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I 4.. a ...).Qo VI' 4609‘ 1.0 . 44‘ -‘g3Quro. .I .2300. ..SL. 4 44. 2.044. .... .. .. 0 .4 ABSTRACT COMPARATIVE VALUE OF FOURIER SHAPE, MOSAIC—STRUCTURAL, AND BINARY SKELETAL CHARACTERS IN A LATE DEVONIAN BRYOZOAN FAUNA (THREEFORKS FM., MONTANA) By Dennis Prezbindowski The purpose of this study is to introduce and examine the relationships among three independently derived sets of morphological characters in a Paleozoic stenolaemate bryozoan fauna. These characters including both intrazoarial means and standard deviations, are sources of biological information. The bryozoan fauna was collected from seven localities within the Upper Devonian Threeforks Formation (Famennian) of southwestern Montana. The fauna consisted of a usable sample of 61 zoaria. The three character sets are Fourier harmonic amplitudes, quantitative (multistate) nonfourier continuous variates, and binary (two-state) characters. R-mode principal components analysis of the six Fourier shape variables and nine quantitative variables reduced the data to the most independent sources of information which accounted for 86.3 percent of the variance observed within the total sample used. Nine of the 15 selected characters were intrazoarial standard deviations. Fisher's exact probability matrix of association was generated for the 53 binary characters used. An R-mode factor analysis of this probability matrix showed that based, on their lack of association, 2O binary characters were the most independent. The residual character sets analyzed with Parks' (1970) R-mode and Q-mode program using simple distance based on principal component values with results illustrated in dendrogram form. Four phenograms were produced using the three basic character sets and various combined sets of characters. The binary character sat alone produced the best phenogram (nine misclassifications), followed by Fourier harmonic amplitudes (1O misclassifications) and the nonfourier continuous variates (15 misclassifications). The combined set of all characters produced five misclassifications. The use of intrazoarial standard deviations measures colony variation within a localized area. This variation is a measure of disorder within the measured area. These measures of variation generally captured more independent information than their associated means. The amount of disorder or variation can be related to the budding pattern. The results of this study strongly support the hypothesis that species have characteristic astogenetic variation patterns. This variation can be used to classify bryozoans. Binary and Fourier shape characters provide more independent information than the standardly used quantitative characters. The newly introduced quantitative characters of nearest neighbor statistc (controlled by budding) and interzooecial area per unit volume have proven to be two of the more important quantitative characters used. Through the use of these three independent character sets, Sokal and Sneath's (1963) Hypothesis of Nonspecificity appears to be only partially true. The resulting phenograms show only a tendence toward similiarity. Two species dominated the bryozoan fauna of the Threeforks Formation, the trepostome Leptotrypella pellucida Duncan, and Nicklesopgra renzettiae n. sp.. The fauna also includes two single specimens, a cystoporate (Fistulipora sp.), and an indeterminate phylloporinid. The unabraded zoaria of Leptotrypella and Nicklesgpora invariably have very thin exozones, suggesting that periodic burial by terrigenous muds prevented the development of mature populations of these bryozoans. COMPARATIVE VALUE OF FOURIER SHAPE, MOSAIC-STRUCTURAL, AND BINARY SKELETAL CHARACTERS IN A LATE DEVONIAN BRYOZOAN FAUNA (THREEFORKS FM., MONTANA) BY Dennis Prezbindowski A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE College of Natural Science Department of Geology 1974 Dedicated to my wife, Debbie, for her help and understanding throughout this study. ACKNOWLEDGMENTS Terry Chase, Jim Welch, and Philip Zink are to be thanked for their assistance in the collection phase of this study. I would like to thank Alan S. Horowitz, curator of the Indiana University Paleontological Collection, for making the loan of specimens in his custody. I would like to thank Sam Upchurch and Chilton Prouty for their constructive criticism of the manuscript. I would finally like to thank Robert L. Anstey for his timely suggestions, interest and perseverance in all phases of this study. 111 TABLE OF CONTENTS LIST OF TABLES . . . . . . . . LIST OF FIGURES . . . . . . . INTRODUCTION . . . . . . . . MATERIAL . . . . . . . . . . METHODS . . . . . . . . . . . Fourier Shape Analysis . . Quantitative Measurements . Interzooecial Surface Area Binary Characters . . . . DATA ANALYSIS . . . . . . . . R-MODE RESULTS . . . . . . . . Q-MODE RESULTS . . . . . . . . THE THREEFORKS BRYOZOAN FAUNA Paleoecology . . . . . . . Systematic Paleontology . . CONCLUSIONS . . . . . . . . . LIST OF REFERENCES . . . . . . APPENDICES . . . . . . . . . . PLATES . . . . . . . . . . . . iv Page vii 11 11 12 18 18 23 29 39 49 49 50 75 77 79 104 10. 11. 12. 13. LIST OF TABLES Page Localities and Specimen Distribution, Indiana University accession numbers . . . . . . 8 Fourier shape and standard quantitative characters . . . . . . . . . . . . . . . . . . 15 Binary characters taken from Eftaxiadis (1973) . 19 Initial R-mode principal components results on quantitative and Fourier shape characters . . 27 Principal component loadings for Fourier shape characters (CLUST6 Program) . . . . . . . . . . 31 Principal component loadings for quantitative character set (CLUST6 Program) . . . . . . . . . 32 Principle component loading of binary character set for initial R-mode analysis of Parks CLUST6 program 0 O O O O O O O O O O O O O O O O O O O 33 Principle component loading of combined character sets Fourier shape, quantitative and binary character sets for initial R-mode analysis of Parks CLUST6 program . . . . . . . . . . . . . . 34 Nicklesopora renzettiae n. sp. binary character Trequences for 28 colonies . . . . . . . . . . . 55 Nicklesopora renzettiae n. sp. means of quantitative character data . . . . . . . . . . 57 Nicklesopora renzettiae n. sp. standard deviations of quantitative character data . . . . . . . . . 58 Nicklesopora renzettiae n. sp. Fourier Haromonic means data statistics . . . . . . . . . . . . . 59 Nicklesopora renzettiae n. sp. Fourier Harmonic standard deviation data statistics . . . . . . . 6O Table 14. 15. 16. 17. 18. 190 20. 21. Comparison of the type species of the genera Nicklesopora and Rhombopora with Nicklesgpora renzettiae . . . . . . . . . . . . . . . . . . Comparison of Nicklesopora renzettiae n. sp. with all previously descrIbed species of the genus Nicklesopora . . . . . . . . . . . . Lgptotrypella pellucida Duncan binary character frequences f6r 33 colonies . . . . . Leptotrypella pellucida quantitative means data statistIcs, based on 33 colonies . . . . Leptotrypella pellucida quantitative standard deviation data statistics, based on 33 colonies . . . . . . . . . . . . . . . . . Leptotrypella pellucida Fourier Harmonic means data statifitics, based on 33 colonies . Leptotrypella pellucida Fourier Harmonic standard deviation data statistics, based on 33 colonies . . . . . . . . . . . . . . . . Comparison of species of the genus Leptotrypella with Threeforks material . . . . vi Page 61 63 66 68 69 7O 71 72 LIST OF FIGURES Map showing location of the seven collecting localities (exact locations in Table 1). . . Diagrammatic illustration of Non-Fourier quantitative characters measured . . . . . . R-mode dendrogram of Fisher's exact probability of the 53 initial binary CharaCters O O O O O O O O O O O O O O O O O Phenogram based on six Fourier shape variables 0 o O O O O O O O O 0 O O O O O O Phenogram based on nine quantitative variables 0 O O O O O O O O O O O O O O I O Phenogram based on 20 binary characters . . Phenogram based on combined set of characters, Fourier shape, quatitative, and binary character sets . . . . . . . . . . . vii Page 14 25 41 43 45 47 INTRODUCTION The purpose of this study is to introduce and examine the relationships and information content of three independently derived morphological character sets in a stenolaemate bryozoan fauna. Secondly, a description and discussion of the bryozoan fauna from seven localities (Figure l) in the Upper Devonian Threeforks Formation (Famennian) of southwestern Montana is based upon the analysis of the morphological information. The character sets used in this study were designed to obtain information from as many aSpects of a fossil bryozoan skelton as possible, including shape, spatial arrangement of individuals in the colony, measurements of internal structures, and coding of nominal state characters. It is generally accepted now that Sokal and Sneath's (1963) Hypothesis of Nonspecificity, is only partially true (Sneath and Sokal, 1973). This hypothesis states "there are no distinct large classes of genes affecting exclusively one class of characters such as morphological, physiological, or ethological, or affecting special regions of the organism such as head, skeletOn, or leaves" (Sokal and Sneath, 1963). The partial failure of this Figure 1. Map showing location of the seven collecting localities (exact locations in Table l). MONTANA 'vv' “A‘A‘AA-A-A ‘ -““-‘A-A ---‘ vvvv ..u’dOr '/ a. .4 Clo". (‘9 ® ® Thu For 6) Whitehall. lazuli \a Field Comp Box man g, C 5 ~ 30'. 