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
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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.
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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
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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
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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.
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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-
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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
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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.
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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.
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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.
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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
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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
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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
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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
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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
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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
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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,
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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
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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
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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
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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
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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).
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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
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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
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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
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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.
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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
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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.
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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
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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
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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
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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
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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
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all links present, the Simple Matching coefficient simply quantifies the degree to which there are
overlapping links.
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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
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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
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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
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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.
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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.
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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
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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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Variable Type
Factor
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Ordinal
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Factor
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Continuous
Continuous
Continuous
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Levels | Measurement
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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
143
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
144
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
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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
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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
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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
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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
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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
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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,
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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.
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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
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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)
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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
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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
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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
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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
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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
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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
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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.
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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-
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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.
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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
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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.
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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
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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
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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
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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.
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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
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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.
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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
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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
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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
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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
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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
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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
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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,
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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.
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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
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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.
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)?
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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
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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-
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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
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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.
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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.
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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
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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.
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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
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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).
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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 –
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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
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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
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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
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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
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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
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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.)
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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.
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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
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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.
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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-
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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.
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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.
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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).
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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
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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.
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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
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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.
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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
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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.
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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
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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
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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",
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"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)
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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)
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# 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
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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,
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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,
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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")
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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),
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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){
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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)) +
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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---------------
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#--------------------------------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
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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
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# 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) +
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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
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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))
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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
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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)
}
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)
# 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
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# 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)
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# 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)] %>%
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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(),
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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")
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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
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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
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# 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)
}
}
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} 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)))
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}
}
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
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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
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# 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") +
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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
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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")
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# 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 %>%
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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
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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")
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# 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`)) %>%
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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$Time4) <- c("Pre-Migration", "Pre- and Post",
"Post-Migration")
# Remove Orendof D and Fouts and plot box and whisker plot
cer_div %>%
filter(Site != "Orendorf D") %>%
filter(Site != "Fouts Village") %>%
ggplot() +
geom_boxplot(aes(x = Time4, y = `Count of Design Categories`)) +
xlab("") +
theme_classic() +
scale_y_continuous(expand = c(0, 0), limits = c(0, 20),
breaks = c(0, 5, 10, 15, 20)) +
ylab("Count of Design Categories Present") +
theme(text = element_text(size=20))
# Regression of number of design categories as explained by sample size
categories <- read_xlsx("Number of Categories and Sample Size from each site for regression.xl
sx")
# Summary of regression
cat_lm <- lm(num_categories ~ sample_size, data = categories)
summary(cat_lm)
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tidy(cat_lm)
# Regression plot - looks strongly positive
categories %>%
filter(Site != "Fouts Village")%>%
ggplot(aes(x = sample_size, y = num_categories)) +
geom_smooth(method = "lm", se = FALSE) +
geom_point()
# Correlation of the number of categories as a function of sample size -
# indeed the larger the sample size, the more plate decoration categories
# are present
cor(categories$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
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# 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)
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#--------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
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# 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))
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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)
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# 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)
}
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)
# 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
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# 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)) +
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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$stat)
# Calculate the absolute value of the slope
abs_BR_all_obs_slope <- lm(weight ~ Distance, data = BR_el_un) %>%
tidy() %>%
filter(term == "Distance") %>%
pull(estimate) %>%
abs()
abs_BR_pre_obs_slope <- lm(weight ~ Distance, data = BR_el_un_pre) %>%
tidy() %>%
filter(term == "Distance") %>%
pull(estimate) %>%
abs()
abs_BR_post_obs_slope <- lm(weight ~ Distance, data = BR_el_un_post) %>%
tidy() %>%
filter(term == "Distance") %>%
pull(estimate) %>%
abs()
# Compute the p-value
BR_all_perm_slope %>%
mutate(abs_BR_all_obs_slope = abs(stat)) %>%
summarize(p_value = mean(abs_BR_all_obs_slope > BR_all_perm_slope))
BR_pre_perm_slope %>%
mutate(abs_BR_pre_obs_slope = abs(stat)) %>%
summarize(p_value = mean(abs_BR_pre_obs_slope > BR_pre_perm_slope))
BR_post_perm_slope %>%
mutate(abs_BR_post_obs_slope = abs(stat)) %>%
summarize(p_value = mean(abs_BR_post_obs_slope > BR_post_perm_slope))
# Linear models sans visualization
# explore residuals
BR_all_lm <- augment(lm(weight ~ Distance, data = BR_el_un))
BR_pre_lm <- augment(lm(weight ~ Distance, data = BR_el_un_pre))
BR_post_lm <- augment(lm(weight ~ Distance, data = BR_el_un_post))
