) 
pweights <- as.numeric(E(pg)$weight) 
pwel <- tbl_df(cbind(pel, pweights)) 
colnames(pwel) <- c("Source", "Target", "weight") 
pwel$weight <- as.numeric(pwel$weight) 
 
# Proportional similarity of plates 
plate_ps <- pwel %>% 
              group_by(Source, Target) %>% 
              summarise(sum = sum(weight, na.rm = TRUE), n = n()) %>% 
              mutate(Prop_sim = sum/n)  
 
# Proportional similarity of jars 
jar_ps <- jwel %>% 
              group_by(Source, Target) %>% 
              summarise(sum = sum(weight, na.rm = TRUE), n = n()) %>% 
              mutate(Prop_sim = sum/n)  
 
# Function to range normalize the proportional similarity weights between 0 and 1 
range01 <- function(x){ 

411 

            (x-min(x))/(max(x)-min(x)) 
  } 
 
# Range normalize the proportional similarity scores 
range_norm_jar_ps <- jar_ps %>% 
                        na.omit() %>% 
                        group_by(Source) %>% 
                        mutate(Range_prop_sim = range01(Prop_sim)) 
         
range_norm_plate_ps <- plate_ps %>% 
                          na.omit() %>% 
                          group_by(Source) %>% 
                          mutate(Range_prop_sim = range01(Prop_sim)) 
 
# Filter to only include scores above 0.5 and remove recursive edges  
# (i.e. node edges pointing to the node itself) 
range_norm_jar_ps_filt <- range_norm_jar_ps %>% 
                            filter(Range_prop_sim > 0.5) %>% 
                            filter(Source != Target) 
                             
range_norm_plate_ps_filt <- range_norm_plate_ps %>% 
                              filter(Range_prop_sim > 0.5) %>% 
                              filter(Source != Target) 

# Read in tables of jar site names, geographic coords., and time distinction 
# For time, 1 is a primary occupation prior to Oneota in-migration 
# and 2 is a primary occupation succeeding Oneota in-migration 
jar_node_table <- read_csv("Jar_node_table.csv") 
colnames(jar_node_table) <- c("Source", "Label", "Long", "Lat", "Time") 
plate_node_table <- read_csv("Plate_node_table.csv") 
colnames(plate_node_table) <- c("Source", "Label", "Long", "Lat", "Time") 
 
# Join the node table columns to the edgelist, dropping the extra  
# columns used to calculate the range normalized similarity 
jar_t1 <- full_join(range_norm_jar_ps_filt[c(-3:-5)], jar_node_table[-2],  
                    by = "Source") 
plate_t1 <- full_join(range_norm_plate_ps_filt[c(-3:-5)], 
                      plate_node_table[-2], by = "Source") 
 
# Prepare node tables to join time designation for the target node 
colnames(jar_node_table) <- c("Target", "Label", "Long", "Lat", "Time2") 
colnames(plate_node_table) <- c("Target", "Label", "Long", "Lat", "Time2") 
 
# Join Time 2 column to Target node  
jar_edgelist_complete <- left_join(jar_t1, jar_node_table[c(-2:-4)],  
                                   by = "Target") 
plate_edgelist_complete <- left_join(plate_t1, plate_node_table[c(-2:-4)], 
                                     by = "Target") 
 
# Change "Range_prop_sim" column name to "weight" for Gephi/igraph 
colnames(jar_edgelist_complete) <- c("Source", "Target", "weight", "Long", 
                                     "Lat", "Time", "Time2") 
colnames(plate_edgelist_complete) <- c("Source", "Target", "weight", "Long", 

412 

                                       "Lat", "Time", "Time2") 
 
# Write complete edgelists 
# write_excel_csv(jar_edgelist_complete, "jar_edgelist_complete_March2018.csv") 
# write_excel_csv(plate_edgelist_complete, "plate_edgelist_complete_March2018.csv") 
 
# Create Pre- and Post-Migration Edgelists 
jar_pre_el_need_dist <- jar_edgelist_complete %>% 
                        filter(Time == Time2) %>% 
                        filter(Time == 1) 
 
jar_post_el_need_Law <- jar_edgelist_complete %>% 
                         filter(Time == Time2) %>% 
                         filter(Time == 2) 
 
plate_pre_el_need_dist <-  plate_edgelist_complete %>% 
                           filter(Time == Time2) %>% 
                           filter(Time == 1) 
 
plate_post_el_need_Law <- plate_edgelist_complete %>% 
                           filter(Time == Time2) %>% 
                           filter(Time == 2) 
 
# Two sites, Lawrenz Gun Club and Buckeye Bend, have occupations in both time periods,  
# so we have to control for that 
Law_jar_post <- jar_edgelist_complete %>% 
                  filter(Time == 2 & Target == "Lawrenz Gun Club" |  
                           Source == "Lawrenz Gun Club" & Time2 == 2 ) %>% 
                    mutate(Time = replace(Time, Time==1, 2)) %>% 
                    mutate(Time2 = replace(Time2, Time2==1, 2)) 
 
Law_plate_post <- plate_edgelist_complete %>% 
                    filter(Time == 2 & Target == "Lawrenz Gun Club" |  
                             Source == "Lawrenz Gun Club" & Time2 == 2 ) %>% 
                    mutate(Time = replace(Time, Time==1, 2)) %>% 
                    mutate(Time2 = replace(Time2, Time2==1, 2)) 
 
Buck_jar_post <- jar_edgelist_complete %>% 
                  filter(Time == 2 & Target == "Buckeye Bend" |  
                           Source == "Buckeye Bend" & Time2 == 2 ) %>% 
                    mutate(Time = replace(Time, Time==1, 2)) %>% 
                    mutate(Time2 = replace(Time2, Time2==1, 2)) 
 
Buck_plate_post <- plate_edgelist_complete %>% 
                    filter(Time == 2 & Target == "Buckeye Bend" |  
                             Source == "Buckeye Bend" & Time2 == 2 ) %>% 
                    mutate(Time = replace(Time, Time==1, 2)) %>% 
                    mutate(Time2 = replace(Time2, Time2==1, 2)) 
 
# Bind the Lawrenz Gun Club post-migration edges to the post-migration edgelists 
jar_post_el_need_dist <- rbind(jar_post_el_need_Law, Law_jar_post, 
                               Buck_jar_post) 
 

413 

plate_post_el_need_dist <- rbind(plate_post_el_need_Law, Law_plate_post, 
                                 Buck_plate_post) 
 
# Adding geographic coordinates 
# Read in matrix of site distances 
site_distances <- read_csv("Site Distances Matrix in km.csv") 
site_distances <- column_to_rownames(site_distances, var = "X1") #first column of site names  
to rownames  
# Convert geographic distance matrix to graph object 
distance_g <- graph_from_adjacency_matrix(as.matrix(site_distances), 
                                          weighted = TRUE,  
                                          mode = "directed") 
 
# Convert geo distance graph object to edgelist 
distance_el <- as_edgelist(distance_g) 
distance_el_weight <- as.numeric(E(distance_g)$weight) 
distance_el <- tbl_df(cbind(distance_el, distance_el_weight)) 
colnames(distance_el) <- c("Source", "Target", "weight") 
distance_el$Distance <- as.numeric(distance_el$weight) 
 
# Merge the geographic distance edgelist with jar and plate edgelists 
jar_pre_el_complete <-merge(jar_pre_el_need_dist, distance_el[-3]) 
jar_post_el_complete <- merge(jar_post_el_need_dist, distance_el[-3]) 
plate_pre_el_complete <- merge(plate_pre_el_need_dist, distance_el[-3]) 
plate_post_el_complete <- merge(plate_post_el_need_dist, distance_el[-3]) 
 
# Combine the pre- and post-migration data sets into a single edgelist 
# Each edgelist will become one layer in a multilayer network analysis 
jar_el_all_time_complete <- rbind(jar_pre_el_complete,  
                                  jar_post_el_complete) 
plate_el_all_time_complete <- rbind(plate_pre_el_complete, 
                                    plate_post_el_complete) 

Analysis of Networks and Network Randomization 
 
# Read in data file for jars 
jel <- read_csv("Jar_complete_edgelist.csv") 
 
# Mississippian period jars 
jelpre <- jel %>% filter(Time == 1) 
 
# Cohabitation period jars 
jelpost <- jel %>% filter(Time == 2) 
 
# Read in data file for plates 
pel <- read_csv("Plate_complete_edgelist.csv") 
 
# Mississippian period plates 
pelpre <- pel %>% filter(Time == 1) 
 
# Cohabitation period plates 
pelpost <- pel %>% filter(Time == 2) 
 

414 

# Convert jar character columns to factor to enable plotting features 
cols <- c(1, 2, 6, 7) 
jel[cols] <- lapply(jel[cols], factor) 
jelpre[cols] <- lapply(jelpre[cols], factor) 
jelpost[cols] <- lapply(jelpost[cols], factor) 
 
# Convert plate character columns to factor to enable plotting features 
pel[cols] <- lapply(pel[cols], factor) 
pelpre[cols] <- lapply(pelpre[cols], factor) 
pelpost[cols] <- lapply(pelpost[cols], factor) 
 
# Create igraph objects from jar data frames 
jg <- graph_from_data_frame(jel, directed = TRUE) 
jgpre <- graph_from_data_frame(jelpre, directed = TRUE) 
jgpost <- graph_from_data_frame(jelpost, directed = TRUE) 
 
# Create igraph objects from plate data frames 
pg <- graph_from_data_frame(pel, directed = TRUE) 
pgpre <- graph_from_data_frame(pelpre, directed = TRUE) 
pgpost <- graph_from_data_frame(pelpost, directed = TRUE) 
 
# Merge together graphs to create flattened multilayer graphs 
mpre <- igraph::union(jgpre, pgpre) 
mpost <- igraph::union(jgpost, pgpost) 
plate_multilayer <- igraph::union(pgpre, pgpost) 
jar_multilayer <- igraph::union(jgpre, jgpost) 
full_multilayer <- igraph::union(plate_multilayer, jar_multilayer) 
 
# igraph union does not combine edge weights so we have to manually mutate them 
# first bind the weights from each graph together 
mpre_weight <- cbind(E(mpre)$weight_1, E(mpre)$weight_2) 
mpost_weight <- cbind(E(mpost)$weight_1, E(mpost)$weight_2) 
plate_multi_weight <- cbind(E(plate_multilayer)$weight_1, E(plate_multilayer)$weight_2) 
jar_multi_weight <- cbind(E(jar_multilayer)$weight_1, E(jar_multilayer)$weight_2) 
full_multi_weight <- cbind(E(full_multilayer)$weight_1, E(full_multilayer)$weight_2) 
 
# Sum across the rows removing NA's 
mpre_weight <- rowSums(mpre_weight, na.rm = TRUE) 
mpost_weight <- rowSums(mpost_weight, na.rm = TRUE) 
plate_multi_weight <- rowSums(plate_multi_weight, na.rm = TRUE) 
jar_multi_weight <- rowSums(jar_multi_weight, na.rm = TRUE) 
full_multi_weight <- rowSums(full_multi_weight, na.rm = TRUE) 
 
# Now we can append the flattened weights to the multilayer graph objects 
E(mpre)$weight <- mpre_weight 
E(mpost)$weight <- mpost_weight 
E(plate_multilayer)$weight <- plate_multi_weight 
E(jar_multilayer)$weight <- jar_multi_weight 
E(full_multilayer)$weight <- full_multi_weight 
 
# Explore jar igraph object 
farthest_vertices(jg)       #which two vertices are farthest apart? 
get_diameter(jg)            #shows the path sequence between two furthest apart vertices 

415 

degree(jg, mode = c("out")) #calculate out-degree of each vertex 
jgd <- edge_density(jg) 
 
#--------------------- Analysis of HUBS and AUTHORITIES ----------------- 
# Developed by Jon Kleinberg, the authorities algorithm was initially  
# used to examine web pages. The idea behind authorities is that these  
# nodes would get many incoming links, and so it is a measure to look  
# at which hubs receive the most connections.  
# Algorithms by Jon Kleinberg 
 
#--------------PRE-MIGRATION HUB/AUTHORITY------------------------------- 
hsjgpre <- hub_score(jgpre)$vector 
hspgpre <- hub_score(pgpre)$vector 
asjgpre <- authority_score(jgpre)$vector 
aspgpre <- authority_score(pgpre)$vector 
 
par(mfrow = c(2,2)) 
jgprel <- layout.kamada.kawai(jgpre) 
pgprel <- layout.kamada.kawai(pgpre) 
plot(jgpre, layout = jgprel, vertex.size = asjgpre*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Authorities in the \n Jar Pre-Migration Network") 
 
plot(pgpre, layout = pgprel, vertex.size = aspgpre*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Authorities in the \n Plate Pre-Migration Network") 
 
plot(jgpre, layout = jgprel, vertex.size = hsjgpre*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Hubs in the \n Jar Pre-Migration Network") 
 
plot(pgpre, layout = pgprel, vertex.size = hspgpre*30, 
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Hubs in the \n Plate Pre-Migration Network") 
 
# Pre-migration multilayer hubs and authorities 
hspremulti <- hub_score(mpre)$vector 
aspremulti <- authority_score(mpre)$vector 
 
par(mfrow = c(1,2)) 
mprel <- layout.kamada.kawai(mpre) 
 
plot(mpre, layout = mprel, vertex.size = hspremulti*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  

416 

     edge.curved = 0.1,  
     main = "Hubs in the \n Multilayer Pre-Migration Network") 
 
plot(mpre, layout = mprel, vertex.size = aspremulti*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Authorities in the \n Multilayer Pre-Migration Network") 
 
#----------POST-MIGRATION HUB/AUTHORITY------------------------------ 
 
hsjgpost <- hub_score(jgpost)$vector 
hspgpost <- hub_score(pgpost)$vector 
asjgpost <- authority_score(jgpost)$vector 
aspgpost <- authority_score(pgpost)$vector 
 
par(mfrow = c(2,2), family = "Times", font = 2) 
jgpostl <- layout.kamada.kawai(jgpost) 
pgpostl <- layout.kamada.kawai(pgpost) 
plot(jgpost, layout = jgpostl, vertex.size = asjgpost*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1, 
     main = "Authorities in the \n Jar Post-Migration Network") 
 
plot(pgpost, layout = pgpostl, vertex.size = aspgpost*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1, 
     main = "Authorities in the \n Plate Post-Migration Network") 
 
plot(jgpost, layout = jgpostl, vertex.size = hsjgpost*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1, main = "Hubs in the \n Jar Post-Migration Network") 
 
plot(pgpost, layout = pgpostl, vertex.size = hspgpost*30,  
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Hubs in the \n Plate Post-Migration Network") 
 
# Post-migration multilayer hubs and authorities 
hspostmulti <- hub_score(mpost)$vector 
aspostmulti <- authority_score(mpost)$vector 
 
par(mfrow = c(1,2)) 
mpostl <- layout.fruchterman.reingold(mpost) 
 
plot(mpost, layout = mpostl, vertex.size = hspostmulti*30, 
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  

417 

     main = "Hubs in the \n Multilayer Post-Migration Network") 
 
plot(mpost, layout = mpostl, vertex.size = aspostmulti*30, 
     vertex.label.color = "gray0", vertex.frame.color = "gray88", 
     vertex.color = "darkolivegreen2", edge.arrow.size = 0.15,  
     edge.curved = 0.1,  
     main = "Authorities in the \n Multilayer Post-Migration Network") 
 
#---------------Centralization Analysis-------------------------------------- 
 
# Calculate degree, betweenness, closeness, and eigenvector centrality  
# for a graph and return a data frame with the scores 
 
centr_all <- function(graph, g_name = "Score") { 
   
  # Check that graph is an igraph object 
  if (!is_igraph(graph)) { 
    stop("Not a graph object") 
  } 
   
  # Prompt user for input on name of graph 
  g_name <- as.character(g_name) 
   
  # Degree centralization 
  res_centr <- centr_degree(graph)$centralization 
   
  # Betweenness centralization 
  res_centr[2] <- centr_betw(graph)$centralization 
   
  # Closeness centralization 
  res_centr[3] <- centr_clo(graph)$centralization 
   
  # Eigenvector centralization 
  res_centr[4] <- centr_eigen(graph)$centralization 
   
  res_centr <- t(as.data.frame(res_centr)) 
   
  # Table of scores 
  colnames(res_centr) <- c("Degree", "Closeness", "Betweenness", "Eigenvector") 
  rownames(res_centr) <- g_name 
   
  res_centr 
} 
 
jprecentr <- centr_all(jgpre, g_name = "Jar Pre-Migration") 
pprecentr <- centr_all(pgpre, g_name = "Plate Pre-Migration") 
mprecent <- centr_all(mpre, g_name = "Multilayer Pre-Migration") 
jpostcentr <- centr_all(jgpost, g_name = "Jar Post-Migration") 
ppostcentr <- centr_all(pgpost, g_name = "Plate Post-Migration") 
mpostcentr <- centr_all(mpost, g_name = "Multilayer Post-Migration") 
platecentr <- centr_all(plate_multilayer, g_name = "Plate Multilayer") 
jarcentr <- centr_all(jar_multilayer, g_name = "Jar Multilayer") 
fullcentr <- centr_all(full_multilayer, g_name = "Complete Multilayer") 

418 

 
rbind(jprecentr, pprecentr, mprecent, jpostcentr,  
      ppostcentr, mpostcentr, platecentr, jarcentr, fullcentr) 
 
#---------------Weighted Degree (Strength) Distributions------------------ 
 
# Pre-migration 
jpredegree <- strength(jgpre) 
hist(strength(jgpre), col = "lightblue", xlab = "Weighted Degree",  
     ylab = "Frequency",  
     main = "Jar Pre-Migration \n Degree Distribution") 
 
hist(strength(pgpre), col = "lightgreen", xlab = "Weighted Degree", 
     ylab = "Frequency",  
     main = "Plate Pre-Migration \n Degree Distribution") 
 
summary(strength(jgpre)) 
summary(strength(pgpre)) 
 
# Post-Migration 
jpostdegree <- strength(jgpost, mode = "total") 
par(mfrow = c(1, 2)) 
hist(strength(jgpost), col = "lightblue", xlab = "Weighted Degree", 
     ylab = "Frequency",  
     main = "Jar Post-Migration \n Degree Distribution") 
 
hist(strength(pgpost), col = "lightgreen", xlab = "Weighted Degree", 
     ylab = "Frequency",  
     main = "Plate Post-Migration \n Degree Distribution") 
 
summary(degree(jgpost)) 
summary(degree(pgpost)) 
#----------------Edge Betweenness Community Detection------------------- 
 
# Edge betweenness extends the concept of vertex betweenness centrality  
# to edges by assigning each edge a score that reflects the number of 
# shortest paths that move through that edge.  
# You might ask the question, which ties in a social network are the  
# most important in the spread of information? 
 
# Some graphs are changed from directed to undirected to enable  
# modularity features 
jgpre_eb <- cluster_edge_betweenness(jgpre) 
jgpost_eb <- cluster_edge_betweenness(jgpost) 
pgpre_eb <- cluster_edge_betweenness(as.undirected(pgpre)) 
pgpost_eb <- cluster_edge_betweenness(pgpost) 
mpre_eb <- cluster_edge_betweenness(as.undirected(mpre)) 
mpost_eb <- cluster_edge_betweenness(mpost) 
 
# Pre-Migration community detection via edge betweenness in jar and  
# plate layers 
par(mfrow = c(1,2)) 
plot(jgpre_eb, jgpre, col = membership(jgpre_eb),  

419 

     vertex.label.cex = c(1.5), edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in the \n Pre-Migration Period Jar Attribut
e Network",  
      cex.main = 1.5) 
 
plot(pgpre_eb, pgpre, col = membership(pgpre_eb),  
     vertex.label.cex = c(1.5), edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in the \n Pre-Migration Period Plate Attrib
tue Network",  
      cex.main = 1.5) 
 
# Pre-migration multilayer communitiy detection using edge betweenness 
par(mfrow = c(1, 1)) 
plot(mpre_eb, mpre, col = membership(mpre_eb), vertex.label.cex = c(1.5),  
     edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in the \n Pre-Migration Period Multilayer J
ar and Plate Attribute Network",  
      cex.main = 1.5) 
 
# Post-migration jar and plate community detection via edge betweenness 
par(mfrow = c(1,2)) 
plot(jgpost_eb, jgpost, col = membership(jgpost_eb),  
     vertex.label.cex = c(1.5), edge.arrow.size = .1) 
title(main = "Edge Betweenness Community Detection in the \n Post-Migration Period Jar Attribu
te Network",  
      cex.main = 1.5) 
 
plot(pgpost_eb, pgpost, col = membership(pgpost_eb),  
     vertex.label.cex = c(1.5), edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in the \n Post-Migration Period Plate Attri
bute Network", 
      cex.main = 1.5) 
 
# Post-migration multilayer community detection via edge betweenness 
par(mfrow = c(1, 1)) 
plot(mpost_eb, mpost, col = membership(mpost_eb),  
     vertex.label.cex = c(1.5), edge.arrow.size = .1, edge.curved = .1, 
     layout = mpostl) 
title(main = "Edge Betweenness Community Detection in the \n Post-Migration Period Multilayer 
Jar and Plate Attribute Network",  
      cex.main = 1.5) 
#dev.off() 
 
#-----------Randomization for Pre-Migration Jar network-------------------- 
#--------------------------------PRE_MIGRATION_JAR-------------------------- 
# Initiate empty list for assessing jar pre-migration average path length and transitivity 
jglpre <- vector('list', 5000) 
 
# Initiate empty list for assessing jar pre-migration density density and mean weighted degree 
jglpre.d <- vector('list', 5000) 
 
# Populate jglpre list with random graphs of same order and size 
for(i in 1:5000){ 

420 

  jglpre[[i]] <- erdos.renyi.game(n = gorder(jgpre), p.or.m = gsize(jgpre), directed = TRUE, t
ype = "gnm") 
} 
 
# Populate jglpre.d list with random graphs of same order and approximate density. A separate 
list  
# of 5000 randmn graphs is necessary for density and mean degree because these statistics woul
d  
# identical in random graphs of the same order and size as our observed graph. Instead, a prob
ability  
# of edge creation equal to the observed density is used. Further, only mean degree (as oppose
d to  
# mean weighted degree) is used because Erdos-Renyi random graphs do not support weights.  
for(i in 1:5000){ 
  jglpre.d[[i]] <- erdos.renyi.game(n = gorder(jgpre), p.or.m = edge_density(jgpre), directed 
= TRUE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (lclustering coefficient), density, and degree a
cross  
# the 5000 random jglpre graphs 
jglpre.pl <- lapply(jglpre.d, mean_distance, directed = TRUE) 
jglpre.trans <- lapply(jglpre, transitivity) 
jglpre.density <- lapply(jglpre.d, edge_density) 
jglpre.degree <- lapply(jglpre.d, function(x){ 
                                      y <- degree(x) 
                                      mean(y) 
                                      } 
                                  ) 
                            
# Unlist and change to a data frame for visualizations 
jglpre.pl <- as.data.frame(unlist(jglpre.pl)) 
jglpre.trans <- as.data.frame(unlist(jglpre.trans)) 
jglpre.density <- as.data.frame(unlist(jglpre.density)) 
jglpre.degree <- as.data.frame(unlist(jglpre.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the pre-migration
  
# jar network's ave. shortest path as line 
p.jpre.pl <- ggplot(jglpre.pl, aes(x = jglpre.pl)) +  
              geom_histogram(aes(y = ..density..)) +  
              geom_vline(xintercept = (mean_distance(jgpre,  
                                                     directed = TRUE)), 
                         linetype = "dashed", color = "red") + 
              geom_density() + 
              ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPre
-Migration Jar Attribute Network Average Shortest Path Length") +  
              xlab("Average Shortest Path Length") + 
              ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration jar network's  
# transitivity path as line 
p.jpre.trans <- ggplot(jglpre.trans, aes(x = jglpre.trans)) +  

421 

                  geom_histogram(aes(y = ..density..)) +  
                  geom_vline(xintercept = (transitivity(jgpre)),  
                             linetype = "dashed", color = "red") + 
                  geom_density() + 
                  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPre-Migratio
n Jar Attribute Network Transitivity") +  
                  xlab("Transitivity (or Clustering Coefficient)") + 
                  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's 
# ave. shortest path as line 
p.jpre.density <- ggplot(jglpre.density, aes(x = jglpre.density)) +  
                    geom_histogram(aes(y = ..density..)) +  
                    geom_vline(xintercept = (edge_density(jgpre)), 
                               linetype = "dashed", color = "red") + 
                    geom_density() + 
                    ggtitle("Distribution of 5000 Random Graph Average Densities &\nPre-Migrat
ion Jar Attribute Network Average Density") +  
                    xlab("Average Density") + 
                    ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration jar network's    
mean 
# degree path as line 
p.jpre.degree <- ggplot(jglpre.degree, aes(x = jglpre.degree)) +  
                  geom_histogram(aes(y = ..density..), bins = 10) +  
                  geom_vline(xintercept = (mean(degree(jgpre,  
                                                       mode = "all"))), 
                             linetype = "dashed", color = "red") + 
                  geom_density() + 
                  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPre-Migration
 Jar Attribute Network Mean Degree") +  
                  xlab("Mean Degree") + 
                  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.jpre.pl, p.jpre.trans, p.jpre.density, p.jpre.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(jglpre.pl < mean_distance(jgpre, directed = TRUE))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient) lower  
than our observed 
sum(jglpre.trans < transitivity(jgpre))/5000*100 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(jglpre.density < edge_density(jgpre))/5000*100 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(jglpre.degree < mean(degree(jgpre)))/5000*100 
 
 
#------------Randomizations for Pre-Migration PLATE network--------------- 

422 

#--------------------------------PRE_MIGRATION_PLATE------------------------ 
 
# Initiate empty list for assessing jar pre-migration average path length and transitivity 
pglpre <- vector('list', 5000) 
 
# Initiate empty list for assessing jar pre-migration density density and mean weighted degree 
pglpre.d <- vector('list', 5000) 
 
# Populate jglpre list with random graphs of same order and size 
for(i in 1:5000){ 
  pglpre[[i]] <- erdos.renyi.game(n = gorder(pgpre), p.or.m = gsize(pgpre), 
                                  directed = TRUE, type = "gnm") 
} 
 
# Populate jglpre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 random graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our observed
  
# graph. Instead, a probability of edge creation equal to the observed density is used.  
# Further, only mean degree (as opposed to mean weighted degree) is used because Erdos-Renyi  
# random graphs do not support weights.  
for(i in 1:5000){ 
  pglpre.d[[i]] <- erdos.renyi.game(n = gorder(pgpre),  
                                    p.or.m = edge_density(pgpre),  
                                    directed = TRUE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density, and degree   
across  
# the 5000 random jglpre graphs 
pglpre.pl <- lapply(pglpre.d, mean_distance, directed = TRUE) 
pglpre.trans <- lapply(pglpre, transitivity) 
pglpre.density <- lapply(pglpre.d, edge_density) 
pglpre.degree <- lapply(pglpre.d, function(x){ 
                                              y <- degree(x) 
                                              mean(y) 
                                              } 
                                            ) 
 
# Unlist and change to a data frame for vizualizations 
pglpre.pl <- as.data.frame(unlist(pglpre.pl)) 
pglpre.trans <- as.data.frame(unlist(pglpre.trans)) 
pglpre.density <- as.data.frame(unlist(pglpre.density)) 
pglpre.degree <- as.data.frame(unlist(pglpre.degree)) 
 
# Plot the distribution of random graph's average shortest path  
# lengths with the pre-migration jar network's ave. shortest path as line 
p.ppre.pl <- ggplot(pglpre.pl, aes(x = pglpre.pl)) +  
  geom_histogram(aes(y = ..density..)) +  
  geom_vline(xintercept = (mean_distance(pgpre, directed = TRUE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPre-Migration P

423 

late Attribute Network Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration jar network's   
transitivity path as line 
p.ppre.trans <- ggplot(pglpre.trans, aes(x = pglpre.trans)) +  
  geom_histogram(aes(y = ..density..)) +  
  geom_vline(xintercept = (transitivity(pgpre)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPre-Migration Plate Attribut
e Network Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's
 density as line 
p.ppre.density <- ggplot(pglpre.density, aes(x = pglpre.density)) +  
  geom_histogram(aes(y = ..density..)) +  
  geom_vline(xintercept = (edge_density(pgpre)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPre-Migration Plate Attribut
e Network Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration jar network's    
mean degree path as line 
p.ppre.degree <- ggplot(pglpre.degree, aes(x = pglpre.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (mean(degree(pgpre, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPre-Migration Plate Attribute
 Network Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs in the same grid 
plot_grid(p.ppre.pl, p.ppre.trans, p.ppre.density, p.ppre.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(pglpre.pl < mean_distance(pgpre, directed = TRUE))/5000 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient) lower  
than our observed 
sum(pglpre.trans < transitivity(pgpre))/5000 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(pglpre.density < edge_density(pgpre))/5000 
 

424 

# Calculate the proportion of graphs with a mean degree lower than observed 
sum(pglpre.degree < mean(degree(pgpre)))/5000 
 
#-----------------------------Randomization for Post-Migration Jar network------------------ 
#--------------------------------POST_MIGRATION_JAR----------------------------------------- 
 
# Initiate empty list for assessing jar pre-migration average path length and transitivity 
jglpost <- vector('list', 5000) 
 
# Initiate empty list for assessing jar pre-migration density density and mean weighted degree 
jglpost.d <- vector('list', 5000) 
 
# Populate jglpre list with random graphs of same order and size 
for(i in 1:5000){ 
  jglpost[[i]] <- erdos.renyi.game(n = gorder(jgpost),  
                                   p.or.m = gsize(jgpost),  
                                   directed = TRUE, type = "gnm") 
} 
 
# Populate jglpre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 randon graphs is necessary for density and mean degree because 
# these statistics would identical in random graphs of the same order and size as our  
# observed graph. Instead, a probability of edge creation equal to the observed density is    
used.  
# Further, only mean degree (as opposed to mean weighted degree) is used because Erdos-Renyi  
# random graphs do not support weights.  
for(i in 1:5000){ 
  jglpost.d[[i]] <- erdos.renyi.game(n = gorder(jgpost),  
                                     p.or.m = edge_density(jgpost),  
                                     directed = TRUE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (lclustering coefficient), density, and degree  
 across the 5000 random jglpre graphs 
jglpost.pl <- lapply(jglpost.d, mean_distance, directed = TRUE) 
jglpost.trans <- lapply(jglpost, transitivity) 
jglpost.density <- lapply(jglpost.d, edge_density) 
jglpost.degree <- lapply(jglpost.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
jglpost.pl <- as.data.frame(unlist(jglpost.pl)) 
jglpost.trans <- as.data.frame(unlist(jglpost.trans)) 
jglpost.density <- as.data.frame(unlist(jglpost.density)) 
jglpost.degree <- as.data.frame(unlist(jglpost.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the pre-migration
 jar network's ave. shortest path as line 
p.jpost.pl <- ggplot(jglpost.pl, aes(x = jglpost.pl)) +  
                geom_histogram(aes(y = ..density..), bins = 18) +  

425 

                geom_vline(xintercept = (mean_distance(jgpost,  
                                                       directed = TRUE)), 
                           linetype = "dashed", color = "red") + 
                geom_density() + 
                ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nP
ost-Migration Jar Attribute Network Average Shortest Path Length") +  
                xlab("Average Shortest Path Length") + 
                ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration jar network's tr
ansitivity path as line 
p.jpost.trans <- ggplot(jglpost.trans, aes(x = jglpost.trans)) +  
                  geom_histogram(aes(y = ..density..), bins = 5) +  
                  geom_vline(xintercept = (transitivity(jgpost)),  
                             linetype = "dashed", color = "red") + 
                  geom_density() + 
                  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPost-Migrati
on Jar Attribute Network Transitivity") +  
                  xlab("Transitivity (or Clustering Coefficient)") + 
                  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's
 ave. shortest path as line 
p.jpost.density <- ggplot(jglpost.density, aes(x = jglpost.density)) +  
                    geom_histogram(aes(y = ..density..), bins = 11) +  
                    geom_vline(xintercept = (edge_density(jgpost)),  
                               linetype = "dashed", color = "red") + 
                    geom_density() + 
                    ggtitle("Distribution of 5000 Random Graph Average Densities &\nPost-Migra
tion Jar Attribute Network Average Density") +  
                    xlab("Average Density") + 
                    ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration jar network's mea
n degree path as line 
p.jpost.degree <- ggplot(jglpost.degree, aes(x = jglpost.degree)) +  
                    geom_histogram(aes(y = ..density..), bins = 10) +  
                    geom_vline(xintercept = (mean(degree(jgpost,  
                                                         mode = "all"))), 
                               linetype = "dashed", color = "red") + 
                    geom_density() + 
                    ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPost-Migrat
ion Jar Attribute Network Mean Degree") +  
                    xlab("Mean Degree") + 
                    ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.jpost.pl, p.jpost.trans, p.jpost.density, p.jpost.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(jglpost.pl < mean_distance(jgpost, directed = TRUE))/5000 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient) lower  

426 

than our observed 
sum(jglpost.trans < transitivity(jgpost))/5000 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(jglpost.density < edge_density(jgpost))/5000 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(jglpost.degree < mean(degree(jgpost)))/5000 
 
 
#-----------------Randomizations for Post-Migration PLATE network--------------- 
#--------------------------------POST_MIGRATION_PLATE----------------------- 
 
# Initiate empty list for assessing jar pre-migration average path length and transitivity 
pglpost <- vector('list', 5000) 
 
# Initiate empty list for assessing jar pre-migration density density and mean weighted degree 
pglpost.d <- vector('list', 5000) 
 
# Populate jglpre list with random graphs of same order and size 
for(i in 1:5000){ 
  pglpost[[i]] <- erdos.renyi.game(n = gorder(pgpost),  
                                   p.or.m = gsize(pgpost),  
                                   directed = TRUE, type = "gnm") 
} 
 
# Populate jglpre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 randon graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our observed
  
# graph. Instead, a probability of edge creation equal to the observed density is used.  
# Further, only mean degree (as opposed to mean weighted degree) is used because Erdos-Renyi  
# random graphs do not support weights.  
for(i in 1:5000){ 
  pglpost.d[[i]] <- erdos.renyi.game(n = gorder(pgpost),  
                                     p.or.m = edge_density(pgpost),  
                                     directed = TRUE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density, and degree  
# across the 5000 random jglpre graphs 
pglpost.pl <- lapply(pglpost.d, mean_distance, directed = TRUE) 
pglpost.trans <- lapply(pglpost, transitivity) 
pglpost.density <- lapply(pglpost.d, edge_density) 
pglpost.degree <- lapply(pglpost.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
pglpost.pl <- as.data.frame(unlist(pglpost.pl)) 
pglpost.trans <- as.data.frame(unlist(pglpost.trans)) 

427 

pglpost.density <- as.data.frame(unlist(pglpost.density)) 
pglpost.degree <- as.data.frame(unlist(pglpost.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the pre-migration
  
# jar network's ave. shortest path as line 
p.ppost.pl <- ggplot(pglpost.pl, aes(x = pglpost.pl)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (mean_distance(pgpost, directed = TRUE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPost-Migration 
Plate Attribute Network Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration jar network's tr
ansitivity path as line 
p.ppost.trans <- ggplot(pglpost.trans, aes(x = pglpost.trans)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (transitivity(pgpost)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPost-Migration Plate Attribu
te Network Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's
 ave. shortest path as line 
p.ppost.density <- ggplot(pglpost.density, aes(x = pglpost.density)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (edge_density(pgpost)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPost-Migration Plate Attribu
te Network Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration jar network's mea
n degree path as line 
p.ppost.degree <- ggplot(pglpost.degree, aes(x = pglpost.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (mean(degree(pgpost, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPost-Migration Plate Attribut
e Network Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs in the same grid 

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plot_grid(p.ppost.pl, p.ppost.trans, p.ppost.density, p.ppost.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(pglpost.pl < mean_distance(pgpost, directed = TRUE))/5000 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient) lower t
han our observed 
sum(pglpost.trans < transitivity(pgpost))/5000 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(pglpost.density < edge_density(pgpost))/5000 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(pglpost.degree < mean(degree(pgpost)))/5000 
 
#---------------------Randomization for Pre-Migration Multilayer network----------- 
#--------------------------------PRE_MIGRATION_MULTILAYER------------------- 
# Initiate empty list for assessing jar pre-migration average path length and transitivity 
mglpre <- vector('list', 5000) 
 
# Initiate empty list for assessing jar pre-migration density density and mean weighted degree 
mglpre.d <- vector('list', 5000) 
 
# Populate jglpre list with random graphs of same order and size 
for(i in 1:5000){ 
  mglpre[[i]] <- erdos.renyi.game(n = gorder(mpre), p.or.m = gsize(mpre), directed = TRUE, typ
e = "gnm") 
} 
 
# Populate jglpre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 randon graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our  
# observed graph. Instead, a probability of edge creation equal to the observed density  
# is used. Further, only mean degree (as opposed to mean weighted degree) is used because  
# Erdos-Renyi random graphs do not support weights.  
for(i in 1:5000){ 
  mglpre.d[[i]] <- erdos.renyi.game(n = gorder(mpre), 
                                    p.or.m = edge_density(mpre),  
                                    directed = TRUE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density,  
# and degree across the 5000 random jglpre graphs 
mglpre.pl <- lapply(mglpre.d, mean_distance, directed = TRUE) 
mglpre.trans <- lapply(mglpre, transitivity) 
mglpre.density <- lapply(mglpre.d, edge_density) 
mglpre.degree <- lapply(mglpre.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 

429 

mglpre.pl <- as.data.frame(unlist(mglpre.pl)) 
mglpre.trans <- as.data.frame(unlist(mglpre.trans)) 
mglpre.density <- as.data.frame(unlist(mglpre.density)) 
mglpre.degree <- as.data.frame(unlist(mglpre.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the  
# pre-migration multilayer network's ave. shortest path as line 
p.mpre.pl <- ggplot(mglpre.pl, aes(x = mglpre.pl)) +  
  geom_histogram(aes(y = ..density..)) +  
  geom_vline(xintercept = (mean_distance(mpre, directed = TRUE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPre-Migration M
ultilayer Attribute Network Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration  
# multilayer network's transitivity path as line 
p.mpre.trans <- ggplot(mglpre.trans, aes(x = mglpre.trans)) +  
  geom_histogram(aes(y = ..density..)) +  
  geom_vline(xintercept = (transitivity(mpre)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPre-Migration Multilayer Att
ribute Network Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration  
# multilayer network's density as line 
p.mpre.density <- ggplot(mglpre.density, aes(x = mglpre.density)) +  
  geom_histogram(aes(y = ..density..)) +  
  geom_vline(xintercept = (edge_density(mpre)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPre-Migration Multilayer Att
ribute Network Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration  
# multilayer network's meandegree path as line 
p.mpre.degree <- ggplot(mglpre.degree, aes(x = mglpre.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (mean(degree(mpre, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPre-Migration Multilayer Attr
ibute Network Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 

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# Use plot_grid to plot all four graphs in the same grid 
plot_grid(p.mpre.pl, p.mpre.trans, p.mpre.density, p.mpre.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(mglpre.pl < mean_distance(mpre, directed = TRUE))/5000 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient) lower  
than our observed 
sum(mglpre.trans < transitivity(mpre))/5000 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(mglpre.density < edge_density(mpre))/5000 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(mglpre.degree < mean(degree(mpre)))/5000 
 
#----------------------Randomization for Post-Migration Multilayer network-------------- 
#--------------------------------POST_MIGRATION_MULTILAYER------------------ 
 
# Initiate empty list for assessing jar pre-migration average path length and transitivity 
mglpost <- vector('list', 5000) 
 
# Initiate empty list for assessing jar pre-migration density density and mean weighted degree 
mglpost.d <- vector('list', 5000) 
 
# Populate jglpost list with random graphs of same order and size 
for(i in 1:5000){ 
  mglpost[[i]] <- erdos.renyi.game(n = gorder(mpost),  
                                   p.or.m = gsize(mpost),  
                                   directed = TRUE, type = "gnm") 
} 
 
# Populate jglpre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 random graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our  
# observed graph. Instead, a probability of edge creation equal to the observed density  
# is used. Further, only mean degree (as opposed to mean weighted degree) is used because  
# Erdos-Renyi random graphs do not support weights.  
for(i in 1:5000){ 
  mglpost.d[[i]] <- erdos.renyi.game(n = gorder(mpost),  
                                     p.or.m = edge_density(mpost),  
                                     directed = TRUE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density, and degree  
# across the 5000 random jglpre graphs 
mglpost.pl <- lapply(mglpost.d, mean_distance, directed = TRUE) 
mglpost.trans <- lapply(mglpost, transitivity) 
mglpost.density <- lapply(mglpost.d, edge_density) 
mglpost.degree <- lapply(mglpost.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 

431 

) 
 
# Unlist and change to a data frame for vizualizations 
mglpost.pl <- as.data.frame(unlist(mglpost.pl)) 
mglpost.trans <- as.data.frame(unlist(mglpost.trans)) 
mglpost.density <- as.data.frame(unlist(mglpost.density)) 
mglpost.degree <- as.data.frame(unlist(mglpost.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the  
# pre-migration multilayer network's ave. shortest path as line 
p.mpost.pl <- ggplot(mglpost.pl, aes(x = mglpost.pl)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (mean_distance(mpost, directed = TRUE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPost-Migration 
Multilayer Attribute Network Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration  
# multilayer network's transitivity path as line 
p.mpost.trans <- ggplot(mglpost.trans, aes(x = mglpost.trans)) +  
  geom_histogram(aes(y = ..density..), bins = 7) +  
  geom_vline(xintercept = (transitivity(mpost)), linetype = "dashed", 
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPost-Migration Multilayer At
tribute Network Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration  
# multilayer network's density as line 
p.mpost.density <- ggplot(mglpost.density, aes(x = mglpost.density)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (edge_density(mpost)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPost-Migration Multilayer At
tribute Network Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration  
# multilayer network's meandegree path as line 
p.mpost.degree <- ggplot(mglpost.degree, aes(x = mglpost.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (mean(degree(mpost, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPost-Migration Multilayer Att
ribute Network Mean Degree") +  

432 

  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs in the same grid 
plot_grid(p.mpost.pl, p.mpost.trans, p.mpost.density, p.mpost.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(mglpost.pl < mean_distance(mpost, directed = TRUE))/5000 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient) lower t
han our observed 
sum(mglpost.trans < transitivity(mpost))/5000 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(mglpost.density < edge_density(mpost))/5000 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(mglpost.degree < mean(degree(mpost)))/5000 

Function to plot results of Monte Carlo Network Randomization 
 
# Function to plot Monte Carlo simulation distributions based on Erdos-Renyi Random Graphs 
 
# Package dependencies 
library(igraph) 
library(cowplot) 
library(ggplot2) 
 
graph_mc_sim <- function(graph, sim = 5000){ 
   
  # Check that graph is an igraph object 
  if (!is_igraph(graph)) { 
    stop("Not a graph object") 
  } 
   
  # Check that graph is directed  
  if(!is_directed(graph)){ 
    stop("Graph is not directed") 
  } 
   
  # Prompt user for input on name of graph 
  g_name <- readline(prompt = "What name would you like to use for the graph in the plots?: ") 
  g_name <- as.character(g_name) 
   
  # Initiate empty list for housing transitivity simulations 
  gl <- vector('list', sim) 
   
  # Initiate empty list for housing density, average path length, and mean degree simulations 
  gl.d <- vector('list', sim) 
   
  # Populate list with random graphs of same order and size 
  for(i in 1:sim){ 
    gl[[i]] <- erdos.renyi.game(n = gorder(graph), p.or.m = gsize(graph), 

433 

                                directed = TRUE, type = "gnm") 
  } 
   
  # Populate gl.d list with random graphs of same order and approximate density.  
  # A separate list of random graphs is necessary for density, average path length, and  
  # mean degree because these statistics would be identical in random graphs of the same 
  # order and size as the observed graph.  
  # Instead, a probability of edge creation equal to the observed density is used.  
  # Further, only mean degree (as opposed to mean weighted degree) is used because  
  # Erdos-Renyi random graphs do not support weights.  
  for(i in 1:sim){ 
    gl.d[[i]] <- erdos.renyi.game(n = gorder(graph),  
                                  p.or.m = edge_density(graph),  
                                  directed = TRUE, type = "gnp") 
  } 
   
  # Calculate average path length, transitivity (clustering coefficient), density, and  
  # degree across the random graphs 
  gl.pl <- lapply(gl.d, mean_distance, directed = TRUE) 
  gl.trans <- lapply(gl, transitivity) 
  gl.density <- lapply(gl.d, edge_density) 
  gl.degree <- lapply(gl.d, function(x){ 
                        y <- degree(x) 
                        mean(y) 
                      } 
                    ) 
   
  # Unlist and change to a data frame for vizualizations 
  gl.pl <- as.data.frame(unlist(gl.pl)) 
  gl.trans <- as.data.frame(unlist(gl.trans)) 
  gl.density <- as.data.frame(unlist(gl.density)) 
  gl.degree <- as.data.frame(unlist(gl.degree)) 
   
  # Plot the distribution of random graph's average shortest path lengths with the  
  # input graphs's ave. shortest path as line 
  p.gl.pl <- ggplot(gl.pl, aes(x = gl.pl)) +  
    geom_histogram(aes(y = ..density..)) +  
    geom_vline(xintercept = (mean_distance(graph, directed = TRUE)), 
               linetype = "dashed", color = "red") + 
    geom_density() + 
    ggtitle(paste0("Distribution of ", sim, " Random Graph Average Shortest Path Lengths & \n 
Observed Average Shortest Path Length in ", g_name)) +  
    xlab("Average Shortest Path Length") + 
    ylab("") 
   
  # Plot the distribution of random graph's transitivity with the input graph's  
  # transitivity path as line 
  p.gl.trans <- ggplot(gl.trans, aes(x = gl.trans)) +  
    geom_histogram(aes(y = ..density..)) +  
    geom_vline(xintercept = (transitivity(graph)), linetype = "dashed", 
               color = "red") + 
    geom_density() + 
    ggtitle(paste0("Distribution of Transitivity in ", sim, " Random Models & \n Observed Tran

434 

sitivity in ", g_name)) +  
    xlab("Transitivity (or Clustering Coefficient)") + 
    ylab("") 
   
  # Plot the distribution of random graph's average density with the input graph's  
  # density as line 
  p.gl.density <- ggplot(gl.density, aes(x = gl.density)) +  
    geom_histogram(aes(y = ..density..)) +  
    geom_vline(xintercept = (edge_density(graph)), linetype = "dashed", 
               color = "red") + 
    geom_density() + 
    ggtitle(paste0("Distribution of ", sim,  " Random Graph Average Densities &\n Observed Ave
rage Density in ", g_name)) +  
    xlab("Average Density") + 
    ylab("") 
   
  # Plot the distribution of random graph's mean degree with the input graph's mean  
  # degree path as line 
  p.gl.degree <- ggplot(gl.degree, aes(x = gl.degree)) +  
    geom_histogram(aes(y = ..density..), bins = 10) +  
    geom_vline(xintercept = (mean(degree(graph, mode = "all"))),  
               linetype = "dashed", color = "red") + 
    geom_density() + 
    ggtitle(paste0("Distribution of Mean Degree in ", sim, " Random Models & \n Observed Mean 
Degree in ", g_name)) +  
    xlab("Mean Degree") + 
    ylab("") 
   