3° .4" Q? g . . fi 0" .3 3;” a: to .5 '0 ’’o O o Vlrolno City A L {>2 30 4 hypothesis is accepted, although the extent of this failure is subject to debate. Sokal and Sneath (1963) suggested a possible test for the hypothesis of non- specificity. If separate classifications could be formed by the division of taxonomic characters into logically independent sets, testing their degree of concordance would test the theory of nonspecificity. This test may shed more light on this problem. The search for new descriptive characters and the evaluation of old as well as new characters within groups of organisms is essential to provide a meaningful basis for numerical taxonomic analysis. Because different parts of an organism carry varying degrees of independent information, an R-mode intercharacter analysis is necessary to understand this distribution. In most numerical taxonomic studies the investigator is faced with several basic questions; how many characters should be measured and which characters will provide the most independent information? Generally the answer to the former question is determined by the structural complexity of the organism and the time and resources of the investigator. Michener and Sokal (1966) stated "The number of characters to be recorded and used is a problem in both orthodox and numerical taxonomy. Further studies are badly needed to determine how many characters are likely to be sufficient to satisfactorily classify groups of various sizes." This problem remains 5 unsolved and because it is not the object of this study, it will not be treated further. The latter question presupposes the existence and use of a large number of taxonomic characters and methods of measurement. In terms of provious bryozoan studies, such is not the case and only a dozen or so measurements are generally used. As noted by Oxnard (1969), numerical taxonomy is an attempt to delineate mathematically, shape as a means of classification. The more precisely we can define the shape both internally and externally, the more taxonomic information can be retrieved. Throckmorton (1968) demonstrated that different taxonomic characters carry different amounts of independent information. The use of characters should be justified by R-mode analysis to determine whether standard or newly introduced characters contribute significant independent information. This I study intends to focus on these questions. MATERIAL The fauna used in this study was collected from seven localities in the trident member of the Threeforks Formation (Upper Devonian) of southwestern Montana (Figure 1). This formation extends from southwestern and central Montana through southeastern Idaho. The characteristic lithology is reddish and yellow brown argillaceous shale with numerous lenticular beds of greenish gray argillaceous limestone. The Threeforks Formation is underlain by the Jefferson Formation, (Middle Devonian) and overlain by the spongiostromated bearing sandstone, and shale of the Sappington Formation (Upper Devonian). The bio-stratigraphic position of the Threeforks Formation is with the Scaphignathus subserratus-Pelekysgnathus inclinatus conodont zone, and the upper Polygnethus styriacus conodont zone of the Upper Famennian Stage (Klapper, 1971). The bryozoan fauna was collected from weathered slopes, The general scarcity of good material necessitated the use of purposeful sampling of as many weathered exposures as were easily accessible in the study area. Additional specimens were obtained from the Renzetti (1963) material, in the Paleontological Collections of Indiana University. 7 A sample of 134 specimens were sectioned using standard sectioning techinques from the seven localities collected. A severe limitation was placed on the amount of material that could be sectioned and feasibly studied because preservation was generally poor. Siderite and pyrite replacement had occured to varying degrees in nearly all material, making the zoaria brittle and difficult to section. Many of the colonies have had their axial areas bored out by other organisms (Plate 1, Figure 7), resulting in crushing and varying degrees of distortion of the zoaria during postdepositional compaction of the sediments. Only 61 sectioned specimens were suitable for study on the basis of their quality. Unfortunately certain localities were better represented than others by this method of selection (Table l). Table 1. Localities and Specimen Distribution, Indiana University accession numbers. 1. Red Hill NWi, NWi, SEi, Sec. 22, T2N, R3W Jefferson Island Quad. Montana. Nicklesopora renzettiae: figured paratypes 6102-1, 6103-19, 6102-2, 6104-1; unfigured paratypes 6101-R, 6102-3R, 6103-1R, 6103-9, 6103-12, 6103-13R, 6103-24, 6103-32, 6103-47, 6103‘48, 6103-49, 6103-50, 6101-R; unfigured specimens 6102-2, 6103-15, 6103-19, 6103-31, 6103-33, 6103-36, 6103-38, 6103-42, 6105-15 Leptotrypella pellucida: figured hypotypes 6100-R, 6103-20, 6103-22R, 6103-43; unfigured hypotypes 6102-3, 6103-1, 6103-4, 6103-5, 6103-6, 6103-7, 6103-11, 6103-13, 6103-21, 6103-22, 6103-23, 6103-27, 6103-28, 6103-29. 6103-30, 6103-45; unfigured specimens 6102-1, 6102-4, 6103-3, 6103-2, 6103-8, 6103-10, 6103-14, 6103-16, 6103-18, 6103-25, 6103-26, 6103-34, 6103-37, 6103-39, 6103-40, 6103-41, 6103-46, 6103-48, 6105-33. 2. Mt. Doherty Sec. 21, T2N, R2W Jefferson Island Quad. Montana. Nicklesopora renzettiae: figured holotype 6107-1; unfigured paratypes 6105-11, 6105-18, 6105-23, 6108-10, 6108-12; unfigured specimens 6104-1, 6104-2, Table 1. Continued. 6105-3, 6105-4, 6105-6, 6105-8, 6105-17, 6105-20, 6105-25, 6105-27, 6105-29. 6105-31, 6105-54. Leptotrypella pellucida: unfigured hypotypes 6105-1, 6105-9, 6105-12, 6105-13, 6105-14, 6105-19, 6105-21, 6105-22, 6105-24; unfigured specimens 6105-2, 6105-7, 6105-10, 6105-16, 6105-26, 6105-28, 6105-30, 6105-32, 6108-11. 3. Carmichael Sec. 33, T1N, R3W Jefferson Island Quad. Montana Inadequate material for sectioning 4. Logan Gulch SEi, Sec. 25 T2N, R2E Manhattan Quad. Montana Nicklesopora renzettiae: figured paratype 6105-R; unfigured specimens 6107-3, 6107-4. Leptotrypella pellucida: unfigured hypotype 6107-2; unfigured specimen 6107-1. Phyloporinid: 6107-5. figured. 5. Nada Mine SEi, Sec. 5, T4N, R1w Radersburg Quad. Montana Nicklesopora renzettiae: unfigured paratypeu6108-2. Leptotrypella pellucida: unfigured hypotype 6108-1; unfigured specimen 6108-3. 10 Table 1. Continued. 6. Horse Gulch NWi, SW1, Sec. 6, TSN, RZW Devils Fence Quad. Montana Leptotrypella pellucida: unfigured specimens 6109-1, 6109-2, 6109-3, 6109-4, 6109-5, 6109-6, 6109-7, 6109-10, 6109-11, 6109-12. 