# Check SSE - how well do the models fit?
augment(lm(weight ~ 1, data = BR_el_un)) %>%
summarize(SSE = var(.resid)) # null
BR_all_lm %>% summarize(SSE = var(.resid))
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augment(lm(weight ~ 1, data = BR_el_un_pre)) %>%
summarize(SSE = var(.resid)) # null
BR_pre_lm %>% summarize(SSE = var(.resid))
augment(lm(weight ~ 1, data = BR_el_un_post)) %>%
summarize(SSE = var(.resid)) # null
BR_post_lm %>% summarize(SSE = var(.resid))
# Looks like the models do fit well
# Breakdown of linear model results for plate attribute networks
summary(lm(weight ~ Distance, data = BR_el_un)) # for each 1 km increase in distance, weight d
rops 0.0006741 and at 0 distance, a weight of 0.5549 is expected
summary(lm(weight ~ Distance, data = BR_el_un))$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)$weight))
}
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# Calculate the mean weighted degree (or strength) for each graph
post.weighted.degree <- lapply(gpost.d, function(x){
y <- strength(x)
mean(y)
}
)
# Unlist and change to a data frame for vizualizations
post.weighted.degree <- as.data.frame(unlist(post.weighted.degree))
ggplot(post.weighted.degree, aes(x = post.weighted.degree)) +
geom_histogram(aes(y = ..density..), bins = 16) +
geom_vline(xintercept = (mean(strength(BR_g_post, mode = "all"))),
linetype = "dashed", color = "red") +
geom_density() +
ggtitle("Distribution of Mean Weighted Degree in 5000 Random Models & \nPost-Migration Perio
d Network Mean Degree") +
xlab("Mean Degree") +
ylab("")
R Code from Chapter 7 Networks of Economic Relationships - Results of the Chemical
Analyses
Create map of sites and clay samples
# Map of sites and clay resources
library(ggmap)
library(tidyverse)
library(ggrepel)
# Read in context data
cc_loc <- read_csv("Clay Ceramic lat long.csv")
# Set center for the map
lat_mid <- mean(cc_loc$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
}
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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$Sample)
orows <- str_detect(dfsamps, "red")
df_samples <- df_shell_corrected[!orows, ]
df_reds <- df_shell_corrected[orows, ]
# Write csv with samples only, Ohio Red standards removed
write_csv(df_samples, "Upton_results_samples_shell_corrected_August_21_2018.csv")
# Write csv with Ohio Reds only
write_csv(df_reds, "Upton_results_OhioRed_August_21_2018.csv")
Ohio Red extraction and analysis
New Ohio Red clay is the common standard used in the chemical analysis of clay and archaeological
samples by LA-ICP-MS and INAA. Here, the standards run each day of LA-ICP-MS anlaysis are
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extracted from the entire data set and analyzed in their own right to determine the accuracy of the
different machines. Ultimately, it was decided to discard a number of sherds that were run on the old
machine at the Field Museum’s Elemental Analysis Facility (circa 2015) and only retain ceramic samples
run on the new machine.