  # Use plot_grid to plot all four graphs in the same grid 
  plot_grid(p.gl.pl, p.gl.trans, p.gl.density, p.gl.degree) 
} 

Function to Calculate Centralization Scores 
 
# Calculate degree, betweenness, closeness, and eigenvector centralization for a graph 
# and return a data frame with the scores 
 
centr_all <- function(graph, g_name = "Score") { 
   
  # Check that graph is an igraph object 
  if (!is_igraph(graph)) { 
    stop("Not a graph object") 
  } 
   
  # Prompt user for input on name of graph 
  g_name <- as.character(g_name) 
   
  # Degree centralization 
  res_centr <- centr_degree(graph)$centralization 
   
  # Betweenness centralization 
  res_centr[2] <- centr_betw(graph)$centralization 
   

435 

  # Closeness centralization 
  res_centr[3] <- centr_clo(graph)$centralization 
   
  # Eigenvector centralization 
  res_centr[4] <- centr_eigen(graph)$centralization 
   
  res_centr <- t(as.data.frame(res_centr)) 
   
  # Table of scores 
  colnames(res_centr) <- c("Degree", "Closeness", "Betweenness", "Eigenvector") 
  rownames(res_centr) <- g_name 
   
  res_centr 
} 

Multilayer Network Analysis of Directed Jar and Plate Attribute Layers 
 
# Multilayer analysis of ceramic attribute interaction networks in the Late Prehistoric CIRV 
 
library(tidyverse) 
library(multinet) 
library(igraph) 
 
# Read in multilayer network into a multinet object 
cnet <- read.ml("ceramicMultilayer_UPDATED_may-2018.csv") 
 
#-----------------Pre-Migration Multilayer Analysis----------------------------------------- 
 
# Checking to see node representation across the layers - degree.deviation.ml returns the  
# standard deviation of the degree of an actor on the input layers. An actor with the same  
# degree on all layers will have deviation 0, while an actor with a lot of neighbors on one  
# layer and only a few on another will have a high degree deviation, showing an uneven usage  
# of the layers (or layers with different densities). 
degree.deviation.ml(cnet, layers = c("Jar_pre", "Plate_pre")) 
 
# connective.redundancy.ml returns 1 minus neighborhood divided by degree and is a  
# measure of how often actors are connected to the same neighbors across multiple layers  
mean(connective.redundancy.ml(cnet, layers = c("Jar_pre", "Plate_pre")), na.rm = TRUE) 
 
# Layer comparison 
# Common edges divided by the union of all edges for all pairs of layers (jaccard) 
layer.comparison.ml(cnet,layers = c("Jar_pre", "Plate_pre"),method="jaccard.edges") 
# Simple matching edges comparison 
layer.comparison.ml(cnet,layers = c("Jar_pre", "Plate_pre"),method="sm.edges") 
 
layer.summary.ml(cnet, "Jar_pre", method = "mean.degree") 
 
#-----------------Post-Migration Multilayer Analysis---------------------------------------- 
 
degree.deviation.ml(cnet, layers = c("Jar_post", "Plate_post")) 
 
mean(connective.redundancy.ml(cnet, layers = c("Jar_post", "Plate_post")), 
     na.rm = TRUE) 

436 

 
# Layer comparison 
# Common edges divided by the union of all edges for all pairs of layers (jaccard) 
layer.comparison.ml(cnet,layers = c("Jar_post", 
                                    "Plate_post"),method="jaccard.edges") 
# Simple matching edges comparison 
layer.comparison.ml(cnet,layers = c("Jar_post", 
                                    "Plate_post"),method="sm.edges") 

Linear Regression Models Assessing the Role of Geographic Distance on the Strength of 
Relational Connections 
 
library(infer) 
library(tidyverse) 
library(igraph) 
library(reshape2) 
library(stringr) 
library(cowplot) 
library(broom) 
 
# Import interaction networks 
jar_el_all_time <- read_csv("Jar_complete_edgelist.csv") 
plate_el_all_time <- read_csv("Plate_complete_edgelist.csv") 
 
# Function to take a random sample from a data set a certain number of times 
rep_sample_n <- function(tbl, size, replace = FALSE, reps = 1) 
{ 
  n <- nrow(tbl) 
  i <- unlist(replicate(reps, sample.int(n, size, replace = replace), 
                        simplify = FALSE)) 
   
  rep_tbl <- cbind(replicate = rep(1:reps,rep(size,reps)), tbl[i,]) 
   
  dplyr::group_by(rep_tbl, replicate) 
} 
 
# Inference testing with linear models 
# Take 100 samples of 50 each from the jar and plate data sets 
# The idea is to explore regression trends on the slope coefficient using samples  
# from each data set. Does the trend with the entire data hold true when  
# sub-samples are taken from the data? 
# This is a two-tailed test to see if a linear relationship (positive or negative) exists 
# between distance (explanatory variable) and weight (response variable) 
jarsamples <- rep_sample_n(jar_el_all_time[, c(8, 3, 6, 7)], size = 50,  
                           reps = 100) 
platesamples <- rep_sample_n(plate_el_all_time[, c(8, 3, 6, 7)],  
                             size = 50, reps = 100) 
 
# Add replicate col to align observed trends with random samples 
jar_observed <- jar_el_all_time[, c(8, 3, 6, 7)] %>% 
                mutate(replicate = 200)  
  
plate_observed <- plate_el_all_time[, c(8, 3, 6, 7)] %>% 

437 

                   mutate(replicate = 200) 
 
# Multilayer models showing relationships across time 
jar_lm_multi <- ggplot(jarsamples, aes(x = Distance, y = weight,  
                                       group = replicate)) +  
  geom_point(size = 2, shape = 20) +  
  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
  ggtitle("Jar Attribute Interaction Network Across Time") +  
  background_grid(major = 'y', minor = "none") + 
  xlab("Distance (km)") + 
  ylab("Strength of Relational Connection") + 
  theme(strip.background = element_blank(), 
        strip.text.x =element_blank()) + 
  stat_smooth(data = jar_observed, aes(x = Distance, y = weight),  
              color ="red3", linetype = "twodash", method = "lm",  
              se = FALSE)  
 
plate_lm_multi <- ggplot(platesamples, aes(x = Distance, y = weight,  
                                           group = replicate)) +  
  geom_point(size = 2, shape = 20) +  
  stat_smooth(geom = "line", alpha = 0.4, method = "lm", se = FALSE) +  
  ggtitle("Plate Attribute Interaction Network Across Time") + 
  background_grid(major = 'y', minor = "none") + 
  xlab("Distance (km)") + 
  ylab("Strength of Relational Connection") + 
  theme(strip.background = element_blank(), 
        strip.text.x =element_blank())+ 
  stat_smooth(data = plate_observed, aes(x = Distance, y = weight),  
              color ="red3",  linetype = "twodash", method = "lm",  
              se = FALSE)  
 
lm_multi_grid_p <- plot_grid(jar_lm_multi, plate_lm_multi) 
 
title <- ggdraw() +  
          draw_label("Distribution of Linear Regression Lines of 100 random samples from the\n
 Multilayer Jar and Plate Attribute Networks Flattened Across Time", fontface = 'bold') 
 
plot_grid(title, lm_multi_grid_p, ncol= 1, rel_heights = c(0.1, 1)) 
 
# How do the trends across time compare to the pre- and post-migration group trends?  
jar_lms <- ggplot(jarsamples, aes(x = Distance, y = weight,  
                                  group = replicate)) +  
            geom_point(size = 2, shape = 20) +  
            stat_smooth(geom = "line", se = FALSE, alpha = 0.4,  
                        method = "lm") +  
            facet_wrap(Time ~ Time2) +  
            ggtitle("Jar Attribute Interaction Networks\nPre-Migration                       P
ost-Migration") +  
            # extra space above accommodates the facet label separation 
            background_grid(major = 'y', minor = "none") + 
            xlab("Distance (km)") + 
            ylab("Strength of Relational Connection") + 
            theme(strip.background = element_blank(), 

438 

                  strip.text.x =element_blank()) + 
            stat_smooth(data = jar_observed, aes(x = Distance, y = weight), 
                        color ="red3",  
                        linetype = "twodash", method = "lm", se = FALSE) +  
            facet_wrap(Time ~ Time2) 
 
plate_lms <- ggplot(platesamples, aes(x = Distance, y = weight,  
                                      group = replicate)) +  
             geom_point(size = 2, shape = 20) +  
             stat_smooth(geom = "line", alpha = 0.4, method = "lm", 
                         se = FALSE) +  
             facet_wrap(Time ~ Time2) +  
             ggtitle("Plate Attribute Interaction Networks\nPre-Migration                     
  Post-Migration") + 
             background_grid(major = 'y', minor = "none") + 
             xlab("Distance (km)") + 
             ylab("Strength of Relational Connection") + 
             theme(strip.background = element_blank(), 
             strip.text.x =element_blank())+ 
             stat_smooth(data = plate_observed, aes(x = Distance,  
                                                    y = weight),  
                         color ="red3", linetype = "twodash",  
                         method = "lm", se = FALSE) +  
             facet_wrap(Time ~ Time2) 
 
lm_grid_p <- plot_grid(jar_lms, plate_lms) 
 
title <- ggdraw() + draw_label("Distribution of Linear Regression Lines of 100 random samples 
from the Jar and Plate Attribute Networks",  
                               fontface = 'bold') 
plot_grid(title, lm_grid_p, ncol= 1, rel_heights = c(0.1, 1)) 
 
# Inference 
# First, let's calculate the observed slope of the lm in the jar and plate attribute networks 
jar_obs_slope <- lm(weight ~ Distance, data = jar_el_all_time) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate)     
 
plate_obs_slope <- lm(weight ~ Distance, data = plate_el_all_time) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate)     
 
# Simulate 500 slopes with a permuted dataset for jars and plates - this will allow us to  
# develop a sampling distribution of the slop under the hypothsis that there is no  
# relationship between the explanatory and response variables.  
set.seed(1568) 
jar_perm_slope <- jar_el_all_time %>% 
  specify(weight ~ Distance) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 500, type = "permute") %>% 
  calculate(stat = "slope")  

439 

 
plate_perm_slope <- plate_el_all_time %>% 
  specify(weight ~ Distance) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 500, type = "permute") %>% 
  calculate(stat = "slope")  
 
ggplot(jar_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
ggplot(plate_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
 
mean(jar_perm_slope$stat) 
mean(plate_perm_slope$stat) 
sd(jar_perm_slope$stat) 
sd(plate_perm_slope$stat) 
 
# Calculate the absolute value of the slope 
abs_jar_obs_slope <- lm(weight ~ Distance, data = jar_el_all_time) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate) %>% 
  abs() 
 
abs_plate_obs_slope <- lm(weight ~ Distance, data = plate_el_all_time) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate) %>% 
  abs() 
 
# Compute the p-value   
jar_perm_slope %>%  
  mutate(abs_jar_perm_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_jar_perm_slope > abs_jar_obs_slope)) 
 
plate_perm_slope %>%  
  mutate(abs_plate_perm_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_plate_perm_slope > abs_plate_obs_slope)) 
 
# Linear models sans visualization 
# First prep the data by splitting it into specific groups by time 
plate_pre <-  plate_el_all_time %>%  
              filter(Time == 1) %>%  
              select(Distance, weight) 
plate_post <- plate_el_all_time %>%  
              filter(Time == 2) %>%  
              select(Distance, weight) 
jar_pre <- jar_el_all_time %>%  
           filter(Time ==1) %>%  
           select(Distance, weight) 
jar_post <- jar_el_all_time %>%  
            filter(Time == 2) %>%  
            select(Distance, weight) 
 
# Plate attribute network linear models - explore residuals  

440 

plate_pre_lm <- augment(lm(weight ~ Distance, data = plate_pre)) 
plate_post_lm <- augment(lm(weight ~ Distance, data = plate_post)) 
 
# Check SSE - how well does the model fit? 
augment(lm(weight ~ 1, data = plate_pre)) %>% summarize(SSE = var(.resid)) 
plate_pre_lm %>% summarize(SSE = var(.resid)) 
 
# Breakdown of linear model results for plate attribute networks  
summary(lm(weight ~ Distance, data = plate_pre)) # for each 1 km increase in distance, weight 
drops 0.0014 and at 0 distance, a weight of 0.7463 is expected 
summary(lm(weight ~ Distance, data = plate_pre))$coefficients # plate pre = p-value of 0.05796
, significant at alpha of 0.06, reject null, significant linear relationship between distance 
and weight in plate pre 
summary(lm(weight ~ Distance, data = plate_post)) # for each 1 km increase in distance, weight
 drops 0.0001292 and at 0 distance, a weight of 0.7782248 is expected 
summary(lm(weight ~ Distance, data = plate_post))$coefficients # plate post p-value of 0.86862
, fail to reject null hypothesis - no significant linear relationship between distance and wei
ght in plate post-migration network 
 
# Check correlations 
cor(plate_pre$Distance, plate_pre$weight)  
cor(plate_post$Distance, plate_post$weight) 
 
summary(lm(weight ~ Distance, data = jar_pre)) # for each 1 km increase in distance, weight in
creases 0.00005609 and at 0 distance, a weight of 0.7559 is expected 
summary(lm(weight ~ Distance, data = jar_pre))$coefficients # jar pre = p-value of 0.925, fail
 to reject null hypothesis - no significant linear relationship between distance and weight in
 jar pre-migration network 
summary(lm(weight ~ Distance, data = jar_post)) # for each 1 km increase in distance, weight d
rops 0.001697 and at 0 distance, a weight of 0.843158 is expected 
summary(lm(weight ~ Distance, data = jar_post))$coefficients # jar post = p-value of 0.003207,
 significant at alpha of 0.01, reject null, significant linear relationship between distance a
nd weight in jar post 
 
cor(jar_pre$Distance, jar_pre$weight) 
cor(jar_post$Distance, jar_post$weight) 

 
 
 
 
R Code from Chapter 6 - Ceramic Design and Networks of Social Identification 
 
Routines to generate and analyze networks of social identification from counts of artifact 
decoration categories 
 
Brainerd Robinson Analysis   
 
# Brainerd Robinson Analysis of Late Prehistoric central Illinois River 
# valley (circa 1200 - 1450 A.D.) plate style groups 
 
# The Brainerd-Robinson coefficient is a similarity metric that is unique  

441 

# to archaeology and is used to compare assemblages based on proportions  
# of categorical data such as vessel or point types. The data used in the 
# site to site proportional similarity comparison include 506 plate 
# fragments, 94 unique stylistic designs, and 29 style groups.  
 
# The Brainerd-Robinson coefficient has been coded in R by Matt Peeples  
# (http://www.mattpeeples.net/BR.html) and by Gianmarco Alberti  
# (http://cainarchaeology.weebly.com/r-function-for-brainerd-robinson-similarity-coefficient.h
tml).  
# Here, I follow Matt Peeple's BRsim implementation because it is 
# substantially less resource intensive. However, I include a rescaling 
# feature to rescale the BR coefficients rom 0 - 200 to 0 - 1, which makes 
# the output amenable for the construction of network graphs.  
 
# The input for the function is a data frame with assemblages to be compared 
# are found in the rows and the categorical variables  
# (such as pottery/lithic types, objects, compositional groups, etc.) 
# comprise the columns. Each variable is the numerical amount of a  
# particular categorical variable found at each site/sample/discrete  
# observation unit.  
 
# Start by loading in some necessary packages 
library(tidyverse) 
library(igraph) 
library(corrplot) 
library(reshape2) 
 
# Here is the BRsim function as coded by Gianmarco 
BRsim <- function(x, correction, rescale) { 
  if(require(corrplot)){ 
    print("corrplot package already installed. Good!") 
  } else { 
    print("trying to install corrplot package...") 
    install.packages("corrplot", dependencies=TRUE) 
    suppressPackageStartupMessages(require(corrplot)) 
  } 
  rd <- dim(x)[1] 
  results <- matrix(0,rd,rd) 
  if (correction == T){ 
    for (s1 in 1:rd) { 
      for (s2 in 1:rd) { 
        zero.categ.a <-length(which(x[s1,]==0)) 
        zero.categ.b <-length(which(x[s2,]==0)) 
        joint.absence <-sum(colSums(rbind(x[s1,], x[s2,])) == 0) 
        if(zero.categ.a==zero.categ.b) { 
          divisor.final <- 1 
        } else { 
          divisor.final <- max(zero.categ.a, zero.categ.b)-joint.absence+0.5 
        } 
        results[s1,s2] <- round((1 - (sum(abs(x[s1, ] / sum(x[s1,]) - x[s2, ] / sum(x[s2,]))))
/2)/divisor.final, digits=3) 
      } 
    }  

442 

  } else {   
    for (s1 in 1:rd) { 
      for (s2 in 1:rd) { 
        results[s1,s2] <- round(1 - (sum(abs(x[s1, ] / sum(x[s1,]) - x[s2, ] / sum(x[s2,]))))/
2, digits=3) 
      } 
    } 
  } 
  rownames(results) <- rownames(x) 
  colnames(results) <- rownames(x) 
  col1 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "white", "cyan", "#007FFF"
, "blue", "#00007F")) 
  if (rescale == F) { 
    upper <- 200 
    results <- results * 200 
  } else {  
    upper <- 1.0 
  } 
  corrplot(results, method="square", addCoef.col="red", is.corr=FALSE, cl.lim = c(0, upper), c
ol = col1(100), tl.col="black", tl.cex=0.8)  
  return(results) 
} 
 
# Here is a more simplified version from Matt Peeples  
# Function for calculating Brainerd-Robinson (BR) coefficients 
# *Note there is data pre-processing for Matt's script not included here 
BR <- function(x) { 
  rd <- dim(x)[1] 
  results <- matrix(0,rd,rd) 
  for (s1 in 1:rd) { 
    for (s2 in 1:rd) { 
      x1Temp <- as.numeric(x[s1, ]) 
      x2Temp <- as.numeric(x[s2, ]) 
      br.temp <- 0 
      results[s1,s2] <- 200 - (sum(abs(x1Temp - x2Temp)))}} 
  row.names(results) <- row.names(x) 
  colnames(results) <- row.names(x) 
  return(results)} 
 
# My editing of the two 
BR_au <- function(x, rescale = F, counts = T) { 
  if (counts == T){ 
    x <- prop.table(as.matrix(x), 1) * 100 
  } else { 
  } 
  rd <- dim(x)[1] 
  results <- matrix(0,rd,rd) 
  for (s1 in 1:rd) { 
    for (s2 in 1:rd) { 
      x1Temp <- as.numeric(x[s1, ]) 
      x2Temp <- as.numeric(x[s2, ]) 
      br.temp <- 0 
      results[s1,s2] <- 200 - (sum(abs(x1Temp - x2Temp))) 

443 

    } 
  }   
  row.names(results) <- row.names(x) 
  colnames(results) <- row.names(x) 
  if (rescale == F) { 
    return(results) 
  } else {  
    results <- results / 200 
    return(results) 
  } 
} 
 
# Now that we have the function constructed, let's bring in our data. 
BRdata <- read.csv("BRsimdata.csv") 
 
# Our first column is the name of the sites. In order for the function to 
# run, we need to turn this first column into our row names and remove  
# the first column so all data are numeric.  
row.names(BRdata) <- BRdata[,1] 
BRdata <- BRdata[, -1] 
 
# Time to use Gianmarco's BRsim function, which produces a nice correlation 
# matrix and corresponding heat map of the results of the Brainerd-Robinson 
# analysis.  
# First we filter out Fouts Village 
BRdata_row_names <- rownames(BRdata) 
BRdata_row_names <- filter(as.data.frame(BRdata_row_names),  
                           BRdata_row_names != "Fouts Village") 
colnames(BRdata_row_names) <- NULL 
BRdata_no_fouts <- filter(BRdata, rownames(BRdata) != "Fouts Village") 
rownames(BRdata_no_fouts) <- sapply(BRdata_row_names, as.character) 
BRsim(BRdata_no_fouts, correction = F, rescale = T) 
 
# Rather than dwelling on the results, let's implement the function using  
# my own function, which is primarily drawn from Matt Peeples’ implementation 
# Since the data provides counts, we first need to convert to proportions  
# for the BR coefficient  
BRdata_prop <- prop.table(as.matrix(BRdata), 1) * 100 
BRresults <- BR_au(BRdata_prop, rescale = T, counts = F) 
 
# Now, let's turn the results into a social network graph. 
 
# The results of the BRsim function come in the form of an adjacency matrix. 
# igraph can easily handle this kind of data to create a network graph. 
# Because the adjacency matrix is between 0 and 1, we need to tell igraph 
# that the resulting network graph is weighted. Otherwise an edge will only 
# be given for the relationship between each site and itself.  
BRgraph <- graph_from_adjacency_matrix(BRresults, weighted = T) 
 
# Now we can manipulate the graph object using igraphs's functions and  
# create a weighted edgelist for work in Gephi and multinet.  
 
# Create edgelist 

444 

BRel <- as_edgelist(BRgraph) 
 
# Create the weights and format as a data frame for column binding 
BRw <- E(BRgraph)$weight 
BRw <- as.data.frame(BRw) 
 
# Add the weights, and viola we have a weighted, directed edgelist for 
# proportional stylistic similarity between sites.  
BRel <- cbind(BRel, BRw) 
 
# Write out complete Brainerd Robinson edgelist 
write_csv(BRel, "complete_BR_edgelist.csv") 
 
# Assessing the distribution of the BR coefficients 
BRel %>% 
  filter(`1` != `2`) %>% 
  ggplot(aes(x = BRw)) +  
  geom_histogram(aes(y=..density..), binwidth=.05, colour="black", 
                 fill="white") + 
  geom_density(alpha = 0.2) + 
  geom_vline(aes(xintercept=mean(BRw, na.rm=T)), # Ignore NA values for mean 
             color="red", linetype="dashed", size=1) + 
  xlab("Rescaled BR Coefficients") + 
  ylab("Density") + 
  theme_minimal()  
 
# Mean of BR coefficients (this will be used as a cutoff point for giving 
# edges) 
BRel %>% 
  filter(`1` != `2`) %>% 
  summarise(Mean = mean(BRw))  
 
# Looks like the mean is 0.4132476. We'll round it down to 0.4 for an edge  
# cutoff value 
 
# But before we apply that cutoff, let's explore the range and frequency of 
# BR scores if they were produced purely by chance based on our data set 
 
# First, we will row and column randomize the BR input 10,000 times and 
# create a list of the results 
# This means that we'll shuffle the order of row and column data with 
# replacement 
BRdata_rand_list <- replicate(10000, BRdata[sample(1:nrow(BRdata),  
                                                   replace = T), 
                                            sample(1:nrow(BRdata),  
                                                   replace = T)],  
                              simplify = F) 
 
# Setup an empty list to hold the BR coefficients for the randomized data 
BR_rand_result <- list() 
 
# Number of simulations 
nsim <- 10000 

445 

 
# Now we can iterate the BR algorithm over the randomized lists 
for (i in 1:nsim) { 
  BR_rand_result[[i]] <- BR_au(BRdata_rand_list[[i]], rescale = T) 
} 
 
# Turn adjacency matrices into three column data frames 
for (i in 1:nsim) { 
  BR_rand_result[[i]] <- setNames(melt(BR_rand_result[[i]]),  
                                  c('1', '2', 'values')) 
} 
 
# Now we can extract the BR values from the data frames in the list 
BR_rand_result_vals <- lapply(BR_rand_result, '[[', 3) 
 
# And collapse that list into one long vector and turn into a  
# tibble data frame 
BR_rand_vals <- tbl_df(unlist(BR_rand_result_vals)) 
 
# Add a column to indicate these are simulated data 
BR_rand_vals <- BR_rand_vals %>% 
                    mutate(Type = "Randomized BR") 
 
# Append the actual data 
BRel <- tbl_df(BRel) 
BR_vals_all <- BRel %>% 
                  select(BRw) %>% 
                  mutate(value = BRw) %>% 
                  select(value) %>% 
                  mutate(Type = "Actual BR") %>% 
                  bind_rows(., BR_rand_vals) 
 
# Drop 0's and 1's since no sites are perfectly dissimilar or similar 
BR_vals_final <- BR_vals_all %>% 
                  filter(value != 1) %>% 
                  filter(value != 0) 
 
# Plot 
ggplot(BR_vals_final, aes(x = value)) +  
  geom_histogram(data = subset(BR_vals_final, Type == "Randomized BR"), 
                 aes(y=..density..), alpha = 0.5, bins = 25, colour="black", 
                 fill="green4") + 
  geom_density(data = subset(BR_vals_final, Type == "Randomized BR"),  
               alpha = 0.1, color = "green4", fill = "green4",  
               adjust = 2.5) +  
  geom_vline(data = subset(BR_vals_final, Type == "Randomized BR"), 
             aes(xintercept=mean(value, na.rm=T)),# Ignore NA values for mean 
             color="green4", linetype="dashed", size=1) + 
  geom_histogram(data = subset(BR_vals_final, Type == "Actual BR"), 
                 aes(y=..density..), bins = 25, colour="black",  
                 fill="navy", alpha = 0.4) + 
  geom_density(data = subset(BR_vals_final, Type == "Actual BR"), 
               alpha = 0.1, color = "navy", fill = "navy") + 

446 

  geom_vline(data = subset(BR_vals_final, Type == "Actual BR"), 
             aes(xintercept=mean(value, na.rm=T)), color = "navy",  
             linetype = "dashed", size = 1) + 
  xlab("Rescaled BR Coefficients") + 
  ylab("Density") + 
  theme_minimal()  
 
# Looks like the mean for the simulated data is well above that of our 
# observed data BR values. Neither the observed nor simulated data closely 
# approximate normal distributions. This suggests some underlying issues 
# related to sampling, in particular the small sample sizes from a  
# number of sites. Nevertheless, the > 0.4 cutoff indicates that edges  
# will be given in situations where the proportional similarity between  
# two assemblages is greater than the average proportional similarity  
# across the Late Prehistoric CIRV.  
 
# Let's now apply our threshold of > 0.4 so that we only give edges to the 
# strongest proportional relationship. We can use dplyr to wrangle the 
# edgelist and also drop recursive edges.  
BRel_t <- BRel %>%  
          filter(BRw > 0.4 & BRel[1] != BRel[2]) 
 
# Change column names to be suitable for Gephi 
colnames(BRel_t) <- c("Source", "Target", "weight") 
 
# Add columns with additional node information 
# Read in tables of site names, geographic coords., and time distinction 
# For time, 1 is a primary occupation prior to Oneota in-migration 
# and 2 is a primary occupation succeeding Oneota in-migration 
plate_node_table <- read_csv("Plate_node_table.csv") 
colnames(plate_node_table) <- c("Source", "Label", "Long", "Lat", "Time") 
 
# Join the node table columns to the edgelist by the Source node 
plate_t1 <- left_join(BRel_t, plate_node_table[-2], by = "Source") 
 
# Prepare node tables to join time designation for the target node 
colnames(plate_node_table) <- c("Target", "Label", "Long", "Lat", "Time2") 
 
# Join Time 2 column to Target node  
plate_edgelist_complete <- left_join(plate_t1, plate_node_table[c(-2:-4)], 
                                     by = "Target") 
 
# Create Pre- and Post-Migration Edgelists 
plate_pre_el_need_dist <-  plate_edgelist_complete %>% 
                            filter(Time == Time2) %>% 
                            filter(Time == 1) 
 
plate_post_el_need_Law <- plate_edgelist_complete %>% 
                            filter(Time == Time2) %>% 
                            filter(Time == 2) 
 
# Two sites have extended or multi-component occupations in both time periods 
# So we need to include their connections in both time periods 

447 

Law_plate_post <- plate_edgelist_complete %>% 
                    filter(Time == 2 & Target == "Lawrenz Gun Club" |  
                             Source == "Lawrenz Gun Club" & Time2 == 2) %>% 
                    mutate(Time = replace(Time, Time == 1, 2)) %>% 
                    mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
Buck_plate_post <- plate_edgelist_complete %>% 
                    filter(Time == 2 & Target == "Buckeye Bend" |  
                             Source == "Buckeye Bend" & Time2 == 2) %>% 
                    mutate(Time = replace(Time, Time == 1, 2)) %>% 
                    mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
# Bind the LCG & Buckeye post-migration edges to the post-migration edgelists 
plate_post_el_need_dist <- rbind(plate_post_el_need_Law, Law_plate_post, 
                                 Buck_plate_post) 
 
# Adding geographic coordinates 
# Read in matrix of site distances 
site_distances <- read_csv("Site Distances Matrix in km.csv") 
 
#first column of site names to rownames  
site_distances <- column_to_rownames(site_distances, var = "X1") 
 
# Convert geographic distance matrix to graph object 
distance_g <- graph_from_adjacency_matrix(as.matrix(site_distances),  
                                          weighted = TRUE,  
                                          mode = "directed") 
 
# Convert geo distance graph object to edgelist 
distance_el <- as_edgelist(distance_g) 
distance_el_weight <- as.numeric(E(distance_g)$weight) 
distance_el <- tbl_df(cbind(distance_el, distance_el_weight)) 
colnames(distance_el) <- c("Source", "Target", "weight") 
distance_el$Distance <- as.numeric(distance_el$weight) 
 
# Merge the geographic distance edgelist with directed plate edgelists 
plate_pre_el_complete <- merge(plate_pre_el_need_dist, distance_el[-3]) 
plate_post_el_complete <- merge(plate_post_el_need_dist, distance_el[-3]) 
 
# Combine the pre- and post-migration data sets into a single edgelist 
plate_el_BR_all_time_complete <- rbind(plate_pre_el_complete, plate_post_el_complete) 
 
# Finally, we can export the complete edgelist for visualization in Gephi 
write_csv(plate_el_BR_all_time_complete, "BR_edgelist_complete_.csv") 
 
###_______UNDIRECTED Network Creation_________### 
###_______________________### 
###_______________________### 
# The edgelists created thus far have been directed. Since we are 
# disregarding directionality, it is important to account for duplicate  
# edges.  
BRgraph_un <- graph_from_adjacency_matrix(BRresults, weighted = T,  
                                          mode = "undirected") 

448 

 
# Create undirected edgelist 
BRel_un <- as_edgelist(BRgraph_un) 
 
# Create the weights and format as a data frame for column binding 
BRw_un <- E(BRgraph_un)$weight 
BRw_un <- as.data.frame(BRw_un) 
 
# Add the weights, and viola we have a weighted, directed edgelist for 
# proportional stylistic similarity between sites.  
BRel_un <- cbind(BRel_un, BRw_un) 
 
# Write out complete Brainerd Robinson edgelist 
write_csv(BRel_un, "complete_BR_UNDIRECTED_edgelist.csv") 
 
# Apply our threshold of > 0.4 so that we only give UNDIRECTED edges to the 
# strongest proportional relationship. We can use dplyr to wrangle the 
# edgelist and also drop recursive edges.  
BRel_t_un <- BRel_un %>%  
  filter(BRw_un > 0.4 & BRel_un[1] != BRel_un[2]) 
 
# Change column names to be suitable for Gephi 
colnames(BRel_t_un) <- c("Source", "Target", "weight") 
 
# Join the node table columns to the edgelist by the Source node 
plate_t1_un <- left_join(BRel_t_un, plate_node_table[-2], by = "Source") 
 
# Prepare node tables to join time designation for the target node 
colnames(plate_node_table) <- c("Target", "Label", "Long", "Lat", "Time2") 
 
# Join Time 2 column to Target node  
plate_edgelist_complete_un <- left_join(plate_t1_un, 
                                        plate_node_table[c(-2:-4)],  
                                        by = "Target") 
 
# Create Pre- and Post-Migration Edgelists 
plate_pre_el_need_dist_un <-  plate_edgelist_complete_un %>% 
  filter(Time == Time2) %>% 
  filter(Time == 1) 
 
plate_post_el_need_Law_un <- plate_edgelist_complete_un %>% 
  filter(Time == Time2) %>% 
  filter(Time == 2) 
 
# Two sites have extended or multi-component occupations in both time periods 
# So we need to include their connections in both time periods 
Law_plate_post_un <- plate_edgelist_complete_un %>% 
  filter(Time == 2 & Target == "Lawrenz Gun Club" |  
           Source == "Lawrenz Gun Club" & Time2 == 2) %>% 
  mutate(Time = replace(Time, Time == 1, 2)) %>% 
  mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
Buck_plate_post_un <- plate_edgelist_complete_un %>% 

449 

  filter(Time == 2 & Target == "Buckeye Bend" |  
           Source == "Buckeye Bend" & Time2 == 2) %>% 
  mutate(Time = replace(Time, Time == 1, 2)) %>% 
  mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
# Bind the LCG & Buckeye post-migration edges to the post-migration edgelists 
plate_post_el_need_dist_un <- rbind(plate_post_el_need_Law_un,  
                                    Law_plate_post_un, Buck_plate_post_un) 
 
# Merge the geographic distance edgelist with undirected plate edgelists 
plate_pre_el_complete_un <- merge(plate_pre_el_need_dist_un, distance_el[-3]) 
plate_post_el_complete_un <- merge(plate_post_el_need_dist_un, 
                                   distance_el[-3]) 
 
# Combine the pre- and post-migration data sets into a single edgelist 
plate_el_BR_all_time_complete_un <- rbind(plate_pre_el_complete_un, 
                                          plate_post_el_complete_un) 
 
# Finally, we can export the complete undirected edgelist for visualization 
# in Gephi 
write_csv(plate_el_BR_all_time_complete_un, 
          "BR_UNDIRECTED_edgelist_complete_.csv") 
write_csv(plate_pre_el_complete_un, 
          "BR_UNDIRECTED_edgelist_pre-migration_.csv") 
write_csv(plate_post_el_complete_un, 
          "BR_UNDIRECTED_edgelist_post-migration_.csv") 

Plate continuous attribute ridgeline plots 
 
# Plate Attributes Ridgeline plot 
 
library(tidyverse) 
library(ggridges) 
 
# Read in plate attribute data 
plates <- read_csv("plate_cont.csv", 
                   col_types = cols(FlareAngle = col_double(),  
                   MaxDiameter = col_double())) 
 
# Assign rownames to unique vessel i.d. 
plate_unique <- read_csv("plate_unique.csv") 
rownames(plates) <- plate_unique$`1` 
 
# Gather data for faceting. Faceting allows the graph to show each 
# attribute's distribution across the different sites 
pGathered <- gather(plates, Attribute, Value, MaxDiameter:MaxTrailing) 
 
# read in node tables to add column to arrange by time period in ridgeline 
# plots 
plate_node_table <- read_csv("Plate_node_table.csv") 
colnames(plate_node_table) <- c("Site", "Label", "Long", "Lat", "Time") 
 
# join node table to allow for separating out sites by time in plots 

450 

pGathered <- pGathered %>% left_join(plate_node_table[c(1, 5)]) 
# Add Time column as factor for discrete color scale 
pGathered$Time1 <- as.factor(pGathered$Time)  
 
# Add a new factor level for Lawrenz and Buckeye, with occupations in both 
# time periods Also factor the Site levels for ordering in the plot 
ppGathered <- pGathered %>% 
  mutate(Time3 = ifelse(Site == "Buckeye Bend", 3, Time1)) %>% 
  mutate(Time4 = ifelse(Site == "Lawrenz Gun Club", 3, Time3)) %>% 
  mutate(Time4 = ifelse(Time4 == 2, 4, Time4)) %>% 
  mutate(Time4 = as.factor(.$Time4)) %>% 
  mutate(Site = as.factor(.$Site)) 
 
# Create vector of columns names to appear in the plot 
attribute_names <- c( 
  "FlareAngle" = "Flare Angle (°)", 
  "FlareLength" = "Flare Length (mm)",  
  "MaxDiameter" = "Diameter (cm)", 
  "MaxIncising" = "Incising (mm)", 
  "MaxTrailing" = "Trailing (mm)", 
  "RimThick" = "Rim Thickness (mm)", 
  "ThickBelowFlare" = "Flare-Well Joint (mm)" 
) 
 
# Create plate ridgeline plot of plate attributes 
ppGathered %>%  
    group_by(Site) %>%  
    arrange(Site, Time4) %>%  
  ggplot(aes(x = Value, y = reorder(fct_rev(Site), desc(Time4)),  
             fill = Time4)) +  
  geom_density_ridges() +  
  facet_wrap(~Attribute, scale = "free",  
             labeller = as_labeller(attribute_names)) +  
  theme(axis.text.y = element_text(size=12)) +  
  xlab("") +  
  ylab("") + ggtitle("Plate Attributes") + 
  scale_fill_brewer(palette = "Greens") +  
  theme_minimal() + 
  theme(strip.text.x = element_text(face = "bold"),  
        panel.grid.major.y = element_blank()) 

Summary and Network Statistics 
 
# Plate design summary and network statistics 
 
library(tidyverse) 
library(readxl) 
library(broom) 
library(igraph) 
library(cowplot) 
 
plate_all <- read_excel("Upton_Dis_Plates.xlsx") 
 

451 

# Count total number of plates by site with decoration data 
plate_all %>%  
  group_by(Site) %>% 
  select(Site, `BR Design Group`) %>%  
  na.omit() %>% 
  summarise(`Decorated Plates` = n())  
 
# Count how many indeterminate vessel designs are present by site 
plate_all %>%  
  group_by(Site) %>% 
  select(Site, `BR Design Group`) %>%  
  mutate(`BR Design Group` = as.numeric(`BR Design Group`)) %>% 
  summarise(NAs = sum(is.na(`BR Design Group`))) 
 
# and missing values overall 
plate_all %>%  
  group_by(Site) %>% 
  select(Site, `BR Design Group`) %>%  
  mutate(`BR Design Group` = as.numeric(`BR Design Group`)) %>% 
  summarise(NAs = sum(is.na(`BR Design Group`))) %>% 
  select(NAs) %>% 
  summarise(sum = sum(.)) 
 
# Count the number of plates with decoration techniques AND identifiable 
# motif by site 
plate_all %>%  
  select(Site, `Primary Design Technique`, `BR Design Group`) %>%  
  group_by(Site) %>% 
  mutate(Tech_BR = ifelse((!is.na(`Primary Design Technique`) & !is.na(`BR Design Group`)),  
                          1, 0)) %>% 
  summarise(`Decorated Plates` = sum(`Tech_BR`)) %>% 
  write_csv(., "Decorated Plates by Site.csv") 
 
# Add a table of the different decoration techniques 
write.csv(table(plate_all$Site, plate_all$`Primary Design Technique`),  
          "plate decoration technique summary.csv") 
 
# Count the total number of decorated plates by site 
plate_all %>%  
  group_by(Site) %>% 
  select(Site, `BR Design Group`) %>% 
  mutate(`Decorated Plates` = ifelse(`BR Design Group` %in% c(-1, 1),  
                                     0, `BR Design Group`)) %>% 
  na.omit() %>% 
  summarise(`Decorated Plates` = n()) %>% 
  write.csv(., "count of decorated plates by site.csv") 
 
# and total number of decorated plates overall 
plate_all %>%  
  group_by(Site) %>% 
  select(Site, `BR Design Group`) %>% 
  mutate(`Decorated Plates` = ifelse(`BR Design Group` %in% c(-1, 1),  
                                     0, `BR Design Group`)) %>% 

452 

  na.omit() %>% 
  summarise(`Decorated Plates` = n()) %>% 
  select(`Decorated Plates`) %>% 
  mutate(`Decorated Plates` = as.numeric(`Decorated Plates`)) %>% 
  summarise(sum = sum(.)) 
 
# Table for BR Design Groups 
BR_table <- table(plate_all$Site, plate_all$`BR Design Group`) 
table(plate_all$Site, plate_all$`Primary Design Technique`) 
write.csv(BR_table, "Plate_BR_table.csv") 
 
# Total number of plates (includes all plates, even those without  
# design data) 
plate_all %>%  
  group_by(Site) %>% 
  select(Site, `BR Design Group`) %>% 
  mutate(`Decorated Plates` = ifelse(`BR Design Group` %in% c(-1, 1),  
                                     0, `BR Design Group`)) %>% 
  summarise(`Decorated Plates` = n()) %>% 
  select(`Decorated Plates`) %>% 
  mutate(`Decorated Plates` = as.numeric(`Decorated Plates`)) %>% 
  summarise(sum = sum(.)) 
 
# Ceramic Diversity at sites 
BR_table_t <- t(BR_table) 
cer_div <- as.data.frame(colSums(BR_table_t != 0)) 
cer_div <- rownames_to_column(cer_div) 
colnames(cer_div) <- c("Site", "Count of Design Categories") 
ppGathered %>% group_by(Site) %>% filter(distinct(Site)) 
cer_div <- left_join(cer_div, unique(ppGathered[, c(1, 7)])) 
levels(cer_div$Time4) <- c("Pre-Migration", "Pre- and Post", 
                           "Post-Migration") 
 
# Remove Orendof D and Fouts and plot box and whisker plot 
cer_div %>% 
  filter(Site != "Orendorf D") %>% 
  filter(Site != "Fouts Village") %>% 
ggplot() + 
    geom_boxplot(aes(x = Time4, y = `Count of Design Categories`)) + 
    xlab("") +  
    theme_classic() + 
    scale_y_continuous(expand = c(0, 0), limits = c(0, 20),  
                       breaks = c(0, 5, 10, 15, 20)) + 
    ylab("Count of Design Categories Present") + 
    theme(text = element_text(size=20)) 
 
# Regression of number of design categories as explained by sample size 
categories <- read_xlsx("Number of Categories and Sample Size from each site for regression.xl
sx") 
 
# Summary of regression 
cat_lm <- lm(num_categories ~ sample_size, data = categories) 
summary(cat_lm) 

453 

tidy(cat_lm) 
 
# Regression plot - looks strongly positive 
categories %>% 
  filter(Site != "Fouts Village")%>% 
  ggplot(aes(x = sample_size, y = num_categories)) +  
  geom_smooth(method = "lm", se = FALSE) +  
  geom_point() 
 
# Correlation of the number of categories as a function of sample size - 
# indeed the larger the sample size, the more plate decoration categories  
# are present 
cor(categories$num_categories, categories$sample_size) 
 
###___________Plate BR Network Stats__________________________### 
 
# Read in finalized, undirected plate BR edgelist  
BR_el_un <- read_csv("BR_UNDIRECTED_edgelist_complete_.csv") 
 
# Read in finalized, undirected pre-migration BR edgelist 
BR_el_un_pre <- read_csv("BR_UNDIRECTED_edgelist_pre-migration_.csv") 
 
# Read in finalized, undirected post-migration BR edgelist 
BR_el_un_post <- read_csv("BR_UNDIRECTED_edgelist_post-migration_.csv") 
 
# Convert to igraph graph 
BR_g <- graph_from_edgelist(as.matrix(BR_el_un[, c(1:2)]),  
                            directed = FALSE) 
BR_g_pre <- graph_from_edgelist(as.matrix(BR_el_un_pre[, c(1:2)]),  
                                directed = FALSE) 
BR_g_post <- graph_from_edgelist(as.matrix(BR_el_un_post[, c(1:2)]), 
                                 directed = FALSE) 
 
# Assign edge weights to graph 
E(BR_g)$weight <- BR_el_un$weight 
E(BR_g_pre)$weight <- BR_el_un_pre$weight 
E(BR_g_post)$weight <- BR_el_un_post$weight 
 
# Function to calculate degree, betweenness, closeness, and eigenvector 
# centrality for a graph and return a data frame with the scores 
centr_all <- function(graph, g_name = "Score") { 
   
  # Check that graph is an igraph object 
  if (!is_igraph(graph)) { 
    stop("Not a graph object") 
  } 
   
  # Name of graph 
  g_name <- as.character(g_name) 
   
  # Degree centralization 
  res_centr <- centr_degree(graph)$centralization 
   

454 

  # Betweenness centralization 
  res_centr[2] <- centr_betw(graph)$centralization 
   
  # Closeness centralization 
  res_centr[3] <- centr_clo(graph)$centralization 
   
  # Eigenvector centralization 
  res_centr[4] <- centr_eigen(graph)$centralization 
   
  res_centr <- t(as.data.frame(res_centr)) 
   
  # Table of scores 
  colnames(res_centr) <- c("Degree", "Betweenness", "Closeness", 
                           "Eigenvector") 
  rownames(res_centr) <- g_name 
   
  res_centr 
} 
 
# Calculate centralization scores for each graph 
all_centr <- centr_all(BR_g, g_name = "Flattened Across Time") 
pre_centr <- centr_all(BR_g_pre,  g_name = "Pre-Migration") 
post_centr <- centr_all(BR_g_post,  g_name = "Post-Migration") 
rbind(pre_centr, post_centr, all_centr) 
 
# Calculated Mean Weighted Degree (or strength) 
mean(strength(BR_g)) 
mean(strength(BR_g_pre)) 
mean(strength(BR_g_post)) 
 
#--------------Edge Betweenness Community Detection----------------- 
# Edge betweenness extends the concept of vertex betweenness centrality to 
# edges by assigning each edge a score that reflects the number of shortest 
# paths that move through that edge.  
# You might ask the question, which ties in a social network are the most 
# important in the spread of information? 
 