7. Milligan Canyon SWfi, NEi, Sec. 36, T2N, R1W Threeforks Quad. Montana Nicklesopora renzettiae: unfigured paratypes 6111-3, 6111-4, 6110-1; unfigured specimens 6110-2, 6110-3, 6110-6, 6111-2. Leptotrypella pellucida: figured hypotype 6110-9; unfigured hypotype 6110-8; unfigured specimens 6110-4, 6110-5, 6110-10, 6110-11, 6111-1. Fistulipora sp. figured 6110-7. METHODS Fourier Shape Analysis The Fourier method of shape characterization (harmonic analysis) was first developed and used in studies of closed forms in geology by Ehrlich and Weinberg (1970). Recently Anstey and Delmet (1972, 1973 ), and Delmet and Anstey (1974) have demonstrated applications of this method to the study of fossil, tubular bryozoans. Descriptions of the underlying mathematics and techniques are provided in the four previously cited papers and Davis (1973). The important aspect of this particular Fourier method is the quantification of closed form shapes as a series of independent harmonic amplitudes (Appendix 2). Twenty, randomly selected, zooecial outlines from the tangential section of each specimen were visually centered and traced onto a starburst pattern. The star- burst consisted of 48 equiangular lines radiating from a center point at 7.5 degree intervals. The intersections of the traced outline and the radiating lines of the starburst pattern were automatically digitized and punched in Cartesian coordinates. The punched coordinates for the 20 outlines of each specimen were used as input to program Fourier (Appendix 2). A zoarial mean and 11 12 intrazoarial standard deviation for the harmonics amplitudes 2-20 and the normalized roughness coefficient were subsequently calculated from the 20 shape replicates per zoarium (zoarium = thin section). The roughness coefficient is the square root of one half the sum of the squared normalized Fourier coefficients (Ehrlich and Weinberg, 1970). In calculating the roughness coefficient, all Fourier amplitudes are normalized by dividing each value by its overall mean in the entire sample. Quantitative Measurements Thirteen quantitative characters were randomly and repetitively measured 20 times in each speimen, nine of these measures are shown in ( Figure 2). These characters include several that are commonly used by bryozoan taxonomists, as for example, those used by Cuffey (1967). Measurements were made on a projected image of the slide on a horizontal screen. Means and intrazoarial standard deviations of the 20 replicates per character per specimen were calculated and punched onto cards for later analysis. Mean radius is the average length of the 48 radial lines from the calculated center of gravity to the zooecial margin for each zooecial shape. The mean and standard deviation of the mean radius were calculated for each section. Included in the quantitative data was the calculation of the nearest neighbor statistic. This statistic, developed by Clark and Evans (1954) in plant ecology, Figure 2. 13 Diagrammatic illustration of Non-Fourier quantitative characters measured. A. Characters measured in tangential section; DA, diameter of acanthopores; ZWT, zooecial wall thickness; APZ, acanthopores per zooecium. B, 0. Characters measured in longitudinal section; AN, angle at which zooecial tubes meet surface of colony; DLC, depth of living chamber (mm); NDPR, number of diaphrams in axial region per 2.5 mm. distance; DAR, diameter of endozone (mm); TMR, thickness of exozone (mm). See table 2 for discription of quantitative and Fourier shape characters. L... .9121... 381' ' .1!!! m 1 15 Table 2. Fourier shape and standard quantitative characters, all means and standard deviations are based on 20 random measurements per colony, see appendix 3 for raw data of the 61 specimens studied. ZRM ZRS ZWTM ZWTS APZM APZS TMRM TMRS DARM DARS ANM ANS NDPRM NDPRS NDARM NDARS DLCM DLCS Zooecial Radius, Mean (mm) Zooecial Radius, Standard Deviation Zooecial Wall thickness, Mean (mm) Zooecial Wall Thickness, Standard Deviation Number of Acanthopores per Zooecium Mean (mm) Number of Acanthopores per Zooecium, Standard Deviation Thickness of Exozone, Mean (mm) Thickness of Exozone, Standard Deviation Diameter of Endozone, Mean (mm) Diameter of Endozone, Standard Deviation Angle at which Zooecial Tubes meet Surface of Colony, Mean (degrees) Angle at which Zooecial Tubes meet Surface of Colony, Standard Deviation Number of Diaphragms in the Exozone, Mean Number of Diaphragms in the Exozone, Standard Deviation Number of Diaphragms in the Endozone per 2.5 mm Distance, Mean Number of Diaphragms in the Endozone per 2.5 mm Distance, Srandard Deviation Depth of Living Chamber, Mean (mm) Depth of Living Chamber, Standard Deviation 16 Table 2. Continued. DAM Diameter of Acanthopores, Mean (mm) DAS Diameter of Acanthopores, Standard Deviation AREAM Interzooecial Surface Area per cubic mm, Mean AREAS Interzooecial Surface Area per cubic mm, Standard Deviation NNS Nearest Neighbor Statistic HM2 to HM2O - Harmonic Mean 2 through Harmonic Mean 20 H82 to H820 - Harmonic Standard Deviation 2 through Harmonic Standard Deviation 20 RCM Roughness Coefficient, Mean RCS Roughness Coefficient, Standard Deviation 17 was used to quantify the spatial arrangement of zooecia in the colony. A randomly selected location on the tangential section was projected onto a horizontal screen. The center points of all neighboring zooecia were visually located and marked, to attain a standard sample size of 33 in a roughly circular area. A noncircular sample area would strongly bias the result. The spatial patterns of the zooecial centers for each specimen were digitized and punched in Cartesfian coordinates. The nearest neighbor statistic was calculated from these data by the NABOR module of the GEOSYS package (Wittick, 1973). 18 Interzooecial Surface Area Zooecial tubes in the mature region of a colony can be thought of as a series of diSpersed particles or empty volumes in a matrix of skeletal material. The surface area of zooecial walls to skeletal volume can be quantified by the following equation: SV = 4N1 (mm2 / mm3). The surface area per cubic mm is equal to four times the number of zooecial tubes to skeletal wall intersections in a random 1 mm line in tangential sectibn (N1). This method is discussed in detail by Underwood (1970). This method provides an absolute measure of surface area only for randomly oriented sections. Because tangential sections are not random in orientation, the measurement is only relative, but serves as a compariative statistic. The intersects for each of the 20 random 1 mm lines were counted and averaged. This average number of intersections was used to calculate the surface area per cubic mm for each specimen. Binary Characters Fifty-three binary characters (Table 3) were choosen from a list of 150 binary characters used by Eftaxiadis (1973). Characters were scored one for positive and zero for negative statement responses. The characters not used were redundant in all of the Threeforks material. 19 Table 3. Binary characters taken from Eftaxiadis (1973), characters were scored one for positive response and zero for negative response, see Appendix 3 for raw binary data values for the 61 specimens studied. I. Characters of Zoarial Growth A. Budding Patterns 1. 2. 5. Zooecia to long Zooecia to long Budding base of arranged in longtdinal rows, parallel axis of zoarium. arranged in diagonal rows, oblique axis of zoarium. of new zooecia mostly limited to colony. Intercalated budding particularly prominent in vicinity of endozone-exozone boundary. Zoarial growth characterized by numerous rejuvenated zones (recurrent mature zones) of zones of iterative budding, commonly containing brown bodies just posterior to plane of rejuvenation. B. Nonzooidal Colony Structures 7. Longitudinal ranges of zooecia separated by continuous dark line in wall. 8. Dark lines in wall forming unbroken polygons around each zooecial aperture. II. Characters Observable in Tangential Section A. Zooecial Apertural Outlines 9. Circular or elliptical to subpolygonal, having rounded corners. 10. Polygonal, having angular corners. Table 3. Continued. 2O 11. More elongate than equidimensional. 12. 13. 14. Rhombic or quadrate. Pentagonal or hexagonal. Invaginated, having a kidney, peanut or dumbbell shape. Zooecial Size and Spacing 15. 16. 17. 18. 19. Maximum greater Maximum greater Maximum greater Minimum greater Maximum greater intermacular diameter generally than 0.15 mm. intermacular diameter generally than 0.20 mm. intermacular diameter generally than 0.25 mm. intermacular diameter generally than 0.20 mm. interzooecial distance generally than one zooecial diameter. Wall Structure 20. Dark divisional line in wall in thick-walled areas between adjacent zooecial apertures. 21. Wall amalgamate, having bread nonlaminated central area in wall in thick-walled areas between adjacent zooecial apertures. 22. 23. Apertural walls lined by sharply differentiated peristome or cingulum. Maximum wall thickness between adjacent zooecial apertures generally greater than 0.04 mm. Intrazooecial Structures 25. Single cystiphragms or curved diaphragms very large, generally constricting more than one third of zooecial aperture. Table 3. E. 21 Continued. Acanthopores 26. 27. 28. 29. 30. 31. 32. 