# Extract Ohio Reds and Calculate Relative Standard Deviation
library(tidyverse)
library(stringr)
library(plotly)
# Import data
dfall <- read_csv("Upton_results_OhioRed_August_21_2018.csv")
# Change Sample column to all lower case to ensure complete string detection
dfall$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() +
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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$Date), format = "%Y-%b-%d", tz = "UTC")
redAVG_group <- ohioreds %>%
mutate(Machine = ifelse(Date > as.POSIXct('2016-01-01', tz = "UTC"),
"New", "Old")) %>%
gather(element, sample, SiO2:Th) %>%
group_by(Machine, element) %>%
summarize(Avg = mean(sample), SD = sd(sample))
# Count the number of Ohio Red samples run on each machine
ohioreds %>%
mutate(Machine = ifelse(Date > as.POSIXct('2016-01-01', tz = "UTC"),
"New", "Old")) %>%
select(Machine) %>%
group_by(Machine) %>%
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summarize(num = n())
write_csv(redAVG_group, "Ohio Reds across Machines_Aug_22_2018.csv")
Analysis of CIRV clay sample
# Clay analysis
library(tidyverse)
library(stringr)
library(plotly)
library(shiny)
library(shinydashboard)
library(ggsci)
library(broom)
library(knitr)
library(ggfortify)
library(stats)
library(ICSNP)
library(factoextra)
library(dendextend)
# Read in full dataset
all_samples <- read_csv("Upton_results_samples_shell_corrected_August_21_2018.csv")
# Read in clay context data
clay_context <- read_csv("clay context data.csv")
# Each clay sample is named "C##_1"
# An expedient way of isolating the clay samples
clay <- arrange(all_samples[str_detect(all_samples$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")
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# 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) %>%
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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$Sample) +
labs(x = "Principal Component 1",
y = "Principal Component 2",
title = "First two principal components of PCA on CIRV Clay dataset")
)
) %>%
pull(pca_graph)
# autoplot is lazy with color. In order to make this publication friendly, have to
# manually edit the color scales
cp1p2_plot[[1]] + scale_fill_manual(values = c("black","black")) +
scale_color_manual(values = c("black","black","black"))
# Plot PCs 1 & 3 against each other
cp1p3_plot <- clay_pca %>%
mutate(
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pca_graph = map2(
.x = pca,
.y = data,
~ autoplot(.x, x = 1, y = 3, loadings = TRUE, loadings.label = TRUE,
loadings.label.repel = TRUE,
loadings.label.colour = "black",
loadings.colour = "gray85",
loadings.label.alpha = 0.5,
frame = TRUE,
frame.type = "norm",
data = .y,
colour = "Geography_2",
shape = "Geography_2",
frame.level = .9,
frame.alpha = 0.001,
size = 2) +
theme_bw() +
#geom_text(label = .y$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')
)
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)
)
############
## 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)") +
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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))
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# 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)], .) %>%
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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$Geography_2))
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# How about using some elements that show good separation between the groups?
group.mem.probs(clay_pcaready[, c("Ni", "Cs")], clay_pc1to7$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)
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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))
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# 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
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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 = "",
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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,
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#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",
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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$Sample) +
labs(x = "Principal Component 1",
y = "Principal Component 2",
title = "First two principal components of PCA on CIRV Ceramic dataset")
)
) %>%
pull(pca_graph)
ggplotly(time_pc1pc2[[1]])