# Calculated edge betweenness score for each network 
pre_eb <- cluster_edge_betweenness(BR_g_pre) 
post_eb <- cluster_edge_betweenness(BR_g_post) 
all_eb <- cluster_edge_betweenness(BR_g) 
 
# Looks like the only interesting graph in terms of community detection is 
# the graph that is flattened across time. It correctly assigns the pre-  
# and post-migration sites to clusters, but with some interesting intricacies 
 
# Community detection via edge betweenness plot 
plot(all_eb, BR_g, col = membership(all_eb), vertex.label.cex = c(1.5),  
     edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in \n the Categorical Identification Networ
k",  
      cex.main = 1.5) 
 

455 

#--------Randomization for Pre-Migration Period BR------------------ 
#------------PRE_MIGRATION------------------------------------------- 
 
# Initiate empty list for assessing BR pre-migration average path length  
# and transitivity 
gpre <- vector('list', 5000) 
 
# Initiate empty list for assessing BR pre-migration density density  
# and mean degree 
gpre.d <- vector('list', 5000) 
 
# Populate gpre list with random graphs of same order and size 
for(i in 1:5000){ 
  gpre[[i]] <- erdos.renyi.game(n = gorder(BR_g_pre), p.or.m = gsize(BR_g_pre), 
                                directed = FALSE, type = "gnm") 
} 
 
# Populate gpre.d list with random graphs of same order and approximate 
# density. A separate list of 5000 random graphs is necessary for density  
# and mean degree because these statistics would identical in random graphs 
# of the same order and size as our observed graph.  
# Instead, a probability of edge creation equal to the observed density is 
# used. Further, only mean degree (as opposed to mean weighted degree) is 
# used because Erdos-Renyi random graphs do not support weights.  
# However, see the bottom of this chapter's code for a method on assigning 
# random edge edgeweights to an Erdo-Renyi graph 
for(i in 1:5000){ 
  gpre.d[[i]] <- erdos.renyi.game(n = gorder(BR_g_pre), p.or.m = edge_density(BR_g_pre), direc
ted = FALSE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), 
# density, and degree across he 5000 random pre-migration graphs 
pre.pl <- lapply(gpre.d, mean_distance, directed = FALSE) 
pre.trans <- lapply(gpre, transitivity) 
pre.density <- lapply(gpre.d, edge_density) 
pre.degree <- lapply(gpre.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
pre.pl <- as.data.frame(unlist(pre.pl)) 
pre.trans <- as.data.frame(unlist(pre.trans)) 
pre.density <- as.data.frame(unlist(pre.density)) 
pre.degree <- as.data.frame(unlist(pre.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths  
# with the pre-migration BR network's ave. shortest path as line 
p.pre.pl <- ggplot(pre.pl, aes(x = pre.pl)) +  
  geom_histogram(aes(y = ..density..), bins = 28) +  
  geom_vline(xintercept = (mean_distance(BR_g_pre, directed = FALSE)),  

456 

             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPre-Migration P
eriod Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration 
# BR network's transitivity path as line 
p.pre.trans <- ggplot(pre.trans, aes(x = pre.trans)) +  
  geom_histogram(aes(y = ..density..), bins = 20) +  
  geom_vline(xintercept = (transitivity(BR_g_pre)), linetype = "dashed", 
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPre-Migration Period Network
 Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the 
# pre-migration jar network's ave. shortest path as line 
p.pre.density <- ggplot(pre.density, aes(x = pre.density)) +  
  geom_histogram(aes(y = ..density..), bins = 20) +  
  geom_vline(xintercept = (edge_density(BR_g_pre)), linetype = "dashed", 
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPre-Migration Preiod Network
 Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration 
# BR network's mean degree path as line 
p.pre.degree <- ggplot(pre.degree, aes(x = pre.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 20) +  
  geom_vline(xintercept = (mean(degree(BR_g_pre, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPre-Migration Period Network 
Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.pre.pl, p.pre.trans, p.pre.density, p.pre.degree) 
 
# Calculate the proportion of graphs with an average path length lower than 
# observed 
sum(pre.pl < mean_distance(BR_g_pre, directed = False))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering 
# coefficient) lower than our observed 
sum(pre.trans < transitivity(BR_g_pre))/5000*100 

457 

 
# Calculate the proportion of graphs with a density lower than our observed 
sum(pre.density < edge_density(BR_g_pre))/5000*100 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(pre.degree < mean(degree(BR_g_pre)))/5000*100 
 
#----------Randomization for Post-Migration Period BR------------ 
#--------------------POST_MIGRATION------------------------------- 
 
# Initiate empty list for assessing BR post-migration average path length and 
# transitivity 
gpost <- vector('list', 5000) 
 
# Initiate empty list for assessing BR post-migration density and 
# mean degree 
gpost.d <- vector('list', 5000) 
 
# Populate gpost list with random graphs of same order and size 
for(i in 1:5000){ 
  gpost[[i]] <- erdos.renyi.game(n = gorder(BR_g_post),  
                                 p.or.m = gsize(BR_g_post),  
                                 directed = FALSE, type = "gnm") 
} 
 
# Populate gpost.d list with random graphs of same order and approximate 
# density. A separate list of 5000 random graphs is necessary for density  
# and mean degree because these statistics would identical in random graphs 
# of the same order and size as our observed graph.  
# Instead, a probability of edge creation equal to the observed density is 
# used. Further, only mean degree (as opposed to mean weighted degree) is 
# used because Erdos-Renyi random graphs do not support weights.  
for(i in 1:5000){ 
  gpost.d[[i]] <- erdos.renyi.game(n = gorder(BR_g_post),  
                                   p.or.m = edge_density(BR_g_post),  
                                   directed = FALSE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), 
# density, and degree across the 5000 random post-migration graphs 
post.pl <- lapply(gpost.d, mean_distance, directed = FALSE) 
post.trans <- lapply(gpost, transitivity) 
post.density <- lapply(gpost.d, edge_density) 
post.degree <- lapply(gpost.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for visualizations 
post.pl <- as.data.frame(unlist(post.pl)) 
post.trans <- as.data.frame(unlist(post.trans)) 
post.density <- as.data.frame(unlist(post.density)) 

458 

post.degree <- as.data.frame(unlist(post.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths  
# with the post-migration BR network's ave. shortest path as line 
p.post.pl <- ggplot(post.pl, aes(x = post.pl)) +  
  geom_histogram(aes(y = ..density..), bins = 18) +  
  geom_vline(xintercept = (mean_distance(BR_g_post, directed = FALSE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPost-Migration 
Period Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the 
# post-migration BR network's transitivity path as line 
p.post.trans <- ggplot(post.trans, aes(x = post.trans)) +  
  geom_histogram(aes(y = ..density..), bins = 12) +  
  geom_vline(xintercept = (transitivity(BR_g_post)), linetype = "dashed", 
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPost-Migration Period Networ
k Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the 
# post-migration BR network's ave. shortest path as line 
p.post.density <- ggplot(post.density, aes(x = post.density)) +  
  geom_histogram(aes(y = ..density..), bins = 15) +  
  geom_vline(xintercept = (edge_density(BR_g_post)), linetype = "dashed", 
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPost-Migration Period Networ
k Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the post-migration 
# BR network's mean degree path as line 
p.post.degree <- ggplot(post.degree, aes(x = post.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 16) +  
  geom_vline(xintercept = (mean(degree(BR_g_post, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPost-Migration Period Network
 Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.post.pl, p.post.trans, p.post.density, p.post.degree) 
 

459 

# Calculate the proportion of graphs with an average path length lower than 
# observed 
sum(post.pl < mean_distance(BR_g_post, directed = FALSE))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering 
# coefficient) lower than our observed 
sum(post.trans < transitivity(BR_g_post))/5000*100 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(post.density < edge_density(BR_g_post))/5000*100 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(post.degree < mean(degree(BR_g_post)))/5000*100 
 
#--------Randomization BR Across Time in the CIRV---------------- 
#--------------ACROSS TIME---------------------------------------- 
 
# Initiate empty list for assessing BR across time average path length and 
# transitivity 
gall <- vector('list', 5000) 
 
# Initiate empty list for assessing BR across time density density and mean 
# degree 
gall.d <- vector('list', 5000) 
 
# Populate gpost list with random graphs of same order and size 
for(i in 1:5000){ 
  gall[[i]] <- erdos.renyi.game(n = gorder(BR_g), p.or.m = gsize(BR_g),  
                                 directed = FALSE, type = "gnm") 
} 
 
# Populate gall.d list with random graphs of same order and approximate 
# density. A separate list of 5000 random graphs is necessary for density  
# and mean degree because these statistics would identical in random graphs 
# of the same order and size as our observed graph.  
# Instead, a probability of edge creation equal to the observed density is used. Further, only
 mean degree (as opposed to mean weighted degree) is used 
# because Erdos-Renyi random graphs do not support weights.  
for(i in 1:5000){ 
  gall.d[[i]] <- erdos.renyi.game(n = gorder(BR_g),  
                                  p.or.m = edge_density(BR_g),  
                                   directed = FALSE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), 
# density, and degree across the 5000 random graphs 
all.pl <- lapply(gall.d, mean_distance, directed = FALSE) 
all.trans <- lapply(gall, transitivity) 
all.density <- lapply(gall.d, edge_density) 
all.degree <- lapply(gall.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 

460 

) 
 
# Unlist and change to a data frame for visualizations 
all.pl <- as.data.frame(unlist(all.pl)) 
all.trans <- as.data.frame(unlist(all.trans)) 
all.density <- as.data.frame(unlist(all.density)) 
all.degree <- as.data.frame(unlist(all.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths  
# with the BR network's ave. shortest path as line 
p.all.pl <- ggplot(all.pl, aes(x = all.pl)) +  
  geom_histogram(aes(y = ..density..), bins = 32) +  
  geom_vline(xintercept = (mean_distance(BR_g, directed = FALSE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \n Average Shorte
st Path Length Across Time in the CIRV") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the observed 
# network's transitivity path as line 
p.all.trans <- ggplot(all.trans, aes(x = all.trans)) +  
  geom_histogram(aes(y = ..density..), bins = 25) +  
  geom_vline(xintercept = (transitivity(BR_g)), linetype = "dashed", 
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \n Transitivity Across Time in
 the CIRV") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the observed 
# BR network's ave. shortest path as line 
p.all.density <- ggplot(all.density, aes(x = all.density)) +  
  geom_histogram(aes(y = ..density..), bins = 20) +  
  geom_vline(xintercept = (edge_density(BR_g)), linetype = "dashed",  
             color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\n Average Density Across Time
 in the CIRV") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the post-migration BR network's    
mean 
# degree path as line 
p.all.degree <- ggplot(all.degree, aes(x = all.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 20) +  
  geom_vline(xintercept = (mean(degree(BR_g, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nMean Degree Across Time in th

461 

e CIRV") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.all.pl, p.all.trans, p.all.density, p.all.degree) 
 
# Calculate the proportion of graphs with an average path length lower than 
# observed 
sum(all.pl < mean_distance(BR_g, directed = FALSE))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering 
# coefficient) lower than our observed 
sum(all.trans < transitivity(BR_g))/5000*100 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(all.density < edge_density(BR_g))/5000*100 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(all.degree < mean(degree(BR_g)))/5000*100 

BR-Geodesic distance regression 
 
library(infer) 
library(tidyverse) 
library(igraph) 
library(reshape2) 
library(stringr) 
library(cowplot) 
library(broom) 
 
# Read in finalized, undirected plate BR edgelist  
BR_el_un <- read_csv("BR_UNDIRECTED_edgelist_complete_.csv") 
 
# Read in finalized, undirected pre-migration BR edgelist 
BR_el_un_pre <- read_csv("BR_UNDIRECTED_edgelist_pre-migration_.csv") 
 
# Read in finalized, undirected post-migration BR edgelist 
BR_el_un_post <- read_csv("BR_UNDIRECTED_edgelist_post-migration_.csv") 
 
# Function from infer to take a random sample from a data set a certain number of times 
rep_sample_n <- function(tbl, size, replace = FALSE, reps = 1) 
{ 
  n <- nrow(tbl) 
  i <- unlist(replicate(reps, sample.int(n, size, replace = replace), simplify = FALSE)) 
   
  rep_tbl <- cbind(replicate = rep(1:reps,rep(size,reps)), tbl[i,]) 
   
  dplyr::group_by(rep_tbl, replicate) 
} 
 
# Inference testing with linear models 
# Take 100 samples of 50 each from the plate BR data sets 

462 

# The idea is to explore regression trends on the slope coefficient using 
# samples from each data set. Does the trend with the entire data hold true 
# when sub-samples are taken from the data? 
# This is a two-tailed test to see if a linear relationship (positive or 
# negative) exists between distance (explanatory variable) and weight 
# (response variable) 
BRpresamples <- rep_sample_n(BR_el_un_pre[, c(3, 8)], size = 12, reps = 100) 
BRpostsamples <- rep_sample_n(BR_el_un_post[, c(3, 8)], size = 7, reps = 100) 
BRallsamples <- rep_sample_n(BR_el_un[, c(3, 8)], size = 18, reps = 100) 
 
# Add replicate col to align observed trends with random samples 
pre_observed <- BR_el_un_pre[, c(3, 8)] %>% 
  mutate(replicate = 200)  
 
post_observed <- BR_el_un_post[, c(3, 8)] %>% 
  mutate(replicate = 200)  
 
all_observed <- BR_el_un[, c(3, 8)] %>% 
  mutate(replicate = 200)  
 
# Model showing proportional similarity across time 
BR_lm_all <- ggplot(BRallsamples, aes(x = Distance, y = weight,  
                                      group = replicate)) +  
  geom_point(size = 2, shape = 20) +  
  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
  ggtitle("Social Categorical Identification Network Across Time") +  
  background_grid(major = 'y', minor = "none") + 
  xlab("Distance (km)") + 
  ylab("Degree of Proportional Categorical Similarity") + 
  theme(strip.background = element_blank(), 
        strip.text.x =element_blank()) + 
  stat_smooth(data = all_observed, aes(x = Distance, y = weight),  
              color ="red3",  
              linetype = "twodash", method = "lm", se = FALSE)  
 
# Model showing proportional similarity in the pre-migration CIRV 
BR_lm_pre <- ggplot(BRpresamples, aes(x = Distance, y = weight,  
                                      group = replicate)) +  
  geom_point(size = 2, shape = 20) +  
  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
  ggtitle("Pre-Migration Social Categorical Identification Network") +  
  background_grid(major = 'y', minor = "none") + 
  xlab("Distance (km)") + 
  ylab("Degree of Proportional Categorical Similarity") + 
  theme(strip.background = element_blank(), 
        strip.text.x =element_blank()) + 
  stat_smooth(data = pre_observed, aes(x = Distance, y = weight),  
              color ="red3",  
              linetype = "twodash", method = "lm", se = FALSE)  
 
# Model showing proportional similarity in the post-migration CIRV 
BR_lm_post <- ggplot(BRpostsamples, aes(x = Distance, y = weight,  
                                        group = replicate)) +  

463 

  geom_point(size = 2, shape = 20) +  
  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
  ggtitle("Post-Migration Social Categorical Identification Network") +  
  background_grid(major = 'y', minor = "none") + 
  xlab("Distance (km)") + 
  ylab("Degree of Proportional Categorical Similarity") + 
  theme(strip.background = element_blank(), 
        strip.text.x =element_blank()) + 
  stat_smooth(data = post_observed, aes(x = Distance, y = weight),  
              color ="red3",  
              linetype = "twodash", method = "lm", se = FALSE)  
 
# Inference 
# First, let's calculate the observed slope of the lm in the jar and plate 
# attribute networks 
BR_all_slope <- lm(weight ~ Distance, data = BR_el_un) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate)     
 
BR_pre_slope <- lm(weight ~ Distance, data = BR_el_un_pre) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate)     
 
BR_post_slope <- lm(weight ~ Distance, data = BR_el_un_post) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate)     
 
# Simulate 500 slopes with a permuted dataset for identification network - 
# this will allow us to develop a sampling distribution of the slop under  
# the hypothesis that there is no relationship between the explanatory 
# (Distance) and response (weight) variables.  
set.seed(1568) 
BR_all_perm_slope <- BR_el_un %>% 
  specify(weight ~ Distance) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 500, type = "permute") %>% 
  calculate(stat = "slope")  
 
BR_pre_perm_slope <- BR_el_un_pre %>% 
  specify(weight ~ Distance) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 500, type = "permute") %>% 
  calculate(stat = "slope")  
 
BR_post_perm_slope <- BR_el_un_post %>% 
  specify(weight ~ Distance) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 500, type = "permute") %>% 
  calculate(stat = "slope")  
 

464 

ggplot(BR_all_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
ggplot(BR_pre_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
ggplot(BR_post_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
 
mean(BR_all_perm_slope$stat) 
mean(BR_pre_perm_slope$stat) 
mean(BR_post_perm_slope$stat) 
sd(BR_all_perm_slope$stat) 
sd(BR_pre_perm_slope$stat) 
sd(BR_post_perm_slope$stat) 
 
# Calculate the absolute value of the slope 
abs_BR_all_obs_slope <- lm(weight ~ Distance, data = BR_el_un) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate) %>% 
  abs() 
 
abs_BR_pre_obs_slope <- lm(weight ~ Distance, data = BR_el_un_pre) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate) %>% 
  abs() 
 
abs_BR_post_obs_slope <- lm(weight ~ Distance, data = BR_el_un_post) %>% 
  tidy() %>%    
  filter(term == "Distance") %>% 
  pull(estimate) %>% 
  abs() 
 
# Compute the p-value   
BR_all_perm_slope %>%  
  mutate(abs_BR_all_obs_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_BR_all_obs_slope > BR_all_perm_slope)) 
 
BR_pre_perm_slope %>%  
  mutate(abs_BR_pre_obs_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_BR_pre_obs_slope > BR_pre_perm_slope)) 
 
BR_post_perm_slope %>%  
  mutate(abs_BR_post_obs_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_BR_post_obs_slope > BR_post_perm_slope)) 
 
# Linear models sans visualization 
# explore residuals  
BR_all_lm <- augment(lm(weight ~ Distance, data = BR_el_un)) 
BR_pre_lm <- augment(lm(weight ~ Distance, data = BR_el_un_pre)) 
BR_post_lm <- augment(lm(weight ~ Distance, data = BR_el_un_post)) 
 
# Check SSE - how well do the models fit? 
augment(lm(weight ~ 1, data = BR_el_un)) %>%  
  summarize(SSE = var(.resid)) # null 
BR_all_lm %>% summarize(SSE = var(.resid)) 

465 

 
augment(lm(weight ~ 1, data = BR_el_un_pre)) %>%  
  summarize(SSE = var(.resid)) # null 
BR_pre_lm %>% summarize(SSE = var(.resid)) 
 
augment(lm(weight ~ 1, data = BR_el_un_post)) %>%  
  summarize(SSE = var(.resid)) # null 
BR_post_lm %>% summarize(SSE = var(.resid)) 
 
# Looks like the models do fit well 
 
# Breakdown of linear model results for plate attribute networks  
summary(lm(weight ~ Distance, data = BR_el_un)) # for each 1 km increase in distance, weight d
rops 0.0006741 and at 0 distance, a weight of 0.5549 is expected 
summary(lm(weight ~ Distance, data = BR_el_un))$coefficients # all = p-value of 0.0464, null  
# hypothesis is rejected at alpha of 0.05. As distance increases, weight moderately decreases 
 
summary(lm(weight ~ Distance, data = BR_el_un_pre)) # for each 1 km increase in distance, weig
ht drops 0.0006655 and at 0 distance, a weight of 0.5765 is expected 
summary(lm(weight ~ Distance, data = BR_el_un_pre))$coefficients # pre p-value of 0.1776, fail
 to 
#reject the null hypothesis - no significant linear relationship b/t distance and weight in pr
e 
 
summary(lm(weight ~ Distance, data = BR_el_un_post)) # for each 1 km increase in distance, wei
ght drops 0.0002517 and at 0 distance, a weight of 0.4949 is expected 
summary(lm(weight ~ Distance, data = BR_el_un_post))$coefficients # post p-value of 0.5007, fa
il  
# to reject null - no significant linear relationship b/t distance and weight in post 
 
# Check correlations 
cor(BR_el_un$Distance, BR_el_un$weight) 
cor(BR_el_un_pre$Distance, BR_el_un_pre$weight) 
cor(BR_el_un_post$Distance, BR_el_un_post$weight) 

Experimental method to randomly assign edge weights to Erdos-Renyi random networks 
 
# Randomly assigning weights to a network  
# runif() is used to assign the weights based on a normal distribution of 
# random weights between the max and min values in the observed data 
# This could be used to assess any statistic that uses edge weights, however, 
# none of these measures proved to be significant for the current analysis 
 
for(i in 1:5000){ 
  gpost.d[[i]] <- erdos.renyi.game(n = gorder(BR_g_post), p.or.m = edge_density(BR_g_post),  
                                   directed = FALSE, type = "gnp") 
} 
 
# Assign random weights to edges based on the min/max in the observed network 
for(i in 1:5000){ 
  E(gpost.d[[i]])$weight <- runif(length(E(gpost.d[[i]])), min = min(E(BR_g_post)$weight), max
 = max(E(BR_g_post)$weight)) 
} 

466 

 
# Calculate the mean weighted degree (or strength) for each graph 
post.weighted.degree <- lapply(gpost.d, function(x){ 
  y <- strength(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
post.weighted.degree <- as.data.frame(unlist(post.weighted.degree)) 
 
ggplot(post.weighted.degree, aes(x = post.weighted.degree)) +  
  geom_histogram(aes(y = ..density..), bins = 16) +  
  geom_vline(xintercept = (mean(strength(BR_g_post, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Weighted Degree in 5000 Random Models & \nPost-Migration Perio
d Network Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 

 
 
 
R Code from Chapter 7 Networks of Economic Relationships - Results of the Chemical 
Analyses 
 
Create map of sites and clay samples 
 
# Map of sites and clay resources 
 
library(ggmap) 
library(tidyverse) 
library(ggrepel) 
 
# Read in context data 
cc_loc <- read_csv("Clay Ceramic lat long.csv") 
 
# Set center for the map 
lat_mid <- mean(cc_loc$lat) 
lon_mid <- mean(cc_loc$lon) 
 
# Get map from google map terrain without any labels (via the style argument) 
b <- get_googlemap(center = c(lon = lon_mid, lat = lat_mid), zoom = 9,  
                   maptype = "terrain", source = "google",  
                   style = 'feature:all|element:labels|visibility:off') 
 
# Create map of sites/clay samples and label to check for accuracy 
ggmap(b) + geom_point(data = cc_loc, aes(x = lon, y = lat, shape = Type)) +  
  geom_text_repel(data = cc_loc[c(1:17),], aes(x = lon, y = lat, label = Site_Sample)) 
 
# Create transparent background map to overlay on bedrock geology map 

467 

map <- ggplot() + geom_point(data = cc_loc, aes(x = lon, y = lat, shape = Type)) +  
  theme( 
    panel.background = element_rect(fill = "transparent"), # bg of the panel 
     plot.background = element_rect(fill = "transparent"), # bg of the plot 
     panel.grid.major = element_blank(), # get rid of major grid 
     panel.grid.minor = element_blank(), # get rid of minor grid 
     legend.background = element_rect(fill = "transparent"), # get rid of legend bg 
     legend.box.background = element_rect(fill = "transparent") # get rid of legend panel bg 
  ) + 
  xlab("") + ylab("") 
 
# Save map with transparent background 
ggsave(map, filename = "site-clay map.png", bg = "transparent") 
 
## After exporting, map of sites/clay samples was overlain on top of a bedrock geology map 
#  of the state of Illinois 

Read in geochemical data from Excel sheets and convert from % Oxide to parts-per-
million (ppm) 
Also included in the following code chunk is a method to correct for the presence of shell tempering. 

## Reading Geochemical data into R and converting from % Oxide to ppm  
 
# Load packages 
library(tidyverse) 
library(readxl) 
library(stringr) 
library(magrittr) 
 
# Determine path to file 
path <- "all.xlsx" 
 
# Use map to iterate read_excel over each worksheet in the workbook 
ld <- path %>% 
  excel_sheets() %>% 
  set_names(., .) %>% # this was giving me problems, but the two dots is a workaround 
  map(read_excel, path = path)  
 
# Bind the columns in the lists together to form one dataframe 
df <- bind_cols(ld) 
 
# Change name of first column to element 
names(df)[names(df) == 'X__1'] <- 'element' 
 
# Now, let's get tidy! 
# Grab the first column as rownames, which will become the variable names 
rnames <- df[,1] 
 
# Then grab the column names, which will become a new column "Sample" once transposed 
Sample <- colnames(df[-1]) #we can drop the first name because it will become the rownames 
 
# Transpose the dataframe 

468 

df <- t(df[, -1]) #have to drop the first column or it will convert the numbers to strings 
 
# Set the column names 
colnames(df) <- unlist(rnames) #rnames is stored as a list, so we have to unlist it  
 
# Convert to tibble dataframe 
df <- tbl_df(df) 
 
# Add the date as a column to our data frame so we know when each sample was run 
# first we need to figure out how many samples were run each day 
ld_lengths <- lapply(ld, length) 
 
# With that information we can create a simple for loop to replicate the dates the  
# appropriatenumber of times for the number of samples run each day 
res1 <- as.data.frame(NULL) 
for(i in names(ld_lengths)) { 
  res <- rep(i, ld_lengths[[i]]) 
  res1 <- c(res1, res) 
} 
 
# Create a dataframe of those dates and add it to our sample data 
date_col <- tbl_df(sapply(res1, paste0, collapse = "")) 
colnames(date_col) <- "Date" 
df <- cbind(date_col[2:nrow(date_col),], df) 
 
# Add column of samples names, which were the columns names before transposing 
df <- cbind(Sample, df) 
 
# Use stringr to get rid of repetitive element row names - which have an "X"  
# in them by default since they don't have a column name 
dfnames <- df$Sample 
x_detect <- str_detect(dfnames, "X") 
df <- df[!x_detect, ] 
 
# One pesky column name has a note in it, let's get rid of it too 
note <- str_detect(df$Sample, "High") 
df <- df[!note, ] 
 
# Convert the sample data to numeric to allow for calculations 
df[,3:ncol(df)] <- sapply(df[,3:ncol(df)], as.numeric) 
 
##---------------------------Correction for Shell Tempering Here-------------------------## 
 
# In analysis, I need to correct the sherd samples for the presence of shell tempering. 
# Shell is composed almost entirely of calcium which is in the same row in the periodic table 
# as strontium and barium.  
 
# First step is to drop the Ohio Red standard samples because they don't need correcting 
orows <- str_detect(tolower(df$Sample), "red") 
df_samples1 <- df[!orows, ] 
 
# Add up all elements calculated in percent oxide aside from Ca and Ba 
CaP_correction <- df_samples1 %>%  

469 

                    select(SiO2, Na2O, MgO, Al2O3, K2O, Sb2O5,  
                           MnO, Fe2O3, CuO, SnO2, Ti, PbO2, BaO, Bi, ZnO) %>%  
                    rowSums() %>% 
                    tbl_df() 
 
# Correct the elements by dividing their amount by the corrected percent oxide 
df_samples1[, c(3:length(df_samples1))] <- sapply(df_samples1[, c(3:length(df_samples1))],  
                                 function(x){x/CaP_correction}) %>% 
                            bind_cols() 
 
# Bind the shell corrected ceramic samples with the Ohio Reds 
df_shell_corrected <- tbl_df(bind_rows(df_samples1, df[orows, ])) 
 
####----------------------------------------------------------------------------------#### 
 
# Converting from %oxide to ppm 
# Each element has a unique coefficient to use when converting, so we'll make a  
# function for each and apply them across the rows 
sio2 <- function(x){ 
            x * 1000000/2.1393 #have to multiply by a million then divide by the coefficient 
} 
 
nao2 <- function(x){ 
  x * 1000000/1.348 
} 
 
mgo <- function(x){ 
  x * 1000000/1.6583 
} 
 
al2o3 <- function(x){ 
  x * 1000000/1.8895 
} 
 
p2o5 <- function(x){ 
  x * 1000000/2.2914 
} 
 
k2o <- function(x){ 
  x * 1000000/1.2046 
} 
 
cao <- function(x){ 
  x * 1000000/1.3992 
} 
 
mno <- function(x){ 
  x * 1000000/1.2912 
} 
 
fe2o3 <- function(x){ 
  x * 1000000/1.4298 
} 

470 

 
ti <- function(x){ 
  x * 1000000/1.6681 
} 
 
bao <- function(x){ 
  x * 1000000/1.1165 
} 
 
# Apply these functions across the appropriate columns 
df_shell_corrected$SiO2 <- sio2(df_shell_corrected$SiO2) 
df_shell_corrected$Na2O <- nao2(df_shell_corrected$Na2O) 
df_shell_corrected$MgO <- mgo(df_shell_corrected$MgO) 
df_shell_corrected$Al2O3 <- al2o3(df_shell_corrected$Al2O3) 
df_shell_corrected$P2O3 <- p2o5(df_shell_corrected$P2O3) 
df_shell_corrected$K2O <- k2o(df_shell_corrected$K2O) 
df_shell_corrected$CaO <- cao(df_shell_corrected$CaO) 
df_shell_corrected$MnO <- mno(df_shell_corrected$MnO) 
df_shell_corrected$Fe2O3 <- fe2o3(df_shell_corrected$Fe2O3) 
df_shell_corrected$Ti <- ti(df_shell_corrected$Ti) 
df_shell_corrected$BaO <- bao(df_shell_corrected$BaO) 
 
# Since we've converted from %oxide, it's a good idea to change the element names 
# Some "O's" are left to differentiate the elements measured as both %oxide and not 
names(df_shell_corrected) <- c("Sample", "Date","Si","Na","Mg","Al","P","Cl","K","Ca", 
                               "SbO","Mn", "Fe","CuO","Sn","Ti","Pb","Ba","Bi","ZnO","Li", 
                               "Be", "B","P","Cl1","Sc","Ti1","V","Cr","Mn","Fe","Ni", 
                               "Co","Cu","Zn","As","Rb","Sr","Zr","Nb","Ag","In","Sn","Sb", 
                               "Cs","Ba","La","Ce","Pr","Ta","Au","Y","Pb","Bi1","U","W", 
                               "Mo","Nd","Sm","Eu","Gd","Tb","Dy","Ho","Er","Tm","Yb", 
                               "Lu","Hf","Th")   
 
# Write the full dataframe to a csv 
write_csv(df_shell_corrected,  
          "Upton_results_samples_and_OhioRed_shell_corrected_all_elements_August_21_2018.csv") 
 
# Drop the Ohio Red Samples 
dfsamps <- tolower(df_shell_corrected$Sample) 
orows <- str_detect(dfsamps, "red") 
df_samples <- df_shell_corrected[!orows, ] 
df_reds <- df_shell_corrected[orows, ] 
 
# Write csv with samples only, Ohio Red standards removed 
write_csv(df_samples, "Upton_results_samples_shell_corrected_August_21_2018.csv") 
 
# Write csv with Ohio Reds only 
write_csv(df_reds, "Upton_results_OhioRed_August_21_2018.csv") 

 
Ohio Red extraction and analysis 
New Ohio Red clay is the common standard used in the chemical analysis of clay and archaeological 
samples by LA-ICP-MS and INAA. Here, the standards run each day of LA-ICP-MS anlaysis are 

471 

extracted from the entire data set and analyzed in their own right to determine the accuracy of the 
different machines. Ultimately, it was decided to discard a number of sherds that were run on the old 
machine at the Field Museum’s Elemental Analysis Facility (circa 2015) and only retain ceramic samples 
run on the new machine. 

# Extract Ohio Reds and Calculate Relative Standard Deviation 
 
library(tidyverse) 
library(stringr) 
library(plotly) 
 
# Import data 
dfall <- read_csv("Upton_results_OhioRed_August_21_2018.csv") 
 
# Change Sample column to all lower case to ensure complete string detection 
dfall$Sample <- tolower(dfall$Sample) 
 
# Search the sample column for the word Ohio based on the abbreviation oh 
ohio <- str_detect(dfall$Sample, "oh") 
 
# Double check by searching same column for Red 
red <- str_detect(dfall$Sample, "red") 
 
# Check to see if the two detection methods are identical 
sum(ohio == red) == nrow(dfall) 
 
# Index to extract all Ohio Red Samples 
ohioreds <- dfall[red,] 
 
# Function to calculate RSD 
RSD <- function(x){ 
  meann <- mean(x) 
  relsd <- sd(x)/meann 
  relsd 
} 
 
# Calculate RSD across the rows 
redRSD <- sapply(ohioreds[, 3:ncol(ohioreds)], RSD) 
 
# Calculate average and standard deviation of values across each of the Ohio Reds 
redAVG <- ohioreds %>% 
              gather(element, sample, Si:Th) %>% 
              group_by(element) %>% 
              summarize(Avg = mean(sample), SD = sd(sample)) 
 
# Plot to check average values 
ohioreds %>% 
  gather(element, sample, Si:Th) %>% 
  group_by(element, Date) %>% 
  summarize(AVG = mean(sample)) %>% 
ggplot(aes(x = Date)) +  
  geom_line(aes(y = AVG, color = element, group = element)) + 
  theme_minimal() + 

472 

  theme(axis.text.x = element_text(angle = 90, hjust = 1)) 
 
# Filter the plot to look at HREE and LREE average values 
p <- ohioreds %>% 
      gather(element, sample, Si:Th) %>% 
      group_by(Date, element) %>% 
      summarize(AVG = mean(sample)) %>% 
      filter(AVG < 100) %>% 
      ggplot(aes(x = Date)) +  
      geom_line(aes(y = AVG, color = element, group = element)) + 
      theme_minimal() + 
      theme(axis.text.x = element_text(angle = 90, hjust = 1)) 
 
ggplotly(p) 
 
# Check very high RSD elements 
all_samples %>% 
  gather(element, sample, Si:Th) %>% 
  group_by(Date, element) %>% 
  summarize(AVG = mean(sample)) %>% 
  filter(element == "Bi") %>% 
  ggplot(aes(x = Date)) +  
  geom_line(aes(y = AVG, color = element, group = element)) + 
  theme_minimal() + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) 
 
 
# Bind Ohio Red averages to relative standard deviations 
redRSD <- data.frame(redRSD) 
redRSD <- rownames_to_column(redRSD, var = "element") 
OHred_avg_rsd <- left_join(redRSD, redAVG, by = "element") 
 
# Add RSD to the Ohio Red Samples 
red_with_RSD <- bind_rows(ohioreds, redRSD) 
 
write_csv(OHred_avg_rsd, "Ohio Red Averages and RSD_Aug-21-2018.csv") 
write_csv(red_with_RSD, "Ohio Reds with RSD_Aug-21-2018.csv") 
 
# Now check for any differences between samples run on different machines 
ohioreds$Date <- as.POSIXct(paste(ohioreds$Date), format = "%Y-%b-%d", tz = "UTC")  
redAVG_group <- ohioreds %>% 
                  mutate(Machine = ifelse(Date > as.POSIXct('2016-01-01', tz = "UTC"),  
                                          "New", "Old")) %>% 
                  gather(element, sample, SiO2:Th) %>% 
                  group_by(Machine, element) %>% 
                  summarize(Avg = mean(sample), SD = sd(sample)) 
 
# Count the number of Ohio Red samples run on each machine 
ohioreds %>% 
  mutate(Machine = ifelse(Date > as.POSIXct('2016-01-01', tz = "UTC"),  
                          "New", "Old")) %>% 
  select(Machine) %>% 
  group_by(Machine) %>% 

473 

  summarize(num = n()) 
 
write_csv(redAVG_group, "Ohio Reds across Machines_Aug_22_2018.csv") 

 

Analysis of CIRV clay sample 
 
# Clay analysis 
 
library(tidyverse) 
library(stringr) 
library(plotly) 
library(shiny) 
library(shinydashboard) 
library(ggsci) 
library(broom) 
library(knitr) 
library(ggfortify) 
library(stats) 
library(ICSNP) 
library(factoextra) 
library(dendextend) 
 
# Read in full dataset 
all_samples <- read_csv("Upton_results_samples_shell_corrected_August_21_2018.csv") 
 
# Read in clay context data  
clay_context <- read_csv("clay context data.csv") 
 
# Each clay sample is named "C##_1" 
# An expedient way of isolating the clay samples 
clay <- arrange(all_samples[str_detect(all_samples$Sample, "C[:digit:]"), ], Sample) 
 
# Clean up clay and clay context sample names 
clay_context$Sample <- str_replace(clay_context$Sample, pattern = "_1" %R% END, "") 
clay$Sample <- str_replace(clay$Sample, pattern = "_1" %R% END, "") 
 
# Join clay data to clay context 
clay <- left_join(clay_context, clay) 
 
# Take the log of the elemental composition data since they are on very different  
# scales 
claylog <- log10(clay[,8:ncol(clay)]) 
claylog <- bind_cols(clay[, 1:7], claylog) 
 
# Number of clay samples analyzed  
claylog %>% 
  summarise(num = n()) 
 
# Remove problem elements. Some elements are known to be unreliably measured using the ICP-MS 
# at the EAF. Following Golitko (2010), these include the following elements.  
problem_elements <- c("P", "Sr", "Ba", "Ca", "Hf", "As", "Cl") 

474 

 
# Other elements such as Ca and Sr are affected by shell tempering.  
# Want to drop those as well.  
 
# Overall these are the Elements retained - 44 in all. 
elems_retained <- c("Al","B", "Be", "Ce", "Co", "Cr", "Cs", "Dy", "Er", "Eu", "FeO", 
                    "Gd", "Ho", "In", "K", "La", "Li", "Lu", "Mg", "MnO", "Mo", "Na", "Nb",  
                    "Nd", "Ni", "Pb", "Pr", "Rb", "Sc", "Si", "Sm", "Sn", "Ta", "Tb", "Th", 
                    "Ti", "Tm", "U", "V", "W", "Y", "Yb", "Zn", "Zr") 
 
names.use <- names(claylog)[(names(claylog) %in% elems_retained)] 
# length(names.use) == length(elems_retained) # check that all elements are retained  
claylog_good <- claylog[, names.use] 
 
# Check to ensure the elements were removed are supposed to be removed 
anti_join(data.frame(names(clay)),  
          data.frame(names(claylog_good)), by = c("names.clay." = "names.claylog_good.")) 
 
# Need to drop the "O" for oxide after elements measured as %oxide composition since they   
# have already been converted to ppm 
names(claylog_good) <- c("Si","Na","Mg","Al","K","Mn","Fe","Ti","Li","Be","B","Sc","V", 
                         "Cr","Ni","Co","Zn","Rb","Zr","Nb","In","Sn","Cs","La","Ce","Pr", 
                         "Ta","Y","Pb","U", "W","Mo","Nd","Sm","Eu","Gd","Tb","Dy","Ho", 
                         "Er","Tm","Yb","Lu","Th")  
 
# Bind sample id and other data to the logged chemical concentrations  
clay_pcaready <- bind_cols(claylog[,c(1:7)], claylog_good) 
 
# Remove two non-clay sample 
clay_pcaready <- filter(clay_pcaready, Sample != "C26") %>% filter(Sample != "C31") 
 
#write_csv(clay_pcaready, "Clay PCA Ready.csv") 
 
# Exploring PCA 
clay_pca <- clay_pcaready %>%  
  nest() %>%  
  mutate(pca = map(data, ~ prcomp(.x %>% select(Si:Th))), 
         pca_aug = map2(pca, data, ~augment(.x, data = .y))) 
 
# Check variance explained by each model 
var_exp <- clay_pca %>%  
  unnest(pca_aug) %>%  
  summarize_at(.vars = vars(contains("PC")), .funs = funs(var)) %>%  
  gather(key = pc, value = variance) %>%  
  mutate(var_exp = variance/sum(variance), 
         cum_var_exp = cumsum(var_exp), 
         pc = str_replace(pc, ".fitted", "")) 
 
# Looks like we need to retain the first 7 PC's to hit 90% of the data's variability 
# Graphing this out might help 
var_exp %>%  
  rename(`Variance Explained` = var_exp, 
    `Cumulative Variance Explained` = cum_var_exp) %>%  

475 

  gather(key = key, value = value,  
         `Variance Explained`:`Cumulative Variance Explained`) %>%  
  mutate(pc = str_replace(pc, "PC", "")) %>% 
  mutate(pc = as.numeric(pc)) %>% 
  ggplot(aes(reorder(pc, sort(as.numeric(as.character(pc)))), value, group = key)) +  
  geom_point() +  
  geom_line() +  
  facet_wrap(~key, scales = "free_y") + 
  theme_bw() + 
  lims(y = c(0, 1)) + 
  labs(y = "Variance", x = "", 
       title = "Variance explained by each principal component") 
 
 
# Plot PCs 1 & 2 against each other 
cp1p2_plot <- clay_pca %>% 
        mutate( 
          pca_graph = map2( 
            .x = pca, 
            .y = data, 
            ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                       scale = FALSE, 
                       #loadings.label.repel = TRUE, 
                       loadings.label.colour = "black", 
                       loadings.colour = "gray85", 
                       loadings.label.alpha = 0.5, 
                       loadings.label.size = 3, 
                       loadings.label.hjust = 1.1, 
                       frame = TRUE, 
                       frame.type = "norm", 
                       data = .y,  
                       colour = "Geography_2",  
                       shape = "Geography_2", 
                       frame.level = .9,  
                       frame.alpha = 0.001,  
                       size = 2) + 
              theme_bw() +  
              #geom_text(label = .y$Sample) + 
              labs(x = "Principal Component 1", 
                   y = "Principal Component 2", 
                   title = "First two principal components of PCA on CIRV Clay dataset") 
          ) 
        ) %>% 
      pull(pca_graph) 
 
# autoplot is lazy with color. In order to make this publication friendly, have to  
# manually edit the color scales 
cp1p2_plot[[1]] + scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black"))  
 
# Plot PCs 1 & 3 against each other 
cp1p3_plot <- clay_pca %>% 
  mutate( 

476 

    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, x = 1, y = 3, loadings = TRUE, loadings.label = TRUE, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Geography_2",  
                 shape = "Geography_2", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 3", 
             title = "First two principal components of PCA on CIRV Clay dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
# autoplot is lazy with color. In order to make this publication friendly, have to  
# manually edit the color scales 
cp1p3_plot[[1]] + scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black"))  
 
# Shiny app to biplot the various elements against one another 
# With 44 elements, there are p(p-1)/2 or 946 biplots to investigate! 
# Therefore, it's a lot easier to make an app to easily and quickly run through the options 
 
############ 
##   UI   ## 
############ 
ui <- fluidPage( 
pageWithSidebar ( 
  headerPanel('Bivariate Plotting'), 
  sidebarPanel( 
    selectInput('x', 'X Variable', names(clay_pcaready),  
                selected = names(clay_pcaready)[[8]]), 
    selectInput('y', 'Y Variable', names(claylog_good), 
                selected = names(clay_pcaready)[[9]]), 
    selectInput('color', 'Color', names(clay_pcaready)), 
    #Slider for plot height 
    sliderInput('plotHeight', 'Height of plot (in pixels)',  
                min = 100, max = 2000, value = 550) 
  ), 
  mainPanel( 
    plotlyOutput('plot1') 
  ) 

477 

) 
) 
 
############ 
## Server ## 
############ 
 
 
server <- function(input, output, session) { 
   
  # Combine the selected variables into a new data frame 
  selectedData <- reactive({ 
    claylog_good[, c(input$x, input$y, input$color)] 
  }) 
 
   
  output$plot1 <- renderPlotly({ 
     
    #Build plot with ggplot syntax  
    p <- ggplot(data = clay_pcaready, aes_string(x = input$x,  
                                          y = input$y,  
                                          color = input$color,  
                                          shape = input$color)) +  
      geom_point() +  
      theme(legend.title = element_blank()) +  
      stat_ellipse(level = 0.9) + 
      scale_color_igv() +  
      theme_bw() + 
      xlab(paste0(input$x, " (log base 10 ppm)")) + 
      ylab(paste0(input$y, " (log base 10 ppm)")) 
     
    ggplotly(p) %>% 
      layout(height = input$plotHeight, autosize = TRUE,  
             legend = list(font = list(size = 12)))  
  }) 
   
} 
 
shinyApp(ui, server) 
 
# Based on the biplots, it looks like there is good separation for the most part  
# in the north and south portions of the valley when comparing Lithium to  
# Vanadium or Beryllium 
 
# Biplot of Li and V 
ggplot(data = clay_pcaready, aes(x = Li, y = V,  
                                 color = Geography_2, shape = Geography_2)) +  
  geom_point() +  
  theme(legend.title = element_blank()) +  
  stat_ellipse(level = 0.9) + 
  scale_color_igv() +  
  theme_bw() + 
  xlab("Lithium (log base 10 ppm)") + 

478 

  ylab("Vanadium (log base 10 ppm)") + 
  scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black"))  
 
# Biplot of Li and Be 
ggplot(data = clay_pcaready, aes(x = Li, y = Be,  
                                 color = Geography_2, shape = Geography_2)) +  
  geom_point() +  
  theme(legend.title = element_blank()) +  
  stat_ellipse(level = 0.9) + 
  scale_color_igv() +  
  theme_bw() + 
  xlab("Lithium (log base 10 ppm)") + 
  ylab("Beryllium (log base 10 ppm)") + 
  scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black"))  
 
# Biplot of Li and Be 
ggplot(data = clay_pcaready, aes(x = Li, y = Be,  
                                 color = Geography_2, shape = Geography_2)) +  
  geom_point() +  
  theme(legend.title = element_blank()) +  
  stat_ellipse(level = 0.9) + 
  scale_color_igv() +  
  theme_bw() + 
  xlab("Lithium (log base 10 ppm)") + 
  ylab("Beryllium (log base 10 ppm)") + 
  scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black"))  
 
# Biplot of Ni and Cs 
ggplot(data = clay_pcaready, aes(x = Ni, y = Cs,  
                                 color = Geography_2, shape = Geography_2)) +  
  geom_point() +  
  theme(legend.title = element_blank()) +  
  stat_ellipse(level = 0.9) + 
  scale_color_igv() +  
  theme_bw() + 
  xlab("Nickel (log base 10 ppm)") + 
  ylab("Cesium (log base 10 ppm)") + 
  scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black"))  
 
# A table of average element concentrations and standard deviations between the two  
# groups may be instructive of their differences numerically as opposed to visually 
clay_group_ave_std <- clay_pcaready %>% 
                        select(Geography_2, Si:Th) %>% 
                        gather(Element, Si:Th, -Geography_2) %>% 
                        mutate(`Si:Th` = 10^`Si:Th`) %>% # convert from log 10 
                        group_by(Geography_2, Element) %>% 
                        summarize(mean = mean(`Si:Th`, na.rm = TRUE),  
                                  std = sd(`Si:Th`, na.rm = TRUE)) 
 

479 

# Count number of clay in the different groups 
clay_pcaready %>% 
  group_by(Geography_2) %>% 
  summarize(count = n()) 
 
write_csv(clay_group_ave_std, "Clay group averages and stds.csv") 
 
# Almost every element is enriched in northerly clays and as a result depleted in the  
# southerly clays, taking a look at that via a histogram is instructive 
clay_pcaready %>% 
  select(Geography_2, Si:Th) %>% 
  gather(Element, Si:Th, -Geography_2) %>% 
  mutate(`Si:Th` = 10^`Si:Th`) %>%  
  filter(Element == "Sn") %>% 
  ggplot(aes(x = Element, group = Geography_2, y = `Si:Th`)) + geom_boxplot() 
   
# It looks like there is a good deal of separation in the geochemistry of clays between the  
# Northern portion of the central Illinois River Valley (including the Spoon/Illinois 
# confluence) and the Southern portion of the CIRV, south of the Spoon River 
# But let's check to see if statistical techniques come to a similar conclusion 
 
###__________________________________HCA______________________________________________### 
# First, we create a data frame for distance calculations including the elemental data only 
clay_for_dist <- claylog_good 
rownames(clay_for_dist) <- claylog$Sample 
 
# Now let's perform some hierarchical clustering using Euclidean distance 
clay_hca <- hclust(dist(clay_for_dist)) 
 
# Create dendrogram object 
dend_clay <- as.dendrogram(clay_hca) 
 
# Plot dendogram object to look for good cut-off heights - 2.5 seems to be a good height 
plot(dend_clay, nodePar = list(lab.cex = .75, pch = NA)) 
 
# Looks like the hierarchical clustering doesn't group precisely as the geographic/geologic 
# prior knowledge would suggest. This is an indication of the hetergeneous nature of clay as  
# well as the complex geological processes that have resulted in clay availability in the  
# CIRV. 
 
 
###___________________________Mahalanobis Distance______________________________________### 
# Since HCA wasn't overly insightful, we can at least check membership probabilities between 
# the north and south groups statistically. The standard method of doing this in  
# archaeology is via Mahalanobis distance, which is commonly used for outlier detection.  
 