33. Small dark spots observable at junction angles of intergrated walled zooecial apertures. Acanthopores of junction angles of most adjacent zooecial apertures. Acanthopores numerous, ringing zooecial apertures. Centered acanthopores common along zooecial walls. Acanthopores differentiated into two distinct size classes (endacanthopores and exacanthopores, or magacanthopores and micracanthOpores). Lumen diameter generally greater than one-half acanthopore diameter. Generally more than two acanthopores associated with each zooecial aperture. Acanthopore diameter (of larger class if bimodal) generally greater than 0.03 mm. III. Characters Observable in Longitudinal Section A. B. Zooecial Geometry 34. 35. 36. Zooecia in exozone inclined at less than 60 degrees to zoarial surface. Zooecia displaying conspicuous bend at endozone-exozone boundary. Zooecia in overgrowth layers displaying short recumbent endozone. Wall Structure 37. 38. 39. Zooecial walls crenulated in endozone. Zooecial walls granular appearing, may be poorly laminated locally. Wall laminae sharply arched, resembling inverted V's, not broadly convex outward (as seen in thick-walled regions of monilae). 22 Table 3. Continued. C. 40. 41. 42. 43. 44. 45. Zooecial walls generally amalgamate, lacking divisional line. Amalgamate wall structure, area of central flexure broad with respect to total wall thickness. Amalgamate wall structure, portions of wall laminae parallel to zooecial length extending posteriorly for a distance greater than one zooecial diameter. Diaphragm laminae continuous across two or more adjacent mesopores or zooecia, represent- ing an unconformity in laminar deposition. Zones of wall laminae separated anteriorly and posteriorly by growth unconformities, the laminae of which do not pass into any diaphragms. Diaphragm (or cystiphragm or hemiphragm) laminae forming lining inside zooecial walls passing upward beneath one or more diaphragms and merging anteriorly with mural laminae, producing a structure resembling a stack of nested tumblers. Diaphragms 47. 48. 49. 50. 51. 52. Diaphragms present in endozonal portions of most zooecia. Distance between successive diaphragms in exozone generally less than one zooecial diameter. Depth of living chamber generally greater than one zooecial diameter. Most diaphragms oriented obliquely to zooecial walls. Most diaphragms slightly curved, concave outward. Most diaphragms slightly curved, convex outward. Cystiphragms 53. Cystiphragms present in most zooecia in exozone. DATA ANALYSIS Fisher's exact probability (Siegel, 1956) was calculated for all possible 2X2 contingency tables for the 53 binary characters, thus generating an R-mode probability matrix. UnlikeTX? approximation values, Fisher's values are exact measures of the probability of dependence of one character state on the other. ( Appendix 1 provides a listing of Fisher's exact probability program DMAT ) This R-mode probability matrix was clustered by means of Bonham-Carter's (1967) CLUST3 program using the weighted pair-group average linkage method. The resulting dendrogram (Figure 3) was the basis for the final selection of the twenty most independent binary characters to be used in the final Q-mode analysis. The 0.38 level of Fisher's exact probability of association was arbitrarily selected as the cutoff level for independent characters, because that level reduced the data to 20 characters. The limit of 20 binary characters for the final analysis was determined by a initial R-mode principal components analysis using the Fisher matrix as input to the FACTOR program of the SPSS package with PA1 and VARIMAX options (Nie, Bent, and Hull 1970), which extracted 23 Figure 3. 24 R-mode dendrogram of Fisher's exact probability of the 53 initial binary characters; the 0.38 level of probability was used as level of character selection. Characters 10 and 29 were dropped from further analysis. These two characters correlated at a zero of a one level with other characters in an off diagonal position in the initial R-mode analysis of Parks' CLUST6 program. This program will not execute with a zero of one in an off diagonal position. The 20 characters selected at the 0.38 level of probability are indicated by an apostrophe. ......OOOOOOOOO ................OOOOOOOOOOOOO......00..........O oosqp 0L0}. or. ope o o e e e 26 20 rotated principal components that collectively accounted for 82.0 percent of the total variance. The standard quantitative and Fourier shape characters were subjected to an R-mode principal components analysis. This analysis was carried out by means of program FACTOR using PA1 and VARIMAX rotation options (Nie, Bent, and Hull, 1970). Fifteen rotated principal components accounted for 86.3 percent of the total variance. The variable showing the highest loading on each component was chosen as the best representative of that component axis. These 15 variables represent the 15 sources of information closest to the rotated components. These 15 variables were converted to logarithms for the final R- and Q-mode analysis. The data were converted in order to approximate better the logarithmic growth pattern of these organisms. These 15 variables included six Fourier shape, and nine quantitative variables (Table 4 ). The final analysis using Parks' (1970) CLUST6 program with all options set to default values was carried out using the 20 binary characters, six Fourier harmonics, and nine quantitative non-Fourier characters, both independently and in combination. CLUST6 is a program designed for use with mixed qualitative and or quantitative data, which uses simple distance as a measure of association. This program first normalizes all data to a 1.0 scale. Table 4. 27 Initial R-mode principal components results on quantitative and Fourier shape characters. 1>.c.1 3.2 P.V.3 C.P.4 v.H.L.P.c.5 1 25.10327 44.0 44.0 HMS 2 5.21582 9.2 53.2 HM18 3 2.86882 5.0 58.2 TMRS 4 2.26567 4.0 62.2 H315 5 2.05877 3.6 65.8 R08 6 1.79911 3.2 69.0 NNS 7 1.59421 2.8 71.8 ANM 8 1.47802 2.6 74.4 NDARM 9 1.24979 2.2 76.6 NDARS 10 1.08057 1.9 78.4 ZWTS 11 1.02140 1.8 80.2 ZRS 12 .94752 1.7 81.9 H82 13 .90617 1.6 83.5 DARS 14 .83662 1.5 85.0 ROM 15 .76730 1.3 86.3 AREAS 1. Principal component 2. Eigenvalue 3. Percent of variance explained 4. Cumulative percent of variance explained 5. Variable with highest loading on principal component 28 It then performs an R-mode principal components analysis on the data, and extracts the principal components which explain 80. percent or more of the variation in the data provided. Factor loadings are calculated and used to convert the original data to orthogonal coordinate values. A final Q-mode cluster analysis using unwieghted pair group average linkage method is carried out using principal component values generated in the R-mode analysis. The results of the Q-mode cluster analysis are then displayed on a line printer generated dendrogram. R-MODE RESULTS Twenty binary characters were chosen from the initial 53 as representing the most independent sources of variation (Figure 3). The SPSS R-mode principal components analysis on the combined quantitative and Fourier shape data sets indicated that the shape characters loaded significantly higher on the first two components than the non-Fourier quantitative characters. Harmonic means three through 16 collectively loaded on the first component at a high level. The standard deviations of harmonics four through 14 also loaded on the first component at a high level. Variable HM8 had the highest laoding on component one. All other variables loaded with significantly lower values. The second factor was closest to the higher harmonics and their standard deviations. Harmonic means 17 through 20 and harmonic standard deviations 15 through 20 loaded on principal component two at a high level. Harmonic mean 18 had the highest loading on principal component two. All other variables had significantly lower loading. Principal components three through 15 were characterized by single characters loading at very high values on each, with all others loaded at very low values (Table 4). 