# Again, this appears similar to the prior PC biplot separated by vessel class - there is
# no general trend of group separation but some interesting insights when considering
# outliers.
# Perhaps Oneota presence may be more revealing
oneota_pc1pc2 <- sample_pca %>%
mutate(
pca_graph = map2(
.x = pca,
.y = data,
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~ autoplot(.x, loadings = TRUE, loadings.label = TRUE,
#loadings.label.repel = TRUE,
loadings.label.colour = "black",
loadings.colour = "gray85",
loadings.label.alpha = 0.5,
loadings.label.size = 3,
loadings.label.hjust = 1.1,
frame = TRUE,
frame.type = "norm",
data = .y,
colour = "Oneota_Present",
shape = "Oneota_Present",
frame.level = .9,
frame.alpha = 0.001,
size = 2) +
theme_bw() +
#geom_text(label = .y$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,
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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)
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# 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)
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# 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))
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# 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$Kmediods_5)] <- 0
# Assess membership probabilities using my heuristic
kmed5_group_mem %>%
mutate(new_assign = ifelse(assigned_val > 10 & `1` < 10 & `2` < 10 & `3` < 10 &
`4` < 10 & `5` < 10,
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Kmediods_5, "unassigned")) %>%
# filter(new_assign != "unassigned")
summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100)
# Ouch, at 95.58% unassigned using the heuristic criteria, this doesn't hold up
########### Kmedoids (pam) 2 #################
# Group probabilities for the kmedoids (pam) 2 cluster solution on PC's 1 to 12
# (90% of variability)
kmed2_group_mem <- group.mem.probs(pc1to12, sample_new_stat_clusters$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$Kmediods_2)] <- 0
# Assess membership probabilities using my heuristic
kmed2_group_mem %>%
mutate(new_assign = ifelse(assigned_val > 10 & `1` < 10 & `2` < 10,
Kmediods_2, "unassigned")) %>%
# filter(assigned_val < `1` | assigned_val < `2`)
summarize(perc_unassigned = sum(new_assign == "unassigned")/n() * 100)
# A 79.01% unassigned using the heuristic criteria is better, but still doesn't hold up
# Since none of these clustering methods were successful when held against Mahalanobis
# Distance, we'll drop them from the augmented PCA data
sample_pca[['pca_aug']][[1]] <- sample_pca[['pca_aug']][[1]] %>%
select(-Kmeans_2:-Kmediods_5)
########### Mahalanobis-first route #######################################################
########### Core and Unassigned Group Assignments #########################################
# Another common method used for constructing core chemical compositional groups in
# archaeology is to initially treat the entire data set as one large group and iteratively
# removing samples with a membership probability of less than 1%. A Core group can thus
# be defined and sub-groups may be identified within the Core.
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# Double the PC data so the group can be compared to itself
pc1to12_twice <- bind_rows(pc1to12, pc1to12)
# Double the stat cluster assignment data
sample_new_stat_clusters_twice <- bind_rows(sample_new_stat_clusters,
sample_new_stat_clusters)
# Create vector of group assignments
one_two <- c(rep(1, 543), rep(2, 543))
# Bind group assignments to cluster data
sample_new_stat_clusters_twice <- cbind(sample_new_stat_clusters_twice, one_two)
# Group probabilities for the group as one data set on PC's 1 through 12
one_group_mem <- group.mem.probs(pc1to12_twice, sample_new_stat_clusters_twice$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$Sample)
### Iteration two
# Bind samples list to PCA data, filter out the unassigned samples after iteration one
# and select PC data only for group membership probability calculation
pc1to12_twice_iter2 <- bind_cols(sample_new_stat_clusters_twice[, c("Sample", "one_two")],
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pc1to12_twice) %>%
filter(Sample %in% iter1$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)
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# 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$Sample)
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# Group probabilities for iteration 4 of the group as one data set on PC's 1 through 12
one_group_mem_iter_4 <- group.mem.probs(pc1to12_twice_iter4,
sample_new_stat_clusters_twice_iter4$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$one_two))
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# Create list of data that is grouped the same as the group probability list