 
# Extract the first 7 PC's (accounting for 90% of variability) and bind to  
# sample/geography data 
clay_pc1to7 <- clay_pca %>%  
                  unnest(pca_aug) %>%  
                  select(starts_with(".fitted")) %>% 
                  bind_cols(clay_pcaready[, c(1,3)], .) %>% 

480 

                  select(c(1:9)) 
 
clay1to7_north <- clay_pc1to7 %>% filter(Geography_2 == "North") 
 
clay1to7_south <- clay_pc1to7 %>% filter(Geography_2 == "South") 
       
# Edit colnames 
colnames(clay_pc1to7) <- str_remove(colnames(clay_pc1to7), ".fitted") 
 
# Mahalanobis distance of North to North 
mahalanobis(clay1to7_north[,3:9], colMeans(clay1to7_north[,3:9]), cov(clay1to7_north[,3:9])) 
 
# With 7 predictor variables (PCs 1-7), the critical chi-square value is 24.32 
# Given that the highest MD value among the northerly clays is 20.92, it doesn't 
# look like there are any outliers 
 
# Have to pair down the number of predictors to 5 for the South, since there are only 7  
# samples. The critical chi-square value is 20.52 for that many, looking good for the south. 
mahalanobis(clay1to7_south[,3:7], colMeans(clay1to7_south[,3:7]), cov(clay1to7_south[,3:7])) 
 
# Let's now look at group membership probabilities. This function written by Matt Peeples 
# allows for for calculating group membership probabilities by chemical compositional  
# distance using Mahalanobis distances and Hotellings T^2 statistic 
group.mem.probs <- function(x2.l,attr1.grp,grps) { 
   
  # x2.l = transformed element data 
  # attr1 = group designation by sample 
  # grps <- vector of groups to evaluate 
   
  probs <- list() 
  for (m in 1:length(grps)) { 
    x <- x2.l[which(attr1.grp==grps[m]),] 
    probs[[m]] <- matrix(0,nrow(x),length(grps)) 
    colnames(probs[[m]]) <- grps 
    rownames(probs[[m]]) <- rownames(x) 
     
    grps2 <- grps[-m] 
     
    p.val <- NULL 
    for (i in 1:nrow(x)) {p.val[i] <- HotellingsT2(x[i,],x[-i,])$p.value} 
    probs[[m]][,m] <- round(p.val,5)*100 
     
    for (j in 1:length(grps2)) { 
      p.val2 <- NULL 
      for (i in 1:nrow(x)) {p.val2[i] <- HotellingsT2(x[i,],x2.l[which(attr1.grp==grps2[j]),])
$p.value} 
      probs[[m]][,which(grps==grps2[j])] <- round(p.val2,5)*100}} 
  return(probs) 
} 
 
# But how do the samples compare to each other on the first 5 PCs  
# (85% ov observed variability)? 
group.mem.probs(clay_pc1to7[3:5], clay_pc1to7$Geography_2, unique(clay_pc1to7$Geography_2))  

481 

 
# How about using some elements that show good separation between the groups? 
group.mem.probs(clay_pcaready[, c("Ni", "Cs")], clay_pc1to7$Geography_2, 
                unique(clay_pc1to7$Geography_2))  
 
# In both cases, there is a marked lack of clear group separation in statistical space for  
# samples in both groups. That is, there are samples defined as North that have a higher  
# probability of grouping with the Southerly sherds and vice versa.  
# To a certain degree, this is expected - this is an experimental analysis looking within a  
# single river valley, and indeed there is not statistically significant separation between  
# the groups as a result.  
# Nevertheless, it is instructive that chemical differences do appear as one moves from the  
# northeast to the southwest in the CIRV, conforming to geologic patterns of exposing parent  
# material of older ages. As a result, an argument can be made that pottery would likely  
# follow this patterning based on raw material availability.  
 
## Exploratory cluster analysis 
 
# Optimal number of clusters based on the elbow method using the total within sum of squares 
fviz_nbclust(clay_pc1to7[3:9], kmeans, method = "wss") 
 
clay_dist <- hclust(dist(clay_pc1to7[3:9])) 
 
View(clay_pc1to7) 
 
# Create dendrogram object 
clay_dend_df_com <- as.dendrogram(clay_dist) 
 
# Plot dendogram object to look for good cut-off heights - 2.5 seems to be a good height 
plot(clay_dend_df_com, nodePar = list(lab.cex = 0.15, pch = NA)) 
 
dend_2.5 <- color_branches(clay_dend_df_com, h = 1.950) 
plot(dend_2.5, cex.axis = 0.75, cex.lab = 0.75, nodePar = list(lab.cex = .85, pch = NA)) 

 

Assignation of ceramic samples into geochemical compositional groups 
The lengthy code chunk below is a linear sequence of unsupervised learning based statistical analysis of 
CIRV ceramic samples. The sequence below was cross referenced against MURRAP GAUSS routines, a 
standard statistical suite in the analysis of geochemical data in archaeology. 

##' Analysis of ceramic LA-ICP-MS data 
 
library(tidyverse) 
library(infer) 
library(broom) 
library(stringr) 
library(plotly) 
library(rebus) 
library(xlsx) 
library(readxl) 
library(plotly) 

482 

library(ggpubr) 
library(cluster) 
library(dendextend) 
library(factoextra) 
library(stats) 
library(ICSNP) 
library(shiny) 
library(shinydashboard) 
library(ggsci) 
 
 
##### Data Import and Cleaning ##### 
samps <- read_csv("Upton_results_samples_shell_corrected_August_21_2018.csv") 
 
# Remove samples that hit shell to the point of being unusable or four samples 
# that were victim to a chamber leakage issue on 2017-Oct-06 
removes <- str_detect(tolower(samps$Sample), "remove") 
samples <- samps[!removes,] 
rm_samps <- samps[removes,] 
 
# Validate removed samples 
rm_samps[,c(1:2)] 
 
# Pull out clay samples (we'll add them back in later on) 
clay_rows <- str_detect(tolower(samples$Sample), "c[:digit:][:digit:]") 
clay_samps <- samples[clay_rows,] 
samples <- samples[!clay_rows,] 
 
# Clean up clay sample names 
clay_samps$Sample <- str_replace(clay_samps$Sample, pattern = "_1" %R% END, "") 
 
# Add clay i.d.'s to a separate column 
clay_samps <- clay_samps %>% 
                mutate(id = parse_number(clay$Sample)) %>% 
                arrange(Sample) 
 
##### Add features to ceramic samples ##### 
# Extract sample unique sherd i.d. number  
# First remove the run information from sample names 
samples$Sample <- str_replace(samples$Sample, pattern = "_1" %R% END, "") 
samples$Sample <- str_replace_all(samples$Sample, c("_run[:digit:][:digit:]" = "",  
                                                    "_run[:digit:]" = "",  
                                                    "__" = "",  
                                                    "_run [:digit:]" = "",  
                                                    "run1" = "", 
                                                    "_r" = "",  
                                                    " run 1" = "",  
                                                    "_" = " ")) 
 
# Now extract the sample i.d.'s to a separate column 
samples <- samples %>% 
            mutate(id = parse_number(samples$Sample))  
 

483 

# Read in contextual data for the ceramic samples 
ceramic_features_by_id <- read_xlsx(path = "ceramic features.xlsx", sheet = 1) 
ceramic_features_by_site <- read_xlsx(path = "ceramic features.xlsx", sheet = 2) 
 
# Join ceramic features to sample data 
samples <- left_join(samples, ceramic_features_by_id) 
samples <- left_join(samples, ceramic_features_by_site) 
 
# Number of sherds by site and by vessel type 
samples %>% 
  group_by(Site, Vessel_Class) %>% 
  summarise(num = n())  # %>% 
  # write_csv("Number of sherds by site and by vessel type.csv") 
 
# Number of sherds by site and by cultural group 
samples %>% 
  group_by(Site, Cultural_Group) %>% 
  summarize(num = n()) 
 
# Check for any linear relationships between Calcium and the other elements 
# Looks like there are some significant at a 0.05 alpha, but there is a significant 
# amount of heteroscedasticity and residual variation in all but Sr, which 
# expectedly does highly correlate with Ca 
summary(lm(Ca ~ ., data = samples[,3:length(samples)])) 
 
# Plotting to show how strong the linear relationships are for some elements 
p <- ggplot(samples, aes(x = Sr, y = Ca)) + geom_smooth() + geom_point() 
#ggplotly(p) 
 
# Remove problem elements. Some elements are known to be unreliably measured using the  
# ICP-MS at the EAF. Following Golitko (2010), these include the following elements.  
problem_elements <- c("P", "Sr", "Ba", "Ca", "Hf", "As", "Cl") 
 
# Other elements such as Ca and Sr are affected by shell tempering. Want to drop those  
# as well.  
 
# Overall these are the Elements retained - 44 in all. 
elems_retained <- c("Al","B", "Be", "Ce", "Co", "Cr", "Cs", "Dy", "Er", "Eu", "FeO", 
                    "Gd", "Ho", "In", "K", "La", "Li", "Lu", "Mg", "MnO", "Mo", "Na", "Nb",  
                    "Nd", "Ni", "Pb", "Pr", "Rb", "Sc", "Si", "Sm", "Sn", "Ta", "Tb", "Th", "T
i", 
                    "Tm", "U", "V", "W", "Y", "Yb", "Zn", "Zr") 
 
ceramic.names.use <- names(samples)[(names(samples) %in% elems_retained)] 
#length(ceramic.names.use) == length(elems_retained) # check that all elements are retained  
samples_good <- samples %>% select(ceramic.names.use) 
 
# Check to ensure the elements were removed are supposed to be removed 
anti_join(data.frame(names(samples)),  
          data.frame(names(samples_good)), by = c("names.samples." = "names.samples_good.")) 
 
# Need to drop the "O" for oxide after elements measured as %oxide composition since they   
# have already been converted to ppm 

484 

names(samples_good) <- str_remove(names(samples_good), "O") 
 
# Bind sample id and other data to the logged chemical concentrations  
sample_pcaready <- bind_cols(samples[,c(1:2, 71:80)], samples_good) 
 
# Some ceramic samples were run on an older ICP-MS machine during an initial pilot study.  
# I need to tease these out pending quality control from Laure Dussubieux, a chemist at the  
# Field Museum.  
sample_old_machine <- sample_pcaready %>% filter(Date < 2016) 
sample_new_pcaready <- sample_pcaready %>% filter(Date > 2016) 
 
######## End of data cleaning, beginnging of statistical analysis ######## 
 
# First step is to take the log base 10 of all samples to account for scalar differences 
# in the magnitude of chemical compositions across the elements, from major to minor to trace 
sample_new_pcaready[,13:56] <- log10(sample_new_pcaready[,13:56]) 
 
##### PCA ##### 
 
# Exploring PCA 
sample_pca <- sample_new_pcaready %>%  
                nest() %>%  
                mutate(pca = map(data, ~ prcomp(.x %>% select(Si:Th))), 
                       pca_aug = map2(pca, data, ~augment(.x, data = .y))) 
 
# Check variance explained by each model 
var_exp_sample <- sample_pca %>%  
  unnest(pca_aug) %>%  
  summarize_at(.vars = vars(contains("PC")), .funs = funs(var)) %>%  
  gather(key = pc, value = variance) %>%  
  mutate(var_exp = variance/sum(variance), 
         cum_var_exp = cumsum(var_exp), 
         pc = str_replace(pc, ".fitted", "")) 
 
# Check eigen values 
get_eigenvalue(prcomp(sample_new_pcaready %>% select(Si:Th))) 
 
# Looks like we need to retain the first 12 PC's to hit 90% of the data's variability 
# Graphing this out might help 
var_exp_sample %>%  
  rename(`Variance Explained` = var_exp, 
         `Cumulative Variance Explained` = cum_var_exp) %>%  
  gather(key = key, value = value,  
         `Variance Explained`:`Cumulative Variance Explained`) %>%  
  mutate(pc = str_replace(pc, "PC", "")) %>% 
  mutate(pc = as.numeric(pc)) %>% 
  ggplot(aes(reorder(pc, sort(as.numeric(as.character(pc)))), value, group = key)) +  
  geom_point() +  
  geom_line() +  
  facet_wrap(~key, scales = "free_y") + 
  theme_bw() + 
  lims(y = c(0, 1)) + 
  labs(y = "Variance", x = "", 

485 

       title = "Variance explained by each principal component") 
 
# Check number of PCs to retain to reach 90% of the variability in the original dataset 
var_exp_sample %>% filter(cum_var_exp < 0.909) # Need to retain the first 12 PCs.  
                                               # 12 PCs is much less than 44 elements 
 
# Plot the first two PCs with Geography_2 as group separation 
geo2_pc1pc2 <-sample_pca %>% 
      mutate( 
        pca_graph = map2( 
          .x = pca, 
          .y = data, 
          ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                     loadings.label.repel = TRUE, 
                     loadings.label.colour = "black", 
                     loadings.colour = "gray45", 
                     loadings.label.alpha = 0.5, 
                     loadings.label.size = 3, 
                     #loadings.label.hjust = 1.1, 
                     frame = TRUE, 
                     frame.type = "norm", 
                     data = .y,  
                     colour = "Geography_2",  
                     shape = "Geography_2", 
                     frame.level = .9,  
                     frame.alpha = 0.001,  
                     size = 2) + 
            theme_bw() +  
            #geom_text(label = .y$Sample) + 
            labs(x = "Principal Component 1", 
                 y = "Principal Component 2", 
                 title = "First two principal components of PCA on CIRV Ceramic dataset") 
        ) 
      ) %>% 
      pull(pca_graph) 
 
geo2_pc1pc2[[1]] + scale_fill_manual(values = c("black","black")) +  
  scale_color_manual(values = c("black","black","black")) + 
  scale_shape_manual(values=c(18, 2))  
 
# This shows significant overlap but a general trend that follows the clay:  
# in general there is less elemental enrichment in clay resources in the  
# southern portion of the CIRV compared to the northern part with the  
# north-south line of demarcation being the Spoon-Illinois River confluence 
# (clay along the Spoon is included in the north) 
 
# Check the first two PCs with Sites as group separation 
site_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 

486 

                 #loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Site",  
                 shape = "Geography_2", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
# Interact with the chart above 
ggplotly(site_pc1pc2[[1]]) # plotly drops the stat_ellipse frames for some reason 
# This is a challenge to interpret, but it doesn't seem as though there is meaningful 
# patterning when considering the different sites on PC1-PC2 aside from some outliers in 
# Walsh/Crable.  
 
# Check the first two PCs with Vessel Class as group separation 
vessel_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 #loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Vessel_Class",  
                 shape = "Vessel_Class", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 

487 

             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
ggplotly(vessel_pc1pc2[[1]]) 
# The vessel graph is interesting. At first glance, it doesn't seem as though there is much  
# in the way of separation by vessel class, but there appears to be some nuances to that   
# upon futher consideration. There are some plates that are low on both PC1 and PC2 axes  
# as well as jars that are significantly more enriched on PC1 
 
# How about separation by time? 
time_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 #loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Time",  
                 shape = "Time", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
ggplotly(time_pc1pc2[[1]]) 
# Again, this appears similar to the prior PC biplot separated by vessel class - there is 
# no general trend of group separation but some interesting insights when considering  
# outliers.  
 
# Perhaps Oneota presence may be more revealing 
oneota_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 

488 

      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 #loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Oneota_Present",  
                 shape = "Oneota_Present", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
ggplotly(oneota_pc1pc2[[1]]) 
# I certainly can't see any meaningful trends here. This suggests that Oneota and  
# Mississippian otters are almost undoubtedly using similar (or the same) clay.  
# However, more work is needed to confirm this hypothesis.  
 
# Does temper percent matter? 
tempperc_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 #loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Temper_Perc",  
                 shape = "Geography_2", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 

489 

             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
ggplotly(tempperc_pc1pc2[[1]]) 
# Can't really discern anything here 
 
# Does temper size matter? 
tempsize_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 #loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Temper_Size",  
                 shape = "Geography_2", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
ggplotly(tempsize_pc1pc2[[1]]) 
# Interestingly, it appears that the smallest temper size only appears in  
# the northern part of the valley.  
# That might suggest that there is either a preference for smaller temper grains there  
# or it is a response to the clay available in the north.  
 
# Finally, let's check Cultural Group 
culture_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 #loadings.label.repel = TRUE, 

490 

                 loadings.label.colour = "black", 
                 loadings.colour = "gray85", 
                 loadings.label.alpha = 0.5, 
                 loadings.label.size = 3, 
                 loadings.label.hjust = 1.1, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Cultural_Group",  
                 shape = "Cultural_Group", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2) + 
        theme_bw() +  
        #geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2", 
             title = "First two principal components of PCA on CIRV Ceramic dataset") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
ggplotly(culture_pc1pc2[[1]]) 
# Very little to no discernible patterning here. This again indicates that both cultural 
# groups are likely to be using the same clays.  
 
# Based on the initial inspection of PCs 1 and 2, it looks like three elements in particular  
# are driving some of the group separation (subtle as it is): Mo, Mn, and Si 
# Let's plot those three elements in a 3D scatter plot 
Mo_Mn_Si <- plot_ly(sample_new_pcaready, x = ~Mo, y = ~Mn, z = ~Si, color = ~Geography_2) 
 
# Explore Samples by date 
ggplotly(ggplot(sample_new_pcaready, aes(x = Mo, y = Mg, color = Date)) +  
  stat_ellipse(aes(color = Geography_2)) + geom_text(aes(label = Date), size = 2)) 
 
# All in all, only a general trend of the north-south distinction holds when considering  
# prior information on PC1-PC2 biplots. That distinction is marked by significant overlap.  
# We'll consider that when running group membership probabilities. But first, it's  
# necessary to explore how a variety of statistical methods will group the data. We'll  
# append that group information to our PC list such that we can consider both prior  
# information and statistical infomation in groups before moving on to group refinement.  
 
 
########################## Cluster Analysis ######################## 
 
##### Hierarchical Cluster Analysis ##### 
 
# Now that I have a sense of the structure of the ceramic data set based on PCA, the next  
# step in compositional analysis is to see how the groups defined from prior  
# information compare to groups constructed using statistical clustering methods such  
# as HCA, kmeans, and kmedoids 
 
# Let's start with some tree-based methods (aka Hierarchical cluster analysis or HCA) 

491 

# We'll use agglomerative methods here (bottom up) as opposed to divisive methods (top down) 
 
# Prep the dataset 
# Set rownames to aid in interpretations of dendrograms and other plots 
rownames(sample_new_pcaready) <- sample_new_pcaready$Sample 
 
# Drop the prior known information features 
sample_new_distready <- sample_new_pcaready %>% select(c(-1:-12)) 
 
# First make a dissimilarity matrix based on Euclidean distance 
euc_dist_ceramics <- dist(sample_new_distready, method = "euclidean") 
 
# We can check agglomerative coefficients with agnes to see which method(s) might 
# work best with the ceramic compositional dataset 
clustmethods <- c( "average", "single", "complete", "ward") 
names(clustmethods) <- c( "average", "single", "complete", "ward") 
 
# function to compute agglomerative coefficient 
ac <- function(x) { 
  agnes(euc_dist_ceramics, method = x)$ac 
} 
 
map_dbl(clustmethods, ac) 
 
# Looks like complete and Ward linkage methods will work best. We'll run those 
 
# Hierarchical clustering using Ward's Linkage 
wardhc1 <- hclust(euc_dist_ceramics, method = "ward.D") 
wardhc1_dend <- as.dendrogram(wardhc1) # create dendrogram object 
 
# Plot Ward dendrogram 
plot(wardhc1_dend, nodePar = list(lab.cex = 0.15, pch = NA)) 
# Looks like there are three well defined clusters at a height of 20.  
# We can color the dendrogram at that height 
wardhc1_dend_20 <- color_branches(wardhc1_dend, h = 20) 
plot(wardhc1_dend_20, cex.axis = 0.75, cex.lab = 0.75,  
     nodePar = list(lab.cex = 0.15, pch = NA)) 
 
# This looks like a good hypothetical groupings to add to our original dataset 
# We'll add all statistical clusters to a dataset sample_new_stat_clusters 
ward_dist_groups <- cutree(wardhc1_dend_20, h = 20) 
table(ward_dist_groups) # How many samples are in each cluster>? 
 
sample_new_stat_clusters <- sample_new_pcaready %>% 
                              select(Sample) %>% 
                              mutate(Ward_HCA_Cluster = ward_dist_groups) 
 
# Visualize the clusters from HCA using Ward's linkage 
fviz_cluster(list(data = sample_new_distready, cluster = ward_dist_groups)) 
 
# Complete linkage also has a high agglomerative coefficient, let's model it 
completehc1 <- hclust(euc_dist_ceramics, method = "complete") 
completehc1_dend <- as.dendrogram(completehc1) 

492 

 
# Plot Complete linkage dendrogram cut at 2.4, which results in 6 clusters (3 main and 3 minor
) 
completehc1_dend_2.4 <- color_branches(completehc1_dend, h = 2.4) 
plot(completehc1_dend_2.4, cex.axis = 0.75, cex.lab = 0.75,  
     nodePar = list(lab.cex = 0.15, pch = NA)) 
complete_dist_groups <- cutree(completehc1_dend, h = 2.4) 
table(complete_dist_groups) 
sample_new_stat_clusters <- sample_new_stat_clusters %>% 
                              mutate(Complete_HCA_Cluster = complete_dist_groups) 
 
# Visualize the clusters from HCA using Complete linkage 
fviz_cluster(list(data = sample_new_distready, cluster = complete_dist_groups)) 
 
# Let's compare the Ward's and Complete Linkage dendrograms with a tanglegram  
# (this is very resource intensive, so I'm commenting it out) 
# tanglegram(wardhc1_dend, completehc1_dend) 
 
# Now let's see how these HCA groups correspond to other clustering methods  
 
##### K-means Cluster Analysis ##### 
# First, it's a good idea to use a few methods to assess the number of clusters to model 
# Elbow Method 
fviz_nbclust(sample_new_distready, kmeans, method = "wss") # 3-8 optimal clusters;  
                                                           # 3-4 looks good 
# Silhouette Method 
fviz_nbclust(sample_new_distready, kmeans, method = "silhouette") # 3 optimal clusters 
# Gap Stat 
#fviz_nbclust(sample_new_distready, kmeans, method = "gap_stat") # 1 optimal cluster 
 
# Based on the optimal cluster methods, it looks like we should run kmeans twice, once with  
# 3 clusters and once with 4 clusters 
 
# 3 Cluster K-means 
k3 <- kmeans(sample_new_distready,  
             centers = 3, # number of clusters 
             nstart = 50, # number of random initial configurations  
                          # out of which the best one is chosen 
             iter.max = 500) # number of allowable iterations allowed  
 
# Visualize 3 cluster kmeans  
fviz_cluster(k3, data = sample_new_distready) 
 
# Assign to clustering assignments data frame 
sample_new_stat_clusters <- sample_new_stat_clusters %>% 
                              mutate(Kmeans_3 = k3$cluster) 
 
# 4 Cluster K-means 
k4 <- kmeans(sample_new_distready, centers = 4, nstart = 50, iter.max = 500) 
 
# Visualize 4 cluster kmeans 
fviz_cluster(k4, data = sample_new_distready) 
 

493 

# Assign to clustering assignments data frame 
sample_new_stat_clusters <- sample_new_stat_clusters %>% 
                              mutate(Kmeans_4 = k4$cluster) 
 
##### K-medoids Cluster Analysis ##### 
 
# For k-medoids, we'll be using the pam function from the cluster package. pam stands for  
# "partitioning around medoids" 
 
# As with k-means, it's a good idea to use a few methods to assess the number of clusters  
 #to model 
# Elbow Method 
fviz_nbclust(sample_new_distready, pam, method = "wss") # 5 looks optimal here 
# Silhouette Method 
fviz_nbclust(sample_new_distready, pam, method = "silhouette") # 2 optimal clusters 
# Gap Stat 
#fviz_nbclust(sample_new_distready, pam, method = "gap_stat") # 1 optimal cluster 
 
# We'll run two clusters - one with 2 and one with 5 
# 2 cluster K-medoids 
pam2 <- pam(sample_new_distready, 2) 
 
# Plot 2 cluster k-medoids 
fviz_cluster(pam2, data = sample_new_distready) 
 
# 5 cluster K-medoids 
pam5 <- pam(sample_new_distready, 5) 
 
# Plot 5 cluster k-medoids 
fviz_cluster(pam5, data = sample_new_distready) 
 
# Assign k-medoids results to clustering assignments data frame 
sample_new_stat_clusters <- sample_new_stat_clusters %>% 
                              mutate(Kmediods_2 = pam2$clustering,  
                                     Kmediods_5 = pam5$clustering) 
 
# One last exploratory metric would be to take the most often occuring group assignment  
# number, the mode 
# Little function to calculate the mode 
Mode <- function(x) { 
  ux <- unique(x) 
  ux[which.max(tabulate(match(x, ux)))] 
} 
 
# Apply this row-wise to the data 
mode_assignment <- apply(sample_new_stat_clusters, 1, Mode) 
 
 
####_______________Begin Mahalanobis distance and membership assignments______________### 
 
# First, create a data frame of the first 12 PC's, which account for 90% of the variability   
# in the elemental data set. This will allow group membership probability assessments with a 
# group as small as 14 (or perhaps 13) 

494 

pc1to12 <- sample_pca[['pca_aug']][[1]] %>%  
  select(.fittedPC1, .fittedPC2, .fittedPC3, .fittedPC4, .fittedPC5, .fittedPC6, .fittedPC7,  
         .fittedPC8, .fittedPC9, .fittedPC10, .fittedPC11, .fittedPC12) 
 
# This function written by Matt Peeples allows for for calculating group membership 
# probabilities by chemical compositional distance using Mahalanobis distances and  
# Hotellings T^2 statistic 
# This is identical to the procedure used in MURRAP GAUSS routines for the same purpose  
# and has been cross referenced against that routine to ensure accuracy for data  
# presented in this analysis 
group.mem.probs <- function(x2.l,attr1.grp,grps) { 
   
  # x2.l = transformed element data 
  # attr1 = group designation by sample 
  # grps <- vector of groups to evaluate 
   
  probs <- list() 
 for (m in 1:length(grps)) { 
    x <- x2.l[which(attr1.grp == grps[m]),] 
    probs[[m]] <- matrix(0,nrow(x),length(grps)) 
    colnames(probs[[m]]) <- grps 
    rownames(probs[[m]]) <- rownames(x) 
     
    grps2 <- grps[-m] 
     
    p.val <- NULL 
    for (i in 1:nrow(x)) {p.val[i] <- HotellingsT2(x[i,], x[-i,])$p.value} 
    probs[[m]][,m] <- round(p.val,5)*100 
     
    for (j in 1:length(grps2)) { 
      p.val2 <- NULL 
      for (i in 1:nrow(x)) {p.val2[i] <- HotellingsT2(x[i,], 
                                                      x2.l[which(attr1.grp == grps2[j]),])$p.v
alue} 
      probs[[m]][,which(grps == grps2[j])] <- round(p.val2, 5)*100}} 
  return(probs) 
} 
 
########### WARD HCA ################# 
# Calculate group membership probabilities for the HCA Ward group assignments based on PCA dat
a 
ward_group_mem <- group.mem.probs(pc1to12, sample_new_stat_clusters$Ward_HCA_Cluster,  
                    unique(sample_new_stat_clusters$Ward_HCA_Cluster))  
 
# Create list of data that is grouped the same as the group probability list 
ward_samp_list <- split(sample_new_stat_clusters[, c(1:2)],  
                        f = sample_new_stat_clusters$Ward_HCA_Cluster) 
 
# Convert the list of matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
ward_group_mem <- map(ward_group_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 

495 

ward_samp_df <- map(ward_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from Ward HCA  
# and convert to data frame for easier handling 
ward_group_mem <- as.data.frame(bind_cols(ward_group_mem, ward_samp_df)) 
 
# New column of membership probability for initially assigned group 
ward_group_mem$assigned_val <- ward_group_mem[1:3][cbind(seq_len(nrow(ward_group_mem)),  
                                                         ward_group_mem$Ward_HCA_Cluster)] 
 
# Set the initial group assignment value to zero to allow for comparisons 
ward_group_mem[cbind(seq_len(nrow(ward_group_mem)), ward_group_mem$Ward_HCA_Cluster)] <- 0 
 
# The heuristic I am using to assess group membership asks whether or not the probability of 
# group membership in the original assigned cluster is greater than 10% and that the  
# probability of membership in any other cluster is less that 10%. This follows  
# Peeples (2010) in part and is a fairly conservative threshold.  
ward_group_mem %>% 
 # mutate(out_group_sum = `1` + `2` + `3`) %>% 
  mutate(assigned_val = as.numeric(assigned_val)) %>% 
  mutate(new_assign = ifelse(assigned_val > 10 & (`1` < 10 & `2` < 10 & `3` < 10),  
                            Ward_HCA_Cluster, "unassigned")) %>%  
#   filter(new_assign != "unassigned")   
  summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100) 
# Applying the heuristic to the initial group assignments for the Ward HCA clusters results  
# in an 77.16% unassignment rate. This is quite high. Let's check other methods to  
# see how they fair.  
 
 
########### Kmeans 4 ################# 
# Group probabilities for the kmeans 4 cluster solution on transformed PCA data  
kmean4_group_mem <- group.mem.probs(pc1to12, sample_new_stat_clusters$Kmeans_4,  
                                      unique(sample_new_stat_clusters$Kmeans_4))  
 
# Create list of data that is grouped the same as the group probability list 
kmean4_samp_list <- split(sample_new_stat_clusters[, c("Sample", "Kmeans_4")],  
                        f = sample_new_stat_clusters$Kmeans_4) 
 
# Reorder list to match the group membership probs 
kmean4_samp_list <- list(kmean4_samp_list$`1`, kmean4_samp_list$`3`, kmean4_samp_list$`4`, 
                         kmean4_samp_list$`2`) 
 
# Convert the matrices of group membership probabilities to data frames and bind  
# rows into one data frame 
kmean4_group_mem <- map(kmean4_group_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
kmean4_samp_df <- map(kmean4_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from Kmean 4 
# and convert to data frame for easier handling 
kmean4_group_mem <- as.data.frame(bind_cols(kmean4_group_mem, kmean4_samp_df)) 
 

496 

# Convert to tibble data frame for easier handling 
kmean4_group_mem <- as.data.frame(kmean4_group_mem) 
 
# New column of membership probability for initially assigned group 
kmean4_group_mem$assigned_val <- kmean4_group_mem[1:4][cbind(seq_len(nrow(kmean4_group_mem)),  
                                                           kmean4_group_mem$Kmeans_4)] 
 
# Set the initial group assignment value to zero to allow for comparisons 
kmean4_group_mem[cbind(seq_len(nrow(kmean4_group_mem)), kmean4_group_mem$Kmeans_4)] <- 0 
 
# Assess membership probabilities using my heuristic 
kmean4_group_mem %>%  
  mutate(assigned_val = as.numeric(assigned_val)) %>% 
  mutate(new_assign = ifelse(assigned_val > 10 & (`1` < 10 & `2` < 10 & `3` < 10 & `4` < 10),  
                             Kmeans_4, "unassigned")) %>%  
  #   filter(new_assign != "unassigned")   
  summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100) 
# At an 99.26%, it doesn't seem like kmeans 4 group clusters faired much better than Ward HCA 
# In fact, this did not do well at all 
 
 
########### Kmedoids (pam) 5 ################# 
# Group probabilities for the kmedoids (pam) 5 cluster solution on PC's 1 to 12  
# (90% of variability) 
kmed5_group_mem <- group.mem.probs(pc1to12, sample_new_stat_clusters$Kmediods_5,  
                                    unique(sample_new_stat_clusters$Kmediods_5))  
 
# Create list of data that is grouped the same as the group probability list 
kmed5_samp_list <- split(sample_new_stat_clusters[, c("Sample", "Kmediods_5")],  
                          f = sample_new_stat_clusters$Kmediods_5) 
 
# Convert the matrices of group membership probabilities to data frames and bind  
# rows into one data frame 
kmed5_group_mem <- map(kmed5_group_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
kmed5_samp_df <- map(kmed5_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from Kmed 5 
# and convert to data frame for easier handling 
kmed5_group_mem <- as.data.frame(bind_cols(kmed5_group_mem, kmed5_samp_df)) 
 
# New column of membership probability for initially assigned group 
kmed5_group_mem$assigned_val <- kmed5_group_mem[1:5][cbind(seq_len(nrow(kmed5_group_mem)),  
                                                           kmed5_group_mem$Kmediods_5)] 
 
# Set the initial group assignment value to zero to allow for comparisons 
kmed5_group_mem[cbind(seq_len(nrow(kmed5_group_mem)), kmed5_group_mem$Kmediods_5)] <- 0 
 
# Assess membership probabilities using my heuristic 
kmed5_group_mem %>%  
  mutate(new_assign = ifelse(assigned_val > 10 & `1` < 10 & `2` < 10 & `3` < 10 & 
                               `4` < 10 & `5` < 10,  

497 

                             Kmediods_5, "unassigned")) %>%  
  #   filter(new_assign != "unassigned")   
  summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100) 
# Ouch, at 95.58% unassigned using the heuristic criteria, this doesn't hold up 
 
########### Kmedoids (pam) 2 ################# 
# Group probabilities for the kmedoids (pam) 2 cluster solution on PC's 1 to 12  
# (90% of variability) 
kmed2_group_mem <- group.mem.probs(pc1to12, sample_new_stat_clusters$Kmediods_2,  
                                   unique(sample_new_stat_clusters$Kmediods_2))  
 
# Create list of data that is grouped the same as the group probability list 
kmed2_samp_list <- split(sample_new_stat_clusters[, c("Sample", "Kmediods_2")],  
                         f = sample_new_stat_clusters$Kmediods_2) 
 
# Convert the matrices of group membership probabilities to data frames and bind  
# rows into one data frame 
kmed2_group_mem <- map(kmed2_group_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
kmed2_samp_df <- map(kmed2_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from Kmed 5 
# and convert to data frame for easier handling 
kmed2_group_mem <- as.data.frame(bind_cols(kmed2_group_mem, kmed2_samp_df)) 
 
# New column of membership probability for initially assigned group 
kmed2_group_mem$assigned_val <- kmed2_group_mem[1:2][cbind(seq_len(nrow(kmed2_group_mem)),  
                                                           kmed2_group_mem$Kmediods_2)] 
 
# Set the initial group assignment value to zero to allow for comparisons 
kmed2_group_mem[cbind(seq_len(nrow(kmed2_group_mem)), kmed2_group_mem$Kmediods_2)] <- 0 
 
# Assess membership probabilities using my heuristic 
kmed2_group_mem %>%  
  mutate(new_assign = ifelse(assigned_val > 10 & `1` < 10 & `2` < 10,  
                             Kmediods_2, "unassigned")) %>%  
 # filter(assigned_val < `1` | assigned_val < `2`)   
  summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100) 
# A 79.01% unassigned using the heuristic criteria is better, but still doesn't hold up 
 
# Since none of these clustering methods were successful when held against Mahalanobis  
# Distance, we'll drop them from the augmented PCA data 
sample_pca[['pca_aug']][[1]] <- sample_pca[['pca_aug']][[1]] %>%  
                                  select(-Kmeans_2:-Kmediods_5) 
 
########### Mahalanobis-first route ####################################################### 
########### Core and Unassigned Group Assignments ######################################### 
# Another common method used for constructing core chemical compositional groups in 
# archaeology is to initially treat the entire data set as one large group and iteratively 
# removing samples with a membership probability of less than 1%. A Core group can thus  
# be defined and sub-groups may be identified within the Core.  
 

498 

# Double the PC data so the group can be compared to itself 
pc1to12_twice <- bind_rows(pc1to12, pc1to12) 
 
# Double the stat cluster assignment data 
sample_new_stat_clusters_twice <- bind_rows(sample_new_stat_clusters,  
                                            sample_new_stat_clusters) 
 
# Create vector of group assignments  
one_two <- c(rep(1, 543), rep(2, 543)) 
 
# Bind group assignments to cluster data 
sample_new_stat_clusters_twice <- cbind(sample_new_stat_clusters_twice, one_two) 
 
# Group probabilities for the group as one data set on PC's 1 through 12 
one_group_mem <- group.mem.probs(pc1to12_twice, sample_new_stat_clusters_twice$one_two,  
                                    unique(sample_new_stat_clusters_twice$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list <- split(sample_new_stat_clusters_twice[, c("Sample", "one_two")],  
                         f = sample_new_stat_clusters_twice$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem <- map(one_group_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df <- map(one_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from  
# and convert to data frame for easier handling 
one_group_mem <- as.data.frame(bind_cols(one_group_mem, one_samp_df)) 
 
# Create data frame of sample to retain after first iteraction 
iter1 <- one_group_mem %>% 
          filter(one_two == 1) %>% 
          filter(`1` > 1) %>% 
          select(Sample)  
 
# Create data frame of unassigned samples after first iteraction 
iter1_unassigned <- one_group_mem %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
   
# Subset initial groups 
one_group_mem1 <- one_group_mem %>% 
                    filter(Sample %in% iter1$Sample) 
 
 
### Iteration two  
# Bind samples list to PCA data, filter out the unassigned samples after iteration one  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter2 <- bind_cols(sample_new_stat_clusters_twice[, c("Sample", "one_two")],  

499 

                                  pc1to12_twice) %>% 
                          filter(Sample %in% iter1$Sample) %>% 
                          select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 2                 
sample_new_stat_clusters_twice_iter2 <- sample_new_stat_clusters_twice[, c("Sample", 
                                                                           "one_two")] %>% 
                                          filter(Sample %in% iter1$Sample) 
 
# Group probabilities for iteration 2 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_2 <- group.mem.probs(pc1to12_twice_iter2,  
                                        sample_new_stat_clusters_twice_iter2$one_two,  
                                 unique(sample_new_stat_clusters_twice_iter2$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter2 <- split(sample_new_stat_clusters_twice_iter2,  
                          f = sample_new_stat_clusters_twice_iter2$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter2 <- map(one_group_mem_iter_2, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter2 <- map(one_samp_list_iter2, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from  
# and convert to data frame for easier handling 
one_group_mem_iter2 <- as.data.frame(bind_cols(one_group_mem_iter2, one_samp_df_iter2)) 
 
# Create data frame of sample to retain after first iteraction 
iter2 <- one_group_mem_iter2 %>% 
            filter(one_two == 1) %>% 
            filter(`1` > 1) %>% 
            select(Sample)  
 
# Create data frame of unassigned samples after first iteraction 
iter2_unassigned <- one_group_mem_iter2 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem2 <- one_group_mem_iter2 %>% 
                     filter(Sample %in% iter2$Sample) 
 
 
### Iteration 3 
# Bind samples list to PCA data, filter out the unassigned samples after iteration two  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter3 <- bind_cols(sample_new_stat_clusters_twice_iter2,  
                                 pc1to12_twice_iter2) %>% 
                            filter(Sample %in% iter2$Sample) %>% 
                            select(-Sample, -one_two) 

500 

 
# Prep the sample names and assignments for iteration 3                
sample_new_stat_clusters_twice_iter3 <- sample_new_stat_clusters_twice_iter2 %>% 
                                            filter(Sample %in% iter2$Sample) 
 
# Group probabilities for iteration 3 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_3 <- group.mem.probs(pc1to12_twice_iter3,  
                                        sample_new_stat_clusters_twice_iter3$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter3$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter3 <- split(sample_new_stat_clusters_twice_iter3,  
                             f = sample_new_stat_clusters_twice_iter3$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter3 <- map(one_group_mem_iter_3, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter3 <- map(one_samp_list_iter3, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter3 <- as.data.frame(bind_cols(one_group_mem_iter3, one_samp_df_iter3)) 
 
# Create data frame of sample to retain after third iteraction 
iter3 <- one_group_mem_iter3 %>% 
            filter(one_two == 1) %>% 
            filter(`1` > 1) %>% 
            select(Sample)  
 
# Create data frame of unassigned samples after third iteraction 
iter3_unassigned <- one_group_mem_iter3 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem3 <- one_group_mem_iter3 %>% 
                    filter(Sample %in% iter3$Sample) 
 
### Iteration 4 
# Bind samples list to PCA data, filter out the unassigned samples after iteration three  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter4 <- bind_cols(sample_new_stat_clusters_twice_iter3,  
                                 pc1to12_twice_iter3) %>% 
                          filter(Sample %in% iter3$Sample) %>% 
                          select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 4              
sample_new_stat_clusters_twice_iter4 <- sample_new_stat_clusters_twice_iter3 %>% 
                                           filter(Sample %in% iter3$Sample) 
 

501 

# Group probabilities for iteration 4 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_4 <- group.mem.probs(pc1to12_twice_iter4,  
                                        sample_new_stat_clusters_twice_iter4$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter4$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter4 <- split(sample_new_stat_clusters_twice_iter4,  
                             f = sample_new_stat_clusters_twice_iter4$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter4 <- map(one_group_mem_iter_4, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter4 <- map(one_samp_list_iter4, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter4 <- as.data.frame(bind_cols(one_group_mem_iter4, one_samp_df_iter4)) 
 
# Create data frame of sample to retain after fourth iteraction 
iter4 <- one_group_mem_iter4 %>% 
            filter(one_two == 1) %>% 
            filter(`1` > 1) %>% 
            select(Sample)  
 
# Create data frame of unassigned samples after fourth iteraction 
iter4_unassigned <- one_group_mem_iter4 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem4 <- one_group_mem_iter4 %>% 
                    filter(Sample %in% iter4$Sample) 
 
 
### Iteration 5 
# Bind samples list to PCA data, filter out the unassigned samples after iteration four  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter5 <- bind_cols(sample_new_stat_clusters_twice_iter4,  
                                 pc1to12_twice_iter4) %>% 
                          filter(Sample %in% iter4$Sample) %>% 
                          select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 5              
sample_new_stat_clusters_twice_iter5 <- sample_new_stat_clusters_twice_iter4 %>% 
                                           filter(Sample %in% iter4$Sample) 
 
# Group probabilities for iteration 5 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_5 <- group.mem.probs(pc1to12_twice_iter5,  
                                        sample_new_stat_clusters_twice_iter5$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter5$one_two))  

502 

 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter5 <- split(sample_new_stat_clusters_twice_iter5,  
                             f = sample_new_stat_clusters_twice_iter5$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter5 <- map(one_group_mem_iter_5, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter5 <- map(one_samp_list_iter5, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter5 <- as.data.frame(bind_cols(one_group_mem_iter5, one_samp_df_iter5)) 
 
# Create data frame of sample to retain after fifth iteraction 
iter5 <- one_group_mem_iter5 %>% 
          filter(one_two == 1) %>% 
          filter(`1` > 1) %>% 
          select(Sample)  
 
# Create data frame of unassigned samples after fifth iteraction 
iter5_unassigned <- one_group_mem_iter5 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem5 <- one_group_mem_iter5 %>% 
                    filter(Sample %in% iter5$Sample) 
 
### Iteration 6 
# Bind samples list to PCA data, filter out the unassigned samples after iteration five  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter6 <- bind_cols(sample_new_stat_clusters_twice_iter5,  
                                 pc1to12_twice_iter5) %>% 
                                filter(Sample %in% iter5$Sample) %>% 
                                select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 6             
sample_new_stat_clusters_twice_iter6 <- sample_new_stat_clusters_twice_iter5 %>% 
                                          filter(Sample %in% iter5$Sample) 
 
# Group probabilities for iteration 6 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_6 <- group.mem.probs(pc1to12_twice_iter6,  
                                        sample_new_stat_clusters_twice_iter6$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter6$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter6 <- split(sample_new_stat_clusters_twice_iter6,  
                             f = sample_new_stat_clusters_twice_iter6$one_two) 
 

503 

# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter6 <- map(one_group_mem_iter_6, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter6 <- map(one_samp_list_iter6, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter6 <- as.data.frame(bind_cols(one_group_mem_iter6, one_samp_df_iter6)) 
 
# Create data frame of sample to retain after sixth iteraction 
iter6 <- one_group_mem_iter6 %>% 
            filter(one_two == 1) %>% 
            filter(`1` > 1) %>% 
            select(Sample)  
 
# Create data frame of unassigned samples after sixth iteraction 
iter6_unassigned <- one_group_mem_iter6 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem6 <- one_group_mem_iter6 %>% 
                    filter(Sample %in% iter6$Sample) 
 
### Iteration 7 
# Bind samples list to PCA data, filter out the unassigned samples after iteration six  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter7 <- bind_cols(sample_new_stat_clusters_twice_iter6,  
                                 pc1to12_twice_iter6) %>% 
                          filter(Sample %in% iter6$Sample) %>% 
                          select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 6             
sample_new_stat_clusters_twice_iter7 <- sample_new_stat_clusters_twice_iter6 %>% 
                                          filter(Sample %in% iter6$Sample) 
 
# Group probabilities for iteration 7 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_7 <- group.mem.probs(pc1to12_twice_iter7, 
                                        sample_new_stat_clusters_twice_iter7$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter7$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter7 <- split(sample_new_stat_clusters_twice_iter7,  
                             f = sample_new_stat_clusters_twice_iter7$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter7 <- map(one_group_mem_iter_7, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 

504 

one_samp_df_iter7 <- map(one_samp_list_iter7, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter7 <- as.data.frame(bind_cols(one_group_mem_iter7, one_samp_df_iter7)) 
 
# Create data frame of sample to retain after seventh iteraction 
iter7 <- one_group_mem_iter7 %>% 
          filter(one_two == 1) %>% 
          filter(`1` > 1) %>% 
          select(Sample)  
 
# Create data frame of unassigned samples after seventh iteraction 
iter7_unassigned <- one_group_mem_iter7 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem7 <- one_group_mem_iter7 %>% 
                     filter(Sample %in% iter7$Sample) 
 
### Iteration 8 
# Bind samples list to PCA data, filter out the unassigned samples after iteration seven  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter8 <- bind_cols(sample_new_stat_clusters_twice_iter7,  
                                 pc1to12_twice_iter7) %>% 
                        filter(Sample %in% iter7$Sample) %>% 
                        select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 7            
sample_new_stat_clusters_twice_iter8 <- sample_new_stat_clusters_twice_iter7 %>% 
                                           filter(Sample %in% iter7$Sample) 
 
# Group probabilities for iteration 8 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_8 <- group.mem.probs(pc1to12_twice_iter8,  
                                        sample_new_stat_clusters_twice_iter8$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter8$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter8 <- split(sample_new_stat_clusters_twice_iter8,  
                             f = sample_new_stat_clusters_twice_iter8$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter8 <- map(one_group_mem_iter_8, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter8 <- map(one_samp_list_iter8, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter8 <- as.data.frame(bind_cols(one_group_mem_iter8, one_samp_df_iter8)) 

505 

 
# Create data frame of sample to retain after fifth iteraction 
iter8 <- one_group_mem_iter8 %>% 
          filter(one_two == 1) %>% 
          filter(`1` > 1) %>% 
          select(Sample)  
 
# Create data frame of unassigned samples after fifth iteraction 
iter8_unassigned <- one_group_mem_iter8 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem8 <- one_group_mem_iter8 %>% 
                     filter(Sample %in% iter8$Sample) 
 
### Iteration 9 
# Bind samples list to PCA data, filter out the unassigned samples after iteration eight  
# and select PC data only for group membership probability calculation 
pc1to12_twice_iter9 <- bind_cols(sample_new_stat_clusters_twice_iter8,  
                                 pc1to12_twice_iter8) %>% 
                          filter(Sample %in% iter8$Sample) %>% 
                          select(-Sample, -one_two) 
 
# Prep the sample names and assignments for iteration 8       
sample_new_stat_clusters_twice_iter9 <- sample_new_stat_clusters_twice_iter8 %>% 
                                          filter(Sample %in% iter8$Sample) 
 
# Group probabilities for iteration 9 of the group as one data set on PC's 1 through 12 
one_group_mem_iter_9 <- group.mem.probs(pc1to12_twice_iter9,  
                                        sample_new_stat_clusters_twice_iter9$one_two,  
                                        unique(sample_new_stat_clusters_twice_iter9$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
one_samp_list_iter9 <- split(sample_new_stat_clusters_twice_iter9,  
                             f = sample_new_stat_clusters_twice_iter9$one_two) 
 
# Convert the matrices of group membership probabilities to data frames  
# and bind rows into one data frame 
one_group_mem_iter9 <- map(one_group_mem_iter_9, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
one_samp_df_iter9 <- map(one_samp_list_iter9, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
one_group_mem_iter9 <- as.data.frame(bind_cols(one_group_mem_iter9, one_samp_df_iter9)) 
 
# Create data frame of sample to retain after eighth iteraction 
iter9 <- one_group_mem_iter9 %>% 
            filter(one_two == 1) %>% 
            filter(`1` > 1) %>% 

506 

            select(Sample)  
 
# Create data frame of unassigned samples after eighth iteraction 
iter9_unassigned <- one_group_mem_iter9 %>% 
                      filter(one_two == 1) %>% 
                      filter(`1` < 1) %>% 
                      select(Sample)  
 
# Subset initial groups 
one_group_mem9 <- one_group_mem_iter9 %>% 
                   filter(Sample %in% iter9$Sample) 
 
# Data frame of unassigned samples 
maha_unassigned <- bind_rows(iter1_unassigned, iter2_unassigned, iter3_unassigned,  
                             iter4_unassigned, iter5_unassigned, iter6_unassigned,  
                             iter7_unassigned, iter8_unassigned) %>%  
                      arrange(Sample) %>% 
                      mutate(one_two = 2) 
 
###### End of Core-Unassigned membership iterations ##### 
 
# Now that I have a core group and an unassigned group, it's important to assess whether or no
t 
# any of the unassigned samples might warrant inclusion back into the core group. 
# To do this, the unassigned samples will be projected against the core group as before.  
# Defined PC loadings for core and unassigned samples 
pc1to12_core_unassigned <-  sample_new_stat_clusters_twice_iter9 %>% 
                              filter(one_two == 1) %>% 
                              bind_rows(maha_unassigned) %>% 
                              left_join(sample_pca[['pca_aug']][[1]], by = "Sample") %>%  
                              select(.fittedPC1:.fittedPC12) 
           
# Prep the sample names and assignments for core|unassigned evaluation  
sample_core_unassigned_clusters <-  sample_new_stat_clusters_twice_iter9 %>% 
                                      filter(one_two == 1) %>% 
                                      bind_rows(maha_unassigned)  
 
# Group probabilities for iteration 9 of the group as one data set on PC's 1 through 12 
core_unassigned_group_prob <- group.mem.probs(pc1to12_core_unassigned,  
                                              sample_core_unassigned_clusters$one_two,  
                                        unique(sample_core_unassigned_clusters$one_two))  
 
# Create list of data that is grouped the same as the group probability list 
core_unassigned_list <- split(sample_core_unassigned_clusters,  
                             f = sample_core_unassigned_clusters$one_two) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows  
# into one data frame 
core_unassigned_group_prob <- map(core_unassigned_group_prob, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
core_unassigned_df <- map(core_unassigned_list, as.data.frame) %>% bind_rows() 
 

507 

# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
core_unassigned_group_prob <- as.data.frame(bind_cols(core_unassigned_group_prob, 
                                                      core_unassigned_df)) 
 
# Check to see if there are any unassigned above the 1% threshold for membership in the core 
core_unassigned_group_prob %>% 
  filter(one_two == 2 & `1` > 1) 
# Does not appear to be the case 
 
# Check to see if there are any core samples below 1% threshold of being assigned to the core  
core_unassigned_group_prob %>% 
  filter(one_two == 1 & `1` < 1) 
# Also does not appear to be the case. This confirms that we have statistically robust   
# core and unassigned groups.  
 