29 30 Parks' CLUST6 program was also used with the six independent Fourier shape variables alone. Two principal components were extracted in the initial R-mode analysis. All variables loaded on the first principal component at high levels (Table 5). Variable RCM had the highest loading on component two. The resulting phenogram was thus based on two non-Fourier quantitative variables, and six shape variables (Figure 4). Three principal components were extracted from the initial R-mode analysis using Park's CLUST6 program on the quantitative character set (Table 6). Variable ZRS loaded the highest on principal component one. All other variables loaded at significantly lower values. Variable NDARM loaded significantly on principal component two. Only variable AREAS loaded on principal component three at a significant level. Nine principal components were extracted from the 20 binary characters. These nine principal components explained 80.553 percent of the variation (Table 7). The final CLUST6 analysis incorporated all the characters previously used in the first three analyses. This combined analysis used 35 binary and continuous variables. Nine principal components were generated which explained 79.34 percent of the variation observed in the data (Table 8). The shape characters and most of the standard quantitative characters loaded at a very high level on the first principal component (Table 5). This 31 Table 5. Principal component loadings for Fourier shape characters (CLUST6 Program), total percent of variance explained by the two components is 84.829 percent. Character Component 1 Component 2 HM8 0.853 -0.382 HM18 0.912 -0.146 H82 0.868 0.271 H315 0.898 -0.236 RCM 0.833 0.404 RCS 0.898 0.111 Eigenvalues 4.619 0.471 Percent of Variance Explained 76.978 7.851 32 Table 6. Principal component loadings for quantitative character set (CLUST6 Program), total percent of variance explained by the three components is 81.826 percent. Character Component 1 Component 2 Component 3 ZRS 0.858 -0.092 -0.004 ZWTS 0.858 0.034 0.229 TMRS 0.793 -0.393 -0.223 DARS 0.814 -0.335 -0.197 ANM 0.765 . 0.497 0.084 NDARM 0.729 0.576 -0.003 NDARS 0.713 0.483 -0.313 AREAS 0.817 -0.209 0.335 NNS 0.762 -0.446 -0.037 Eigenvalues 5.638 1.330‘ 0.397 Percent of Variance Explained 62.640 14.778 4.408 33 600 r.mir0 98100 tU l nuvh 01) 804 000 0 r. nU.fi/n£ ad nu 1LAQ.KJ he- 00 Ck?) ’9 rx1i ...H/nU VJ nu 00 4| 0‘ r“: :2 ad I) nf 0.00.0 (L nv .UJn/_1L ku .o AQFH/ nufii file. 0.9 AU flu .5104AUJ Va 0211 Do1;nd n8 0 in 80000 Au Auc- RJAUJ no AH, n5/A4 0e ’00 1;.flu1l.fil a: 0 nv Ocnfl/oo tmr all n . e 0 nvnn.tvfll n c 0000 nv1$nd Afioo “Ina n; ooqfillfi m1. 88 oth1.. nu.1.flv n£_71 n ’11 null (O 1 0 prm 00 00 41 nund cent-h} cf r734 n 31 ito .... her 016 an hrpH/1&.l‘ Table 7. 39 PRINCIPAL AXIS FACTO? LOAJIN F Character F 1 7013.01.09 01.070103124391593! 711. an... .0.“ .01.?92167933 211340171.9319310809,.2 .....OOOOOQOCOCIIIOO ow 00*33936938Q.“911633“5 7.37 1.J3.L.(12C.0 1...). *7 3101.3. 0.011.1112303313223110 00.000.00.000000000. 72430:??337“ 1379.01.996 91973652113556993290 022183100100111.03201 00000000000000.0000. “07 10.01.1010 00202? .0527 1 36 “In 30.1.2510 “08904210596 2 L521CC3227.135202281 1,125.55; 0935135253709 313.» 917636535735 .1035 .leGOlCoLllltuZJZGIIQH 0. 08327 8709317920. .0596 35.55191. 0.55 n «33733 .96 137.11.»n.0051 031010 0013 0 OOOOOOOOOOCOOOOOOOOO . 00410-5536 07..0633’.337 525 133.95559b3.355k).35751 5.).).0Ln)]3?.7.).7.7.9..0141)1121 00.0.000000000000000 B7qc356.01.5195192.0103 53’357L7673.996960925 22“1.LJS‘J?655212213“11 00000000000000000000 1237 2.0.1.30. It, .4327 5565:. 06.0377 . .6. q .4 39535110.- 5 55555565666557 5555.95 123556700. «0.123 956739 0 111.111.11.112 EIgenvaluem Percent of variance accounted for o 2 Q 5 .9 .0 I O 2 7. .9 .4 3 5 7 0 O 2 Z 0 .b 1 .D 3 O O 3 1 7 Q. 5 7 9 O 0 3 6 .0 0 3 8 .0 O I 19 2.983 1.55“ 1.J29 10.917 7.771 5.160 7.177 35. 837 19. 16; 31; 45; 2, HM18; NDARS; 13, 25, 31. 28; 43; 12, NDARM; 25; 24. 30. Character 1, HM8; 5, ROM; 6, RC8; 7, ZRS; 8, ZWTS; lO, DARS; 16, 9; 17, 11; 18, 13; 23, quantitative and binary 23; character sets for initial R-mode analysis of Park's CLUST6 program. 3. H52: 9. 11, ANM; 34 15, NNS; 22, 21, 18; 279 343 28, 35; 299 42; 4, H815; -03521'1‘0’.) AREAS; Principle component loading of combined character TMRS; sets Fourier shape, 32. 48; 33. 49; 34. 51; 35. 52. 20, 17; 26. 32; 14, Pelagi'it 411, cactu— Charactcr r 1 Table 8. 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J J a J 02 4.,4 .011UJ.J.U\JIQ3.J.J.JJ1_D—3 ..............O....I.....I.I....... 7 055...}...10.“ 7’55“)...“ ~3.062810.¢59.3“756.05 .erljl w) C1 .. 3:: (.151. we; 0.1.1. 5.0233767t69.01_ ~71 ..- 2 .JJ1)_.J11.J 0 <15. :22 130.7322). 0 WH.UJJ)C~UH)_J1U 93.J° ~95.) 11.032.33.421 0 “.61 .0. 01.? 47J311G/3.’ rl.91 L...5G.1.C7 1131.752). .5278. . 1.x“118k61..../>¢.50.1§[0.3.2 1.Jh41..). .21....7...1)15 Olv S‘s-J 4P)3.H Q 02.0231btfl21 0.00.0.0... 000000000 .0... 00000 0.... 01.3 1... 9:123 286-302—239793206315975“52 h 113 95310;. .- 01 $8.09 a 1... c )9: O 0 ~ s7L7b31 e19“: .- 7.10.1H 1.47.0.1 18.9.165.0.35A...)5.75.0..).9'D5.D765.9S55 12395576 9.91239567593123956759 1.12305 11111111112222222222333 .1033 .575 1.638 .051 1.561 .695 1.967 U odb 2.956 .915 2.615 2.I90 lthi 2.9?5 ,0980' 3.125 5.929 16.578 Percent of variance «7.365 accounted for Eigenvalue 35 principal component accounts for 47.365 percent of the observed variance in the data. Blackith and Reyment (1971) noted that the first principal component often represents size variation of a growth vector. In this study characters which are accepted as controlled by growth, such as thickness of the mature region and number of diaphragms per unit area loaded at very high levels on the.first factor. This would tend to confirm the idea that the first principal component generally represnets a growth vector. Because the loading of the Fourier shape variables are generally larger than the standard quantitative characters, these shape variables must be to a large extent controlled by growth. Binary characters, on the other hand, are far less sensitive to this source of variation due to their nominal level of measurement. These characters dominate principal components two through nine. Oxnard (1969) stated, "The mathematical delineation of shape has frequently been aimed at problems of classification; some of the most recent attempts have been described as numerical taxonomy by Sokal and Sneath." Quantitative measurements are commonly used as a crude attempt at the description of the internal and external structure of the organism being studied. As noted by Oxnard, "The shape of a biological specimen may be represented by a series of measurements of different 36 kinds taken on the specimen." The Fourier shape analysis provides an exact description of shape. This description represents an advancement over the use of one or two measures of length or width as a measure of shape. The degree and rate of astogenetic variation of different Species may be as diagnostic as the measures of characters free from such variation. Blackith and Reyment (1971) have pdinted out that astogenetic variation differs from one species to another. This variation is thought to be a product of both genetic and environmental influence. A combined influence of these factors makes the interpretation of variation in widely scattered localities representing substantially different environments difficult. In this study a generally uniform lithology points to an environment in which genetic influences might possibly outweigh environmental ones. The importance of intracolonial variation is in- dicated by the large proportion of standard deviations that were better measures of the rotated components than the means. Nine of the 15 Fourier shape and quantitative characters so chosen were standard deviations or measures of localized intra-colony variation. The nearest neighbor statistic loaded significantly on both principal components one and three, and thus contribute significantly independent information. Clark 37 and Evans (1954) pointed out that the pattern of distribution of a population of plants or of animals is a fundamental characteristic of that population. Inasmuch as a colony can be treated as a collection of individuals with varying degrees of interdependence, the pattern of distribution of the individuals, in the case of this study, the zooids, should also be of fundamental importance. The only apparent control on the spatial pattern of distribution is the degree of budding. This pattern is spatially controlled, as demonstrated by Anstey and Pachut (1974) in Amplexopora filiasa. "The distributions exhibited by populations of living organisms in their natural environments include an almost infinite variety of patterns" (Clark and Evans, 1954). Such a variety of spatial budding patterns are certain to exist in colonial organisms, especially the ectoprocts. The standard deviation of interzooecial surface area (Underwood, 1970), also contributed independent information. This character also appears to be controlled by the budding pattern. In this study the variance of the characters measured in the exozone of the zoarium appear