one_samp_list_iter5 <- split(sample_new_stat_clusters_twice_iter5,
f = sample_new_stat_clusters_twice_iter5$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)
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# 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
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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))
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# 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()
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# 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, '
Site:', Site, "
Geography_2:",
Geography_2, "
Time:", Time,
"
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()
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########################### 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
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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)
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# 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))
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## 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$`2`)
#colnames(out_kmeans2_mem) <- c(1, 2)
# Convert the list of matrices of sample names to data frames and bind into one data frame
out_kmeans2_samp_df <- map(out_kmeans2_samp_list, as.data.frame) %>% bind_rows()
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# Bind to initial sample id and group assignment and convert to data frame for easier handling
out_kmeans2_mem <- as.data.frame(bind_cols(out_kmeans2_mem, out_kmeans2_samp_df))
# New column of membership probability for initially assigned group
out_kmeans2_mem$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
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# 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$Sample) +
labs(x = "Principal Component 1",
y = "Principal Component 2")
)
) %>%
pull(pca_graph)
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core_outgroup_pc1pc5[[1]] +
scale_fill_manual(values = c("black","black", "black",
"black", "black", "black")) +
scale_color_manual(values = c("black","black","black", "black", "black", "black")) +
stat_ellipse(data = filter(sample_pca[["pca_aug"]][[1]], Outgroup != "unassigned"),
aes(x = .fittedPC1, y = .fittedPC2, color = Outgroup)) +
scale_shape_manual(values=c(2, 15, 18, 43))
# Create plot of PC 1 and PC 5 with the 90% conf intervals around the core and outgroups
core_outgroup_pc1pc5 <- sample_pca %>%
mutate(
pca_graph = map2(
.x = pca,
.y = data,
~ autoplot(.x, x = 1, y = 5, loadings = TRUE, loadings.label = TRUE,
scale = 0,
loadings.label.repel = TRUE,
loadings.label.colour = "black",
loadings.colour = "gray45",
loadings.label.alpha = 0.9,
loadings.label.size = 2.5,
loadings.label.hjust = -0.5,
#frame = TRUE,
#frame.type = "norm",
data = .y,
colour = "Outgroup",
shape = "Outgroup",
frame.level = .9,
frame.alpha = 0.001,
size = 2,
alpha = core_alpha) +
theme_bw() +
# geom_text(label = .y$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]]
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# 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
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# 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$Kmeans_2))
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# Create list of data that is grouped the same as the group probability list
core_kmean2_samp_list <- split(core_pc1to12_samps[, c("Sample", "Kmeans_2")],
f = core_pc1to12_samps$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$Kmeans_2_iter2))
# Create list of data that is grouped the same as the group probability list
core_kmean2_samp_list_iter2 <- split(core_pc1to12_samps[, c("Sample", "Kmeans_2_iter2")],
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f = core_pc1to12_samps$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")
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# 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
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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$cluster)
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# Group probabilities for the core kmeans 2 cluster solution on PC's 1 to 12
# (90% of variability)
core_A_kmed2_group_prob <- group.mem.probs(core_A_pc1to12, core_A$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$Kmedoids_2))] <- 0
# Assess membership probabilities using an outlier heuristic of less than 10% probability
# in another group
core_A_kmed2_group_prob_iter1 <- core_A_kmed2_group_prob %>%
mutate(new_assign = ifelse(assigned_val > 10 & `1` < 10 & `2` < 10,
Kmedoids_2, "Core A")) %>%
#summarize(perc_unassigned = sum(new_assign == Kmedoids_2)/n() * 100)