# Create interactive 3D scatter plot showing first three PC's and the core and unassigned samp
les       
p <-  sample_new_stat_clusters_twice_iter9 %>% 
        filter(one_two == 1) %>% 
        bind_rows(maha_unassigned) %>% 
        left_join(sample_pca[['pca_aug']][[1]], by = "Sample") %>% 
        mutate(one_two = factor(one_two, labels = c("Core", "Unassigned"))) %>% 
        mutate(symbols1 = ifelse(one_two == "Core", "plus", "triangle-up")) %>% 
       # ggplot(aes(x = .fittedPC1, y = .fittedPC3, color = one_two)) + geom_point()  
        plot_ly(type = "scatter3d", x = ~.fittedPC1, y = ~.fittedPC2, z = ~.fittedPC3,  
                color = ~as.factor(one_two), size = 3, colors = c('grey40', 'black'),  
                alpha = 0.8, 
                text = ~(paste("Sample ID", Sample, '<br>Site:', Site, "<br>Geography_2:",  
                               Geography_2, "<br>Time:", Time,  
                               "<br>Cultural Group:", Cultural_Group)), 
             #  marker = list(symbol = ~I(symbols1)), size = .3, 
                symbol = ~one_two, #symbols = ~symbols1, 
              mode = "markers") %>% 
        layout(scene = list(xaxis = list(title = 'Principal Component 1'), 
                            yaxis = list(title = 'Principal Component 2'), 
                            zaxis = list(title = 'Principal Component 3'))) 
 
# Adjust plot features 
pb <- plotly_build(p) 
pb$x$data[[1]]$marker$symbol <- 'diamond-open' 
pb$x$data[[2]]$marker$symbol <- 'circle-open' 
pb # Display interactive 3D scattergram 
 
# Table of core and unassigned group membership 
sample_new_stat_clusters_twice_iter9 %>% 
  filter(one_two == 1) %>% 
  bind_rows(maha_unassigned) %>% 
  left_join(sample_pca[['pca_aug']][[1]], by = "Sample") %>% 
  mutate(one_two = factor(one_two, labels = c("Core", "Unassigned"))) %>% 
  select(one_two) %>% 
  table() 
 

508 

 
########################### Unassigned Group Structure ##################################### 
# There are 127 unassigned samples (or 23.4% of the original ceramic sample) 
unassigned <- maha_unassigned %>% 
                left_join(sample_pca[['pca_aug']][[1]], by = "Sample") %>% 
                select(-starts_with(".")) # Drop PC's from full data set PCA 
 
# In taking a look at a table of the sites from where the outliers were recovered,  
# it looks like five sites in particular have outlier vessels: Crable, Morton Village, 
# Orendorf C, Ten Mile Creek, and Walsh 
table(unassigned$Site) 
# Looking through the other pieces of a prior information, there don't appear to be  
# any "smoking-gun" trends that may help guide cluster analysis of the Unassigned group 
 
# Prepare samples for distance and clustering methods, we'll consider the elemental data here 
unassigned_distready <- unassigned %>% 
                          select(Si:Th) 
 
##### Kmeans of Unassigned ##### 
# First, it's a good idea to use a few methods to assess the number of clusters to model 
# Elbow Method 
fviz_nbclust(unassigned_distready, kmeans, method = "wss") # 4 - 8 optimal clusters;  
                                                           # 4-5 looks good 
# Silhouette Method 
fviz_nbclust(unassigned_distready, kmeans, method = "silhouette") # 2 optimal clusters 
# Gap Stat 
#fviz_nbclust(unassigned_distready, kmeans, method = "gap_stat") # 1 optimal cluster 
 
# Based on the optimal cluster methods, it looks like we should run kmeans twice, once with  
# 2 clusters and once with 5 clusters 
 
# 2 Cluster K-means 
unassigned_k2 <- kmeans(unassigned_distready,  
                         centers = 2, # number of clusters 
                         nstart = 50, # number of random initial configs  
                                      # out of which best is chosen 
                         iter.max = 500) # number of allowable iterations allowed  
 
# Visualize 2 cluster kmeans  
fviz_cluster(unassigned_k2, data = unassigned_distready) 
 
# Assign to clustering assignments data frame 
unassigned_stat_clusters <- maha_unassigned %>% 
                                select(Sample) %>% 
                                mutate(Kmeans_2 = unassigned_k2$cluster) 
 
# 5 Cluster K-means 
unassigned_k5 <- kmeans(unassigned_distready, centers = 5, nstart = 50, iter.max = 500) 
 
# Visualize 5 cluster kmeans 
fviz_cluster(unassigned_k5, data = unassigned_distready) 
 
# Assign to clustering assignments data frame 

509 

unassigned_stat_clusters <- unassigned_stat_clusters %>% 
                              mutate(Kmeans_5 = unassigned_k5$cluster,  
                                     Kmeans_2 = unassigned_k2$cluster) 
 
##### K-medoids of Unassigned ##### 
 
# For k-medoids, we'll be using the pam function from the cluster package. pam stands for  
# "partitioning around medoids" 
 
# As with k-means, it's a good idea to use a few methods to assess the number of clusters to m
odel 
# Elbow Method 
fviz_nbclust(unassigned_distready, pam, method = "wss") # 5 looks optimal here 
# Silhouette Method 
fviz_nbclust(unassigned_distready, pam, method = "silhouette") # 2 optimal clusters 
# Gap Stat 
#fviz_nbclust(unassigned_distready, pam, method = "gap_stat") # 1 optimal cluster 
 
# We'll run two clusters - one with 2 and one with 5 
# 2 cluster K-medoids 
pam2_unassigned <- pam(unassigned_distready, 2) 
 
# Plot 2 cluster k-medoids 
fviz_cluster(pam2_unassigned, data = unassigned_distready) 
 
# 5 cluster K-medoids 
pam5_unassigned <- pam(unassigned_distready, 5) 
 
# Plot 5 cluster k-medoids 
fviz_cluster(pam5_unassigned, data = unassigned_distready) 
 
# Assign k-medoids results to clustering assignments data frame 
unassigned_stat_clusters <- unassigned_stat_clusters %>% 
                                mutate(Kmediods_2 = pam2_unassigned$clustering,  
                                       Kmediods_5 = pam5_unassigned$clustering) 
 
# There appears to be fairly broad agreement between kmeans and kmedoids about the different 
# clusters present, but it is important to see how these hold up to comparison using  
# visual inspection 
 
# Convert all unassigned statistical cluster assignments to character for joining 
unassigned_stat_clusters[,2:5] <- sapply(unassigned_stat_clusters[,2:5], as.character) 
 
# Make data frame with core sample assignments and unassigned cluster assignments 
core_and_unassigned_clusters <- sample_new_stat_clusters_twice_iter9 %>% 
                                  filter(one_two == 1) %>% 
                                  mutate(Kmeans_2 = "Core",  
                                         Kmeans_5 = "Core",  
                                         Kmediods_2 = "Core", 
                                         Kmediods_5 = "Core") %>% 
                                  select(-one_two) %>% 
                                  bind_rows(unassigned_stat_clusters) 
 

510 

# Join the core assignments to the original PCA data, which is stored in a nested  
# prcomp list object 
sample_pca[["data"]][[1]] <- left_join(sample_pca[["data"]][[1]], core_and_unassigned_clusters
, by = "Sample") 
 
# Join the core assignments to the augmented PCA data, which is stored in a nested 
# prcomp list object 
sample_pca[["pca_aug"]][[1]] <- left_join(sample_pca[["pca_aug"]][[1]],  
                                          core_and_unassigned_clusters, by = "Sample") 
 
# Create column to apply alpha to core group points in biplots for easier interpretation 
# sample_pca[["data"]][[1]] <- sample_pca[["data"]][[1]] %>% 
#                                 mutate(alpha = ifelse(Kmeans_5 == "Core", 0.25, 1)) %>% 
#                                 mutate(alpha = as.vector(alpha)) 
 
# Vectorize the alpha column 
# core_alpha <- as.vector(sample_pca[["data"]][[1]]$alpha) 
 
# Create plot of PC 1 and PC 2 with the 90% conf intervals around the core and outgroups 
unass_pc1pc2_kmean2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray45", 
                 loadings.label.alpha = 0.9, 
                 loadings.label.size = 3.5, 
                 loadings.label.hjust = -0.5, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Kmeans_5",  
                 shape = "Kmeans_5", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 #alpha = core_alpha, 
                 size = 2) + 
        theme_bw() +  
       # geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
 
unass_pc1pc2_kmean2[[1]] + scale_fill_manual(values = c("black","black", "black",  
                                                        "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  scale_shape_manual(values=c(3, 18, 16, 2, 43, 1))  

511 

 
 
## Add final assignments to shiny app data 
sample_pca[["pca_aug"]][[1]] <- sample_pca[["pca_aug"]][[1]] %>% 
  left_join(pca_aug[, c("Sample", "Final_Assign")], by = "Sample") 
   
###### Shiny app to biplot the various elements and PCs against one another ##### 
##   UI   ## 
ui_sample <- fluidPage( 
  pageWithSidebar ( 
    headerPanel('Bivariate Plotting'), 
    sidebarPanel( 
      selectInput('x', 'X Variable', names(sample_pca[["pca_aug"]][[1]]),  
                  selected = names(sample_pca[["pca_aug"]][[1]])[[14]]), 
      selectInput('y', 'Y Variable', names(sample_pca[["pca_aug"]][[1]]), 
                  selected = names(sample_pca[["pca_aug"]][[1]])[[15]]), 
      selectInput('color', 'Color', names(sample_pca[["pca_aug"]][[1]]), 
                  selected = names(sample_pca[["pca_aug"]][[1]])[[103]]), 
      #Slider for plot height 
      sliderInput('plotHeight', 'Height of plot (in pixels)',  
                  min = 100, max = 2000, value = 550) 
    ), 
    mainPanel( 
      plotlyOutput('plot1') 
    ) 
  ) 
) 
 
## Server ## 
server_sample <- function(input, output, session) { 
   
  # Combine the selected variables into a new data frame 
  selectedData <- reactive({ 
    sample_pca[["pca_aug"]][[1]][, c(input$x, input$y, input$color)] 
  }) 
   
  output$plot1 <- renderPlotly({ 
     
    #Build plot with ggplot syntax  
    p <- ggplot(data = sample_pca[["pca_aug"]][[1]], aes_string(x = input$x,  
                                                 y = input$y,  
                                                 color = input$color,  
                                                 shape = input$color)) +  
      geom_point() +  
      theme(legend.title = element_blank()) +  
      stat_ellipse(level = 0.9) + 
      scale_color_igv() +  
      theme_bw() + 
      xlab(paste0(input$x, " (log base 10 ppm)")) + 
      ylab(paste0(input$y, " (log base 10 ppm)")) 
     
    ggplotly(p) %>% 
      layout(height = input$plotHeight, autosize = TRUE,  

512 

             legend = list(font = list(size = 12)))  
  }) 
   
} 
 
shinyApp(ui_sample, server_sample) 
 
## Membership probabilties for outgroup Kmeans 5 group assignments 
 
# Assess membership probabilities of the outgroup samples 
# Out-groups 2, 3, and 4 are large enough to be assessed for Mahalanobis  
# distance probabilities 
table(sample_pca[["pca_aug"]][[1]]$Kmeans_5) 
 
# Pull sample data for the Kmeans_5 samples 
kmeans234_samps <- sample_pca[["pca_aug"]][[1]] %>% 
                    filter(Kmeans_5 == 2 | Kmeans_5 == 3 | Kmeans_5 == 4) %>% 
                    select(Sample, Kmeans_5, .fittedPC1:.fittedPC12) %>% 
                    mutate(Kmeans_5 = as.numeric(Kmeans_5) - 1) 
 
# Pull PC data for the Kmeans_5 samples 
kmeans234_pcs <- kmeans234_samps %>% 
                  select(.fittedPC1:.fittedPC12) 
 
# Group membership probabilities for the groups large enough to be assessed  
kmeans234_mem <- group.mem.probs(kmeans234_pcs, kmeans234_samps$Kmeans_5,  
                   unique(kmeans234_samps$Kmeans_5)) 
 
# Create list of data that is grouped the same as the group probability list 
kmeans234_samp_list <- split(kmeans234_samps,  
                         f = kmeans234_samps$Kmeans_5) 
 
# Convert the matrices of group membership probabilities to data frames and bind  
# rows into one data frame 
kmeans234_mem <- map(kmeans234_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
kmeans234_samp_df <- map(kmeans234_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from Kmed 5 
# and convert to data frame for easier handling 
kmeans234_mem <- as.data.frame(bind_cols(kmeans234_mem, kmeans234_samp_df)) 
 
# Reorder columns 
kmeans234_mem <- kmeans234_mem[, c(3, 1, 2, 4, 5)] 
 
# New column of membership probability for initially assigned group 
kmeans234_mem$assigned_val <- kmeans234_mem[1:3][cbind(seq_len(nrow(kmeans234_mem)),  
                                                       as.numeric(kmeans234_mem$Kmeans_5))] 
 
# Determine column with the maximum value and assign to new column 
kmeans234_mem$max_value <- colnames(kmeans234_mem[1:3])[max.col(kmeans234_mem[1:3])] 
 

513 

# There is broad disagreement in group assignment between the Kmeans/Kmedoids 5 group methods 
# and the group membership probabilities. This isn't surprising since there is much overlap 
# between the groups on PC biplots. As a result, I'll take the maximum group membership 
# probability as assessed via Mahalanobis/Hotelling's T2 and re-run the assignments to  
# refine the non-core group membership assignments.  
 
# Samples and PCs for maximum membership after iteration one 
kmeans234_iter2_samps <- kmeans234_mem %>% 
                            select(Sample, max_value) %>% 
                            left_join(kmeans234_samps[-2], by = "Sample") 
 
# PC data for iteration 2 of Kmeans assignments 
kmeans234_iter2_pcs <- kmeans234_iter2_samps %>% select(.fittedPC1:.fittedPC12) 
 
# Group membership probs for iteration 2 of Kmeans 
kmeans234_mem_iter2 <- group.mem.probs(kmeans234_iter2_pcs, kmeans234_iter2_samps$max_value,  
                                       unique(kmeans234_iter2_samps$max_value)) 
 
# Unfortunatly, it appears that the groups as defined and refined from Kmeans do not  
# hold up to statistical rigor. Let's try the Kmeans 2 group assignments  
 
## Membership probabilties for outgroup Kmeans 2 group assignments 
 
# Assess membership probabilities of the outgroup samples for Kmeans_2 
table(sample_pca[["pca_aug"]][[1]]$Kmeans_2) 
 
# Pull sample data for the Kmeans_2 samples 
out_kmeans2_samps <- sample_pca[["pca_aug"]][[1]] %>% 
                        filter(Kmeans_2 != "Core") %>% 
                        select(Sample, Kmeans_2, .fittedPC1:.fittedPC12)  
 
# Pull PC data for the Kmeans_2 samples 
out_kmeans2_pcs <- out_kmeans2_samps %>% 
                    select(.fittedPC1:.fittedPC12) 
 
# Group membership probabilities for the groups large enough to be assessed  
out_kmeans2_mem <- group.mem.probs(out_kmeans2_pcs, out_kmeans2_samps$Kmeans_2,  
                                 c("1", "2")) 
 
# Create list of data that is grouped the same as the group probability list 
out_kmeans2_samp_list <- split(out_kmeans2_samps[1:2],  
                             f = out_kmeans2_samps$Kmeans_2) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows into one
 data frame 
out_kmeans2_mem <- map(out_kmeans2_mem, as.data.frame) %>% bind_rows() 
 
# Reorder column to put them in the correct position 
#out_kmeans2_mem <- data.frame(out_kmeans2_mem$`1`, out_kmeans2_mem$`2`) 
#colnames(out_kmeans2_mem) <- c(1, 2) 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
out_kmeans2_samp_df <- map(out_kmeans2_samp_list, as.data.frame) %>% bind_rows() 

514 

 
# Bind to initial sample id and group assignment and convert to data frame for easier handling 
out_kmeans2_mem <- as.data.frame(bind_cols(out_kmeans2_mem, out_kmeans2_samp_df)) 
 
# New column of membership probability for initially assigned group 
out_kmeans2_mem$assigned_val <- out_kmeans2_mem[1:2][cbind(seq_len(nrow(out_kmeans2_mem)),  
                                                       as.numeric(out_kmeans2_mem$Kmeans_2))] 
 
# Set the initial group assignment value to zero to allow for comparisons 
out_kmeans2_mem[cbind(as.numeric(seq_len(nrow(out_kmeans2_mem))),  
                      as.numeric(out_kmeans2_mem$Kmeans_2))] <- 0 
 
# Assess membership probabilities using my heuristic 
out_kmeans2_mem %>%  
  mutate(assigned_val = as.numeric(assigned_val)) %>% 
  mutate(`1` = as.numeric(`1`)) %>% 
  mutate(`2` = as.numeric(`2`)) %>% 
  mutate(new_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10,  
                             Kmeans_2, "unassigned")) %>%  
  #   filter(new_assign != "unassigned")   
  summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100) 
# 50.4% unassigned rate suggests that there is some support for a two group soluation here 
# Let's remove the unassigned samples and run another iteration to firm up the outgroups 
 
#### Data frame of Outgroup Kmeans 2 assignments for group mem iteration 2 
out_kmeans2_iter2 <- out_kmeans2_mem %>%  
                      mutate(assigned_val = as.numeric(assigned_val)) %>% 
                      mutate(`1` = as.numeric(`1`)) %>% 
                      mutate(`2` = as.numeric(`2`)) %>% 
                      mutate(new_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10,  
                             Kmeans_2, "unassigned")) %>% 
                      filter(new_assign != "unassigned") 
 
# Data frame of Outgroup Kmeans 2 unassigned sherds after group mem iteration 1 
out_kmeans2_iter2_unassigned <- out_kmeans2_mem %>%  
                        mutate(assigned_val = as.numeric(assigned_val)) %>% 
                        mutate(`1` = as.numeric(`1`)) %>% 
                        mutate(`2` = as.numeric(`2`)) %>% 
                        mutate(new_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10,  
                                                   Kmeans_2, "unassigned")) %>% 
                        filter(new_assign == "unassigned") 
 
# Sample and PC data for Kmeans 2 iteration 2 
out_kmeans2_iter2_samps <- out_kmeans2_iter2 %>% 
                            select(Sample, new_assign) %>% 
                            left_join(out_kmeans2_samps[-2], by = "Sample") 
 
# PC data for Kmenas sample 2 
out_kmeans2_iter2_pcs <- out_kmeans2_iter2_samps %>% 
                          select(.fittedPC1:.fittedPC12) 
 
# Membership probabilities for iteration 2 - only two samples need to become unassigned 
out_kmeans2_iter2_mem <- group.mem.probs(out_kmeans2_iter2_pcs,  

515 

                                         out_kmeans2_iter2_samps$new_assign,  
                                         unique(out_kmeans2_iter2_samps$new_assign)) 
 
# Create list of data that is grouped the same as the group probability list 
out_kmeans2_iter2_samps_list <- split(out_kmeans2_iter2_samps[1:2],  
                                   f = out_kmeans2_iter2_samps$new_assign) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows  
# into one data frame 
out_kmeans2_iter2_mem <- map(out_kmeans2_iter2_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
out_kmeans2_iter2_samps_df <- map(out_kmeans2_iter2_samps_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment and convert to data frame for easier handling 
out_kmeans2_iter2_mem <- as.data.frame(bind_cols(out_kmeans2_iter2_mem, out_kmeans2_iter2_samp
s_df)) 
 
# New column of membership probability for initially assigned group 
out_kmeans2_iter2_mem$assigned_val <- out_kmeans2_iter2_mem[1:3][cbind(seq_len(nrow(out_kmeans
2_iter2_mem)),  
                                                           as.numeric(out_kmeans2_iter2_mem$ne
w_assign))] 
 
# Set the initial group assignment value to zero to allow for comparisons 
out_kmeans2_iter2_mem[cbind(as.numeric(seq_len(nrow(out_kmeans2_iter2_mem))),  
                      as.numeric(out_kmeans2_iter2_mem$new_assign))] <- 0 
 
# Assess membership probabilities using my heuristic but reduced in-group membership to >2.5% 
out_kmeans2_iter2_mem %>%  
  mutate(assigned_val = as.numeric(assigned_val)) %>% 
  mutate(`1` = as.numeric(`1`)) %>% 
  mutate(`2` = as.numeric(`2`)) %>% 
  mutate(iter2_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10,  
                             new_assign, "unassigned")) %>%  
  #   filter(new_assign != "unassigned")   
  summarize(perc_unassigned = sum(iter2_assign == "unassigned")/n() * 100) 
# Great, only dropped 6.3% of the samples. Seems like we have statistically robust outgroups 
# Let's go ahead and define those here.  
 
# Data frame of assigned outgroup samples 
outgroup_assignments <- out_kmeans2_iter2_mem %>% 
                      mutate(assigned_val = as.numeric(assigned_val)) %>% 
                      mutate(`1` = as.numeric(`1`)) %>% 
                      mutate(`2` = as.numeric(`2`)) %>% 
                      mutate(iter2_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10,  
                                                   new_assign, "unassigned")) %>% 
                      filter(iter2_assign != "unassigned") %>% 
                      mutate(Outgroup = iter2_assign) %>% 
                      select(Sample, Outgroup) 
 
# Table of outgroup sample assignments 
table(outgroup_assignments$Outgroup) 

516 

 
# Data frame of unassigned outgroup samples 
outgroup_unassigned <- out_kmeans2_iter2_mem %>% 
                        mutate(assigned_val = as.numeric(assigned_val)) %>% 
                        mutate(`1` = as.numeric(`1`)) %>% 
                        mutate(`2` = as.numeric(`2`)) %>% 
                        mutate(new_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10,  
                                                     new_assign, "unassigned")) %>% 
                        filter(new_assign == "unassigned") %>% 
                        full_join(out_kmeans2_iter2_unassigned, by = "Sample") %>% 
                        mutate(Outgroup = "unassigned") %>% 
                        select(Sample, Outgroup) 
 
# Data frame of all outgroup samples 
outgroup_assignments <- bind_rows(outgroup_assignments, outgroup_unassigned) 
 
# Change the Label of 1 to Outgroup 2 and 2 to Outgroup 1 
outgroup_assignments <- outgroup_assignments %>% 
                      mutate(Outgroup = ifelse(Outgroup == 1, "Outgroup 2", Outgroup)) %>% 
                      mutate(Outgroup = ifelse(Outgroup == 2, "Outgroup 1", Outgroup)) 
   
### Visualize core and outgroup samples 
# Make data frame with core sample assignments and unassigned cluster assignments 
core_and_outgroup_assignments <- sample_new_stat_clusters_twice_iter9 %>% 
                                    filter(one_two == 1) %>% 
                                    mutate(Outgroup = "Core") %>% 
                                    select(-one_two) %>% 
                                    bind_rows(outgroup_assignments) 
 
# Join the core assignments to the original PCA data, which is stored in a nested  
# prcomp list object 
sample_pca[["data"]][[1]] <- left_join(sample_pca[["data"]][[1]], core_and_outgroup_assignment
s, by = "Sample") 
 
# Join the core assignments to the augmented PCA data, which is stored in a nested  
# prcomp list object 
sample_pca[["pca_aug"]][[1]] <- left_join(sample_pca[["pca_aug"]][[1]],  
                                          core_and_outgroup_assignments, by = "Sample") 
 
# Create column to apply alpha to core group points in biplots for easier interpretation 
sample_pca[["data"]][[1]] <- sample_pca[["data"]][[1]] %>% 
                                mutate(core_alpha = ifelse(Outgroup == "Core", 0.25, 1)) %>% 
                                mutate(core_alpha = as.vector(core_alpha)) 
 
# Vectorize the alpha column 
core_alpha <- as.vector(sample_pca[["data"]][[1]]$core_alpha) 
 
# Create plot of PC 1 and PC 2 with the 90% conf intervals around the core and outgroups 
core_outgroup_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 

517 

      ~ autoplot(.x, loadings = TRUE, loadings.label = TRUE, 
                 scale = 0, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray45", 
                 loadings.label.alpha = 0.9, 
                 loadings.label.size = 2.5, 
                 loadings.label.hjust = -0.5, 
                 #frame = TRUE, 
                 #frame.type = "norm", 
                 data = .y,  
                 colour = "Outgroup",  
                 shape = "Outgroup", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2, 
                 alpha = core_alpha) + 
        theme_bw() +  
        # geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
 
core_outgroup_pc1pc2[[1]] + 
  scale_fill_manual(values = c("black","black", "black",  
                                                        "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  stat_ellipse(data = filter(sample_pca[["pca_aug"]][[1]], Outgroup != "unassigned"),  
                             aes(x = .fittedPC1, y = .fittedPC2, color = Outgroup)) + 
  scale_shape_manual(values=c(2, 15, 18, 43))  
 
 
# Group membership probabilities for Outgroup 1, 2, unassigned, and core 
core_out_unass_samps <- sample_pca[["pca_aug"]][[1]] %>% 
                          select(Sample, Outgroup, .fittedPC1:.fittedPC12) 
 
core_out_unass_pcs <- core_out_unass_samps %>% select(.fittedPC1:.fittedPC12) 
 
core_out_unass_mem <- group.mem.probs(core_out_unass_pcs, core_out_unass_samps$Outgroup,  
                                      unique(core_out_unass_samps$Outgroup)) 
 
# Create list of data that is grouped the same as the group probability list 
core_out_samp_list <- split(core_out_unass_samps[, c("Sample", "Outgroup")],  
                         f = core_out_unass_samps$Outgroup) 
 
# Reorder list to match the order of the group membership probs 
core_out_samp_list <- list(core_out_samp_list$Core, core_out_samp_list$`Outgroup 1`,  
                           core_out_samp_list$unassigned, core_out_samp_list$`Outgroup 2`) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows  

518 

# into one data frame 
core_out_unass_mem <- map(core_out_unass_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
core_out_samp_df <- map(core_out_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment from Kmed 5 
# and convert to data frame for easier handling 
core_out_unass_mem <- as.data.frame(bind_cols(core_out_unass_mem, core_out_samp_df)) 
 
# Create table for dissertation 
outgroup_core_table <- core_out_unass_mem %>% 
                        right_join(sample_pca[["pca_aug"]][[1]][, c("Sample", "Site")]) %>% 
                        filter(Outgroup != "unassigned", Outgroup != "Core") %>% 
                        select(-unassigned) %>% 
                        arrange(Outgroup) %>% 
                        mutate(Sample = parse_number(Sample)) 
 
# Write table to csv 
# write_csv(outgroup_core_table, "outgroups - core.csv") 
 
 
# Create plot of PC 1 and PC 2 with the 90% conf intervals around the core and outgroups 
core_outgroup_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, x = 1, y = 2, loadings = TRUE, loadings.label = TRUE, 
                 scale = 0, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray45", 
                 loadings.label.alpha = 0.9, 
                 loadings.label.size = 2.5, 
                 loadings.label.hjust = -0.5, 
                 #frame = TRUE, 
                 #frame.type = "norm", 
                 data = .y,  
                 colour = "Outgroup",  
                 shape = "Outgroup", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2, 
                 alpha = core_alpha) + 
        theme_bw() +  
        # geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2") 
    ) 
  ) %>% 
  pull(pca_graph) 
 

519 

core_outgroup_pc1pc5[[1]] + 
  scale_fill_manual(values = c("black","black", "black",  
                               "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  stat_ellipse(data = filter(sample_pca[["pca_aug"]][[1]], Outgroup != "unassigned"),  
               aes(x = .fittedPC1, y = .fittedPC2, color = Outgroup)) + 
  scale_shape_manual(values=c(2, 15, 18, 43))  
 
 
# Create plot of PC 1 and PC 5 with the 90% conf intervals around the core and outgroups 
core_outgroup_pc1pc5 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, x = 1, y = 5, loadings = TRUE, loadings.label = TRUE, 
                 scale = 0, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray45", 
                 loadings.label.alpha = 0.9, 
                 loadings.label.size = 2.5, 
                 loadings.label.hjust = -0.5, 
                 #frame = TRUE, 
                 #frame.type = "norm", 
                 data = .y,  
                 colour = "Outgroup",  
                 shape = "Outgroup", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2, 
                 alpha = core_alpha) + 
        theme_bw() +  
        # geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 5") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
core_outgroup_pc1pc5[[1]] + 
  scale_fill_manual(values = c("black","black", "black",  
                               "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  stat_ellipse(level = 0.9, data = filter(sample_pca[["pca_aug"]][[1]],  
                                          Outgroup != "unassigned"),  
               aes(x = .fittedPC1, y = .fittedPC5, color = Outgroup)) + 
  scale_shape_manual(values=c(2, 15, 18, 43))  
 
# Create plot of Mo and Sc for elemental separation 
# Prep data 
pca_aug <- sample_pca[["pca_aug"]][[1]] 
 

520 

# Plot of ytterbium and magnesium of core-outgroup separation 
ggplot(pca_aug, aes(x = Yb, y = Mg, color = Outgroup, shape = Outgroup)) +  
  geom_point() +  
  stat_ellipse(level = 0.9, data = filter(sample_pca[["pca_aug"]][[1]], Outgroup != "unassigne
d"),  
               aes(x = Yb, y = Mg, color = Outgroup)) + 
  scale_shape_manual(values=c(2, 15, 18, 43)) + 
  scale_fill_manual(values = c("black","black", "black",  
                                  "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  xlab("Yb (log base 10 ppm)") + 
  ylab("Mg (log base 10 ppm)") + 
  theme_bw() 
 
# Explore Outgroup 1 sherds 
pca_aug %>% 
  select(Sample, Site, Outgroup, Cultural_Group, Vessel_Class, Geography_2) %>% 
  group_by(Outgroup, Site, Vessel_Class) %>% 
  summarize(n = n()) %>% View() 
 
pca_aug %>% 
    select(Sample, Site, Outgroup, Cultural_Group, Vessel_Class) %>% 
    mutate(Outgroup = factor(Outgroup),  
           Site = factor(Site)) %>% 
    group_by(Outgroup, Vessel_Class) %>% 
    summarize(n = n()) %>% View() 
       
pca_aug %>% 
    select(Sample, Site, Outgroup, Cultural_Group, Vessel_Class, Time) %>% 
    mutate(Outgroup = factor(Outgroup),  
           Site = factor(Site)) %>%  
    group_by(Time, Outgroup) %>% 
    summarize(total = n()) %>% View() 
 
 
################################ Core Group Structure ####################################### 
 
# Let's explore here structure within the core group 
# First, isolate the core group samples and their accompanying elemental and PC data 
core_group_data <- sample_pca[["pca_aug"]][[1]] %>% 
                    filter(Outgroup == "Core") 
 
# Let's run some cluster analyses to see if the core group can be sub-divded  
# Prepare a data frame of the elemental data for distance calculations 
core_distready <- core_group_data %>% 
                    select(Si:Th) 
   
# Kmeans of Core # 
# First, it's a good idea to use a few methods to assess the number of clusters to model 
# Elbow Method 
fviz_nbclust(core_distready, kmeans, method = "wss") # 4-6 optimal clusters; 4-5 looks good 
# Silhouette Method 
fviz_nbclust(core_distready, kmeans, method = "silhouette") # 2 optimal clusters 

521 

# Gap Stat 
#fviz_nbclust(core_distready, kmeans, method = "gap_stat") # 1 optimal cluster 
 
# Based on the optimal cluster methods, it looks like we should run kmeans twice, once with  
# 2 clusters and once with 5 clusters 
 
# 2 Cluster K-means 
core_k2 <- kmeans(core_distready,  
                        centers = 2, # number of clusters 
                        nstart = 50, # number of random initial configs  
                                     # out of which best is chosen 
                        iter.max = 500) # number of allowable iterations allowed  
   
# Visualize 2 cluster kmeans  
fviz_cluster(core_k2, data = core_distready) 
 
# Assign to clustering assignments data frame 
core_stat_clusters <- core_group_data %>% 
                              select(Sample) %>% 
                                mutate(Kmeans_2 = core_k2$cluster) 
 
# Let's compare the kmeans to kmedoids 
core_kmed2 <- pam(core_distready, 2) 
fviz_cluster(core_kmed2, data = core_distready) 
 
fviz_cluster(core_kmed2, data = core_distready, geom = text, label = ) 
 
core_group_data %>% 
  filter(Outgroup == "Core") %>% 
  select(-Kmeans_2:-Kmediods_5) %>% 
  left_join(core_stat_clusters, by = "Sample") %>% 
ggplot(aes(x = .fittedPC4, y = .fittedPC2, color = Geography_2, label = Site)) + 
  stat_ellipse(level = 0.9) + 
  geom_text(size = 2.5) 
 
# It appears as though there is broad agreement between the two cluster methods about  
# there being two clusters at approximately the same locations (with primary separation  
# in the first PC).  
# Kmeans seems to offer a more conservative soluation. We'll use that and see how it fairs in  
# mahalanobis distance calculations.  
 
core_pc1to12_samps <- core_group_data %>% 
                        select(Sample, .fittedPC1:.fittedPC12) %>% 
                        left_join(core_stat_clusters, by = "Sample") 
 
core_pc1to12 <- core_pc1to12_samps %>% select(.fittedPC1:.fittedPC12) 
 
 
# Group probabilities for the core kmeans 2 cluster solution on PC's 1 to 12  
# (90% of variability) 
core_kmean2_group_mem <- group.mem.probs(core_pc1to12, core_pc1to12_samps$Kmeans_2,  
                                   unique(core_pc1to12_samps$Kmeans_2))  
 

522 

# Create list of data that is grouped the same as the group probability list 
core_kmean2_samp_list <- split(core_pc1to12_samps[, c("Sample", "Kmeans_2")],  
                           f = core_pc1to12_samps$Kmeans_2) 
 
# Convert the matrices of group membership probabilities to data frames and bind  
# rows into one data frame 
core_kmean2_group_mem <- map(core_kmean2_group_mem, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
core_kmean2_samp_df <- map(core_kmean2_samp_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
core_kmean2_group_mem <- as.data.frame(bind_cols(core_kmean2_group_mem, core_kmean2_samp_df)) 
 
# New column of membership probability for initially assigned group 
core_kmean2_group_mem$assigned_val <- core_kmean2_group_mem[1:2][cbind(seq_len(nrow(core_kmean
2_group_mem)),  
                                                                       core_kmean2_group_mem$K
means_2)] 
 
# Set the initial group assignment value to zero to allow for comparisons 
core_kmean2_group_mem[cbind(seq_len(nrow(core_kmean2_group_mem)), core_kmean2_group_mem$Kmeans
_2)] <- 0 
 
# Assess membership probabilities using an outlier heuristic of less than 1%  
# probability in another group 
core_kmean_iter1 <- core_kmean2_group_mem %>%  
                      mutate(new_assign = ifelse(assigned_val > 2.5 & `1` < 1 & `2` < 1,  
                                                 Kmeans_2, "Core")) %>%  
                      #summarize(perc_unassigned = sum(new_assign == "Core")/n() * 100) 
                      mutate(Kmeans_2_iter2 = new_assign) %>% 
                      select(Sample, Kmeans_2_iter2) 
# Results in a 81.97% remaining in Core and shaving off the difference 
 
# Assign Core, Core1 and Core2 memberships after iteration 1 
core_stat_clusters <- core_stat_clusters %>%   
                        left_join(core_kmean_iter1, by = "Sample") 
 
# Append Kmeans_2 + Core groups to PC data 
core_pc1to12_samps <- core_pc1to12_samps %>%  
                        left_join(core_stat_clusters[,c("Sample", "Kmeans_2_iter2")], 
                                  by = "Sample") 
 
## Iteration 2 of Core group structure 
# Group probabilities for the core kmeans 2 cluster solution on PC's 1 to 12 (90% of variabili
ty) 
core_kmean2_group_mem_iter2 <- group.mem.probs(core_pc1to12, core_pc1to12_samps$Kmeans_2_iter2
, 
                                         unique(core_pc1to12_samps$Kmeans_2_iter2))  
 
# Create list of data that is grouped the same as the group probability list 
core_kmean2_samp_list_iter2 <- split(core_pc1to12_samps[, c("Sample", "Kmeans_2_iter2")],  

523 

                                     f = core_pc1to12_samps$Kmeans_2_iter2) 
 
# Reorder list so it matches the order of the group probs 
core_kmean2_samp_list_iter2 <- list(core_kmean2_samp_list_iter2$Core, core_kmean2_samp_list_it
er2$`2`,  
                                    core_kmean2_samp_list_iter2$`1`) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows  
# into one data frame 
core_kmean2_group_mem_iter2 <- map(core_kmean2_group_mem_iter2, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
core_kmean2_samp_df_iter2 <- map(core_kmean2_samp_list_iter2, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
core_kmean2_group_mem_iter2 <- as.data.frame(bind_cols(core_kmean2_group_mem_iter2,  
                                                       core_kmean2_samp_df_iter2)) 
 
# Change "Core" column name to "3" for data handling 
colnames(core_kmean2_group_mem_iter2) <- c("3", "2", "1", "Sample", "Kmeans_2_iter2") 
 
# Change "Core" assignments to the character "3" to match the new column name 
# and reorder the columns 
core_kmean2_group_mem_iter2 <- core_kmean2_group_mem_iter2 %>% 
                                mutate(Kmeans_2_iter2 = ifelse(Kmeans_2_iter2 == "Core", "3",  
                                                               Kmeans_2_iter2)) %>% 
                                select(`1`, `2`, `3`, Sample, Kmeans_2_iter2) 
 
# New column of membership probability for initially assigned group 
core_kmean2_group_mem_iter2$assigned_val <- core_kmean2_group_mem_iter2[1:3][cbind(seq_len(nro
w(core_kmean2_group_mem_iter2)), as.numeric(core_kmean2_group_mem_iter2$Kmeans_2_iter2))] 
   
# Set the initial group assignment value to zero to allow for comparisons 
core_kmean2_group_mem_iter2[cbind(seq_len(nrow(core_kmean2_group_mem_iter2)),  
                            as.numeric(core_kmean2_group_mem_iter2$Kmeans_2_iter2))] <- 0 
 
# Assess membership probabilities using an outlier heuristic of less than 10% probability  
# in another group 
core_kmean_iter2 <- core_kmean2_group_mem_iter2 %>%  
  mutate(new_assign = ifelse(assigned_val > 2.5 & `1` < 10 & `2` < 10 & `3` < 10,  
                             Kmeans_2_iter2, 3)) %>%  
  #summarize(perc_unassigned = sum(new_assign == Kmeans_2_iter2)/n() * 100) 
  mutate(Kmeans_2_iter3 = new_assign)#%>% 
  #select(Sample, Kmeans_2_iter3) 
# Results in a 90.14% remaining in their iteration 2 assignment 
 
# Explore Core sub-group assignments 
core_kmean_iter2 %>% 
  filter(Kmeans_2_iter3 == 1 | Kmeans_2_iter3 == 2) %>% 
  left_join(pca_aug[, c("Sample", "Site")]) %>% 
  mutate(id = parse_number(Sample)) %>% 
  write_csv("Core A B and C.csv") 

524 

 
# Assign Core, Core1 and Core2 memberships  
core_stat_clusters <- core_stat_clusters %>%   
                        left_join(core_kmean_iter2, by = "Sample") 
 
# Add group designations to the Sample PCA augmented data 
sample_pca[["pca_aug"]][[1]] <- sample_pca[["pca_aug"]][[1]] %>%  
        left_join(core_stat_clusters[, c("Sample", "Kmeans_2_iter3")]) %>% 
        mutate(Kmeans_2_iter3 = ifelse(Kmeans_2_iter3 == 3, "Core A", Kmeans_2_iter3)) %>% 
        mutate(Kmeans_2_iter3 = ifelse(Kmeans_2_iter3 == 1, "Core C", Kmeans_2_iter3)) %>% 
        mutate(Kmeans_2_iter3 = ifelse(Kmeans_2_iter3 == 2, "Core B", Kmeans_2_iter3)) %>%  
        mutate(Core_Outgroup = ifelse(Kmeans_2_iter3 %in% c("Core A", "Core B", "Core C"),  
                                       Kmeans_2_iter3, Outgroup))  
 
pca_aug <- pca_aug %>% 
        #select(-Kmeans_2:-Kmediods_5) %>% 
        left_join(core_stat_clusters[, c("Sample", "Kmeans_2_iter3")]) %>% 
        mutate(Kmeans_2_iter3 = ifelse(Kmeans_2_iter3 == 3, "Core A", Kmeans_2_iter3)) %>% 
        mutate(Kmeans_2_iter3 = ifelse(Kmeans_2_iter3 == 1, "Core C", Kmeans_2_iter3)) %>% 
        mutate(Kmeans_2_iter3 = ifelse(Kmeans_2_iter3 == 2, "Core B", Kmeans_2_iter3)) %>%  
        mutate(Core_Outgroup = ifelse(Kmeans_2_iter3 %in% c("Core A", "Core B", "Core C"),  
                                       Kmeans_2_iter3, Outgroup))  
 
pca_aug <- pca_aug %>% 
            mutate(Core_ABC = Kmeans_2_iter3) %>% 
            mutate(Kmeans_2_iter3 = NULL) 
 
# Plot Core A, B, C 
pca_aug %>% 
  filter(!is.na(Core_ABC)) %>% 
  ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Core_ABC, shape = Core_ABC)) +  
  geom_point() +  
  stat_ellipse(level = 0.9) + 
  scale_shape_manual(values=c(2, 15, 18)) + 
  scale_fill_manual(values = c("black","black", "black",  
                               "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  xlab("Principal Component 1") + 
  ylab("Principal Component 2") + 
  theme_bw() 
             
# Out of the original 416 Core sherds, we've now identified three sub-groups - Core A, B, & C 
# Core B and C are quite small, but that they could be removed from the main Core group 
# is instructive of variation within the core group.  
# Next, we'll set about searching for structure within the Core A Sub-Group 
 
###### Core A Sub-Group Structure ####### 
 
# Append Kmeans_2 + Core groups to PC data 
core_pc1to12_samps <- core_pc1to12_samps %>%  
                        left_join(pca_aug[,c("Sample", "Core_ABC", "Site")], by = "Sample") 
 
# Extract the Core A Sherds 

525 

core_A <- core_pc1to12_samps %>% 
            filter(Core_ABC == "Core A") 
 
# First 12 PCs of Core A sherds 
core_A_pc1to12 <- core_A %>% select(.fittedPC1:.fittedPC12) 
 
# No obvious structure by vessel class or by geography or by site 
core_A %>% 
  left_join(pca_aug[, c(2, 6, 9)], by = "Sample") %>% 
  ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Geography_2, shape = Geography_2)) + 
  #ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Vessel_Class, shape = Vessel_Class)) + 
  #ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Site))  
  geom_point() + 
  stat_ellipse(level = .9) 
 
# Explore Core sherds 
pca_aug %>% 
  select(Sample, Site, Outgroup, Cultural_Group, Vessel_Class,  
         Geography_2, Core_Outgroup, Core_ABC) %>% 
  group_by(Core_Outgroup, Site) %>% 
  summarize(n = n()) %>% View() 
 
# Elbow Method 
fviz_nbclust(core_A_pc1to12, kmeans, method = "wss") # 4 - 6 optimal clusters; 4 looks good 
# Silhouette Method 
fviz_nbclust(core_A_pc1to12, kmeans, method = "silhouette") # 2 optimal clusters 
 
# Ward linkage hierarchical agglomerative clustering 
plot(as.dendrogram(hclust(dist(core_A_pc1to12), method = "ward.D")), 
                   cex.axis = 0.75, cex.lab = 0.75, nodePar = list(lab.cex = 0.5, pch = NA)) 
# Two or three primary clusters seems optimal here 
 
# 2 Cluster K-means for Core A 
coreAkmean2 <- kmeans(core_A_pc1to12,  
               centers = 2, # number of clusters 
               nstart = 50, # number of random initial configurations  
                            # out of which the best one is chosen 
               iter.max = 500) # number of allowable iterations allowed  
 
# Visualize 2 cluster kmeans  
fviz_cluster(coreAkmean2, data = core_A_pc1to12) 
 
# Visualize a two cluster kmedoids soluation 
fviz_cluster(pam(core_A_pc1to12, 2), data = core_A_pc1to12) 
 
## From all of this cluster analysis, it seems to me that the kmedoids 2 cluster solution  
#  captures separation in the data that can be best refined via Mahalanobis distance 
coreA_pam2 <- pam(core_A_pc1to12, 2) 
 