to be controlled by the budding pattern. The budding of Lgptotrypella pellucida for the most part takes place in the exozone. This budding leads to a wide range of zooecial sizes and shapes at the surface and sub- sequently to large degrees of variation for all characters measured in this region. In Nicklesopora renzettiae n. sp. budding generally occurs in the endozone and zooecia 38 at the surface are for the most part ontogenetically uniform. Such uniformity leads to lower standard deviations and more consistent spatial patterns and surface area per unit volume. This difference explains the greater information content of most standard deviations in comparison with their associated means. Further studies are needed to determine if this discrimination holds true at lower, more similar taxonomic levels. Q-MODE RESULTS The taxonomic placement of the specimens was based on comparison with previously published literature (Tables 14, 15, and 21), The two species were sufficiently distinct to make visual sorting easy and reliable. The two species clusters were constructed so as to minimize misclassifications. The number of misclass- ifications was determined by counting the number of OTU's (Operational Taxonomic Units) of one species found in the other Species' cluster. The phenograms generated from the three character sets, (shape, quantitative, and binary) (Figure 4, 5, 6, 7), indicate that the binary character set provided the best phenogram on the basis of the fewest misclassifications. The Fourier shape character set provided nearly as good a phenogram, while the quantitative character set provided the worst phenogram. The same OTU misclassifications are not always present in any two of the character set generated phengorams, and never in all three basic phenograms. Each of these sets provide a certain amount of independent information. One can not say exactly how much unique information is being carried by each character set. It has been 39 40 Figure 4. Phenogram based on six Fourier shape variables; HM8, HM18, H82, H815, RCM, RCS; ten mis- classifications present in phenogram, asteriSks indicate misclassifications; see Table 1 for explanation of character abbreviations. Asterisk indicates specimen clustered in the wrong group, or is misclassified. 0.2 0.3 Us! 41 1.) rLu.x r orafisnu cwgrrxctrvr OI VOLI‘ 111111111111 . . . . . . . . . . . . . . . o . . n . . _ . . . . - g . _ . . . . — 7.171111111111111 . _ . . . - . . . . a c - Tflfiflfiw 11”“54l111-..1? 9L-»V?nil . . - o o . o o . o . . c - . . . . . - . . . . . u . o . . . . . . . . _ . . . . . . . . . . . . u o . g — . . . . . - .. . . . . - o n o a o . . . . . — . . . . . . . . . . 11111.... 1111111111111 111 . . . . . . . . . . . o . . . . . . . n . . . . . a . . . a . o g . - . . . . . . . - . . . . . . o u . . . . . . . . . . . . o . _ . . . . . . . u . . . . o . . . . . . . . . . . . . . . . . u . . . . . . . - . . . . . . . . . . . . . . 11.111111111111111 - . . . . 1.1.11 . . . . c c . . . . n . . . . . . . . n u u u . . . . . . . . . . . . - . . . . . . . . . . . a . . . . . . . o o . o g . o . . a o . . . . - . . . . . . . . . . . - 11111117811117.1111... . o . . . . . . . . c c . u . o o . c o . . . . ~ . . . . . . . . . . . . . . - . . . . . . . . . . . . . . - 13111.11 T31111- o . u . 7.111. a . u . c o c c - . o c . c . . . . . . . . g . . . . . n . . . . . . . . . . . - . . . . . . . . . . . . . 1? 7.1.7.1.]... . . . - . . . . . 17.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . . . . . . . . . . . . . . . . . . . . c . . . . . . . . . . . . _ . . v 7.7.11 . . 1?.TTT It. . a 7:111 11.7.. 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I/... 1n! ... 1 ..1...11.4......l.ov.... .....1....22125.<2.)....7.21n1.17..unusual-((1 h 1 “A 1.... .¢.P.m.fl.h. q" . 9 1 1 3 . 3. .33 .. . . ... r 1...... .... ......ui..,...,wm1wo.1uh:u;...uw”FWNMArTIHM ~N..:.w.Ph.. (Libyan... -vthJBLaruivxuSC t J. v33 3 3 5 051...) )1. u a 1.. .L butr b1111lr 011c111..s111.n..u L11. L 0111‘ 53 L1L1‘L1111f‘ l.- 1 {v 110 L1 L41 ... (1111.11 1;..3! .. 111D 01.6.u“1".56-111131161.511 m 1611.31.53.51“ 1 a 1 511.1 01¢ .h m . . e .H mmfipvcaroa anomcmm.axofiz . mvaosfifio caflmmxmvopmm . . . . 630...... 3L.J7.1t)?P3.h.-.O7?LBFC .(67054(7?o.17r.16#1936383275 1 r» .... 1.1.9.19 £16 159.1132 516 3&11733 £56..» 221L53H51 27.53.» 2.45 1123 3 r) h 1h23315 ‘51 Figure 5. 42 whenogram based on nine quantitative variables; TMRS, NNS, ANM, NDARM, NDARS, ZWTS, ZRS, DARS, AREAS; 15 misclassifications present in phenogram, asterisks indicate misclassifications; see Table 1 for explanation of character abbreviations. Asterisk indicates specimen clustered in the wrong group (misclassified). ‘43 CLUSTiq 013G533 VILUL OF COTFFICIEWI 0.3 0.2 0.1 1.0 I if 1111 II} IIIIIIIIIIII 1 Id-—--- ...-0..... goon-mam“ i f i I E I II II 1111 III-l. . — . . . . .— . . - . u _ u . u . . - 111111111 . — . . . . . . . . - . . . IIIIIiIIIIIIIIIIII - u - IIIIIII . . . . u . . . . . . . . . . . . . . . . - . . . . . . . . - 1731.11. 11.11 11.1 . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . - 111111.. . . . . . . . . . ... . . . . . . . . - . ... . . . . . . . . u . ... . . . . 11111 11111111 . . 1.11111 . . . . . . . . . . . . . . u . . ... . . . . . . . . . . . . . ... . . . . . . . . . . . _ . . ... . . . . 11911.11 . III . 111911111 o c 11.11 . o n 111117.. . o . ............... . ...... ...... ......qun..."33:31.. . . .731 . .11 11 . . o . . . Pv11'u.1 1.1.5... . . . o . . . .Y. 7.7.. . . . .. . . .. ... .. .. . r .. . . ... ... .. ... ... .. . .... . ... ... .... .-... . ......... ........ . . ... . ... ... .... .Ifi... . ......... ........ T1111...IT.1...11..11...T.T...ITII........1....... 31.92.51. 132.1. 1.9.1.11. 1.1.5.1....) 7.“..122 15.1171... 1,370.... 1.151.123.4131. 1.1.1.7...1.b9..1.15.(.1.29.1?323. . . . . . . .7.24?413.1..~.3114.. . .. ..?a3.31....8.5 ........1...571 5:....73.......?. 54.... .5? 3r; .. .r: .533... (95333333615 . 330...... T...1r..r~J3335332.~63.-3833...... .. . IIIiIIiIII-i ii {1111719111 1 I.----------.------- I I 6111-3 -o---—-----------------------------------.--------------}--- { 1---.--O..----------I -. .-.---I------00’--.-------------.---.-----.-------.-C-------.- .-------C-.-1--------O-------.------------.-.------..--. a ------------—-----------------------1 p --------I------------------------..- I . . . 1 o I c . a o . a . . . o o p . . . . . o . . . . . u 1 11?. r):- f11 1. .. 7. . . . 5 3.1 .135 (I... "...... 1.9.0 [.1 1.1 6...... 16 “w HC31r.MM.. .31? My: .anICCCOENCIuCCMMM “MMMMCCGCCCHQMQIGN”MUN...“ 1 9101 1. 1 1 1111 1:11 11.1111 1 m an t.nu it; u p mufiosflflom maammmuvopmoq“ omfivpmscoh . . 711169 83.50111...) an“ f).01726276 “89221867120551.58265;1’09631736 1‘21“ 23‘555131227huu12235 6353512231431 5337.53 f)... anomommeOHz 37L. .0 00. 09 5 .5 6 hr) 1..) 1 Q3 Figure 6. 44 shenogram based on 20 binary characters; 9, 11, 13, 16, 17, 18, 23, 25, 28, 31, 32, 34, 35, 42, 43, 45, 48, 49, 51, 52; nine misclassifications present in phenogram; asterisks indicate misclassifications; see Table 1 for explanation of character abbreviations. 45 ”LUSTTIIJIflu=Ai Of COE1FIFISNT VILJ" o . n . “ IIIIIIIIIIIIIIIIIIII . - . . III'LIIVIIIIIITII'AIIIIIIIIIIIIIIIII}IIIIIIIIIIIIIIIIIIII . . u a . . . Iiillfll . . III . . . - u 7. o . p - 0 o . o n o o . c - I!II1111'stIEIIiIIIIEIIII'fIIIIIIIII . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . o . IIIIIIIII . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III . . . . IIIIII . . . . . . . . . . - . . . . . . . . . . . o u o o u o o a o o o a o o o . . . . - . . . . . . . . . . . IIIIIIIIII . . . . . . I... . . . III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . - . . . . . 9 . . . . . . . IIIIII . c . c . - . II . o o . o o o o I... . III! . . . . . . . . . . .. . . . . . . . . .. . . . . . . . . . . . .. . .. . . . . . . . . .. . . . . . . . . . . . .- . .. . . . . . . . . .. . . . . . . . . . . . .. . .. . . . III . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . .. . . . I . . . . . . . . .— . .. . . . . . . . . . .. . . . . . . . . . . . . .. . .. . . . . . . . . . .. . . . a o o u - III-I . o o o a II. o o o o . III 0 o o c a o o . . . . . . .. . . . .- . ... . . . . . ... . . . .. . . . . . . . . .. . . . .- . ... . . . . . ... . . . .. . . . . . . . . .. . . . .__ . ... . . . . . ... . . . .. . . . . . II . e .. . II II . III ... . . III . . ... . . . .o . o . . . .. . . .. . .. .. .