mutate(Kmedoids_iter1 = new_assign) %>%
select(Sample, Kmedoids_iter1)
# Results in a 57.85% remaining in their Kmedoids assignment - suggests a good
# cluster solution
### End Iteration 1 of Core A group structure membership probabilities
# Append retained Kmed_2 sherds to PC data
core_A <- core_A %>%
left_join(core_A_kmed2_group_prob_iter1, by = "Sample")
# PC data for Core A group membership probabilities iteration 2
core_A_iter1pc1to12 <- core_A %>%
filter(Kmedoids_iter1 != "Core A") %>%
select(.fittedPC1:.fittedPC12)
# Group Membership data for kmeds iteration 2 Core A
core_A_iter2 <- core_A %>% filter(Kmedoids_iter1 != "Core A")
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# Group probabilities for the core kmeans 2 cluster solution on PC's 1 to 12 (90% of
# variability)
core_A_kmed2_group_prob_iter2 <- group.mem.probs(core_A_iter1pc1to12, core_A_iter2$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")
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# 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$data[[1]] %>%
left_join(core_A_subs[, c("Sample", "Core_A_Sub")])
# Plot Core A and Core A sub-groups using autoplot
core_A_pc1pc2 <- sample_pca %>%
mutate(
pca_graph = map2(
.x = pca,
.y = data,
~ autoplot(.x, x = 1, y = 2, loadings = TRUE, loadings.label = TRUE,
scale = 0,
loadings.label.repel = TRUE,
loadings.label.colour = "black",
loadings.colour = "gray45",
loadings.label.alpha = 0.9,
loadings.label.size = 2.5,
loadings.label.hjust = -0.5,
#frame = TRUE,
#frame.type = "norm",
data = .y,
colour = "Core_A_Sub",
shape = "Core_A_Sub",
frame.level = .9,
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frame.alpha = 0.001,
size = 2,
alpha = .00001) +
theme_bw() +
# geom_text(label = .y$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$Final_Assign)
# Plot of Mg - Ni of the Core A, A1 and A2 group assignments
pca_aug %>%
filter(Core_A_Sub == "Core A1" | Core_A_Sub == "Core A2") %>%
ggplot(aes(x = Mg, y = Ni, color = Core_A_Sub, shape = Core_A_Sub)) +
geom_point() +
stat_ellipse(level = 0.9) +
scale_shape_manual(values=c(43, 15, 18)) +
scale_fill_manual(values = c("black","black", "black",
"black", "black", "black")) +
scale_color_manual(values = c("black","black","black",
"black", "black", "black")) +
xlab("Magnesium (log base 10 ppm)") +
ylab("Nickel (log base 10 ppm)") +
geom_point(data = filter(pca_aug[, c("Mg", "Ni", "Mo", "Core_A_Sub")],
Core_A_Sub == "Core A"),
aes(x = Mg, y = Ni, alpha = 0.2)) +
theme_bw()
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# Plot all assignments along PC1 and PC2
pca_aug %>%
filter(Final_Assign != "unassigned") %>%
ggplot(aes(x = .fittedPC1, y = .fittedPC2, color = Final_Assign)) +
geom_point() +
stat_ellipse(level = 0.9) +
xlab("Principal Component 1") +
ylab("Principal Component 2") +
geom_point(data = filter(pca_aug, Final_Assign == "unassigned"),
aes(x = .fittedPC1, y = .fittedPC2, color = Final_Assign, alpha = 0.4)) +
theme_bw() +
scale_color_d3()
# Plot all assignments along Mg and Mo
pca_aug %>%
filter(Final_Assign != "unassigned") %>%
ggplot(aes(x = Mg, y = Mo, color = Final_Assign)) +
geom_point() +
stat_ellipse(level = 0.9) +
xlab("Mg (log base 10 ppm)") +
ylab("Mo (log base 10 ppm)") +
geom_point(data = filter(pca_aug, Final_Assign == "unassigned"),
aes(x = Mg, y = Mo, color = Final_Assign, alpha = 0.4)) +
theme_bw() +
scale_color_d3()
# Append Final Assignments to PCA data
sample_pca$data[[1]] <- sample_pca$data[[1]] %>%
left_join(pca_aug[, c("Sample", "Final_Assign")])
# Plot Core A and Core A sub-groups using autoplot
final_assign_pc1pc2 <- sample_pca %>%
mutate(
pca_graph = map2(
.x = pca,
.y = data,
~ autoplot(.x, x = 1, y = 2, loadings = TRUE, loadings.label = TRUE,
scale = 0,
loadings.label.repel = TRUE,
loadings.label.colour = "black",
loadings.colour = "gray25",
loadings.label.alpha = 0.9,
loadings.label.size = 3.5,
#loadings.label.hjust = -0.5,
frame = TRUE,
frame.type = "norm",
data = .y,
colour = "Final_Assign",
#shape = "Final_Assign",
frame.level = .9,
frame.alpha = 0.001,
size = 2,
alpha = .3) +
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theme_bw() +
# geom_text(label = .y$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$Final_Assign)
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# Regression of the number of compositional groups as a function of sample size
# Also included are lines to look at potential differences in the average number of
# compositional groups by geography of site or time period of occupation
group_assign_by_site %>%
select(1, 3:8) %>%
mutate(group_count = rowSums(!is.na(.))) %>%
mutate(group_count = group_count - 1) %>% # need to subtract the Site col
#left_join(group_assign_by_site_geo[c(1:3)]) %>%
#group_by(Geography_2, Time) %>%