# Record kmeans Core A clustering assignments 
core_A  <- core_A %>% 
            mutate(Kmedoids_2 = coreA_pam2$cluster) 
 

526 

# Group probabilities for the core kmeans 2 cluster solution on PC's 1 to 12  
# (90% of variability) 
core_A_kmed2_group_prob <- group.mem.probs(core_A_pc1to12, core_A$Kmedoids_2, 
                                               unique(core_A$Kmedoids_2))  
 
# Create list of data that is grouped the same as the group probability list 
core_A_kmed2_list <- split(core_A[, c("Sample", "Kmedoids_2")],  
                                     f = core_A$Kmedoids_2) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows  
# into one data frame 
core_A_kmed2_group_prob <- map(core_A_kmed2_group_prob, as.data.frame) %>% bind_rows() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
core_A_kmed2_df <- map(core_A_kmed2_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
core_A_kmed2_group_prob <- as.data.frame(bind_cols(core_A_kmed2_group_prob,  
                                                   core_A_kmed2_df)) 
 
# New column of membership probability for initially assigned group 
core_A_kmed2_group_prob$assigned_val <- core_A_kmed2_group_prob[1:2][cbind(seq_len(nrow(core_A
_kmed2_group_prob)), as.numeric(core_A_kmed2_group_prob$Kmedoids_2))] 
 
# Set the initial group assignment value to zero to allow for comparisons 
core_A_kmed2_group_prob[cbind(seq_len(nrow(core_A_kmed2_group_prob)),  
                                  as.numeric(core_A_kmed2_group_prob$Kmedoids_2))] <- 0 
 
# Assess membership probabilities using an outlier heuristic of less than 10% probability 
# in another group 
core_A_kmed2_group_prob_iter1 <- core_A_kmed2_group_prob %>%  
      mutate(new_assign = ifelse(assigned_val > 10 & `1` < 10 & `2` < 10,  
                                 Kmedoids_2, "Core A")) %>%  
      #summarize(perc_unassigned = sum(new_assign == Kmedoids_2)/n() * 100) 
      mutate(Kmedoids_iter1 = new_assign) %>% 
      select(Sample, Kmedoids_iter1) 
    # Results in a 57.85% remaining in their Kmedoids assignment - suggests a good 
    # cluster solution 
 
### End Iteration 1 of Core A group structure membership probabilities 
 
# Append retained Kmed_2 sherds to PC data 
core_A <- core_A %>%  
            left_join(core_A_kmed2_group_prob_iter1, by = "Sample") 
 
# PC data for Core A group membership probabilities iteration 2 
core_A_iter1pc1to12 <- core_A %>% 
                        filter(Kmedoids_iter1 != "Core A") %>% 
                        select(.fittedPC1:.fittedPC12) 
 
# Group Membership data for kmeds iteration 2 Core A 
core_A_iter2 <- core_A %>% filter(Kmedoids_iter1 != "Core A") 

527 

 
 
# Group probabilities for the core kmeans 2 cluster solution on PC's 1 to 12 (90% of 
# variability) 
core_A_kmed2_group_prob_iter2 <- group.mem.probs(core_A_iter1pc1to12, core_A_iter2$Kmedoids_it
er1, 
                                           unique(core_A_iter2$Kmedoids_iter1))  
 
# Create list of data that is grouped the same as the group probability list 
core_A_kmed2_iter_list <- split(core_A_iter2[, c("Sample", "Kmedoids_iter1")],  
                           f = core_A_iter2$Kmedoids_2) 
 
# Convert the matrices of group membership probabilities to data frames and bind rows into 
# one data frame 
core_A_kmed2_group_prob_iter2 <- map(core_A_kmed2_group_prob_iter2, as.data.frame) %>% bind_ro
ws() 
 
# Convert the list of matrices of sample names to data frames and bind into one data frame 
core_A_kmed2_group_prob <- map(core_A_kmed2_iter_list, as.data.frame) %>% bind_rows() 
 
# Bind to initial sample id and group assignment  
# and convert to data frame for easier handling 
core_A_kmed2_group_prob_iter2 <- as.data.frame(bind_cols(core_A_kmed2_group_prob_iter2,  
                                                         core_A_kmed2_group_prob)) 
 
# New column of membership probability for initially assigned group 
core_A_kmed2_group_prob_iter2$assigned_val <- core_A_kmed2_group_prob_iter2[1:2][cbind(seq_len
(nrow(core_A_kmed2_group_prob_iter2)), as.numeric(core_A_kmed2_group_prob_iter2$Kmedoids_iter1
))] 
 
# Set the initial group assignment value to zero to allow for comparisons 
core_A_kmed2_group_prob_iter2[cbind(seq_len(nrow(core_A_kmed2_group_prob_iter2)),  
                              as.numeric(core_A_kmed2_group_prob_iter2$Kmedoids_iter1))] <- 0 
 
# Assess membership probabilities using a tighter heuristic of less than 2.5% probability  
# in another group and greater than 3% probability in-group 
core_A_kmed2_group_prob_iter2 <- core_A_kmed2_group_prob_iter2 %>%  
  mutate(new_assign = ifelse(assigned_val > 3 & `1` < 2.5 & `2` < 2.5,  
                             Kmedoids_iter1, "Core A")) %>%  
  #summarize(perc_assigned = sum(new_assign == Kmedoids_iter1)/n() * 100) 
  mutate(Kmedoids_iter2 = new_assign) #%>% 
  #select(Sample, Kmedoids_iter2) 
# Results in a 100% remaining in their Kmedoids iter1 assignment - suggests a great  
# cluster solution 
 
# Prep data for export 
core_A_kmed2_group_prob_iter2_table <- core_A_kmed2_group_prob_iter2 %>% 
                                        left_join(pca_aug[, c("Sample", "Site")]) %>% 
                                        mutate(id = parse_number(Sample))  
 
# Export csv of Core A1 and A2 Groups 
write_csv(core_A_kmed2_group_prob_iter2_table, "Core A groups.csv") 
 

528 

# Make table of Core A1/A2 sherd assignments 
core_A_kmed2_group_prob_iter2_table <- core_A_kmed2_group_prob_iter2_table %>% 
                                        mutate(Core_A_Sub = paste0("Core A", Kmedoids_iter1)) 
 
# Bind the Core A1/A2 table to Core A PC data 
core_A_subs <- core_A %>% 
                left_join(core_A_kmed2_group_prob_iter2_table[, c("Sample", "Core_A_Sub")],  
                          by = "Sample") %>% 
                mutate(Core_A_Sub = ifelse(is.na(Core_A_Sub), "Core A", Core_A_Sub)) %>%  
                select(-Kmeans_2:-Kmeans_2_iter2, -Kmedoids_2)  
 
# Plot of PC1 - PC2 of the Core A, A1, and A2 group assignments 
core_A_subs %>% 
  filter(Core_A_Sub == "Core A1" | Core_A_Sub == "Core A2") %>% 
  ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Core_A_Sub, shape = Core_A_Sub)) +  
  geom_point() +  
  stat_ellipse(level = 0.9) + 
  scale_shape_manual(values=c(43, 15, 18)) + 
  scale_fill_manual(values = c("black","black", "black",  
                               "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black",  
                                "black", "black", "black")) + 
  xlab("Principal Component 1") + 
  ylab("Principal Component 2") + 
  geom_point(data = filter(core_A_subs[, c(".fittedPC1", ".fittedPC2", "Core_A_Sub")],  
                           Core_A_Sub == "Core A"),  
             aes(x = .fittedPC1, y = .fittedPC2, alpha = 0.2)) + 
  theme_bw() 
 
# Add Core A sub-groups to pca data 
sample_pca$data[[1]] <- sample_pca$data[[1]] %>% 
                          left_join(core_A_subs[, c("Sample", "Core_A_Sub")]) 
 
# Plot Core A and Core A sub-groups using autoplot 
core_A_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, x = 1, y = 2, loadings = TRUE, loadings.label = TRUE, 
                 scale = 0, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray45", 
                 loadings.label.alpha = 0.9, 
                 loadings.label.size = 2.5, 
                 loadings.label.hjust = -0.5, 
                 #frame = TRUE, 
                 #frame.type = "norm", 
                 data = .y,  
                 colour = "Core_A_Sub",  
                 shape = "Core_A_Sub", 
                 frame.level = .9,  

529 

                 frame.alpha = 0.001,  
                 size = 2, 
                 alpha = .00001) + 
        theme_bw() +  
        # geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
core_A_pc1pc2[[1]] + 
  scale_fill_manual(values = c("black","black", "black",  
                               "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black", "black", "black", "black")) + 
  stat_ellipse(data = filter(sample_pca[["pca_aug"]][[1]],  
                             !is.na(Core_A_Sub) | Core_A_Sub != "Core A"),  
               aes(x = .fittedPC1, y = .fittedPC2, color = Core_A_Sub)) + 
  scale_shape_manual(values=c(2, 15, 18, 43))  
 
# Add Core A sub-group data to the augmented PCA data for Shiny app biplotting  
# (using the above shiny app) 
sample_pca[["pca_aug"]][[1]] <- sample_pca[["pca_aug"]][[1]] %>% 
  left_join(core_A_subs[, c("Sample", "Core_A_Sub")],  
            by = "Sample") 
 
# Do the same to the non-list pca aug data object  
pca_aug <- pca_aug %>% 
  left_join(core_A_subs[, c("Sample", "Core_A_Sub")], by = "Sample") %>% 
  mutate(Final_Assign = Core_A_Sub) %>% 
  mutate(Final_Assign = ifelse(is.na(Core_A_Sub), Core_Outgroup, Core_A_Sub))  
 
table(pca_aug$Final_Assign) 
 
# Plot of Mg - Ni of the Core A, A1 and A2 group assignments 
pca_aug %>% 
  filter(Core_A_Sub == "Core A1" | Core_A_Sub == "Core A2") %>% 
  ggplot(aes(x = Mg, y = Ni, color = Core_A_Sub, shape = Core_A_Sub)) +  
  geom_point() +  
  stat_ellipse(level = 0.9) + 
  scale_shape_manual(values=c(43, 15, 18)) + 
  scale_fill_manual(values = c("black","black", "black",  
                               "black", "black", "black")) +  
  scale_color_manual(values = c("black","black","black",  
                                "black", "black", "black")) + 
  xlab("Magnesium (log base 10 ppm)") + 
  ylab("Nickel (log base 10 ppm)") + 
  geom_point(data = filter(pca_aug[, c("Mg", "Ni", "Mo", "Core_A_Sub")],  
                           Core_A_Sub == "Core A"),  
             aes(x = Mg, y = Ni, alpha = 0.2)) + 
  theme_bw() 
   
 

530 

# Plot all assignments along PC1 and PC2 
pca_aug %>% 
  filter(Final_Assign != "unassigned") %>% 
  ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Final_Assign)) +  
  geom_point() +  
  stat_ellipse(level = 0.9) + 
  xlab("Principal Component 1") + 
  ylab("Principal Component 2") +  
  geom_point(data = filter(pca_aug, Final_Assign == "unassigned"),  
             aes(x = .fittedPC1, y = .fittedPC2, color = Final_Assign, alpha = 0.4)) + 
  theme_bw() + 
  scale_color_d3() 
 
# Plot all assignments along Mg and Mo 
pca_aug %>% 
  filter(Final_Assign != "unassigned") %>% 
  ggplot(aes(x = Mg, y = Mo, color = Final_Assign)) +  
  geom_point() +  
  stat_ellipse(level = 0.9) + 
  xlab("Mg (log base 10 ppm)") + 
  ylab("Mo (log base 10 ppm)") +  
  geom_point(data = filter(pca_aug, Final_Assign == "unassigned"),  
             aes(x = Mg, y = Mo, color = Final_Assign, alpha = 0.4)) + 
  theme_bw() + 
  scale_color_d3() 
 
# Append Final Assignments to PCA data 
sample_pca$data[[1]] <- sample_pca$data[[1]] %>% 
                          left_join(pca_aug[, c("Sample", "Final_Assign")]) 
 
# Plot Core A and Core A sub-groups using autoplot 
final_assign_pc1pc2 <- sample_pca %>% 
  mutate( 
    pca_graph = map2( 
      .x = pca, 
      .y = data, 
      ~ autoplot(.x, x = 1, y = 2, loadings = TRUE, loadings.label = TRUE, 
                 scale = 0, 
                 loadings.label.repel = TRUE, 
                 loadings.label.colour = "black", 
                 loadings.colour = "gray25", 
                 loadings.label.alpha = 0.9, 
                 loadings.label.size = 3.5, 
                 #loadings.label.hjust = -0.5, 
                 frame = TRUE, 
                 frame.type = "norm", 
                 data = .y,  
                 colour = "Final_Assign",  
                 #shape = "Final_Assign", 
                 frame.level = .9,  
                 frame.alpha = 0.001,  
                 size = 2,  
                 alpha = .3) + 

531 

        theme_bw() +  
        # geom_text(label = .y$Sample) + 
        labs(x = "Principal Component 1", 
             y = "Principal Component 2") 
    ) 
  ) %>% 
  pull(pca_graph) 
 
final_assign_pc1pc2[[1]] + 
  theme_bw() + 
  scale_color_d3() 
 
 
# Averages and standard deviations of each of the identified compositional groups 
pca_aug %>% 
  select(Final_Assign, Si:Th) %>% 
  gather(Element, Si:Th, -Final_Assign) %>% 
  mutate(`Si:Th` = 10^`Si:Th`) %>% # convert from log 10 
  group_by(Final_Assign, Element) %>% 
  summarize(mean = mean(`Si:Th`, na.rm = TRUE), std = sd(`Si:Th`, na.rm = TRUE)) %>% 
  write_csv("Ceramic final group assignment element ave and std.csv") 
 
 
# Pickup here with a PCA graph of Core A1 and A2 sherds as well as a table of membership  
# probs for both of these groups 
 
# Next step is to start a new script that looks at constructing networks based on BR  
# coefs of similarities in site=based representation in the different groups  
# (Outgroup 1, Outgroup 2, Core A, Core A1, Core A1, Core B and Core C) 
 
# Table of all group assignments by site 
group_assign_by_site <- pca_aug %>% 
                          select(Sample, Site, Final_Assign) %>% 
                          group_by(Final_Assign, Site) %>% 
                          summarize(count = n()) %>% 
                          spread(Final_Assign, count) 
 
# Table of all group assignments by site AND geography 
group_assign_by_site_geo <- pca_aug %>% 
                              select(Sample, Site, Final_Assign, Geography_2, Time) %>% 
                              group_by(Final_Assign, Site, Geography_2, Time) %>% 
                              summarize(count = n()) %>% 
                              spread(Final_Assign, count) 
 
group_assign_by_geo_class <- pca_aug %>% 
                    select(Sample, Final_Assign, Geography_2, Vessel_Class) %>% 
                    group_by(Final_Assign, Geography_2, Vessel_Class) %>% 
                    summarize(count = n()) %>% 
                    spread(Final_Assign, count) 
 
# Confirm assignments 
colSums(group_assign_by_site[, -1], na.rm = TRUE) 
table(pca_aug$Final_Assign)   

532 

 
# Regression of the number of compositional groups as a function of sample size 
# Also included are lines to look at potential differences in the average number of  
# compositional groups by geography of site or time period of occupation 
group_assign_by_site %>% 
  select(1, 3:8) %>% 
  mutate(group_count = rowSums(!is.na(.))) %>% 
  mutate(group_count = group_count - 1) %>% # need to subtract the Site col 
  #left_join(group_assign_by_site_geo[c(1:3)]) %>% 
  #group_by(Geography_2, Time) %>% 
  #summarize(avg_grou = mean(group_count)) # check average group count 
  mutate(sample_size = rowSums(.[2:7], na.rm = TRUE)) %>% 
  #ggplot(aes(x = sample_size, y = group_count)) + 
  #geom_point() + 
  #geom_smooth(method = "lm") 
  lm(group_count ~ sample_size, data = .) %>% 
  glance()  
 
 
# Write out csv file of group assignments 
# write_csv(group_assign_by_site, "group assignments by site.csv") 
# write_csv(group_assign_by_site_geo, "group assignments by site-geo.csv")  
# write_csv(group_assign_by_geo_class, "group assignments by geo-vessel class.csv") 
 
pca_aug %>% 
  filter(Final_Assign == "Core A2") %>% View() 
 
# Component loadings for first 12 principal components 
pc_loadings <- sample_pca$pca[[1]]$rotation %>% 
                as.data.frame() %>% 
                rownames_to_column(var = "element") %>% 
                select(element:PC12) 
 
# write_csv(pc_loadings, "pc1 - 12 loadings.csv") 

Creation of Economic Networks from Compositional Membership Data 
 
## Turning membership in LA-ICP-MS compositional groups into networks of economic  
#  relationships 
 
#'  The basic idea here is that, leveraging the criterion of abundance (Bishop et al., 1982), 
#'  as similarities in membership in different compositional groups increases between 
#'  archaeological communities, so does the likelihood that individuals from those  
#'  communities are engaging in direct economic interactions. As used here, economic 
#'  interactions are built around the concept of weak ties (Granovetter 1973). In contrast  
#'  to ties that are built on deep affinity such as close friendships, family or marriage 
#'  relationships, weak ties might be acquaintances or a stranger  with a common cultural 
#'  background. Weak ties emanating from economic relationships related to 
#'  ceramic industry are constructed through such behaviors as exchange relationships, 
#'  overlapping resource exploitation areas, or similar production regimes.   
#'   
#'  Using the Brainerd Robinson coefficient of similarity, it is possible to create networks 
#'  of economic relationships through community-based membership in compositional groups.  

533 

#'  That is,beginning with raw elemental data produced from LA-ICP-MS of 543 ceramic  
#'  artifacts, several compositional groups were identified in the Late Prehistoric central 
#'  Illinois River valley.  
#'  The Brainerd Robinson coefficient of similarity assesses how similar any two given sites  
#'  are based on similarities in the number of individual sherd assignments in different  
#'  compositional groups. This method provides means to model relational economic interactions 
#'  in an archaeological region.  
 
# Statistically robust compositional groups were identified in `Ceramic Analysis.R`.  
# Beginning with hose counts, we'll clean the data and apply the Brainerd Robinson  
# coefficient of similarity.  
# Networks are then constructed and analyzed to reveal changing patterns of economic 
# relationships in Illinois' archaeological heritage.  
 
# First, we'll load in some package libraries 
library(tidyverse) 
library(igraph) 
library(corrplot) 
library(reshape2) 
 
# Then read in compositional group count data by site 
comp_group <- read_csv("group assignments by site.csv") 
 
# Two of the eight compositional groups are based on equivocal membership probabilities 
# While a core group was extracted and refined, we need to drop the sherds that were  
# unable to be assigned to a core sub-group as well as those that were not able to be 
# assigned to any other group.  
comp_group_refined <- comp_group %>% 
                        select(-`Core A`, -unassigned) 
 
# Sum up all of the retained sherds for compositional group construction 
comp_group_refined %>% 
  gather(key = Site, value = `Core A1`:`Outgroup 2`) %>% 
  rename(count = "\`Core A1\`:\`Outgroup 2\`") %>% 
  summarize(total_count = sum(count, na.rm = TRUE)) 
# Total is 314 out of the original 543, or 63% of the original data set 
 
# Look at total number of sherds from each site 
comp_group_refined %>% 
  gather(key = group, value = `Core A`:`Outgroup 2`, -Site) %>% 
  rename(count = "\`Core A\`:\`Outgroup 2\`") %>% 
  group_by(Site) %>% 
  summarize(total = sum(count, na.rm = TRUE)) 
# Perhaps the most problematic site here is Star Bridge, which had a massive drop from  
# ~30 or so sherds analyzed but only 9 placed within compositional groups.  
# Nevertheless, all 18 sites are represented by at least 8 sherds - not too bad.  
 
# The Brainerd-Robinson coefficient is a similarity metric that is unique to archaeology, 
# and is used to compare assemblages based on proportions of categorical data such as 
# vessel or point types.  
 
# The Brainerd-Robinson coefficient has been coded in R by Matt Peeples  
# (http://www.mattpeeples.net/BR.html) and by Gianmarco Alberti  

534 

# (http://cainarchaeology.weebly.com/r-function-for-brainerd-robinson-similarity-coefficient.h
tml).  
# Here, I follow Matt Peeple's BRsim implementation because it is substantially less resource 
# intensive. However, I include a rescaling feature to rescale the BR coefficients 
# from 0 - 200 to 0 - 1, which makes the output amenable for the construction 
# of network graphs.  
 
# The input for the function is a dataframe with assemblages to be compared are found in  
# the rows and the categorical variables (such as pottery/lithic types, objects,  
# compositional groups, etc.) comprise the columns. Each variable is the numerical  
# amount of a particular categorical variable found at each site/sample/discrete  
# observation unit.  
 
# Here is the BRsim function as coded by Gianmarco 
BRsim <- function(x, correction, rescale) { 
  if(require(corrplot)){ 
    print("corrplot package already installed. Good!") 
  } else { 
    print("trying to install corrplot package...") 
    install.packages("corrplot", dependencies=TRUE) 
    suppressPackageStartupMessages(require(corrplot)) 
  } 
  rd <- dim(x)[1] 
  results <- matrix(0, rd, rd) 
  if (correction == T){ 
    for (s1 in 1:rd) { 
      for (s2 in 1:rd) { 
        zero.categ.a <-length(which(x[s1,] == 0)) 
        zero.categ.b <-length(which(x[s2,] == 0)) 
        joint.absence <-sum(colSums(rbind(x[s1,], x[s2,])) == 0) 
        if(zero.categ.a == zero.categ.b) { 
          divisor.final <- 1 
        } else { 
          divisor.final <- max(zero.categ.a, zero.categ.b) - joint.absence+0.5 
        } 
        results[s1,s2] <- round((1 - (sum(abs(x[s1,] / sum(x[s1,]) - x[s2,] / sum(x[s2,]))))/2
)/divisor.final, 
                                digits=3) 
      } 
    }  
  } else {   
    for (s1 in 1:rd) { 
      for (s2 in 1:rd) { 
        results[s1,s2] <- round(1 - (sum(abs(x[s1,] / sum(x[s1,]) - x[s2, ] / sum(x[s2,]))))/2
, digits=3) 
      } 
    } 
  } 
  rownames(results) <- rownames(x) 
  colnames(results) <- rownames(x) 
  col1 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "white", "cyan", "#007FFF"
, "blue", "#00007F")) 
  if (rescale == F) { 

535 

    upper <- 200 
    results <- results * 200 
  } else {  
    upper <- 1.0 
  } 
  corrplot(results, method="square", addCoef.col="red", is.corr=FALSE, cl.lim = c(0, upper), c
ol = col1(100), tl.col="black", tl.cex=0.8)  
  return(results) 
} 
 
# Here is a more simplified version from Matt Peeples  
# Function for calculating Brainerd-Robinson (BR) coefficients 
# *Note there is data pre-processing for Matt's script not included here 
BR <- function(x) { 
  rd <- dim(x)[1] 
  results <- matrix(0,rd,rd) 
  for (s1 in 1:rd) { 
    for (s2 in 1:rd) { 
      x1Temp <- as.numeric(x[s1, ]) 
      x2Temp <- as.numeric(x[s2, ]) 
      br.temp <- 0 
      results[s1,s2] <- 200 - (sum(abs(x1Temp - x2Temp)))}} 
  row.names(results) <- row.names(x) 
  colnames(results) <- row.names(x) 
  return(results)} 
 
# My editing of the two 
BR_au <- function(x, rescale = FALSE, counts = TRUE) { 
  if (counts == T){ 
    x <- prop.table(as.matrix(x), 1) * 100 
  } else { 
  } 
  rd <- dim(x)[1] 
  results <- matrix(0,rd,rd) 
  for (s1 in 1:rd) { 
    for (s2 in 1:rd) { 
      x1Temp <- as.numeric(x[s1, ]) 
      x2Temp <- as.numeric(x[s2, ]) 
      br.temp <- 0 
      results[s1,s2] <- 200 - (sum(abs(x1Temp - x2Temp))) 
    } 
  }   
  row.names(results) <- row.names(x) 
  colnames(results) <- row.names(x) 
  if (rescale == F) { 
    return(results) 
  } else {  
    results <- results / 200 
    return(results) 
  } 
} 
 
# Before we run the BR functions, the data frame needs to have the Sites become a row name 

536 

# because the BR functions all take as inputs counts or percentages only.  
rownames(comp_group_refined) <- comp_group_refined$Site  
comp_group_refined <- comp_group_refined[, -1] 
 
# Also need to change NAs into 0 (two methods provided below) 
comp_group_refined <- comp_group_refined %>% 
                        mutate_all(funs(replace(., is.na(.), 0))) 
 
#    comp_group_refined %>% 
#      mutate_all(funs(coalesce(., 0L))) 
 
# Lost the rownames during manipulation, need to add them again 
rownames(comp_group_refined) <- comp_group$Site 
 
# A big advantage of Gianmarco's BR function is a succinct correlation plot. It can be  
# thought of as a "heat-map" for BR similarities.  
BRsim(comp_group_refined, correction = FALSE, rescale = TRUE) 
 
eco_BR <- BR_au(comp_group_refined, rescale = TRUE) 
 
# The results of the BRsim function come in the form of an adjacency matrix. igraph  
# can easily handle this kind of data to create a network graph. Because the adjacency 
# matrix is between 0 and 1, we need to tell igraph that the resulting network graph is 
# weighted. Otherwise an edge will only be given for the relationship between each site  
# and itself.  
ecoBRgraph <- graph_from_adjacency_matrix(eco_BR, weighted = T) 
BRel <- as_edgelist(ecoBRgraph) # convert to 2 column edgelist 
BRw <- as.data.frame(E(ecoBRgraph)$weight) # extract edge weights 
BRwel <- cbind(BRel, BRw) # append edge weights to edgelist 
BRwel <- rename(BRwel, weight = `E(ecoBRgraph)$weight`) # rename weight column 
 
# Assessing the distribution of the BR coefficients 
BRwel %>% 
  filter(`1` != `2`) %>% # drop recursive edges 
  ggplot(aes(x = weight)) +  
  geom_histogram(aes(y = ..density..), bins = 25, colour = "black", fill = "white") + 
  geom_density(alpha = 0.2) + 
  geom_vline(aes(xintercept = mean(weight, na.rm = T)),   # Ignore NA values for mean 
             color = "red", linetype = "dashed", size = 1) + 
  xlab("Rescaled BR Coefficients") + 
  ylab("Density") + 
  theme_minimal()  
 
# Mean of BR coefficients (this will be used as a cutoff point for giving edges) 
BRwel %>% 
  filter(`1` != `2`) %>% 
  filter(weight != 1) %>% 
  filter(weight != 0) %>% 
  summarise(Mean = mean(weight))  
# Looks like the mean is 0.556. This can be round down to 0.55 for edge cutoffs 
 
 
# But before we apply that cutoff, let's explore the range and frequency of BR 

537 

# scores if they were produced purely by chance based on our data set 
 
# First, we will row and column randomize the BR input 10,000 times and create a list  
# of the results 
# This means that we'll shuffle the order of row and column data with replacement 
BReco_rand_list <- replicate(10000, comp_group_refined[sample(1:nrow(comp_group_refined), 
                                                              replace = T), 
                                            sample(1:ncol(comp_group_refined),  
                                                   replace = T)], simplify = F) 
 
# Setup an empty list to hold the BR coefficients for the randomized data 
BReco_rand_result <- list() 
 
# Number of simulations 
nsim <- 10000 
 
# Now we can iterate the BR algorithm over the randomized lists 
for (i in 1:nsim) { 
  BReco_rand_result[[i]] <- BR_au(BReco_rand_list[[i]], rescale = T) 
} 
 
# Turn adjacency matrices into three column data frames 
for (i in 1:nsim) { 
  BReco_rand_result[[i]] <- setNames(melt(BReco_rand_result[[i]]), c('1', '2', 'values')) 
} 
 
# Now we can extract the BR values from the data frames in the list 
BReco_rand_result_vals <- lapply(BReco_rand_result, '[[', 3) 
 
# And collapse that list into one long vector and turn into a tibble data frame 
BReco_rand_vals <- tbl_df(unlist(BReco_rand_result_vals)) 
 
# Add a column to indicate these are simulated data 
BReco_rand_vals <- BReco_rand_vals %>% 
  mutate(Type = "Randomized BR") 
 
# Append the actual data 
BRwel <- tbl_df(BRwel) 
BReco_vals_all <- BRwel %>% 
  select(weight) %>% 
  mutate(value = weight) %>% 
  select(value) %>% 
  mutate(Type = "Actual BR") %>% 
  bind_rows(., BReco_rand_vals) 
 
# Drop 0's and 1's since no sites are perfectly dissimilar or similar 
BReco_vals_all <- BR_vals_all %>% 
  filter(value != 1) %>% 
  filter(value != 0) 
 
# Plot density histograms of the observed and simulated BR coefficients 
ggplot(BReco_vals_all, aes(x = value)) +  
  geom_histogram(data = subset(BReco_vals_all, Type == "Randomized BR"), aes(y=..density..), 

538 

                 alpha = 0.5, bins = 30, colour = "black", fill = "#2ca02c") + 
  geom_density(data = subset(BReco_vals_all, Type == "Randomized BR"),  
               alpha = 0.1, color = "#2ca02c" , fill = "#2ca02c" , adjust = 2.5) +  
  geom_vline(data = subset(BReco_vals_all, Type == "Randomized BR"), 
             aes(xintercept = mean(value, na.rm = T)),   # Ignore NA values for mean 
             color = "#2ca02c" , linetype = "dashed", size = 1) + 
  geom_histogram(data = subset(BReco_vals_all, Type == "Actual BR"), 
                 aes(y = ..density..), bins = 30, colour = "black",  
                 fill = "#1f77b4" , alpha = 0.4) + 
  geom_density(data = subset(BReco_vals_all, Type == "Actual BR"), 
               alpha = 0.1, color = "#1f77b4" , fill = "#1f77b4" ) + 
  geom_vline(data = subset(BReco_vals_all, Type == "Actual BR"), 
             aes(xintercept = mean(value, na.rm = T)), color = "#1f77b4" ,  
             linetype = "dashed", size = 1) + 
  xlab("Rescaled BR Coefficients") + 
  ylab("Density") + 
  theme_minimal()  
 
# "#1f77b4" = d3 blue 
# "#2ca02c" = d3 green 
 
# Looks like the simulated and observed data actually share similar distributions.  
# Nevertheless, there are significant nuances seen in the observed data, suggesting  
# deviations from random chance and a slightly lower than expected mean BR 
# coefficient. This could reflect the small number of compositional groups (6),  
# limited number of samples from a few sites (some have 8 or 9 samples), or  
# simply a reflection of the limited geological diversity present in the CIRV.  
# However, applying the the > 0.55 cutoff indicates that edges will be  
# given in situations where the proportional similarity between two assemblages is  
# greater than the average proportional similarity across economic relationships in  
# the Late Prehistoric CIRV. 
 
# Let's apply the 0.55 threshold 
BRel_t <- BRwel %>%  
  filter(weight > 0.55 & `1` != `2`) 
 
# Change column names to be suitable for Gephi 
colnames(BRel_t) <- c("Source", "Target", "weight") 
 
# Add columns with additional node information 
# Read in tables of site names, geographic coords., and time distinction 
# For time, 1 is a primary occupation prior to Oneota in-migration 
# and 2 is a primary occupation succeeding Oneota in-migration 
node_table <- read_csv("Jar_node_table.csv") 
colnames(node_table) <- c("Source", "Label", "Long", "Lat", "Time") 
 
# Join the node table columns to the edgelist by the Source node 
econet_t1 <- left_join(BRel_t, node_table[-2], by = "Source") 
 
# Prepare node tables to join time designation for the target node 
colnames(node_table) <- c("Target", "Label", "Long", "Lat", "Time2") 
 
# Join Time 2 column to Target node  

539 

econet_edgelist_complete <- left_join(econet_t1, node_table[c(-2:-4)], by = "Target") 
 
# Create Pre- and Post-Migration Edgelists 
econet_pre_el_need_dist <-  econet_edgelist_complete %>% 
                              filter(Time == Time2) %>% 
                              filter(Time == 1) 
 
econet_post_el_need_Law <- econet_edgelist_complete %>% 
                              filter(Time == Time2) %>% 
                              filter(Time == 2) 
 
# Two sites have extended or multi-component occupations in both time periods 
# So we need to include their connections in both time periods 
Law_econet_post <- econet_edgelist_complete %>% 
                      filter(Time == 2 & Target == "Lawrenz Gun Club" |  
                               Source == "Lawrenz Gun Club" & Time2 == 2) %>% 
                      mutate(Time = replace(Time, Time == 1, 2)) %>% 
                      mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
Buck_econet_post <- econet_edgelist_complete %>% 
                      filter(Time == 2 & Target == "Buckeye Bend" |  
                               Source == "Buckeye Bend" & Time2 == 2) %>% 
                      mutate(Time = replace(Time, Time == 1, 2)) %>% 
                      mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
# Bind the LCG & Buckeye post-migration edges to the post-migration edgelists 
econet_post_el_need_dist <- rbind(econet_post_el_need_Law, Law_econet_post, Buck_econet_post) 
 
# Adding geographic coordinates 
# Read in matrix of site distances 
site_distances <- read_csv("Site Distances Matrix in km.csv") 
 
#first column of site names to rownames  
site_distances <- column_to_rownames(site_distances, var = "X1") 
 
# Convert geographic distance matrix to graph object 
distance_g <- graph_from_adjacency_matrix(as.matrix(site_distances), weighted = TRUE,  
                                          mode = "directed") 
 
# Convert geo distance graph object to edgelist 
distance_el <- as_edgelist(distance_g) 
distance_el_weight <- as.numeric(E(distance_g)$weight) 
distance_el <- tbl_df(cbind(distance_el, distance_el_weight)) 
colnames(distance_el) <- c("Source", "Target", "weight") 
distance_el$Distance <- as.numeric(distance_el$weight) 
 
# Merge the geographic distance edgelist with directed plate edgelists 
econet_pre_el_complete <- merge(econet_pre_el_need_dist, distance_el[-3]) 
econet_post_el_complete <- merge(econet_post_el_need_dist, distance_el[-3]) 
 
# Combine the pre- and post-migration data sets into a single edgelist 
econet_el_BR_all_time_complete <- rbind(econet_pre_el_complete, econet_post_el_complete) 
 

540 

# Finally, we can export the complete edgelist for visualization in Gephi 
write_csv(econet_el_BR_all_time_complete, "Economic_network_BR_edgelist_complete_.csv") 
 
#### Undirected Economic Networks #### 
 
# The edgelists created thus far have been directed. Since we are disregarding  
# directionality, it is imporant to account for duplicate edges.  
BRgraph_un <- graph_from_adjacency_matrix(eco_BR, weighted = T, mode = "undirected") 
 
# Create undirected edgelist 
BRel_un <- as_edgelist(BRgraph_un) 
 
# Create the weights and format as a data frame for column binding 
BRw_un <- E(BRgraph_un)$weight 
BRw_un <- as.data.frame(BRw_un) 
 
# Add the weights, and viola we have a weighted, directed edgelist for proportional 
# stylistic similarity between sites.  
BRel_un <- cbind(BRel_un, BRw_un) 
 
# Write out complete Brainerd Robinson edgelist 
write_csv(BRel_un, "complete_ECO_BR_UNDIRECTED_edgelist.csv") 
 
# Apply our threshold of > 0.4 so that we only give UNDIRECTED edges to the strongest 
# proportional relationship. We can use dplyr to wrangle the edgelist and also drop 
# recursive edges.  
BRel_t_un <- BRel_un %>%  
  filter(BRw_un > 0.55 & BRel_un[1] != BRel_un[2]) 
 
# Change column names to be suitable for Gephi 
colnames(BRel_t_un) <- c("Source", "Target", "weight") 
 
colnames(node_table) <- c("Source", "Label", "Long", "Lat", "Time") 
 
# Join the node table columns to the edgelist by the Source node 
eco_t1_un <- left_join(BRel_t_un, node_table[-2], by = "Source") 
 
# Prepare node tables to join time designation for the target node 
colnames(node_table) <- c("Target", "Label", "Long", "Lat", "Time2") 
 
# Join Time 2 column to Target node  
econet_edgelist_complete_un <- left_join(eco_t1_un, node_table[c(-2:-4)], by = "Target") 
 
# Create Pre- and Post-Migration Edgelists 
econet_pre_el_need_dist_un <-  econet_edgelist_complete_un %>% 
                                  filter(Time == Time2) %>% 
                                  filter(Time == 1) 
 
econet_post_el_need_Law_un <- econet_edgelist_complete_un %>% 
                                filter(Time == Time2) %>% 
                                filter(Time == 2) 
 
# Two sites have extended or multi-component occupations in both time periods 

541 

# So we need to include their connections in both time periods 
Law_econet_post_un <- econet_edgelist_complete_un %>% 
                        filter(Time == 2 & Target == "Lawrenz Gun Club" |  
                                 Source == "Lawrenz Gun Club" & Time2 == 2) %>% 
                        mutate(Time = replace(Time, Time == 1, 2)) %>% 
                        mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
Buck_econet_post_un <- econet_edgelist_complete_un %>% 
                        filter(Time == 2 & Target == "Buckeye Bend" |  
                                 Source == "Buckeye Bend" & Time2 == 2) %>% 
                        mutate(Time = replace(Time, Time == 1, 2)) %>% 
                        mutate(Time2 = replace(Time2, Time2 == 1, 2)) 
 
# Bind the LCG & Buckeye post-migration edges to the post-migration edgelists 
econet_post_el_need_dist_un <- rbind(econet_post_el_need_Law_un,  
                                    Law_econet_post_un, Buck_econet_post_un) 
 
# Merge the geographic distance edgelist with undirected plate edgelists 
econet_pre_el_complete_un <- merge(econet_pre_el_need_dist_un, distance_el[-3]) 
econet_post_el_complete_un <- merge(econet_post_el_need_dist_un, distance_el[-3]) 
 
# Combine the pre- and post-migration data sets into a single edgelist 
econet_el_BR_all_time_complete_un <- rbind(econet_pre_el_complete_un, 
                                           econet_post_el_complete_un) 
 
# Finally, we can export the complete undirected edgelist for visualization in Gephi 
write_csv(econet_el_BR_all_time_complete_un, "Econet_BR_UNDIRECTED_edgelist_complete_.csv") 
write_csv(econet_pre_el_complete_un, "Econet_BR_UNDIRECTED_edgelist_pre-migration_.csv") 
write_csv(econet_post_el_complete_un, "Econet_BR_UNDIRECTED_edgelist_post-migration_.csv") 

 

CIRV Economic Network Analysis 
 
# Geochemical compositional group economic network statistics 
 
library(tidyverse) 
library(readxl) 
library(broom) 
library(igraph) 
library(cowplot) 
 
 
#----------------------------Economic BR Network Stats----------------------------#### 
 
# Read in finalized, undirected economic BR edgelist  
BReco_el_un <- read_csv("Econet_BR_UNDIRECTED_edgelist_complete_.csv") 
 
# Read in finalized, undirected pre-migration BR edgelist 
BReco_el_un_pre <- read_csv("Econet_BR_UNDIRECTED_edgelist_pre-migration_.csv") 
 
# Read in finalized, undirected post-migration BR edgelist 
BReco_el_un_post <- read_csv("Econet_BR_UNDIRECTED_edgelist_post-migration_.csv") 

542 

 
# Convert to igraph graph 
BReco_g <- graph_from_edgelist(as.matrix(BReco_el_un[, c(1:2)]), directed = FALSE) 
BReco_g_pre <- graph_from_edgelist(as.matrix(BReco_el_un_pre[, c(1:2)]), directed = FALSE) 
BReco_g_post <- graph_from_edgelist(as.matrix(BReco_el_un_post[, c(1:2)]), directed = FALSE) 
 
# Assign edge weights to graph 
E(BReco_g)$weight <- BReco_el_un$weight 
E(BReco_g_pre)$weight <- BReco_el_un_pre$weight 
E(BReco_g_post)$weight <- BReco_el_un_post$weight 
 
# Function to calculate degree, betweenness, closeness, and eigenvector centrality  
# for a graphand return a data frame with the scores 
centr_all <- function(graph, g_name = "Score") { 
   
  # Check that graph is an igraph object 
  if (!is_igraph(graph)) { 
    stop("Not a graph object") 
  } 
   
  # Name of graph 
  g_name <- as.character(g_name) 
   
  # Degree centralization 
  res_centr <- centr_degree(graph)$centralization 
   
  # Betweenness centralization 
  res_centr[2] <- centr_betw(graph)$centralization 
   
  # Closeness centralization 
  res_centr[3] <- centr_clo(graph)$centralization 
   
  # Eigenvector centralization 
  res_centr[4] <- centr_eigen(graph)$centralization 
   
  res_centr <- t(as.data.frame(res_centr)) 
   
  # Table of scores 
  colnames(res_centr) <- c("Degree", "Betweenness", "Closeness", "Eigenvector") 
  rownames(res_centr) <- g_name 
   
  res_centr 
} 
 
# Calculate centralization scores for each graph 
all_centr <- centr_all(BReco_g, g_name = "Flattened Across Time") 
pre_centr <- centr_all(BReco_g_pre,  g_name = "Pre-Migration") 
post_centr <- centr_all(BReco_g_post,  g_name = "Post-Migration") 
rbind(pre_centr, post_centr, all_centr) 
 
# Calculated Mean Weighted Degree (or strength) 
mean(strength(BReco_g)) 
mean(strength(BReco_g_pre)) 

543 

mean(strength(BReco_g_post)) 
 
## The following network statistics were calculated in Gephi 0.9.2: 
# Average Degree, Avg. Weighted Degree, Avg. Clustering Coefficient, Avg. Path Length,  
# Graph Density, Network Diameter 
 
#-------------------------Edge Betweenness Community Detection-------------------#### 
 
# Edge betweenness extends the concept of vertex betweenness centrality to edges by  
# assigning each edge a score that reflects the number of shortest paths that move  
# through that edge.  
# You might ask the question, which ties in a social network are the most important in  
# the spread of information? 
 