__ . . ... . . . . . . ... . . . .. . . . . . . . . o o o o o . . . . _ o . o . . . . o . o . . . . o o. . . . . . . c o c o o o o o o o u o . o o a o o c o o . c p o a o o o o p o a o o a o g c u o II. o o '81! o c o c o _ u o o o o o a o . III! o o o o o p o o . XIII . . .. . .. .. . . .. .. ._ . . ... . . . . .... ... . . . .. . .... . . .. . .. .. . . .. .. ._ . . ... . . . . .... ... . . . .. . .... . . .. . .. .. . . .. .. . . . ... . . . . .... ... . . . .. . .... . . ..lI .. .. . . .. .. . III. ... . . . . .... ... . . . .. . .... . . .... .. .. . . .. .. ._ . .. ... . . . . .... ... . . . .. . .... . . .... .. .. . . .. .. . . .. ... . . . . .... ... . . . .. . .... a o .... a. o. o . o. o. . o .— ... a o o - .... ... o u o .o o .... III. .... .. .. II. .. .. . . .. ... . . . . .... ... . . . .. . .... . .. .... .. .. ... .. .. . . .. ... . . . . .... ... . . . .. . .... . .. .... .. .. ... .. .. . . .. ... . . . . .... ... . . . .. . .... . .. .... .. .. ... .. .. . . .. ... . . . . .... ... . . . .. . .... o .- .... .u .. ... o. o. - ... ... on . ...-. .... o... o a... . .. .... .- .- ... .. ... o .- ... . c c ...-a co. a. u a. . .... 0 . .. .... .. .. ... .. .. . . .. ... . . . . .... ... . . . .. . .... . . .. .... .. .. ... .. .. . . .. ... . . . . .... ... . . . .. . .... a! . .. .... .. ..II.. .. .. . .II. ... . .IIII.... ... . . . .. .II... . .. .... a. .. .... o. o. o a... ... a . .... o... no. u o o .o c on... . .. .... .. .. .... .. .. . .... ... . . .... .... ... . . . .. . ..... ... .... o. .. .... a. o. - .... ... o o .... co.- co. a. g n. o ....o II.. .... ..II. .... .. .. . 1T... ... . . .... .... ... . . . .. . ..... .... .... ..... .... .. .. . ..... ... . . .... .... ... . . . .. . ..... .... .... ..... .... .. .. .=..... ... . . .... .... ... . . . .. . ..... .... .... ..... .... .. .. ....... ... . . .... .... ... . . . .. . ..... II...II... ..... .... .. .. .-..... ... . . .... .... ... . . . .. . ..... R0908K19PJ ?9911 Raw“ “7 R3 1.55702 192 h C 3769 Q931 016 2 1 3 98 1 19162 1.5N.II.... .I... 311. 29 .2 .7923. .12 . 1 .22. 222?. 2.. 3 1 .... ..w 2 1...). 1.....)ogd351. 2.1575 ...1. o. 01. ,.-5.3-7 1).. 3 . 2...J 2... ..JJ . o . nJ- — .533. .33Jt)3 .-.(1 7.2., ....Uf. 9.89.)... 3.6 cs 0 .9593-» 055 a 3 033.. o 335 3.11 3 5 5 «U7. 3 (uh)... U3 \ L VICIUIII.‘ I 01.1... .9 U 91. .00 100 1.1...ch 1..U.U 1. .v 1.0.101. 3,950 011 (U L U 1rd .0 c111|u 0116116b66 61.66” 11.16 1.1. 6... 6 9016.86 611. 6 1. 61.1.6 01.1.1 1.66 1*. 1 1. 6 I 16561 a . i u a. m . . mwfivpmNth whomdmmaxoaz . avaOSHHom mHHmmHuvoemcq . 6557u763“.b ‘30:]. 5631 “2 2° 3 tag/32 Ill-.33“ 31.?)6 1,555 5146 23 15 1.51.25 857 314.5 55 6‘69 1.736 973 9 C 2 13 C #9812 225 2226 155 2 h M 3 21.312 11111!!! If. (11.-LII I I I I I $05.12 .---------.-O-OOIODCCOOOOCDO---00-o--------------------. 63-h} ---. -c-uno.--------onconouocuc-oo------- 1 1 * 103-12 -----.----o---------:-oooooou--..--------g-.-----.---—--- ------------- . 03-1.5 --------uuoccccooooocooooouoooooocuno-QOI 1c 33 81 17 15 46 Figure 7. Phenogram based on combined set of characters, Fourier shape, quatitative, and binary character sets; five misclassifications present in phenogram; asterisks indicate misclassifications. v NJ-wtro PM» \NLGNNQC‘ WM“ bl C “N VIN 3‘0! Ntl‘tNN 0‘ u» POWU‘OU‘ W0 UNO‘HNH V 0““ 01th NO (NOON NCU‘O‘ CPD ““30“!“ ON U“? SKIN-DUI HUN” PO‘U LLU3I.: VALUL Nicklesopora renzettiae Leptorypella pellucida 1' 11' 0‘ t“ F‘ 000‘» Own-r“ 060‘ PC‘HH 477 l Ala-3.: C‘ 30CrchIi1l ICJfll b1u7-3 153-13 3-’22 .' )’ \A. IOIIII ' I 2 2 z UU'H'\ OJ (“Vt-fir. r: (PM ”(a pup-MM: OH. 1.00- FHHC‘d‘w ...L‘nrspb-ac‘ I)... d C'b'tu‘W‘U V‘r‘ so. INHI Ilval 00» HI Al“‘dwwm 15.-21 165-13 6113-1 -3 0‘ ya u L 1C2-3? a- 0 M O raw-Mo H' -r-u HHH (‘Pcc H m rum... mug-l ... 0 mt (a r- I wt. ulllr- mm.» Ian! I P DOOM 3“qu l0. O—Iv-‘r- r u: Out-‘10 Aunt-us) ' 19H .0 I *- ...Jl ... c u: I V e1;--1‘ --------------- ------ --------- ---- ----- ----oi {----- ------ i its-.9 --- ----------- ---- ------ --------—----------o1---I 1 1.3.12 -. ----------- ----- .......... .-1 :cb-11 - ---------------------- ------—-—------------------- --------- ----I :cs-s? -------------------- - ------ -------------- ------ ----- -------- - ----------- 0.1 . 1 -------- III:3:2:I:2:1:::::::£-,,_,_______-___--_§----------- ............... ----------------..--O.---1 - ) --.. COCO--.-..-ooooolnoc----.--‘O...1.--.-.OCOOP1 J.2 ....... 1 ; ::::::::::::::::::::::::::::::::i‘"'°" ' § - ....... .---.---------.------------.-.------.-.---.-1 ................ .---1 i =5a:2332Izzszzzzgrfiixxré """"" i --------- - ----- i ---------------- 1-------1-----------1 I-------I ------------ ------------, g g ---------- ----------------—-----1 1 I ------ ----------—---------------1-------------------i . I x I I...........; I I ::::::::::::I"""‘} ..... ----------§_-----.---- I i--- ::::::::::::::::::::£...............I i I , ---------- "'1 } -- ..... -.--...------...-----------..-- 1 -°°--~°----‘-'------------'-'-'-°--?‘-'-""----I I ::::::::::::::::::::::::I .......... .---.--- ..... - ......... .-. .------’----------------------------—---------4-----_----- I-.-‘-----.-. ....... ---“I C ............ -.---C'----1 WH ---.----1 -------- I---------------I---------°-----r-------I .............. -------.--1 ----I ----1---1 ----t.--. ----1 .-.-;-----.---.-1.--; h HHHHHHHHH I O | H HI—WHHW IIIIZZIIIIZZIIII----§"' """" " """" """' -.--.-- .......... --- ........... .-- ......... ----.--.-1 ....................... -------------------°---------I I ................ .-------.---.-------.---.-----------1------- I --- ....................... .......-..I I ------------------------------------ 1---------------x I I I I--- { HHHHHWHHH HHHHHD-dHHHHHH—‘HHHHHHHHHHH-‘HHM HHHHHHHHHHHWHHHH b—HHhOdM-‘HH HM 48 demonstrated that the standard quantitative character set does not provide as much independent information as the other two sets. As seen in Figures 4, S, and 6 the quantitative character based phenograms generate no clear boundary between the two species, whereas the other two basic phenograms demonstrate a somewhat shaprer break between the two species. In the case of the binary character set, the larger amount of independent information retrieved can be accounted for by the larger number of characters measured. This large number of characters makes up for the information loss due to the nominal level . of measurement as opposed to the ratio level of the quantitative and Fourier shape character sets. The larger amount of independent information retrieved by the Fourier shape character set can be attributed to its greater accuracy of mathematical description of the zooecial shape. The failure of the standard quantitative character set to provide a comparable classification of the studied OTU's appears to be due to the lesser ability, accuracy and number of these characters to describe the skeletal shapes both internally and externally. As expected, the combined character sets provided a substantially better phenogram. Sneath and Sokal (1973) suggest the use of all possible characters, and indeed this study indicates that the greater the number of characters used, the better the resulting phenograms. THE THREEFORKS BRYOZOAN FAUNA Paleoecology The bryozoan fauna of the Threeforks Formation is characterized by juvenile forms, which lack well developed exozones. Zoaria are generally small and ramose. The predominatly shaley lithology indicated deposition of large amounts of terrigenous muds. The sporadic deposition of muds apparently prevented the growth of fully mature bryozoan colonies. The two species Leptotrypella pellucida Duncan, and Eicklesopora renzettiae n. sp. dominate the fauna of the Threeforks Formation. These two species, although widely separated by systematists, are morphologically quite similar in external form. This suggest functional morphological selection of these zoarial forms. As suggested by the abundance of juvenile zoaria, the environment was one of stress leading to a large environmentally induced change in skeletal morphology, which probably brought about convergence of gross colony form in divergent taxa. 49 Systematic Paleontology Phylum Ectoprocta Nitsche, 1869 Superclass Tubulobryozoa Cuffey, 1973 Class Stenolaemata Borg, 1926 Subclass Curtaulata Cuffey, 1973 Order Cryptostomida Vine, 1883 Suborder Habrovirgatina Cuffey, 1973 Infraorder Rhabdomesita Astrova and Morozova, 1956 Family Rhabdomesidae Vine, 1883 Genus Nicklesopora Bassler, 1952 Type species.