#summarize(avg_grou = mean(group_count)) # check average group count
mutate(sample_size = rowSums(.[2:7], na.rm = TRUE)) %>%
#ggplot(aes(x = sample_size, y = group_count)) +
#geom_point() +
#geom_smooth(method = "lm")
lm(group_count ~ sample_size, data = .) %>%
glance()
# Write out csv file of group assignments
# write_csv(group_assign_by_site, "group assignments by site.csv")
# write_csv(group_assign_by_site_geo, "group assignments by site-geo.csv")
# write_csv(group_assign_by_geo_class, "group assignments by geo-vessel class.csv")
pca_aug %>%
filter(Final_Assign == "Core A2") %>% View()
# Component loadings for first 12 principal components
pc_loadings <- sample_pca$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.
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#' 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
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# (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) {
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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
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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
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# 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")
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# 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))
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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
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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") +
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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)
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# 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()
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# 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
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# 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 %>%
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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
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# 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
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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) %>%
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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$Target,
c(" " = "_", "-" = "_", "\\." = ""))
# Plates directed all
plates %>%
select(Source, Target, weight) %>%
unite(sep = " ") %>%
write.table("edge_list_ptech_directed_all.txt", row.names = FALSE,
col.names = FALSE, quote = FALSE)
# Plates directed pre
plates %>%
filter(Time == 1) %>%
select(Source, Target, weight) %>%
unite(sep = " ") %>%
write.table("edge_list_ptech_directed_pre.txt", row.names = FALSE,
col.names = FALSE, quote = FALSE)
# Plates directed post
plates %>%
filter(Time == 2 |
(Source == "Buckeye_Bend" & Target == "Lawrenz_Gun_Club") |
(Source == "Lawrenz_Gun_Club" & Target == "Buckeye_Bend")) %>%
select(Source, Target, weight) %>%
unite(sep = " ") %>%
write.table("edge_list_ptech_directed_post.txt", row.names = FALSE,
col.names = FALSE, quote = FALSE)
# Now, create UNDIRECTED graph txt files for plates
# To do this, any reciprocal edge weights will be the mean of the two
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# directed edge weights
# Plate undirected all
pg <- graph.data.frame(plates, directed = TRUE)
pg_un <- as.undirected(pg, edge.attr.comb = "mean", mode = "collapse")
as.data.frame(as_edgelist(pg_un)) %>%
mutate(weight = E(pg_un)$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')
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# 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
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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"))$weight) %>%
mutate(Layer = "Jar_pre") %>%
select(V1, V2, Layer, weight) %>%
unite(sep = ",") %>%
write_delim("jar_pre_mulitnet_el.txt", delim = "")
# Post-migration
j %>%
filter(Time == 2 |
(Source == "Buckeye_Bend" & Target == "Lawrenz_Gun_Club") |
(Source == "Lawrenz_Gun_Club" & Target == "Buckeye_Bend")) %>%
graph.data.frame(directed = TRUE) %>%
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as.undirected(edge.attr.comb = "mean", mode = "collapse") %>%
as_edgelist(.) %>%
as.data.frame(.) %>%
mutate(weight = E(as.undirected(graph.data.frame(filter(j, Time == 2 |
(Source == "Buckeye_Bend" &
Target == "Lawrenz_Gun_Club") |
(Source == "Lawrenz_Gun_Club" &
Target == "Buckeye_Bend")), directed = TRUE),
edge.attr.comb = "mean", mode = "collapse"))$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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