# Calculated edge betweenness score for each network 
ecopre_eb <- cluster_edge_betweenness(BReco_g_pre) 
ecopost_eb <- cluster_edge_betweenness(BReco_g_post) 
ecoall_eb <- cluster_edge_betweenness(BReco_g) 
 
# Edge betweenness correctly assigns the pre- and post-migration 
# sites to clusters, but with some interesting intricacies - Buckeye in pre and 
# Lawrenz in post 
 
# The pre- and post-migration eb communities are interesting as well 
 
# Community detection via edge betweenness plot_across time 
plot(ecoall_eb, BReco_g, col = membership(ecoall_eb), vertex.label.cex = c(1),  
     edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in \n the Economic Network",  
      cex.main = 1.5) 
 
# Community detection via edge betweenness plot_pre-migration 
plot(ecopre_eb, BReco_g_pre, col = membership(ecopre_eb), vertex.label.cex = c(1),  
     edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in \n the Economic Network",  
      cex.main = 1.5) 
 
# Community detection via edge betweenness plot_post-migration 
plot(ecopost_eb, BReco_g_post, col = membership(ecopost_eb), vertex.label.cex = c(1),  
     edge.arrow.size = .1, edge.curved = .1) 
title(main = "Edge Betweenness Community Detection in \n the Economic Network",  
      cex.main = 1.5) 
 
#------------------Pre Randomization for Pre-Migration Period Economic BR-------------#### 
#----------------------------------PRE_MIGRATION-----------------------------------------# 
 
# Initiate empty list for assessing BR pre-migration average path length and transitivity 
gecopre <- vector('list', 5000) 
 
# Initiate empty list for assessing BR pre-migration density density and mean degree 
gecopre.d <- vector('list', 5000) 
 
# Populate gpre list with random graphs of same order and size 

544 

for(i in 1:5000){ 
  gecopre[[i]] <- erdos.renyi.game(n = gorder(BReco_g_pre), p.or.m = gsize(BReco_g_pre), 
                                   directed = FALSE, type = "gnm") 
} 
 
# Populate gecopre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 random graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our  
# observed graph.  
# Instead, a probability of edge creation equal to the observed density is used. Further,  
# only mean degree (as opposed to mean weighted degree) is used because Erdos-Renyi  
# random graphs do not support weights.  
for(i in 1:5000){ 
  gecopre.d[[i]] <- erdos.renyi.game(n = gorder(BReco_g_pre),  
                                     p.or.m = edge_density(BReco_g_pre),  
                                     directed = FALSE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density, and degree ac
ross  
# the 5000 random pre-migration graphs 
ecopre.pl <- lapply(gecopre.d, mean_distance, directed = FALSE) 
ecopre.trans <- lapply(gecopre, transitivity) 
ecopre.density <- lapply(gecopre.d, edge_density) 
ecopre.degree <- lapply(gecopre.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
ecopre.pl <- as.data.frame(unlist(ecopre.pl)) 
ecopre.trans <- as.data.frame(unlist(ecopre.trans)) 
ecopre.density <- as.data.frame(unlist(ecopre.density)) 
ecopre.degree <- as.data.frame(unlist(ecopre.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the pre-migration
  
# BR network's ave. shortest path as line 
p.ecopre.pl <- ggplot(ecopre.pl, aes(x = unlist(ecopre.pl))) +  
  geom_histogram(aes(y = ..density..), bins = 24) +  
  geom_vline(xintercept = (mean_distance(BReco_g_pre, directed = FALSE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPre-Migration P
eriod Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration BR network's  
# transitivity path as line 
p.ecopre.trans <- ggplot(ecopre.trans, aes(x = unlist(ecopre.trans))) +  
  geom_histogram(aes(y = ..density..), bins = 22) +  

545 

  geom_vline(xintercept = (transitivity(BReco_g_pre)), linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPre-Migration Period Network
 Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's 
# ave. shortest path as line 
p.ecopre.density <- ggplot(ecopre.density, aes(x = unlist(ecopre.density))) +  
  geom_histogram(aes(y = ..density..), bins = 22) +  
  geom_vline(xintercept = (edge_density(BReco_g_pre)), linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPre-Migration Preiod Network
 Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration BR network's mean 
# degree path as line 
p.ecopre.degree <- ggplot(ecopre.degree, aes(x = unlist(ecopre.degree))) +  
  geom_histogram(aes(y = ..density..), bins = 22) +  
  geom_vline(xintercept = (mean(degree(BReco_g_pre, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPre-Migration Period Network 
Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.ecopre.pl, p.ecopre.trans, p.ecopre.density, p.ecopre.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(ecopre.pl < mean_distance(BReco_g_pre, directed = FALSE))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient)  
# lower than our observed 
sum(ecopre.trans < transitivity(BReco_g_pre))/5000*100 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(ecopre.density < edge_density(BReco_g_pre))/5000*100 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(ecopre.degree < mean(degree(BReco_g_pre)))/5000*100 
 
#------------------Post Randomization for Post-Migration Period Economic BR-------------#### 
#----------------------------------POST_MIGRATION-----------------------------------------# 
 
# Initiate empty list for assessing BR pre-migration average path length and transitivity 
gecopost <- vector('list', 5000) 
 
# Initiate empty list for assessing BR pre-migration density density and mean degree 

546 

gecopost.d <- vector('list', 5000) 
 
# Populate gpre list with random graphs of same order and size 
for(i in 1:5000){ 
  gecopost[[i]] <- erdos.renyi.game(n = gorder(BReco_g_post), p.or.m = gsize(BReco_g_post), 
                                   directed = FALSE, type = "gnm") 
} 
 
# Populate gecopre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 random graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our  
# observed graph.  
# Instead, a probability of edge creation equal to the observed density is used. Further,  
# only mean degree (as opposed to mean weighted degree) is used because Erdos-Renyi  
# random graphs do not support weights.  
for(i in 1:5000){ 
  gecopost.d[[i]] <- erdos.renyi.game(n = gorder(BReco_g_post), 
                                      p.or.m = edge_density(BReco_g_post),  
                                     directed = FALSE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density, and  
# degree across the 5000 random pre-migration graphs 
ecopost.pl <- lapply(gecopost.d, mean_distance, directed = FALSE) 
ecopost.trans <- lapply(gecopost, transitivity) 
ecopost.density <- lapply(gecopost.d, edge_density) 
ecopost.degree <- lapply(gecopost.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
ecopost.pl <- as.data.frame(unlist(ecopost.pl)) 
ecopost.trans <- as.data.frame(unlist(ecopost.trans)) 
ecopost.density <- as.data.frame(unlist(ecopost.density)) 
ecopost.degree <- as.data.frame(unlist(ecopost.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the pre-migration
  
# BR network's ave. shortest path as line 
p.ecopost.pl <- ggplot(ecopost.pl, aes(x = unlist(ecopost.pl))) +  
  geom_histogram(aes(y = ..density..), bins = 24) +  
  geom_vline(xintercept = (mean_distance(BReco_g_post, directed = FALSE)),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nPost-Migration 
Period Average Shortest Path Length") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration BR network's  
# transitivity path as line 

547 

p.ecopost.trans <- ggplot(ecopost.trans, aes(x = unlist(ecopost.trans))) +  
  geom_histogram(aes(y = ..density..), bins = 10) +  
  geom_vline(xintercept = (transitivity(BReco_g_post)), linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nPost-Migration Period Networ
k Transitivity") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's 
# ave. shortest path as line 
p.ecopost.density <- ggplot(ecopost.density, aes(x = unlist(ecopost.density))) +  
  geom_histogram(aes(y = ..density..), bins = 19) +  
  geom_vline(xintercept = (edge_density(BReco_g_post)), linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nPost-Migration Preiod Networ
k Average Density") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration BR network's mean 
# degree path as line 
p.ecopost.degree <- ggplot(ecopost.degree, aes(x = unlist(ecopost.degree))) +  
  geom_histogram(aes(y = ..density..), bins = 19) +  
  geom_vline(xintercept = (mean(degree(BReco_g_post, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nPost-Migration Period Network
 Mean Degree") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.ecopost.pl, p.ecopost.trans, p.ecopost.density, p.ecopost.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(ecopost.pl < mean_distance(BReco_g_post, directed = FALSE))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient)  
# lower than our observed 
sum(ecopost.trans < transitivity(BReco_g_post))/5000*100 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(ecopost.density < edge_density(BReco_g_post))/5000*100 
 
# Calculate the proportion of graphs with a mean degree lower than observed 
sum(ecopost.degree < mean(degree(BReco_g_post)))/5000*100 
 
# There is a change from the pre-migration to post-migration period centralization scores 
# Let's check to see which site-nodes are driving that change 
betweenness(BReco_g_post, directed = FALSE) 
closeness(BReco_g_post) 
 

548 

 
#------------Across Time Randomization for Post-Migration Period Economic BR----------#### 
#-----------------------------------ACROSS TIME-----------------------------------------# 
 
# Initiate empty list for assessing BR pre-migration average path length and transitivity 
gecoall <- vector('list', 5000) 
 
# Initiate empty list for assessing BR pre-migration density density and mean degree 
gecoall.d <- vector('list', 5000) 
 
# Populate gpre list with random graphs of same order and size 
for(i in 1:5000){ 
  gecoall[[i]] <- erdos.renyi.game(n = gorder(BReco_g), p.or.m = gsize(BReco_g), 
                                    directed = FALSE, type = "gnm") 
} 
 
# Populate gecopre.d list with random graphs of same order and approximate density.  
# A separate list of 5000 random graphs is necessary for density and mean degree because  
# these statistics would identical in random graphs of the same order and size as our  
# observed graph.  
# Instead, a probability of edge creation equal to the observed density is used. Further,  
# only mean degree (as opposed to mean weighted degree) is used because Erdos-Renyi  
# random graphs do not support weights.  
for(i in 1:5000){ 
  gecoall.d[[i]] <- erdos.renyi.game(n = gorder(BReco_g), p.or.m = edge_density(BReco_g),  
                                      directed = FALSE, type = "gnp") 
} 
 
# Calculate average path length, transitivity (clustering coefficient), density, and degree ac
ross  
# the 5000 random pre-migration graphs 
ecoall.pl <- lapply(gecoall.d, mean_distance, directed = FALSE) 
ecoall.trans <- lapply(gecoall, transitivity) 
ecoall.density <- lapply(gecoall.d, edge_density) 
ecoall.degree <- lapply(gecoall.d, function(x){ 
  y <- degree(x) 
  mean(y) 
} 
) 
 
# Unlist and change to a data frame for vizualizations 
ecoall.pl <- as.data.frame(unlist(ecoall.pl)) 
ecoall.trans <- as.data.frame(unlist(ecoall.trans)) 
ecoall.density <- as.data.frame(unlist(ecoall.density)) 
ecoall.degree <- as.data.frame(unlist(ecoall.degree)) 
 
# Plot the distribution of random graph's average shortest path lengths with the pre-migration
  
# BR network's ave. shortest path as line 
p.ecoall.pl <- ggplot(ecoall.pl, aes(x = unlist(ecoall.pl))) +  
  geom_histogram(aes(y = ..density..), bins = 24) +  
  geom_vline(xintercept = (mean_distance(BReco_g, directed = FALSE)),  
             linetype = "dashed", color = "red") + 

549 

  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Shortest Path Lengths & \nAverage Shortes
t Path Length Across Time in the CIRV") +  
  xlab("Average Shortest Path Length") + 
  ylab("") 
 
# Plot the distribution of random graph's transitivity with the pre-migration BR network's  
# transitivity path as line 
p.ecoall.trans <- ggplot(ecoall.trans, aes(x = unlist(ecoall.trans))) +  
  geom_histogram(aes(y = ..density..), bins = 25) +  
  geom_vline(xintercept = (transitivity(BReco_g)), linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Transitivity in 5000 Random Models & \nTransitivity Across Time in 
the CIRV") +  
  xlab("Transitivity (or Clustering Coefficient)") + 
  ylab("") 
 
# Plot the distribution of random graph's average density with the pre-migration jar network's 
# ave. shortest path as line 
p.ecoall.density <- ggplot(ecoall.density, aes(x = unlist(ecoall.density))) +  
  geom_histogram(aes(y = ..density..), bins = 24) +  
  geom_vline(xintercept = (edge_density(BReco_g)), linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of 5000 Random Graph Average Densities &\nAverage Density Across Time 
in the CIRV") +  
  xlab("Average Density") + 
  ylab("") 
 
# Plot the distribution of random graph's mean degree with the pre-migration BR network's mean 
# degree path as line 
p.ecoall.degree <- ggplot(ecoall.degree, aes(x = unlist(ecoall.degree))) +  
  geom_histogram(aes(y = ..density..), bins = 23) +  
  geom_vline(xintercept = (mean(degree(BReco_g, mode = "all"))),  
             linetype = "dashed", color = "red") + 
  geom_density() + 
  ggtitle("Distribution of Mean Degree in 5000 Random Models & \nMean Degree Across Time in th
e CIRV") +  
  xlab("Mean Degree") + 
  ylab("") 
 
# Use plot_grid to plot all four graphs on the same grid 
plot_grid(p.ecoall.pl, p.ecoall.trans, p.ecoall.density, p.ecoall.degree) 
 
# Calculate the proportion of graphs with an average path length lower than observed 
sum(ecoall.pl < mean_distance(BReco_g, directed = FALSE))/5000*100 
 
# Calculate the proportion of graphs with a transitivity (mean clustering coefficient)  
# lower than our observed 
sum(ecoall.trans < transitivity(BReco_g))/5000*100 
 
# Calculate the proportion of graphs with a density lower than our observed 
sum(ecoall.density < edge_density(BReco_g))/5000*100 
 

550 

# Calculate the proportion of graphs with a mean degree lower than observed 
sum(ecoall.degree < mean(degree(BReco_g)))/5000*100 

 

Economic Network Distance Regressions 
Is the strength or degree of economic network relationships related to the distance between sites? The 
following analyses show that there is no support for a linear relationship between these variables. 

library(infer) 
library(tidyverse) 
library(igraph) 
library(reshape2) 
library(stringr) 
library(cowplot) 
library(broom) 
 
# Read in finalized, undirected plate BR edgelist  
BReco_el_un <- read_csv("Econet_BR_UNDIRECTED_edgelist_complete_.csv") 
 
# Read in finalized, undirected pre-migration BR edgelist 
BReco_el_un_pre <- read_csv("Econet_BR_UNDIRECTED_edgelist_pre-migration_.csv") 
 
# Read in finalized, undirected post-migration BR edgelist 
BReco_el_un_post <- read_csv("Econet_BR_UNDIRECTED_edgelist_post-migration_.csv") 
 
# Inference testing with linear models 
# Take 100 samples of half the network size each from the economic BR data sets 
# The idea is to explore regression trends on the slope coefficient using samples  
# from each data set. Does the trend with the entire data hold true when  
# sub-samples are taken from the data? 
# This is a two-tailed test to see if a linear relationship (positive or negative) exists 
# between distance (explanatory variable) and weight (response variable) 
BRecopresamples <- rep_sample_n(BReco_el_un_pre[, c(3, 8)], size = 21, reps = 100) 
BRecopostsamples <- rep_sample_n(BReco_el_un_post[, c(3, 8)], size = 5, reps = 100) 
BRecoallsamples <- rep_sample_n(BReco_el_un[, c(3, 8)], size = 26, reps = 100) 
 
# Add replicate col to align observed trends with random samples 
ecopre_observed <- BReco_el_un_pre[, c(3, 8)] %>% 
                      mutate(replicate = 200)  
 
ecopost_observed <- BReco_el_un_post[, c(3, 8)] %>% 
                      mutate(replicate = 200)  
 
ecoall_observed <- BReco_el_un[, c(3, 8)] %>% 
                      mutate(replicate = 200)  
 
# Model showing proportional similarity across time 
BReco_lm_all <- ggplot(BRecoallsamples, aes(x = Distance, y = weight, group = replicate)) +  
                  geom_point(size = 2, shape = 20) +  
                  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
                  ggtitle("Ceramic Industry Economic Network Across Time") +  

551 

                  background_grid(major = 'y', minor = "none") + 
                  xlab("Distance (km)") + 
                  ylab("Degree of Proportional Similarity in Compositional Groups") + 
                  theme(strip.background = element_blank(), 
                        strip.text.x = element_blank()) + 
                  stat_smooth(data = ecoall_observed, aes(x = Distance, y = weight),  
                              color ="red3",  
                              linetype = "twodash", method = "lm", se = FALSE)  
 
# Model showing proportional similarity in the pre-migration CIRV 
BReco_lm_pre <- ggplot(BRecopresamples, aes(x = Distance, y = weight, group = replicate)) +  
                  geom_point(size = 2, shape = 20) +  
                  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
                  ggtitle("Pre-Migration Ceramic Industry Economic Network") +  
                  background_grid(major = 'y', minor = "none") + 
                  xlab("Distance (km)") + 
                  ylab("Degree of Proportional Similarity in Compositional Groups") + 
                  theme(strip.background = element_blank(), 
                        strip.text.x = element_blank()) + 
                  stat_smooth(data = ecopre_observed, aes(x = Distance, y = weight),  
                              color ="red3",  
                              linetype = "twodash", method = "lm", se = FALSE)  
 
# Model showing proportional similarity in the post-migration CIRV 
BReco_lm_post <- ggplot(BRecopostsamples, aes(x = Distance, y = weight, group = replicate)) +  
                  geom_point(size = 2, shape = 20) +  
                  stat_smooth(geom = "line", se = FALSE, alpha = 0.4, method = "lm") +  
                  ggtitle("Post-Migration Ceramic Industry Economic Network") +  
                  background_grid(major = 'y', minor = "none") + 
                  xlab("Distance (km)") + 
                  ylab("Degree of Proportional Similarity in Compositional Groups") + 
                  theme(strip.background = element_blank(), 
                        strip.text.x = element_blank()) + 
                  stat_smooth(data = ecopost_observed, aes(x = Distance, y = weight),  
                              color ="red3",  
                              linetype = "twodash", method = "lm", se = FALSE)  
 
# Inference 
# First, let's calculate the observed slope of the lm in the jar and plate attribute networks 
BReco_all_slope <- lm(weight ~ Distance, data = BReco_el_un) %>% 
                        tidy() %>%    
                        filter(term == "Distance") %>% 
                        pull(estimate)     
 
BReco_pre_slope <- lm(weight ~ Distance, data = BReco_el_un_pre) %>% 
                        tidy() %>%    
                        filter(term == "Distance") %>% 
                        pull(estimate)     
 
BReco_post_slope <- lm(weight ~ Distance, data = BReco_el_un_post) %>% 
                        tidy() %>%    
                        filter(term == "Distance") %>% 
                        pull(estimate)     

552 

 
# Simulate 500 slopes with a permuted dataset for economic network - this will allow us to  
# develop a sampling distribution of the slop under the hypothesis that there is no  
# relationship between the explanatory (Distance) and response (weight) variables.  
set.seed(1568) 
BReco_all_perm_slope <- BReco_el_un %>% 
                          specify(weight ~ Distance) %>% 
                          hypothesize(null = "independence") %>% 
                          generate(reps = 500, type = "permute") %>% 
                          calculate(stat = "slope")  
 
BReco_pre_perm_slope <- BReco_el_un_pre %>% 
                          specify(weight ~ Distance) %>% 
                          hypothesize(null = "independence") %>% 
                          generate(reps = 500, type = "permute") %>% 
                          calculate(stat = "slope")  
 
BReco_post_perm_slope <- BReco_el_un_post %>% 
                          specify(weight ~ Distance) %>% 
                          hypothesize(null = "independence") %>% 
                          generate(reps = 500, type = "permute") %>% 
                          calculate(stat = "slope")  
 
ggplot(BReco_all_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
ggplot(BReco_pre_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
ggplot(BReco_post_perm_slope, aes(x = stat)) + geom_density() + theme_classic() 
 
mean(BReco_all_perm_slope$stat) 
mean(BReco_pre_perm_slope$stat) 
mean(BReco_post_perm_slope$stat) 
sd(BReco_all_perm_slope$stat) 
sd(BReco_pre_perm_slope$stat) 
sd(BReco_post_perm_slope$stat) 
 
# Calculate the absolute value of the slope 
abs_BRco_all_obs_slope <- lm(weight ~ Distance, data = BReco_el_un) %>% 
                            tidy() %>%    
                            filter(term == "Distance") %>% 
                            pull(estimate) %>% 
                            abs() 
 
abs_BReco_pre_obs_slope <- lm(weight ~ Distance, data = BReco_el_un_pre) %>% 
                              tidy() %>%    
                              filter(term == "Distance") %>% 
                              pull(estimate) %>% 
                              abs() 
 
abs_BReco_post_obs_slope <- lm(weight ~ Distance, data = BReco_el_un_post) %>% 
                              tidy() %>%    
                              filter(term == "Distance") %>% 
                              pull(estimate) %>% 
                              abs() 
 

553 

# Compute the p-value   
BReco_all_perm_slope %>%  
  mutate(abs_BReco_all_obs_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_BReco_all_obs_slope > BReco_all_perm_slope)) 
 
BReco_pre_perm_slope %>%  
  mutate(abs_BReco_pre_obs_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_BReco_pre_obs_slope > BReco_pre_perm_slope)) 
 
BReco_post_perm_slope %>%  
  mutate(abs_BReco_post_obs_slope = abs(stat)) %>% 
  summarize(p_value = mean(abs_BReco_post_obs_slope > BReco_post_perm_slope)) 
 
# Linear models sans visualization 
# explore residuals  
BReco_all_lm <- augment(lm(weight ~ Distance, data = BReco_el_un)) 
BReco_pre_lm <- augment(lm(weight ~ Distance, data = BReco_el_un_pre)) 
BReco_post_lm <- augment(lm(weight ~ Distance, data = BReco_el_un_post)) 
 
# Check SSE - how well do the models fit? 
augment(lm(weight ~ 1, data = BReco_el_un)) %>% summarize(SSE = var(.resid)) # null 
BReco_all_lm %>% summarize(SSE = var(.resid)) 
 
augment(lm(weight ~ 1, data = BReco_el_un_pre)) %>% summarize(SSE = var(.resid)) # null 
BReco_pre_lm %>% summarize(SSE = var(.resid)) 
 
augment(lm(weight ~ 1, data = BReco_el_un_post)) %>% summarize(SSE = var(.resid)) # null 
BReco_post_lm %>% summarize(SSE = var(.resid)) 
 
# Looks like the models do fit very well 
 
# Breakdown of linear model results for plate attribute networks  
summary(lm(weight ~ Distance, data = BReco_el_un))  
# for each 1 km increase in distance, weight drops 0.0007723 and at 0 distance,  
# a weight of 0.7378 is expected 
summary(lm(weight ~ Distance, data = BReco_el_un))$coefficients  
# all = p-value of 0.1454, fail to   
# reject null hypothesis - no significant linear relationship b/t distance and weight  
# across time 
 
summary(lm(weight ~ Distance, data = BReco_el_un_pre))  
# for each 1 km increase in distance, weight drops 0.0003959 and at 0 distance, a weight of 
# 0.7385 is expected 
summary(lm(weight ~ Distance, data = BReco_el_un_pre))$coefficients  
# pre p-value of 0.6918, fail to reject the null hypothesis - no significant linear 
# relationship b/t distance and weight in pre 
 
summary(lm(weight ~ Distance, data = BReco_el_un_post)) # for each 1 km increase in distance, 
# weight drops 0.0004263 and at 0 distance, a weight of 0.6835 is expected 
summary(lm(weight ~ Distance, data = BReco_el_un_post))$coefficients  
# post p-value of 0.5499, fail to reject null - no significant linear relationship b/t  
# distance and weight in post 
 

554 

# Check r.squared 
glance(lm(weight ~ Distance, data = BReco_el_un)) 
glance(lm(weight ~ Distance, data = BReco_el_un_pre)) 
glance(lm(weight ~ Distance, data = BReco_el_un_post)) 
 
ggplot(BReco_el_un_post, aes(Distance, weight)) + geom_point() + geom_smooth() 
ggplot(BReco_el_un_pre, aes(Distance, weight)) + geom_point() + geom_smooth() 
 
# Check correlations 
cor(BReco_el_un$Distance, BReco_el_un$weight) 
cor(BReco_el_un_pre$Distance, BReco_el_un_pre$weight) 
cor(BReco_el_un_post$Distance, BReco_el_un_post$weight) 
 
 
### No relationship between distance and degree of economic interactions is able to be 
#   identified this is interesting, as it would be expected that sites closer in proximity 
#   would exhibit stronger economic relationships via a higher degree of exchange of  
#   finished vessels, overlapping resource exploitation areas, or similar paste preparation  
#   and production regimes.  

 
R Code from Chapter 8 – Toward Explaining Social Interrelationships through a Ceramic 
Industry Multilayer Network 

 

Network Date Pre-Treatment for Multilayer Network Construction 
 

#' Data munging to convert network data into a form amenable  
#' to the construction of multilayer networks using multinet 
#' and muxViz. 
 
library(tidyverse) 
library(multinet) 
library(igraph) 
 
# First, read in the social identification network built based on 
# proportional similarity in plate stylistic designs between sites  
style_all <- read_csv("BR_UNDIRECTED_edgelist_complete_.csv") 
eco_all <- read_csv("Econet_BR_UNDIRECTED_edgelist_complete_.csv") 
 
# Multinet is implement in a variant of the C language and as such 
# is bound by different rules. One of those is avoiding spaces in 
# the actor (or in this case archaeological site) names 
 
# Replace all spaces and dashes with an underscore for style layers 
style_all$Source <- str_replace_all(style_all$Source, c(" " = "_", "-" = "_")) 
style_all$Target <- str_replace_all(style_all$Target, c(" " = "_", "-" = "_")) 
    
# Decompose edge table to edge vectors for style layers                      
style_all %>% 

555 

  mutate(Layer = ifelse(Time == 1, "Style_pre", "Style_post")) %>% 
  select(Source, Target, Layer, weight) %>% 
  unite(Style, sep = ",") %>% 
  write_csv("style_edge_table_multinet.csv") 
 
# Style node table 
style_all %>% 
  mutate(Layer = ifelse(Time == 1, "Style_pre", "Style_post")) %>% 
  select(Source, Target, Layer) %>% 
  gather(Site, Source:Layer, -Layer) %>% 
  select(`Source:Layer`, Layer) %>% 
  distinct(`Source:Layer`, Layer) %>% 
  unite(Nodes_style, sep = ",") %>%  
  write_csv("style_node_table_multinet.csv") 
 
# Economic network layer node cleaning 
# '\\.' matches a . 
eco_all$Source <- str_replace_all(eco_all$Source,  
                                  c(" " = "_", "-" = "_", "\\." = "")) 
eco_all$Target <- str_replace_all(eco_all$Target,  
                                  c(" " = "_", "-" = "_", "\\." = "")) 
 
# Decompose edge table to edge vectors for economic layers   
eco_all %>% 
  mutate(Layer = ifelse(Time == 1, "Eco_pre", "Eco_post")) %>% 
  select(Source, Target, Layer, weight) %>% 
  unite(Economic, sep = ",") %>% 
  write_csv("economic_edge_table_multinet.csv") 
 
# Economic networks node table 
eco_all %>% 
  mutate(Layer = ifelse(Time == 1, "Eco_pre", "Eco_post")) %>% 
  select(Source, Target, Layer) %>% 
  gather(Site, Source:Layer, -Layer) %>% 
  select(`Source:Layer`, Layer) %>% 
  distinct(`Source:Layer`, Layer) %>% 
  unite(Nodes_style, sep = ",") %>% 
  write_csv("economic_node_table_multinet.csv") 
 
# At this point, node and edge table information is combined using the RStudio 
# content editor. It's easier working in the content editor because Excel and text 
# editing software often append spaces, commas, or other unwanted characters to 
# the data, which multinet cannot handle. For information on how to create 
# multilayer or multiplex networks in multinet, see the documentation on CRAN 
# or you can view the file below once it is posted.  
  
test <- read.ml("ceramicMultilayer_complete_in progress.csv")   
test 
plot(test) 
 
# Pre-Treatment for muxViz #### 
# muxViz is a powerful tool for multilayer network anlaysis and visualization 
# Here, I'll work with the network data I have to create files for use in muxViz 

556 

 
# Style network edge lists for muxViz 
# Pre-migration 
style_all %>% 
  filter(Time == 1) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_style_pre.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE) 
 
# Post-migration 
style_all %>% 
  filter(Time == 2) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_style_post.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE) 
 
# Across time 
style_all %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_style_all.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE) 
 
# Economic network edge lists for muxViz 
# Pre-migration 
eco_all %>% 
  filter(Time == 1) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_eco_pre.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE) 
   
# Post-migration 
eco_all %>% 
  filter(Time == 2) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_eco_post.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE)  
 
# Across time 
eco_all %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_eco_all.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Interaction through cultural transmission network edge lists for muxViz 
 
# Jars muxViz #### 
# Import jar edgelist and munge the site names 

557 

jars <- read_csv('jar_complete_edgelist.csv') 
jars$Source <- str_replace_all(jars$Source,  
                               c(" " = "_", "-" = "_", "\\." = "")) 
jars$Target <- str_replace_all(jars$Target, 
                               c(" " = "_", "-" = "_", "\\." = "")) 
 
# First, make directed graph txt files for muxZiv 
# Jar directed all 
jars %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_jtech_directed_all.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Jar directed pre 
jars %>% 
  filter(Time == 1) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_jtech_directed_pre.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Jar directed post 
jars %>% 
  filter(Time == 2) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_jtech_directed_post.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Now, create UNDIRECTED graph txt files for jars 
# To do this, any reciprocal edge weights will be the mean of the two  
# directed edge weights 
 
# Jar undirected all 
jg <- graph.data.frame(jars, directed = TRUE) 
jg_un <- as.undirected(jg, edge.attr.comb = "mean", mode = "collapse") 
 
as.data.frame(as_edgelist(jg_un)) %>% 
  mutate(weight = E(jg_un)$weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_jtech_undirected_all.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Jar undirected pre 
jars %>% 
  filter(Time == 1) %>%  
  graph.data.frame(directed = TRUE) -> jg_pre 
jg_un_pre <- as.undirected(jg_pre, edge.attr.comb = "mean",  
                           mode = "collapse") 
 
as.data.frame(as_edgelist(jg_un_pre)) %>% 
  mutate(weight = E(jg_un_pre)$weight) %>% 

558 

  unite(sep = " ") %>% 
  write.table("edge_list_jtech_undirected_pre.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Jar undirected post 
jars %>% 
  filter(Time == 2 |  
           (Source == "Buckeye_Bend" & Target == "Lawrenz_Gun_Club") | 
           (Source == "Lawrenz_Gun_Club" & Target == "Buckeye_Bend")) %>% 
  graph.data.frame(directed = TRUE) -> jg_post 
jg_un_post <- as.undirected(jg_post, edge.attr.comb = "mean",  
                            mode = "collapse") 
 
as.data.frame(as_edgelist(jg_un_post)) %>% 
  mutate(weight = E(jg_un_post)$weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_jtech_undirected_post.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Plates muxViz ####  
plates <- read_csv('plate_complete_edgelist.csv') 
plates$Source <- str_replace_all(plates$Source,  
                                 c(" " = "_", "-" = "_", "\\." = "")) 
plates$Target <- str_replace_all(plates$Target,  
                                 c(" " = "_", "-" = "_", "\\." = "")) 
 
# Plates directed all 
plates %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_ptech_directed_all.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Plates directed pre 
plates %>% 
  filter(Time == 1) %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_ptech_directed_pre.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE) 
 
# Plates directed post 
plates %>% 
  filter(Time == 2 |  
           (Source == "Buckeye_Bend" & Target == "Lawrenz_Gun_Club") | 
           (Source == "Lawrenz_Gun_Club" & Target == "Buckeye_Bend"))  %>% 
  select(Source, Target, weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_ptech_directed_post.txt", row.names = FALSE,  
              col.names = FALSE, quote = FALSE) 
   
# Now, create UNDIRECTED graph txt files for plates 
# To do this, any reciprocal edge weights will be the mean of the two  

559 

# directed edge weights 
 
# Plate undirected all 
pg <- graph.data.frame(plates, directed = TRUE) 
pg_un <- as.undirected(pg, edge.attr.comb = "mean", mode = "collapse") 
 
as.data.frame(as_edgelist(pg_un)) %>% 
  mutate(weight = E(pg_un)$weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_ptech_undirected_all.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Plate undirected pre 
plates %>% 
  filter(Time == 1) %>% 
  graph.data.frame(directed = TRUE) -> pg_pre 
pg_un_pre <- as.undirected(pg_pre, edge.attr.comb = "mean",  
                           mode = "collapse") 
 
as.data.frame(as_edgelist(pg_un_pre)) %>% 
  mutate(weight = E(pg_un_pre)$weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_ptech_undirected_pre.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE) 
 
# Plate undirected post 
plates %>% 
  filter(Time == 2 |  
           (Source == "Buckeye_Bend" & Target == "Lawrenz_Gun_Club") | 
           (Source == "Lawrenz_Gun_Club" & Target == "Buckeye_Bend")) %>% 
  graph.data.frame(directed = TRUE) -> pg_post 
pg_un_post <- as.undirected(pg_post, edge.attr.comb = "mean",  
                            mode = "collapse") 
 
as.data.frame(as_edgelist(pg_un_post)) %>% 
  mutate(weight = E(pg_un_post)$weight) %>% 
  unite(sep = " ") %>% 
  write.table("edge_list_ptech_undirected_post.txt", row.names = FALSE, 
              col.names = FALSE, quote = FALSE)  
 
## UNDIRECTED Edgelists for Gephi 
# Here I take directed jar and plate technological attribute networks and  
# decompose them into undirected networks based on the average edge weights 
# among any two given sites (if there is no reciprocal edge, the present 
# edge weight is used to define the relationship).  
# Filtering can be applied in Gephi, so only one edge table is needed for 
# each vessel class.  
 
# Import jar/plate data again (no special modifications to site names is  
# needed for Gephi) 
p <- read_csv('plate_complete_edgelist.csv') 
j <- read_csv('jar_complete_edgelist.csv') 
 

560 

# Jars for Gephi 
j %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  as_edgelist(.) %>% 
  as.data.frame(.) %>% 
  mutate(weight = E(as.undirected(graph.data.frame(j,directed = TRUE),  
                                  edge.attr.comb = "mean",  
                                  mode = "collapse"))$weight) %>% 
  rename(Source = V1, Target = V2) %>% 
  write_csv("Jars_tech_UN_across_time.csv") 
   
# Plates for Gephi 
p %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  as_edgelist(.) %>% 
  as.data.frame(.) %>% 
  mutate(weight = E(as.undirected(graph.data.frame(p,directed = TRUE),  
                                  edge.attr.comb = "mean",  
                                  mode = "collapse"))$weight) %>% 
  rename(Source = V1, Target = V2) %>% 
  write_csv("Plates_tech_UN_across_time.csv") 
 
# Function to calculate degree, betweenness, closeness, and eigenvector centrality  
# for a graphand return a data frame with the scores 
centr_all <- function(graph, g_name = "Score") { 
   
  # Check that graph is an igraph object 
  if (!is_igraph(graph)) { 
    stop("Not a graph object") 
  } 
   
  # Name of graph 
  g_name <- as.character(g_name) 
   
  # Degree centralization 
  res_centr <- centr_degree(graph)$centralization 
   
  # Betweenness centralization 
  res_centr[2] <- centr_betw(graph)$centralization 
   
  # Closeness centralization 
  res_centr[3] <- centr_clo(graph)$centralization 
   
  # Eigenvector centralization 
  res_centr[4] <- centr_eigen(graph)$centralization 
   
  res_centr <- t(as.data.frame(res_centr)) 
   
  # Table of scores 
  colnames(res_centr) <- c("Degree", "Betweenness", "Closeness", "Eigenvector") 
  rownames(res_centr) <- g_name 

561 

   
  res_centr 
} 
 
## Centralization values for undirected jar and plate networks 
 
# Jar pre-migration, post-migration, and all 
j %>% 
  #filter(Time == 1) %>% 
  #filter(Time == 2) %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  centr_all(.) 
   
# Plate pre-migration, post-migration, and all 
p %>% 
  #filter(Time == 1) %>% 
  #filter(Time == 2) %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  centr_all(.) 
 
# Undirected networks for multinet #### 
 
# First, correct site (node) names for the convention I used previously 
j$Source <- str_replace_all(j$Source, c(" " = "_", "-" = "_", "\\." = "")) 
j$Target <- str_replace_all(j$Target, c(" " = "_", "-" = "_", "\\." = "")) 
p$Source <- str_replace_all(p$Source, c(" " = "_", "-" = "_", "\\." = "")) 
p$Target <- str_replace_all(p$Target, c(" " = "_", "-" = "_", "\\." = "")) 
 
# Jars undirected multinet 
# Pre-migration 
j %>% 
  filter(Time == 1) %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  as_edgelist(.) %>% 
  as.data.frame(.) %>% 
  mutate(weight = E(as.undirected(graph.data.frame(filter(j, Time == 1), 
                                                   directed = TRUE),  
                                  edge.attr.comb = "mean",  
                                  mode = "collapse"))$weight) %>% 
  mutate(Layer = "Jar_pre") %>% 
  select(V1, V2, Layer, weight) %>% 
  unite(sep = ",") %>% 
  write_delim("jar_pre_mulitnet_el.txt", delim = "") 
 
# Post-migration 
j %>% 
  filter(Time == 2 |  
           (Source == "Buckeye_Bend" & Target == "Lawrenz_Gun_Club") | 
           (Source == "Lawrenz_Gun_Club" & Target == "Buckeye_Bend"))  %>% 
  graph.data.frame(directed = TRUE) %>% 

562 

  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  as_edgelist(.) %>% 
  as.data.frame(.) %>% 
  mutate(weight = E(as.undirected(graph.data.frame(filter(j, Time == 2 |  
                      (Source == "Buckeye_Bend" &  
                         Target == "Lawrenz_Gun_Club") | 
                        (Source == "Lawrenz_Gun_Club" &  
                           Target == "Buckeye_Bend")), directed = TRUE),  
                      edge.attr.comb = "mean", mode = "collapse"))$weight) %>% 
  mutate(Layer = "Jar_post") %>% 
  select(V1, V2, Layer, weight) %>% 
  unite(sep = ",") %>% 
  write_delim("jar_post_mulitnet_el.txt", delim = "") 
 
# Plates undirected multinet 
# Pre-migration 
p %>% 
  filter(Time == 1) %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  as_edgelist(.) %>% 
  as.data.frame(.) %>% 
  mutate(weight = E(as.undirected(graph.data.frame(filter(p, Time == 1), 
                                                   directed = TRUE), 
                                  edge.attr.comb = "mean",  
                                  mode = "collapse"))$weight) %>% 
  mutate(Layer = "Plate_pre") %>% 
  select(V1, V2, Layer, weight) %>% 
  unite(sep = ",") %>% 
  write_delim("plate_pre_mulitnet_el.txt", delim = "") 
 
# Post-migration 
p %>% 
  filter(Time == 2) %>% 
  graph.data.frame(directed = TRUE) %>% 
  as.undirected(edge.attr.comb = "mean", mode = "collapse") %>% 
  as_edgelist(.) %>% 
  as.data.frame(.) %>% 
  mutate(weight = E(as.undirected(graph.data.frame(filter(p, Time == 2), 
                                                   directed = TRUE),  
                                  edge.attr.comb = "mean",  
                                  mode = "collapse"))$weight) %>% 
  mutate(Layer = "Plate_post") %>% 
  select(V1, V2, Layer, weight) %>% 
  unite(sep = ",") %>% 
  write_delim("plate_post_mulitnet_el.txt", delim = "") 

 

Multilayer Network Analysis Using Multinet and MuxViz 

563 

# Multilayer Network Analysis using Multinet (and MuxViz) 
 
# Multilayer networks of ceramic industry from the Late Prehistoric central   
# IllinoisRiver valley (1200-1450 A.D.) are analyzed here.  
# There are four distinct layers in this multilayer network: 
# 1) attributes likely constrained by social forces, or imbued with social information,  
# on domestic cooking jars and 2) likely serving plates, 3) proportional stylistic 
# similarity in design groups present at sites, and 4) economic networks related  
# to ceramic industry as gleaned from geochemical compositional groups.  
# Networks are considered both prior to and preceding a circa 1300 A.D. in-migration  
# of an Oneota group into a Mississippian chiefly environment.  
 
# All network ties are unweighted and undirected in Multinet analysis -  
# it does not yet support these network attributes yet. Nevertheless, significant   
# insight can be gained when exploring the multilayer nature of the networks  
# based on the threshold values for giving an edge between two sites across  
# the different network layers.  
 
# Load multinet 
library(multinet) 
library(igraph) 
library(tidyverse) 
library(ggsci) 
library(magrittr) 
 
# Import Ceramic Industry Multilayer Network 
cnet <- read.ml("ceramicMultilayer_complete_in progress_UNDIRECTED.csv") 
cnet_pre <- read.ml("ceramicMultilayer_PRE_in progress_UNDIRECTED_2.0.0.csv") 
cnet_post <- read.ml("ceramicMultilayer_POST_in progress_UNDIRECTED_2.0.0.csv") 
 
# Let's take a look at some basic Network Analysis Measures for actors in the network 
 
# Degree of all actors, considering edges on all layers 
# This does not consider edge weights 
degree.ml(cnet) 
degree.ml(cnet_pre) 
degree.ml(cnet_post) 
 
# Degree deviation is an interesting measure. It is the standard deviation of the 
# degree of an actor on the input layers. An actor with the same degree on all layers 
# will have deviation 0, while an actor with a lot of neighbors on one layer and  
# only a few on another will have a high degree deviation, showing an uneven usage  
# of layers (or layers with different densities).  
# The values are quite high because of the many layers on which many of the sites are 
# not represented.  
degree.deviation.ml(cnet) 
deviation_pre <- cnet_pre %>%  
                  degree.deviation.ml() %>% 
                  as.data.frame() %>% 
                  rownames_to_column() %>% 
                  as_tibble() %>% 
                  set_colnames(c("Site", "Degree Deviation")) %>% 
                  mutate(Time = "Pre-Migration") 

564 

 
deviation_post <- cnet_post %>% 
                    degree.deviation.ml() %>% 
                    as.data.frame() %>% 
                    rownames_to_column() %>% 
                    as_tibble() %>% 
                    set_colnames(c("Site", "Degree Deviation")) %>% 
                    mutate(Time = "Post-Migration") 
 
# Plotting degree deviation for pre-migration time period 
deviation_pre %>% 
  mutate(Site = str_replace_all(Site, "_", " ")) %>% 
  ggplot() +  
  geom_col(aes(x = reorder(Site,`Degree Deviation`), y = `Degree Deviation`, 
               fill = `Degree Deviation`), color = "black") + 
  theme_bw() + 
  scale_fill_material("blue-grey") + 
  labs(y = "Degree Deviation", 
       x = "",  
       fill = "Degree Deviation") + 
  coord_flip() +  
  theme(axis.text.y = element_text(size = 10)) 
 
# Plotting degree deviation for post-migration time period 
deviation_post %>% 
  mutate(Site = str_replace_all(Site, "_", " ")) %>% 
  ggplot() +  
  geom_col(aes(x = reorder(Site,`Degree Deviation`), y = `Degree Deviation`,  
               fill = `Degree Deviation`), color = "black") + 
  theme_bw() + 
  scale_fill_material("blue-grey") + 
  labs(y = "Degree Deviation", 
       x = "", 
       fill = "Degree Deviation") + 
  coord_flip() +  
  #scale_y_continuous(limits = c(0.0, 4.0)) + 
  theme(axis.text.y = element_text(size = 10)) 
 
# Let's refine this to only look at specific layers - either before or after  
# the migration 
degree.deviation.ml(cnet, layers = c("Jar_pre", "Plate_pre")) 
degree.deviation.ml(cnet, layers = c("Jar_post", "Plate_post")) 
 
# Two sites are off the charts for these measures - Eveland and CW_Cooper  
# This is because one of the vessel classes is not present at these sites 
# Overall, there is significantly less degree deviation in the post-migration 
# period, indicating a more even usage of the layers overall compared to the  
# pre-migration period. This might indicate that social relationships became 
# more developed (which doesn't necessary connote positive or negative) kinds 
# of relationships, only that interaction perhaps became more routinized in 
# some way. Perhaps this is related to the presence of an internal frontier,  
# which could act to structure inter-site relationships in ways not possible 
# in the pre-migration period.  

565 

 
# What about measures for the multiplexity of an actor's relationships?  
# Connective redundancy assesses whether or not sites that share a relationship 
# on one layer also share that same relationships across other layers 
connective.redundancy.ml(cnet) 
connective.redundancy.ml(cnet_pre) 
connective.redundancy.ml(cnet_post) 
 
# Storing connective redundancy as a tidy tibble 
redundancy_pre <- cnet_pre %>%  
                    connective.redundancy.ml() %>% 
                    as.data.frame() %>% 
                    rownames_to_column() %>% 
                    as_tibble() %>% 
                    set_colnames(c("Site", "Connective Redundancy")) %>% 
                    mutate(Time = "Pre-Migration") 
 
# Storing connective redundancy as a tidy tibble 
redundancy_post <- cnet_post %>% 
                      connective.redundancy.ml() %>% 
                      as.data.frame() %>% 
                      rownames_to_column() %>% 
                      as_tibble() %>% 
                      set_colnames(c("Site", "Connective Redundancy")) %>% 
                      mutate(Time = "Post-Migration") 
 
# Plotting connective redundancy in the pre-migration period 
redundancy_pre %>% 
  mutate(Site = str_replace_all(Site, "_", " ")) %>% 
  ggplot() +  
  geom_col(aes(x = reorder(Site,`Connective Redundancy`),  
               y = `Connective Redundancy`, 
               fill = `Connective Redundancy`), 
           color = "black") + 
  theme_bw() + 
  labs(y = "Connective Redundancy", 
       x = "", 
       fill = "Connective Redundancy") + 
  scale_fill_material("green") + 
  coord_flip() +  
  scale_y_continuous(limits = c(0.0, 0.7)) + 
  theme(axis.text.y = element_text(size = 10))  
 
# Plotting connective redundancy in the post-migration period 
redundancy_post %>% 
  mutate(Site = str_replace_all(Site, "_", " ")) %>% 
  ggplot() +  
  geom_col(aes(x = reorder(Site,`Connective Redundancy`),  
               y = `Connective Redundancy`,  
               fill = `Connective Redundancy`), 
           color = "black") + 
  theme_bw() + 
  labs(y = "Connective Redundancy", 

566 

       x = "",  
       fill = "Connective Redundancy") + 
  scale_fill_material("green") + 
  coord_flip() +  
  scale_y_continuous(limits = c(0.0, 0.7)) + 
  theme(axis.text.y = element_text(size = 10)) 
 
# Comparing layers - looks at overlapping and distribution similarity (0 to 1)  
layer.comparison.ml(cnet) 
layer.comparison.ml(cnet_pre) 
layer.comparison.ml(cnet_post) 
layer.comparison.ml(cnet,method="jaccard.edges") 
layer.comparison.ml(cnet,method="sm.edges") 
jaccard_pre <- layer.comparison.ml(cnet_pre,method="jaccard.edges") 
jaccard_post <- layer.comparison.ml(cnet_post,method="jaccard.edges") 
sm_pre <- layer.comparison.ml(cnet_pre,method="sm.edges") 
sm_post <- layer.comparison.ml(cnet_post,method="sm.edges") 
 
 
# Let's plot the different layer comparisons as two barcharts for the  
# pre- and post-migration periods respectively 
# Make weighted, undirected graph from Pre-migration Jaccard coefficient 
jac_pre_g <- jaccard_pre %>% 
              as.matrix() %>% 
              graph_from_adjacency_matrix(., weighted = TRUE,  
                                        mode = "undirected") 
 
# Weighted, undirected pre-migration period simple matching coefficient graph 
sm_pre_g <- sm_pre %>% 
              as.matrix() %>% 
              graph_from_adjacency_matrix(., weighted = TRUE,  
                                          mode = "undirected") 
 
# Convert pre-migration graphs to tbl_dfs and combine 
e_pre <- jac_pre_g %>% 
          as_edgelist() %>% 
          as_tibble() %>% 
          mutate(Jaccard = E(jac_pre_g)$weight) %>% 
          filter(V1 != V2) %>% 
          left_join(as_tibble(as_edgelist(sm_pre_g)) %>%  
                      mutate(Simple_Matching = E(sm_pre_g)$weight)) %>% 
          unite("layers", c("V1", "V2"), sep = "-") %>% 
          # Add edge overlapping from MuxViz (edge weights are factored in) 
          mutate(Edge_Overlap = c(0.727, 0.474, 0.629, 0.495, 0.544, 0.345)) 
 
# Make weighted, undirected graph from Post-migration Jaccard coefficient 
jac_post_g <- jaccard_post %>% 
                as.matrix() %>% 
                graph_from_adjacency_matrix(., weighted = TRUE, 
                                            mode = "undirected") 
 
# Weighted, undirected post-migration period simple matching coefficient graph 
sm_post_g <- sm_post %>% 

567 

              as.matrix() %>% 
              graph_from_adjacency_matrix(., weighted = TRUE,  
                                          mode = "undirected") 
 
# Convert post-migration graphs to tbl_dfs and combine 
e_post <- jac_post_g %>% 
            as_edgelist() %>% 
            as_tibble() %>% 
            mutate(Jaccard = E(jac_post_g)$weight) %>% 
            filter(V1 != V2) %>% 
            left_join(as_tibble(as_edgelist(sm_post_g)) %>%  
                        mutate(Simple_Matching = E(sm_post_g)$weight)) %>% 
            unite("layers", c("V1", "V2"), sep = "-") %>% 
            # Add edge overlapping from MuxViz (edge weights factored in) 
            mutate(Edge_Overlap = c(0.520, 0.819, 0.469, 0.620, 0.488, 0.454)) 
 
# Pre-migration edge correlation barplot 
e_pre %>% 
  gather(Metric, value, Jaccard:Edge_Overlap, -layers) %>% 
  mutate(layers = str_replace(layers, "_pre", ""), 
         layers = str_replace(layers, "_pre", ""), 
         layers = str_replace(layers, "Eco", "Economic"),  
         Metric = str_replace(Metric, "_", " "),  
         layers = str_replace(layers, "-", " - ")) %>% 
  arrange(layers) %>% 
  ggplot() +  
  geom_col(aes(x = reorder(layers, value), y = value, fill = Metric),  
           position = "dodge") + 
  theme_bw() + 
  scale_fill_nejm() + 
  labs(y = "Layer Overlap", 
       x = "",  
       subtitle = "Pre-migration period layer edge overlaps") + 
  coord_flip() +  
  scale_y_continuous(limits = c(0.0, 1.0)) + 
  theme(axis.text.y = element_text(size = 10)) 
 
# Post-migration edge correlation barplot 
e_post %>% 
  gather(Metric, value, Jaccard:Edge_Overlap, -layers) %>% 
  mutate(layers = str_replace(layers, "_post", ""), 
         layers = str_replace(layers, "_post", ""), 
         layers = str_replace(layers, "Eco", "Economic"),  
         Metric = str_replace(Metric, "_", " "),  
         layers = str_replace(layers, "-", " - ")) %>% 
  arrange(layers) %>% 
  ggplot() +  
  geom_col(aes(x = reorder(layers, value), y = value, fill = Metric),  
           position = "dodge") + 
  theme_bw() + 
  scale_fill_nejm() + 
  labs(y = "Layer Overlap", 
       x = "", 

568 

       subtitle = "Post-migration period layer edge overlaps") + 
  coord_flip() +  
  scale_y_continuous(limits = c(0.0, 1.0)) + 
  theme(axis.text.y = element_text(size = 10)) 
 
 
# Plotting MuxViz Multilayer Centrality Measures 
#' Three centrality measures were calculated in MuxViz 2.0 - strength,  
#' degree, and eigenvector. These provide assessments of the influence of 
#' individual nodes in a network layer. Combining the results across the  
#' layers provides an indirect assessment of the influence of a layer 
#' on the entire multilayer network  
pre_centr <- read_delim("pre-migration muxviz centrality.csv", ";",  
                         escape_double = FALSE, trim_ws = TRUE) 
post_centr <- read_delim("post-migration muxviz centrality.csv", ";",  
                         escape_double = FALSE, trim_ws = TRUE) 
 
# Plot pre-migration centrality scores across the layers 
pre_centr %>% 
  filter(Layer != "Aggr") %>% 
  select(Layer, Label, Degree, Strength, Eigenvector) %>% 
  gather(key = Statistic, value = value, Degree:Eigenvector, -Layer) %>% 
  mutate(Label = str_replace_all(Label, "_", " ")) %>% 
  mutate(Layer = ifelse(Layer == "1", "Plate attributes",  
                 ifelse(Layer == "2", "Jar attributes",  
                 ifelse(Layer == "3", "Style",  
                 ifelse(Layer == "4", "Economic", 0))))) %>% 
  rename(Site = Label) %>% 
  ggplot() + 
  geom_bar(aes(x = reorder(Site, value), 
               y = value, fill = Layer), stat = "identity") +  
  facet_wrap(~Statistic, scales = "free_x") + 
  coord_flip() + 
  scale_fill_nejm() + 
  theme_bw() + 
  xlab("") + 
  ylab("Centrality Score") + 
  facet_wrap(~Statistic, scales = "free_x") 
 
 
# Plot post-migration centrality scores across the layers 
post_centr %>% 
  filter(Layer != "Aggr") %>% 
  select(Layer, Label, Degree, Strength, Eigenvector) %>% 
  gather(key = Statistic, value = value, Degree:Eigenvector, -Layer) %>% 
  mutate(Label = str_replace_all(Label, "_", " ")) %>% 
  mutate(Layer = ifelse(Layer == "1", "Plate attributes",  
                 ifelse(Layer == "2", "Jar attributes",  
                 ifelse(Layer == "3", "Style",  
                 ifelse(Layer == "4", "Economic", 0))))) %>% 
  rename(Site = Label) %>% 
  ggplot() + 
  geom_bar(aes(x = reorder(Site, value), 

569 

               y = value, fill = Layer), stat = "identity") +  
  facet_wrap(~Statistic, scales = "free_x") + 
  coord_flip() + 
  scale_fill_nejm() + 
  theme_bw() + 
  xlab("") + 
  ylab("Centrality Score") + 
  facet_wrap(~Statistic, scales = "free_x") 
 
# Summary of centrality scores, pre-migration  
pre_centr %>% 
  filter(Layer != "Aggr") %>% 
  select(Layer, Label, Degree, Strength) %>% 
  gather(key = Statistic, value = value, Degree:Strength, -Layer) %>% 
  mutate(Label = str_replace_all(Label, "_", " ")) %>% 
  mutate(Layer = ifelse(Layer == "1", "Plate attributes",  
                 ifelse(Layer == "2", "Jar attributes",  
                 ifelse(Layer == "3", "Style",  
                 ifelse(Layer == "4", "Economic", 0))))) %>% 
  rename(Site = Label) %>% 
  group_by(Layer, Statistic) %>% 
  summarize(Total_Centrality = sum(value)) %>% 
  ggplot() + 
  geom_bar(aes(x = reorder(Layer, Total_Centrality), y= Total_Centrality, 
               fill = Statistic),  
           stat = "identity") + 
  coord_flip() + 
  scale_fill_jama() + 
  theme_bw() + 
  xlab("") + 
  ylab("Centrality Score")  
   
# Summary of centrality scores, post-migration 
post_centr %>% 
  filter(Layer != "Aggr") %>% 
  select(Layer, Label, Degree, Strength) %>% 
  gather(key = Statistic, value = value, Degree:Strength, -Layer) %>% 
  mutate(Label = str_replace_all(Label, "_", " ")) %>% 
  mutate(Layer = ifelse(Layer == "1", "Plate attributes",  
                 ifelse(Layer == "2", "Jar attributes",  
                 ifelse(Layer == "3", "Style",  
                 ifelse(Layer == "4", "Economic", 0))))) %>% 
  rename(Site = Label) %>% 
  group_by(Layer, Statistic) %>% 
  summarize(Total_Centrality = sum(value)) %>% 
  ggplot() + 
  geom_bar(aes(x = reorder(Layer, Total_Centrality), y= Total_Centrality, 
               fill = Statistic),  
           stat = "identity") + 
  coord_flip() + 
  scale_fill_jama() + 
  theme_bw() + 
  xlab("") + 

570 

  ylab("Centrality Score")  
   
 
 
# Plotting 
plot(cnet, vertex.labels.cex = .6) 
plot(cnet_pre, vertex.labels.cex = .6) 
plot(cnet_post, vertex.labels.cex = .6) 
 
# Circular layout 
l <- layout.circular.ml(cnet) 
plot(cnet, layout = l, vertex.labels.cex = .6) 
 
# Community Detection 
com <- clique.percolation.ml(cnet) 
com_pre <- clique.percolation.ml(cnet_pre) 
com_pre_4 <- clique.percolation.ml(cnet_pre, m = 4) 
com_post <- clique.percolation.ml(cnet_post) 
com_post_4 <- clique.percolation.ml(cnet_post, m = 4) 
plot(cnet, com = com, layout = l, vertex.labels.cex = .6) 
plot(cnet_pre, com = com_pre, vertex.labels.cex = .6) 
plot(cnet_pre, com = com_pre_4, vertex.labels.cex = .6) 
plot(cnet_post, com = com_post, vertex.labels.cex = .6) 
plot(cnet_post, com = com_post_4, vertex.labels.cex = .6) 
 
glouvain.ml(cnet_post) 
com_lart_pre <- lart.ml(cnet_pre) 
plot(cnet_pre, com = com_lart_pre, vertex.labels.cex = .6) 
com_lart_post <- lart.ml(cnet_post) 
plot(cnet_post, com = com_lart_post, vertex.labels.cex = .6) 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

571 

LA-ICP-MS Data and Supplementary Statistical Documentation for Group Assignments 

APPENDIX D  

 

 

Figure D.1 Percent variance explained by each principal component for the sherd data set 

 
 
Table D.1 Component loadings for the first 12 principal components, accounting for 90.4% of 
the variance in the 44 element data set 
 
Element 
Si 
Na 
Mg 
Al 
K 
Mn 
Fe 
Ti 

PC4 
-0.034 
-0.160 
0.226 
0.120 
0.087 
-0.361 
-0.001 
0.075 

PC11 
-0.035 
-0.376 
0.041 
0.137 
-0.013 
0.251 
0.054 
-0.004 

PC5 
-0.024 
-0.002 
0.241 
0.079 
0.043 
-0.350 
0.056 
-0.035 

PC8 
0.001 
0.450 
0.063 
-0.034 
0.104 
0.109 
0.011 
-0.065 

PC1 
-0.033 
0.021 
0.175 
0.066 
0.055 
0.282 
0.081 
0.058 

PC2 
0.026 
-0.262 
-0.532 
-0.030 
-0.152 
-0.226 
0.018 
-0.066 

PC3 
0.016 
0.059 
-0.085 
0.045 
-0.019 
-0.582 
-0.160 
0.092 

PC9 
-0.029 
0.359 
-0.215 
0.117 
0.158 
-0.068 
0.035 
0.206 

PC10 
0.009 
0.035 
0.293 
-0.114 
-0.198 
-0.133 
0.051 
0.122 

PC7 
-0.016 
-0.015 
-0.135 
0.047 
-0.104 
-0.207 
0.037 
0.043 

PC6 
0.011 
0.102 
0.567 
-0.079 
0.024 
-0.138 
-0.085 
0.101 

572 

 

PC12 
0.023 
-0.345 
0.213 
-0.055 
-0.342 
0.058 
-0.192 
-0.074 

 
0.079 
0.088 
0.138 
0.097 
0.109 
0.103 
0.183 
0.195 
0.165 
0.073 
0.098 
0.085 
0.136 
0.158 
0.104 
0.190 
0.187 
0.189 
0.106 
0.207 
0.169 
0.152 
0.084 
0.117 
0.178 
0.174 
0.196 
0.182 
0.193 
0.184 
0.196 
0.184 
0.185 
0.173 
0.180 
0.154 

 
0.167 
0.120 
0.288 
-0.048 
0.134 
0.185 
0.135 
-0.043 
0.277 
0.113 
0.018 
0.050 
0.068 
0.217 
0.171 
-0.102 
-0.128 
-0.109 
0.015 
-0.184 
0.184 
0.110 
0.155 
0.366 
-0.035 
-0.049 
-0.100 
-0.082 
-0.158 
-0.074 
-0.159 
-0.058 
-0.133 
-0.033 
-0.126 
0.018 

 
0.068 
0.051 
0.106 
-0.136 
0.095 
0.086 
0.152 
-0.024 
-0.105 
-0.071 
0.056 
-0.107 
-0.414 
-0.539 
-0.097 
-0.008 
-0.065 
0.005 
-0.117 
0.037 
-0.097 
-0.111 
-0.080 
0.085 
0.146 
0.150 
0.048 
0.160 
0.048 
0.178 
0.060 
0.183 
0.031 
0.168 
0.017 
0.011 

 
0.083 
-0.026 
0.023 
0.083 
-0.075 
-0.002 
-0.174 
-0.218 
0.036 
0.061 
0.089 
0.114 
0.019 
0.156 
0.095 
0.084 
0.018 
0.069 
0.166 
0.065 
0.032 
0.129 
0.137 
-0.557 
0.045 
0.039 
0.087 
0.043 
0.067 
0.055 
0.071 
0.073 
0.071 
0.072 
0.087 
0.128 

 
-0.042 
-0.052 
-0.187 
0.031 
-0.043 
-0.063 
-0.138 
-0.201 
-0.068 
-0.018 
-0.092 
0.002 
0.003 
-0.061 
0.062 
0.025 
0.021 
0.055 
0.059 
0.091 
0.103 
0.140 
0.065 
0.569 
0.019 
0.044 
0.062 
0.063 
0.111 
0.062 
0.112 
0.054 
0.104 
0.046 
0.105 
0.043 

Table D.1 (cont.) 
 
Li 
Be 
B 
Sc 
V 
Cr 
Ni 
Co 
Zn 
Rb 
Zr 
Nb 
In 
Sn 
Cs 
La 
Ce 
Pr 
Ta 
Y 
Pb 
U 
W 
Mo 
Nd 
Sm 
Eu 
Gd 
Tb 
Dy 
Ho 
Er 
Tm 
Yb 
Lu 
Th 
 
 
 
Table D.2 Posterior classification probabilities based on jackknifed Mahalanobis for Core A1 
and Core A2 Sub-Groups 

 
-0.129 
0.176 
-0.259 
-0.095 
0.051 
0.110 
0.338 
0.081 
-0.005 
-0.226 
0.020 
-0.052 
0.071 
0.517 
-0.358 
-0.040 
-0.066 
-0.052 
-0.197 
0.038 
-0.011 
-0.174 
-0.125 
-0.034 
0.101 
0.105 
0.043 
0.145 
0.005 
0.116 
-0.024 
0.115 
-0.045 
0.072 
-0.066 
-0.173 

 
-0.106 
0.020 
-0.581 
0.213 
0.049 
-0.013 
0.035 
0.097 
0.476 
-0.051 
-0.021 
0.093 
-0.068 
-0.223 
-0.014 
-0.010 
0.017 
-0.042 
0.037 
0.151 
0.182 
0.095 
-0.084 
0.011 
-0.131 
-0.109 
0.023 
-0.063 
0.018 
-0.079 
0.007 
-0.057 
0.013 
-0.076 
0.028 
0.013 

 
0.344 
0.065 
-0.449 
-0.116 
0.187 
0.132 
-0.179 
-0.079 
-0.043 
0.206 
-0.071 
0.001 
-0.141 
0.098 
0.270 
-0.089 
-0.157 
-0.083 
-0.099 
-0.054 
-0.166 
0.002 
0.122 
-0.174 
0.081 
0.078 
-0.008 
0.070 
-0.041 
0.108 
-0.024 
0.111 
-0.057 
0.121 
-0.060 
0.003 

 
-0.144 
-0.061 
0.028 
-0.114 
-0.009 
0.021 
-0.116 
0.076 
-0.178 
-0.257 
-0.045 
-0.037 
-0.100 
-0.010 
-0.123 
0.152 
0.289 
0.116 
0.013 
-0.221 
0.332 
0.179 
0.158 
-0.098 
0.190 
0.140 
0.046 
0.036 
-0.078 
-0.038 
-0.135 
-0.060 
-0.153 
-0.041 
-0.142 
0.068 

 
0.010 
-0.146 
-0.179 
0.067 
-0.060 
-0.113 
-0.203 
-0.150 
-0.416 
-0.007 
0.016 
0.009 
0.106 
0.287 
0.007 
0.070 
0.010 
0.057 
0.005 
0.082 
-0.278 
0.000 
-0.080 
0.330 
0.003 
0.009 
0.036 
-0.004 
0.040 
-0.020 
0.033 
-0.021 
0.050 
-0.019 
0.048 
0.036 

 
-0.119 
-0.190 
-0.103 
-0.357 
-0.168 
-0.114 
-0.277 
-0.104 
0.206 
0.037 
0.005 
-0.099 
-0.079 
0.094 
-0.103 
-0.186 
-0.175 
-0.122 
-0.036 
-0.165 
0.279 
0.162 
0.198 
0.087 
0.077 
0.096 
0.023 
0.119 
-0.013 
0.144 
-0.005 
0.160 
-0.002 
0.178 
-0.010 
-0.034 

 
0.100 
0.032 
-0.317 
-0.035 
0.148 
0.111 
0.120 
0.288 
-0.347 
0.040 
0.243 
0.234 
-0.054 
-0.108 
0.001 
0.020 
0.183 
0.029 
0.222 
-0.200 
0.032 
0.101 
0.161 
0.100 
0.070 
0.021 
-0.031 
-0.040 
-0.118 
-0.066 
-0.118 
-0.049 
-0.102 
-0.027 
-0.088 
0.097 

  
Sample # 
5 
23 
50 
67 
68 
70 
145 
159 
166 
180 
245 
246 
252 
 

  
Site 
Orendorf C 
Orendorf C 
Orendorf C 
Orendorf C 
Orendorf C 
Orendorf C 
Crable 
Crable 
Crable 
Crable 
C.W. Cooper 
C.W. Cooper 
Emmons 
Emmons 

  
Core A Sub-Group 

Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 

573 

Membership Probability 

Core A1  Core A2 
0.0000 
0.0000 
0.0000 
0.0000 
0.0080 
0.1430 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 

37.3690 
42.4300 
18.7800 
8.2790 
48.9720 
14.1390 
58.1420 
27.1720 
15.1250 
9.2120 
91.1720 
78.0740 
74.8250 
89.6390 

Table D.2 (cont.) 
253 
254 
261 
263 
266 
276 
277 
279 
280 
281 
291 
307 
319 
320 
327 
328 
329 
345 
394 
457 
499 
508 
511 
535 
537 
544 
545 
552 
561 
562 
563 
564 
580 
584 
630 
648 
655 
687 
728 
729 
737 
738 
740 
742 
745 
746 
748 
749 
750 
751 
755 
756 
757 
758 
763 
773 

Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Baehr South 
Myer-Dickson 
Myer-Dickson 
Myer-Dickson 
Myer-Dickson 
Myer-Dickson 
Myer-Dickson 
Star Bridge 
Star Bridge 
Ten Mile Creek 
Ten Mile Creek 
Ten Mile Creek 
Eveland 
Eveland 
Eveland 
Eveland 
Eveland 
Eveland 
Eveland 
Eveland 
Eveland 
Kingston Lake 
Kingston Lake 
Kingston Lake 
Kingston Lake 
Kingston Lake 
Lawrenz Gun Club 
Buckeye Bend 
Buckeye Bend 
Buckeye Bend 
Buckeye Bend 
Buckeye Bend 
Buckeye Bend 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Fouts Village 
Larson 

Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 

574 

91.7550 
83.7390 
59.3840 
80.6780 
95.6590 
35.5950 
17.2490 
28.3420 
90.3640 
43.1060 
9.9830 
10.0350 
88.1220 
55.3070 
18.0850 
87.9720 
31.0480 
30.6000 
83.2690 
79.3510 
13.8100 
83.6280 
69.5660 
44.0550 
57.0680 
13.6720 
28.6070 
37.8710 
42.6800 
67.0610 
64.9730 
30.5190 
53.6350 
81.5830 
10.1500 
72.6500 
12.3050 
31.3320 
17.1650 
19.6050 
64.7170 
29.1350 
6.0980 
86.6640 
34.3180 
88.9660 
42.8830 
75.3320 
63.9540 
44.7540 
45.2520 
88.4720 
34.2740 
60.3590 
50.7510 

0.0000 
0.0030 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.1650 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0010 
0.0790 
0.0000 
0.0000 
0.2990 
0.0000 
0.0110 
0.0330 
0.0180 
0.0050 
0.0160 
0.0000 
1.3380 
0.0080 
0.0260 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0290 
0.0010 
0.0000 
0.0000 
0.0330 
0.0020 
0.0680 
0.2640 
0.0500 
0.2800 
0.0000 
0.0010 
0.0100 
0.0320 
0.0660 
0.1320 
0.0000 
0.2340 
0.0000 

Table D.2 (cont.) 
 
780 
786 
788 
793 
796 
797 
810 
815 
819 
822 
826 
838 
842 
843 
845 
867 
882 
884 
888 
895 
896 
898 
900 
908 
910 
915 
918 
920 
921 
927 
930 
1061 
1068 
1070 
1072 
1163 
1170 
1171 
1177 
1178 
1184 
1187 
1194 
1201 
1202 
1207 
1211 
1213 
1223 
1226 
1235 
1242 
1251 
1257 
1282 

Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Larson 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Crable 
Crable 
Crable 
Crable 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Morton Village 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
Orendorf D 
C.W. Cooper 

Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 

575 

8.9070 
96.4890 
29.3050 
28.4760 
65.5530 
37.6950 
24.9180 
56.0440 
66.0180 
37.5620 
98.4980 
56.1790 
23.8470 
55.3470 
54.5590 
8.8500 
14.2240 
23.7390 
61.5110 
32.0750 
77.4130 
63.5530 
35.0040 
30.7550 
98.3630 
25.8110 
87.0970 
3.9680 
53.5450 
82.8340 
61.6430 
30.3960 
21.5850 
81.4990 
64.6400 
61.4770 
63.4230 
23.8940 
71.1460 
15.5530 
20.1310 
25.9160 
30.8080 
80.6520 
50.4840 
21.9190 
6.4620 
55.1570 
42.9220 
16.1780 
36.6980 
77.6970 
18.4250 
6.7060 
60.1370 

0.0030 
0.0000 
0.0000 
0.0000 
0.0110 
0.0000 
0.0010 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0010 
0.0000 
0.0000 
0.0000 
0.0000 
0.0040 
0.0010 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0330 
0.0000 
0.4320 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0390 
0.0030 
0.0000 
0.2160 
0.0260 
0.0010 
0.0000 
0.0000 
0.0000 
0.0040 
0.8890 
0.0370 
0.0110 
0.0050 
0.0110 
0.0150 
0.1340 
0.0540 
0.0000 

Table D.2 (cont.) 
 
1283 
1284 
1286 
1291 
1294 
1296 
1298 
1299 
1309 
66 
104 
105 
107 
118 
148 
162 
194 
199 
203 
206 
219 
221 
231 
241 
243 
257 
262 
270 
275 
285 
294 
298 
303 
310 
332 
346 
387 
398 
407 
427 
479 
488 
515 
520 
531 
538 
546 
553 
560 
565 
597 
600 
602 
608 
626 

C.W. Cooper 
C.W. Cooper 
C.W. Cooper 
C.W. Cooper 
C.W. Cooper 
C.W. Cooper 
C.W. Cooper 
C.W. Cooper 
Orendorf D 
Orendorf C 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Walsh 
Walsh 
Walsh 
Walsh 
Walsh 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
C.W. Cooper 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Emmons 
Baehr South 
Baehr South 
Baehr South 
Myer-Dickson 
Myer-Dickson 
Star Bridge 
Star Bridge 
Star Bridge 
Star Bridge 
Star Bridge 
Ten Mile Creek 
Ten Mile Creek 
Ten Mile Creek 
Ten Mile Creek 
Eveland 
Eveland 
Eveland 
Eveland 
Eveland 
Kingston Lake 
Kingston Lake 
Kingston Lake 
Kingston Lake 
Kingston Lake 

Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A1 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 

576 

63.9300 
47.1060 
93.8340 
83.6530 
11.5030 
68.0910 
63.6830 
53.0830 
83.0500 
0.1010 
0.0070 
0.0450 
0.0000 
0.0000 
0.0310 
0.0020 
0.0000 
0.0000 
0.0310 
0.0010 
0.0100 
0.0010 
0.0000 
0.0000 
0.0030 
0.2250 
0.0730 
0.3500 
0.0270 
0.1750 
0.0260 
0.0240 
0.0000 
0.0470 
0.0380 
0.0010 
0.0090 
0.3380 
0.0240 
0.0540 
0.0510 
0.0470 
0.0000 
0.0100 
0.0020 
0.0010 
0.0000 
0.1270 
0.0450 
0.0000 
0.0000 
0.0040 
0.0000 
0.0050 
0.0000 

0.0000 
0.0000 
0.0000 
0.0000 
0.0060 
0.0000 
0.0000 
0.0000 
0.3540 
11.8990 
82.0550 
91.9200 
50.8880 
54.1540 
68.3250 
31.3960 
94.4490 
77.8040 
27.7130 
55.3620 
82.0530 
3.5200 
41.7300 
49.0670 
54.0250 
54.5390 
71.1940 
26.0490 
70.7010 
5.1830 
74.6740 
27.7340 
51.8190 
49.1890 
10.8800 
64.6110 
59.4270 
8.6740 
67.7540 
26.5990 
4.0320 
22.1940 
20.9620 
26.4740 
60.0270 
38.5250 
10.6350 
9.7980 
9.3670 
19.0490 
88.7310 
16.4530 
17.8080 
67.1550 
66.3040 

0.0000 
0.1480 
0.0000 
0.0000 
0.0000 
0.0160 
0.0010 
0.0010 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0130 
0.2360 
0.5420 
0.1180 
0.0030 
0.0960 
0.1510 
0.0000 
0.0000 
0.0000 
0.0040 
0.0000 
0.0000 
0.0160 
0.0000 
0.0000 
0.0000 
0.0130 
1.4160 
0.0030 
0.0010 
2.3470 
0.0000 
0.1030 
0.0130 
0.0180 
0.0030 

77.4090 
58.4460 
55.7460 
43.4560 
91.4010 
96.2420 
79.5940 
40.9220 
75.7870 
97.3340 
47.3040 
15.8450 
59.8090 
83.3410 
6.8130 
23.3610 
4.9930 
22.2100 
15.6590 
66.7800 
49.9000 
56.2730 
44.9240 
36.0610 
23.7950 
82.1710 
28.5450 
93.3400 
96.2150 
88.7430 
95.8950 
21.0460 
11.6420 
7.2310 
88.9410 
22.2370 
27.6440 
45.4390 
98.0840 
39.6200 
98.5290 
85.4870 

 
Table D.2 (cont.) 
 
631 
650 
652 
661 
662 
663 
665 
673 
677 
680 
681 
682 
683 
685 
724 
739 
762 
850 
883 
901 
902 
913 
919 
1058 
1059 
1062 
1065 
1074 
1075 
1077 
1078 
1174 
1175 
1176 
1198 
1229 
1247 
1302 
1303 
1305 
1306 
1310 

Kingston Lake 
Kingston Lake 
Kingston Lake 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Lawrenz Gun Club 
Buckeye Bend 
Buckeye Bend 
Fouts Village 
Larson 
Morton Village 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Houston-Shryock 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Crable 
Morton Village 
Morton Village 
Morton Village 
Orendorf D 
Orendorf D 
Orendorf D 
Crable 
Crable 
Crable 
Crable 
Orendorf D 

 
 
 
 

Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 
Core A2 

577 

 

  

Al 
B 
Be 
Ce 
Co 
Cr 
Cs 
Dy 
Er 
Eu 
Fe 
Gd 
Ho 
In 
K 
La 
Li 
Lu 
Mg 
Mn 
Mo 
Na 
Nb 
Nd 
Ni 
Pb 
Pr 
Rb 
Sc 
Si 
Sm 
Sn 
Ta 
Tb 
Th 
Ti 
Tm 
U 
V 
W 
Y 
Yb 
Zn 
Zr 

 

Std Dev 
7826.4 
22.2 
0.4 
16.7 
2.3 
11.5 
0.8 
0.8 
0.5 
0.3 
6394.8 
0.9 
0.3 
0.0 
2369.6 
8.9 
6.2 
0.1 
6526.7 
291.2 
0.2 
1043.8 
2.4 
4.8 
9.9 
5.2 
2.2 
10.9 
4.0 
9357.3 
1.0 
0.4 
0.2 
0.2 
2.3 
570.7 
0.1 
0.5 
19.2 
0.2 
7.5 
0.4 
44.5 
20.5 

  
 

  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Average 
  
83861.7  ± 
61.0  ± 
2.4  ± 
82.0  ± 
11.3  ± 
83.5  ± 
5.4  ± 
5.1  ± 
2.9  ± 
1.7  ± 
46978.7  ± 
5.8  ± 
1.2  ± 
0.1  ± 
18879.7  ± 
41.8  ± 
37.4  ± 
0.5  ± 
8250.3  ± 
451.8  ± 
0.8  ± 
5537.5  ± 
18.3  ± 
33.5  ± 
39.6  ± 
25.5  ± 
10.7  ± 
104.2  ± 
20.1  ± 
336540.2  ± 
6.8  ± 
2.4  ± 
1.3  ± 
1.0  ± 
13.8  ± 
5049.6  ± 
0.5  ± 
3.4  ± 
122.2  ± 
1.6  ± 
30.8  ± 
2.9  ± 
157.1  ± 
130.8  ± 

Std Dev 
8462.4 
15.9 
0.3 
13.9 
1.5 
11.3 
0.9 
0.7 
0.5 
0.3 
7554.3 
0.8 
0.2 
0.0 
3005.5 
7.0 
5.5 
0.1 
1305.4 
198.3 
0.4 
924.0 
3.1 
4.1 
8.2 
4.0 
1.8 
12.1 
3.4 
10783.4 
0.9 
0.4 
0.2 
0.2 
1.9 
628.1 
0.1 
0.6 
22.8 
0.2 
7.6 
0.4 
31.6 
19.0 

Table D.3 Mean and standard deviation values for the ceramic geochemical compositional groups 
 

Core A (n = 161) 

Core A1 (n = 133) 

Core A2 (n = 88) 

Average 
  
89977.7  ± 
72.7  ± 
2.5  ± 
91.4  ± 
14.6  ± 
97.3  ± 
5.2  ± 
5.7  ± 
3.2  ± 
1.8  ± 
53982.3  ± 
6.4  ± 
1.3  ± 
0.1  ± 
21042.0  ± 
47.3  ± 
37.8  ± 
0.5  ± 
11606.3  ± 
678.6  ± 
0.8  ± 
6381.7  ± 
18.7  ± 
38.7  ± 
53.2  ± 
24.8  ± 
12.0  ± 
99.6  ± 
19.7  ± 
321719.5  ± 
7.7  ± 
2.5  ± 
1.3  ± 
1.0  ± 
14.6  ± 
5225.7  ± 
0.5  ± 
3.2  ± 
150.9  ± 
1.5  ± 
32.5  ± 
3.1  ± 
150.4  ± 
146.7  ± 

Std Dev 
7292.8 
20.7 
0.3 
15.6 
2.7 
11.6 
1.0 
0.8 
0.4 
0.3 
7132.0 
0.9 
0.2 
0.0 
2361.0 
8.6 
5.7 
0.1 
3376.1 
285.7 
0.3 
1223.8 
2.5 
4.7 
9.8 
4.1 
1.9 
13.1 
3.5 
9731.1 
0.9 
0.5 
0.2 
0.2 
2.3 
563.0 
0.1 
0.6 
24.2 
0.2 
7.0 
0.4 
36.5 
25.2 

  
 

  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Average 
  
93785.0  ± 
83.1  ± 
2.7  ± 
97.4  ± 
17.3  ± 
104.7  ± 
5.0  ± 
5.9  ± 
3.3  ± 
1.9  ± 
55216.3  ± 
6.6  ± 
1.3  ± 
0.1  ± 
22175.4  ± 
50.9  ± 
40.1  ± 
0.5  ± 
17914.7  ± 
820.8  ± 
0.7  ± 
6998.3  ± 
18.8  ± 
41.0  ± 
62.7  ± 
25.6  ± 
12.7  ± 
99.0  ± 
20.5  ± 
311372.4  ± 
8.0  ± 
2.6  ± 
1.3  ± 
1.1  ± 
15.1  ± 
5287.9  ± 
0.5  ± 
3.1  ± 
153.5  ± 
1.4  ± 
34.2  ± 
3.2  ± 
170.2  ± 
155.9  ± 

578 

 

  

Al 
B 
Be 
Ce 
Co 
Cr 
Cs 
Dy 
Er 
Eu 
Fe 
Gd 
Ho 
In 
K 
La 
Li 
Lu 
Mg 
Mn 
Mo 
Na 
Nb 
Nd 
Ni 
Pb 
Pr 
Rb 
Sc 
Si 
Sm 
Sn 
Ta 
Tb 
Th 
Ti 
Tm 
U 
V 
W 
Y 
Yb 
Zn 
Zr 

 

Std Dev 
5172.5 
11.7 
0.3 
14.4 
1.6 
7.4 
1.0 
0.8 
0.4 
0.3 
8966.9 
0.9 
0.2 
0.0 
2662.9 
6.6 
7.3 
0.1 
1558.2 
208.1 
0.5 
1313.4 
2.2 
3.3 
8.8 
2.4 
1.6 
17.0 
3.9 
7977.0 
0.6 
0.2 
0.2 
0.2 
2.0 
732.8 
0.1 
0.5 
14.0 
0.2 
6.8 
0.3 
31.5 
19.4 

  
 

  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Outgroup 1 (n = 39) 
Average 
  
96053.4  ± 
79.2  ± 
3.0  ± 
106.3  ± 
16.7  ± 
108.8  ± 
5.8  ± 
7.3  ± 
4.1  ± 
2.3  ± 
66075.9  ± 
8.4  ± 
1.7  ± 
0.1  ± 
20123.8  ± 
58.3  ± 
41.9  ± 
0.7  ± 
11976.4  ± 
1258.6  ± 
3.4  ± 
5273.9  ± 
19.6  ± 
46.4  ± 
67.4  ± 
37.1  ± 
14.8  ± 
104.7  ± 
23.5  ± 
308608.6  ± 
9.5  ± 
5.3  ± 
1.3  ± 
1.4  ± 
16.3  ± 
5268.8  ± 
0.7  ± 
4.2  ± 
165.5  ± 
1.5  ± 
47.3  ± 
3.8  ± 
226.0  ± 
144.7  ± 

Std Dev 
13944.9 
33.9 
0.5 
20.8 
4.4 
17.9 
1.7 
1.9 
1.0 
0.6 
22711.5 
2.3 
0.5 
0.0 
5145.7 
13.9 
18.8 
0.2 
6433.8 
972.3 
4.0 
2337.8 
3.5 
9.0 
16.9 
17.5 
3.4 
22.0 
4.9 
15673.1 
2.1 
6.1 
0.2 
0.5 
2.7 
1049.6 
0.2 
1.1 
38.8 
0.3 
17.4 
0.7 
100.3 
33.3 

Table D.3 (cont.) 

 
 

Core B (n = 21) 

Core C (n = 13) 

Average 
  
101189.3  ± 
86.7  ± 
3.1  ± 
109.6  ± 
18.5  ± 
112.2  ± 
5.2  ± 
6.7  ± 
3.8  ± 
2.1  ± 
58195.8  ± 
7.5  ± 
1.4  ± 
0.1  ± 
22769.6  ± 
58.4  ± 
41.1  ± 
0.6  ± 
18059.4  ± 
752.9  ± 
0.7  ± 
6789.3  ± 
20.7  ± 
46.5  ± 
67.9  ± 
29.4  ± 
14.4  ± 
103.9  ± 
22.0  ± 
301631.5  ± 
9.0  ± 
3.3  ± 
1.5  ± 
1.2  ± 
17.1  ± 
5848.9  ± 
0.6  ± 
3.9  ± 
152.4  ± 
1.6  ± 
39.1  ± 
3.7  ± 
229.1  ± 
172.0  ± 

Std Dev 
8878.5 
31.3 
0.4 
14.1 
3.0 
13.6 
1.3 
1.0 
0.6 
0.2 
6574.8 
1.0 
0.1 
0.0 
3066.7 
7.5 
8.7 
0.1 
8689.8 
376.0 
0.3 
1304.1 
2.0 
5.6 
12.2 
6.0 
1.8 
14.7 
3.5 
11596.5 
1.1 
0.7 
0.2 
0.1 
2.6 
512.1 
0.1 
0.8 
21.8 
0.2 
4.7 
0.6 
77.4 
21.2 

  
 

  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Average 
  
77825.0  ± 
47.1  ± 
2.2  ± 
65.6  ± 
10.1  ± 
77.4  ± 
4.4  ± 
4.6  ± 
2.6  ± 
1.5  ± 
48996.8  ± 
5.3  ± 
1.0  ± 
0.1  ± 
16410.1  ± 
33.6  ± 
32.4  ± 
0.4  ± 
7792.6  ± 
406.0  ± 
0.8  ± 
6971.0  ± 
16.5  ± 
29.3  ± 
37.5  ± 
22.0  ± 
8.8  ± 
87.2  ± 
16.9  ± 
341586.2  ± 
6.0  ± 
2.0  ± 
1.2  ± 
0.8  ± 
11.6  ± 
4927.8  ± 
0.4  ± 
2.8  ± 
114.9  ± 
1.4  ± 
25.7  ± 
2.5  ± 
129.3  ± 
112.5  ± 

579 

Table D.3 (cont.) 

 
 

 

  

Al 
B 
Be 
Ce 
Co 
Cr 
Cs 
Dy 
Er 
Eu 
Fe 
Gd 
Ho 
In 
K 
La 
Li 
Lu 
Mg 
Mn 
Mo 
Na 
Nb 
Nd 
Ni 
Pb 
Pr 
Rb 
Sc 
Si 
Sm 
Sn 
Ta 
Tb 
Th 
Ti 
Tm 
U 
V 
W 
Y 
Yb 
Zn 
Zr 

 

Outgroup 2 (n = 20) 
Average 
  
78046.1  ± 
46.6  ± 
2.4  ± 
68.1  ± 
11.1  ± 
78.3  ± 
4.0  ± 
3.8  ± 
2.0  ± 
1.2  ± 
55708.7  ± 
4.2  ± 
0.9  ± 
0.1  ± 
18096.4  ± 
33.7  ± 
29.9  ± 
0.4  ± 
5107.6  ± 
574.3  ± 
0.7  ± 
5138.9  ± 
15.6  ± 
25.4  ± 
43.3  ± 
17.8  ± 
8.8  ± 
83.7  ± 
18.3  ± 
339954.2  ± 
5.2  ± 
1.8  ± 
1.0  ± 
0.8  ± 
10.3  ± 
3980.7  ± 
0.4  ± 
2.3  ± 
119.6  ± 
1.1  ± 
23.4  ± 
2.0  ± 
111.2  ± 
112.3  ± 

Std Dev 
14533.7 
9.3 
0.8 
15.2 
2.7 
11.9 
0.9 
1.2 
0.6 
0.3 
12989.9 
1.2 
0.3 
0.0 
4451.8 
6.7 
5.7 
0.1 
3595.6 
309.4 
0.3 
1736.7 
2.3 
6.8 
15.6 
6.3 
2.3 
15.7 
4.5 
19989.5 
1.4 
0.4 
0.3 
0.2 
3.1 
903.0 
0.1 
0.8 
25.1 
0.3 
4.8 
0.6 
30.9 
18.0 

  
 

  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Unassigned (n = 68) 
Average 
  
83732.1  ± 
61.2  ± 
2.5  ± 
107.8  ± 
22.7  ± 
93.7  ± 
5.0  ± 
5.1  ± 
2.9  ± 
1.7  ± 
55436.1  ± 
5.9  ± 
1.2  ± 
0.1  ± 
19804.1  ± 
46.4  ± 
33.4  ± 
0.5  ± 
11089.3  ± 
1333.5  ± 
1.4  ± 
5818.7  ± 
18.1  ± 
35.3  ± 
59.0  ± 
29.2  ± 
11.8  ± 
94.6  ± 
21.7  ± 
327378.5  ± 
7.0  ± 
3.9  ± 
1.2  ± 
1.0  ± 
13.4  ± 
5094.2  ± 
0.5  ± 
3.3  ± 
141.9  ± 
1.4  ± 
33.3  ± 
2.8  ± 
175.9  ± 
141.4  ± 

Std Dev 
16282.0 
24.1 
0.8 
131.8 
65.4 
53.8 
1.7 
1.6 
0.9 
0.5 
14790.8 
1.8 
0.4 
0.2 
5626.1 
14.1 
7.9 
0.1 
8066.7 
3842.3 
1.5 
1934.0 
4.1 
10.4 
50.2 
27.0 
3.5 
24.3 
5.6 
24369.5 
2.0 
3.7 
0.3 
0.3 
3.2 
1315.8 
0.1 
1.7 
49.1 
0.4 
10.4 
0.9 
169.0 
79.5 

580 

APPENDIX E  

 

Plate Stylistic Design Group Sketches 

Sketch-tracings or design sketches are provided for each of the plate style groups 

 
 
 

presented in Chapter 6. Sketch-tracings are denoted by the presence of 1 cm square scales and 

were sketched using a re-purposed computer monitor that was laid flat for accuracy of tracing. 

Certain design-only sketches appear without a scale. Unique Type numbers are provided that 

correspond to narrative descriptions of plate decoration presented in the Coding Sheet in 

Appendix A. These unique decoration categories total 94 across the 429 vessels with design 

techniques present. Additionally, a Brainerd Robinson (BR) group number is specified, which 

correspond to the 29 decoration motif grouping categories. Decoration categories were 

determined based on perceived similarities in decoration motifs alone (i.e. disregarding design 

technique) in order to focus solely on symbolism.    

 

The term ‘share’ is used in sketches to denote unique types that share the decoration 

motif but were assessed as distinct in initial classification. The term ‘also’ is used below to 

denote vessels that were assessed as the same unique type number in initial classification.  

Sketches are ordered by BR group number and by unique decoration category. 

581 

582 

 

583 

 

584 

 

585 

 

586 

 

587 

 

588 

 

589 

 

590 

 

591 

 

592 

 

593 

 

594 

 

595 

 

596 

 

597 

 

598 

 

599 

 

600 

 

601 

 

602 

 

603 

 

604 

 

605 

 

606 

 

607 

 

608 

 

609 

 

610 

 

611 

 

612 

 

613 

 

614 

 

615 

 

616 

 

617 

 

618 

 

619 

 

620 

 

621 

 

622 

 

623 

 

624 

APPENDIX F  

 

Jar and Plate Profile Sample 

The following samples of jar and plate profiles are provided for heuristic purposes as well 

 
 

as to highlight the artifacts themselves that form the basis of the analyses and interpretations 

presented in this study. The sherds chosen for profiling follow no pre-defined sampling strategy 

but are meant to be representative of each assemblage. Profiles are scaled appropriately within a 

tolerance of approximately one cm, but no indications are provided for the presence of 

decoration or cord marking since detailed photographs of all vessels were taken and may be 

made available for research or teaching purposes by contacting the author. The orientations of 

vessels based on rim profiles are of course approximate. Numbering indicates the unique vessel 

identification number assigned to each vessel. A ‘J’ preceding a vessel number indicates a 

domestic jar, while a ‘P’ indicates a plate. Vessel identification numbers are sequential and do 

not consider the vessel class, which are provided here for ease of vessel type interpretation.  

 

Jar and plate rim profiles from three sites are not presented here since they are already 

published elsewhere. See Conrad (1991) for profiles of vessels from Orendorf Settlement C and 

D (as well as for select other sites). See Conner (2016) for profiles of vessels from Myer-

Dickson.   

 

625 

626 

 

627 

 

628 

 

629 

 

630 

 

631 

 

632 

 

633 

 

634 

 

635 

 

636 

637 

638 

639 

640 

 

641 

 

642 

 

 
 
XRD #

APPENDIX G  

 

Mineralogical Analysis Results 

Provenance/notes
Jar sherd from Orendorf Settlement D; refired in village confligration
Jar sherd from Orendorf Settlement D; refired in village confligration
Jar sherd from Orendorf Settlement D; refired in village confligration
Jar sherd from Orendorf Settlement D; refired in village confligration
F270 L2024; Jar sherd from Larson; un-refired
F137 L1491; Jar sherd from Larson; un-refired
H55; Plate sherd from Larson; un-refired
F71 L365; Plate sherd from Larson; un-refired
East Creek outcrop, strata above lowest red layer above creek
East Creek outcrop, red strata above Sample #33

Sample # Type
sherd
sherd
sherd
sherd
sherd
sherd
sherd
sherd
outcrop
outcrop
outcrop Manito sand pit; layers of sand above and below clay; collected with Ed
outcrop? Recovered from pit at Lawrenz Gun Club at depth of 45-55 cmbd; manuport
outcrop
outcrop
outcrop
outcrop
core
core
core
outcrop
core
sherd

bottom of sand bank/river bend from Tenmile Creek near Caterpillar Peoria proving ground
taken from bank of Coal Creek; iron? inclusion/coloration?
taken from bank of West Branch LaMarsh Creek; red inclusions in matrix
taken from creek that feeds La Moine River
Illinois Valley, Emiquon 3.53 - 3.55 m
Kimmswick; 12.70 - 12.71 m
Illinois Valley, NW of Meredosia  3.78 - 3.85 m; 705926.959 4414752.135
East Creek outcrop; red clay - lowest strata exposed by creek
Spunky Bottom - cored to 160-182cm; very low in the B-Horizon; collected with Ed
L2099/F345/H12; Plate sherd from Myer-Dickson

1 1198
2 1207
3 1214
4 1218
5 776
6 796
7 810
8 844
9 33
10 34
11 36
12 38
13 16
14 18
15 21
16 25
17 EMQ-40
18 KMM-01
19 DPL-003
20 32
21 37
22 338

Kaolinite Illite I/S Calcite dolomite Quartz Orthoclase Plagioclase
5
6
8
10
6
5
5
3
12
8
3
0
7
4
5
13
10
6
3
2
1
6

74 3
34 0
42 1
51 10
47 2
43 1
46 5
32 2
55 7
42 2
38 1
7 1
39 3
50 1
64 5
61 1
41 7
25 4
37 1
54 1
41 3
42 2

0 18
0 60
0 49
0 29
0 36
0 51
0 44
0 33
20 6
35 10
29 29
0 7
15 11
22 17
13 13
13 12
15 18
23 10
29 39
18 25
27 28
0 50
Clays

0
0
0
0
9
0
0
30
0
3
0
85
0
0
0
0
0
7
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
25
6
0
0
9
5
0
0
0
0

 
Table G.1 X-ray Diffraction Results 
 
XRD analysis was performed at University of Cincinnati College of Engineering and Applied Science Advanced Materials 
Characterization Center. See Chapter 4 for a discussion of methodology and interpretations.  
 
Sample numbers for ceramic sherds are those used in artifact attribute recordings. Sample numbers for clay outcrop or cores are 
unique to this XRD analysis.  

Carbonates

Silicates

 

643 

APPENDIX H  

 

Site Identification Codes and Radiocarbon Probabilities 

 
 
Table H.1 Site IAS and ISM Identification Numbers 
 

IAS Number(s) 
11Br47 
11F310 
11F15 
11F249 
11F218 
11F353 
11F164 
11F114 
11P11 
11F3 
11Cs4, Cs11 - 19 
11F2 
11F10 
11F1284 
11Br105 or 11Br17 
11T2 
11Br11 

Site Name 
Baehr South 
Buckeye Bend 
C.W. Cooper 
Crable 
Emmons Village 
Eveland 
Fouts Village 
Houston-Shryock 
Kingston Lake 
Larson 
Lawrenz Gun Club 
Morton Village 
Myer-Dickson 
Orendorf 
Star Bridge 
Ten Mile Creek  
Walsh 
 
IAS - Illinois Archaeological Survey or Smithsonian Trinomial 
ISM - Illinois State Museum 

ISM Number(s) 
11Br2? 
11Fv1079 
11Fv47 
11Fv891-898 
11Fv962 
11Fv900 
11Fv664 
11Fb901-904 (11Fv902-903) 
11Pv1-5 
11Fv1109 
- 
11Fv19 
11Fv33 
11Fv1284 
11Brv55 
11Tv4 
11Brv46 

 

 

 

 
 
 
 
 
 
 

644 

1975-0080
1975-0080
1959-0025
1958-0100
1960-0043
-
-
-
-
-
-
-
-
-

Sample Material Provenience
maize kernel
deer astragalus
maize kernels
thatch
charred twig
bone (collagen)
bone (collagen)
hazelnut

11F310 - 1
11F310 - 2
11P11 - 1
11F114 - 1
11F218 - 1
11Br47 - 1
11F164 - 1
F321-2
Str 26-5SW PP286 willow twig
Str 34 Bl18-1A
11T2 - 1
11T2 - 2
11Br105 - 1
11Br105 - 2

CIRV Site Radiocarbon assay probabilities 
 
 
Table H.2 Radiocarbon assay probabilities and results 
 
ISM Site # ISM Accession Sample #
Site
11F310
Buckeye Bend
11F310
Buckeye Bend
Kingston Lake
11P11
Houston-Shryock 11F114
Emmons Village 11F218
11Br47
Baehr South
11F164
Fouts Village
Morton Village
11F2
11F2
Morton Village
11F2
Morton Village
Ten Mile Creek
11T1
11T2
Ten Mile Creek
11Br105
Star Bridge
Star Bridge
11Br105
 
 
Calibrated probability assessments for the 11 successful radiocarbon assays are presented below courtesy of OxCal.  
 
 
 
 
 
 
 
 
 
 
 

Pit 4 
House 26
unknown
House 2
house excavation
unknown
unknown structure
F321 Level 2
Str 26-5SW PP286
Str34 Bl18-1A
Unknown feature
Burned house w/cm jar
unknown burnt structure
unknown burnt structure

hazelnuts
antler tine
elk long bone
antler tine
antler tine

961
651

failed in measurement

modern
625
880

Radiocarbon Age BP 1σ error DirectAMS code
D-AMS 026576
30 D-AMS 026579
25 D-AMS 026577
D-AMS 026578
30 D-AMS 026575
23 D-AMS 027116
D-AMS 027296
32 D-AMS 030550
29 D-AMS 030535
28 D-AMS 030536
29 D-AMS 020156
34 D-AMS 020157
25 D-AMS 020158
27 D-AMS 020159

insufficient collagen preservation

561
586
620
624
625
635
569

 

645 

 

 

Figure H.1 Emmons Lake radiocarbon assay probability 

Figure H.2 Kingston Lake radiocarbon assay probability 

646 

 

 

 

Figure H.3 Baehr South radiocarbon assay probability 

Figure H.4 Buckeye Bend radiocarbon assay probability 

647 

 

 

Morton Village (11F2) 

 

Figure H.5 Morton Village radiocarbon assay probability (1) 

Morton Village (11F2) 

Figure H.6 Morton Village radiocarbon assay probability (2) 

648 

 

 

Morton Village (11F2) 

Figure H.7 Morton Village radiocarbon assay probability (3) 

 

Figure H.8 Star Bridge radiocarbon assay probability (1) 

 

649 

 

 

 

 

Figure H.9 Star Bridge radiocarbon assay probability (2) 

Figure H.10 Ten Mile Creek radiocarbon assay probability (1) 

 

650 

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Figure H.11 Ten Mile Creek radiocarbon assay probability (2) 

 

651 

 

 

 

 

 

 

 

 

 

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