-Nicklesopora elegantula (Ulrich), 1882 Nicklesopora renzettiae n. sp. pl. 1, figs. 1-7 pl. 2, figs. 1-5 Diagnosis- Zoarium ramose, low monticules, generally 4 mm apart, composed of larger zooecia. In longitudinal section, endozonal walls uncrenulated diverge gently outward, abruptly thickening at base of exozone, numerous well defined simple diaphragms in endozone. Well developed superior hemisepta; inferior hemisepta present. B-acanthOpores observable in thickened exozonal walls as series of pustule like grains. In tangential section, zooecia thick walled, generally ovate, surrounded by single row of poorly defined small B-acanthopores centered on walls, forming polygonal zooecial outlines. Description- Qualitative and quantitative characters given in tables 9-13. 50 51 Discussion- Due to the confused status of the genus Rhombopora, and Nicklesopora, generic placement of the Threeforks taxa was carried out by compariosns of the type species of each genus with the Threeforks material (Table 14). Nicklesopora renzettiae is compared with named species of Nicklesopora in (Table 15). Nicklesopora renzettiae is most similar to E. elegantula (Ulrich), the type species of the genus, but differs in having superior and inferior hemisepta, and well develOped numerous diaphragms in the axial region. In the description of E- elegantula, Ulrich (1884, p. 33) stated, "... it seems quite certian that an occasional diaphragm crosses the tubes in the axial region, but as they are not sharply defined in my sections, and might not really be such structures, I have not allowed them to appear in the figure." The presence of axial diaphragms in the type species remains in doubt but Nicklesopora renzettiae has well defined and numerous axial diaphragms which are very distinct; fiicklesopora has not previously been reported from the Devonian. Origin of name- Nicklesopora renzettiae is named after Dr. Phyllis Renzetti for her unpublished study of the Threeforks fauna in 1963. Through the recollections of Dr. Renzetti's localities and the use of material previously collected by her, this study was made possible. Type specimens- Holotype: 6107-1 52 Paratypes; Figured, 6102-l, 6102-2, 6103-19, 6104-1, 6105-R. Unfigured, 6101-R, 6102-3R, 6103-1R, 6103-9, 6103-12, 6103-13R, 6103-24, 6103-32, 6103-47, 6103-48, 6103-49, 6103-50, 6106-R, 6105-11, 6105—18, 6105-23, 6108-10, 6108-12, 6108-2, 6111-3, 6111-4, 6110-1. Suborder Fenestrina Elias and Condra, 1957 Family Phylloporinidae Genus Indeterminate p10 3, figSO 7-8 Diagnosis- Zoaria composed of anastomosing branches with four rows of apertures on celluliferous side and none on back. Zooecia and fenestrules sharply ovate in outline. Fenestrule mean length 1.75 mm; mean width of 1.00 mm; branches average 0.35 mm wide; zooecial apertures 0.1 mm x 0.04 mm. Remarks- Only one specimen of this taxon was found. This is the first reported occurence of a phylloporinid of Devonian age. This specimen closely resembles the genera Cariniphylloporina and Phylloporina but lacks hexagonal fenestrules and a sharp keel in oompariosn with the former, and lacks observable mesopores and possesses elongate zooecia which are strongly diagonally aligned in contrast to theilstter. Therefore, this specimen possibly belongs to a new genus. This specimen was collected from locality four. 53 Subclass Leptaulata Cuffey, 1973 Infraclass Expletocystata Cuffey, 1973 Order Expletocystida Cuffey, 1973 Suborder Trepostomina Ulrich, 1882 Family Heterotrypidae Ulrich, 1890 Genus Leptotrypella Vinassa de Regny, 1920 Subgenus Leptotrypella Vinassa de Regny emend. Boardman 2122 species Leptotrypella barrandei (Nicholson), 1874 Leptotrypella pellucida Duncan, 1939 pl. 4, figs. 1-6 pl. 5, figs. 1-5 Diagnosis- Zoarium ramose, monticles average 3 mm apart, walls thin, crenulate with complete simple diaphragms in axial region. Walls thin to moderately thick, thickening slightly irregular in peripheral region. Numerous complete simple diaphragms. Mesopores absent; occasionally small zooecia present. A-acanthopores occasionally present, zooecial subpolygonal to subcircular. Description- Qualitative and quantitative characters given in tables 16-20. Remarks- This taxon agrees with Duncan's L. pellucida in all respects (Table 21) except in length of mature zone, axial ratio and substantially larger size of zooecia. Because of the very narrow mature region and high axial ratio, this material probably represents astogenetically younger stages of Duncan's L. pellucida. 54 Hypotypes Figured, 6100-R, 6103-20, 6103-22, 6103-43, 6110-9. Unfigured, 6102-3, 6103-1, 6103-4, 6103-5, 6103-6, 6103-7, 6103-11, 6103-13, 6103-21, 6103-22, 6103-23, 6103-27, 6103-28, 6103-29, 6103-30, 6103-45, 6105-1, 6105-9, 6105-12, 6105-13, 6105-14, 6105-19, 6105-21, 6105-22, 6105-24, 6107-2, 6107-5, 6108-1, 6110-8. Suborder Cystoporina Astrova, 1964 Family Fistuliporidae Ulrich, 1882 Genus Fistulipora McCoy, 1850 Type species.- Fistulipora minor McCoy P1. 3, figs. 1-6 Disgnosis- Zoarium lamellate, well developed lunaria projected into zooecial chamber almost appearing trilobate in cross section. Three to four upright series of vesicular material between zooecia, mean redius of zooecia 0.26 mm, mean distance between zooecia, 0.21 mm diaphrams average one zooecial width apart. This zoarial fragment measured 1.0 cm x 1.7 cm x 0.4 cm, and was collected from locality number six. Remarks- Depending upon generic revision of fistuliporids, this specimen conforms in all respects to the genus Dybowskiella, and could be assigned to that genus pending clarification of the concepts of Fistulipora, Dybowskiella, and Cyclotrypa. 55 Table 9. Nicklesopora renzettiae n. sp. binary character requences for 28 colonies. Frequency of Frequency of Character positive character Character positive char. (Table 3) states states (percent of all zoaria) (percent of all zoaria) 1 13.8 19 6,9 2 86.2 20 3.4 3 0.0 21 96.6 4 3.4 22 10.3 5 96.6 23 86.2 6 3.4 25 10.3 7 0.0 26 3.4 8 0.0 27 10.3 9 96.6 28 65.5 10 3.4 29 65.5 11 89.7 30 20.7 12 3.4 31 69.0 13 13.8 32 58.6 14 0.0 33 13.8 15 96.6 34 31.0 16 58.6 35 62.1 17 27.6 36 0.0 18 17.2 37 3.4 Table 9. 38 39 40 41 42 43 44 45 Continued. 3.4 93.1 89.7 10.3 17.2 6.9 3.4 58.6 56 47 48 49 50 51 52 53 93.1 51.7 86.2 96.6 58.6 41.4 3.4 57 Table 10. Nicklesopora renzettiae n. sp. means of quantitative character data, means based on 28 colonies of N. renzettiae. Character Mean Standard Deviation Minimum Maximum ZRM 0.111 0.023 0.072 0.166 ZWTM 0.229 0.078 0.054 0.423 APZM 16.860 11.783 0.0 38.200 TMRM 0.294 0.173 0.070 0.607 DARM 4.027 1.565 1.488 6.943 ANM 79.389 17.880 9.00 90.00 NDPRM 0.716 1.660 0.0 5.8 NDARM 2.324 0.939 0.0 4.0 DLCM 0.357 0.153 0.103 0.685 DAM 0.020 0.015 0.0 0.083 AREAM 19.263 4.340 10.11 29.800 NNS 0.841 0.142 0.651 1.449 58 Table 11. Nicklesopgra renzettiae n. sp. standard dEvIatIOns of quantitative character data, represents mean of 28 colony standard deviat- ions. Character Mean Standard Deviation Minimum Maximum ZRS 0.014 0.004 0.006 0.023 ZWTS 0.042 0.016 0.001 0.077 APZS 4.273 2.829 0.0 10.89 TMRS 0.046 0.039 0.011 0.156 DARS 0.195 0.192 0.035 0.883 ANS 3.093 3.576 0.0 13.39 NDPRS 0.116 0.305 0.0 1.056 NDARS 0.576 0.257 0.0 1.005 DLCS 0.074 0.065 0.011 0.333 DAS 0.006 0.008 0.0 0.043 AREAS 1.461 0.242 1.046 1.963 59 Table 12. Nicklesopora renzettiae n. sp. Fourier Harmonic Means data statistics, based on 28 colonies. Character Mean Standard Deviation Minimum Maximum HM2 0.184 0.046 0.106 0.300 HM3 0.410 0.011 0.021 0.066 HM4 0.036 0.013 0.015 0.072 HMS 0.018 0.007 0.008 0.040 HM6 0.013 0.005 0.007 0.024 HM7 0.008 0.004 0.005 0.019 HM8 0.006 0.003 0.004 0.015 HM9 0.005 0.002 0.003 0.012 HM10 0.004 0.001 0.002 0.009 HM11 0.003 0.001 0.002 0.005 HM12 0.003 0.001 0.002 0.006 HM13 0.002 0.001 0.002 0.005 HM14 0.002 0.001 0.001 0.004 HM1S 0.002 0.001 0.001 0.004 HM16 0.002 0.000 0.001 0.002 HM17 0.001 0.000 0.001 0.003 HM18 0.001 0.000 0.001 0.002 HM19 0.001 0.000 0.001 0.002 HM20 0.001 0.000 0.001 0.001 RCM 3.417 0.037 3.324 3.506 60 Table 13. Nicklesopora renzettiae n. sp. Fourier Harmonié standErd deviation data statistics, based on 28 colonies. Character Mean Standard Deviation Minimum Maximum H32 0.063 0.016 0.040 0.102 H33 0.023 0.008 0.013 0.042 HS4 0.018 0.007 0.007 0.033 H35 0.010 0.004 0.004 0.019 H36 0.007 0.003 0.003 0.014 H37 0.005 0.002 0.002 0.011 H38 0.003 0.002 0.002 0.007 H39 0.003 0.001 0.001 0.006 H310 0.002 0.001 0.001 0.004 H311 0.002 0.001 0.001 0.003 H312 0.001 0.000 0.001 0.003 H313 0.001 0.000 0.001 0.003 H314 0.001 0.000 0.001 0.002 H315 0.001 0.000 0.001 0.002 H316 0.001 0.000 0.001 0.002 H317 0.001 0.000 0.001 0.001 H318 0.001 0.000 0.000 0.001 H319 0.001 0.000 0.000 0.001 H320 0.000 0.000 0.000 0.001 R03 0.740 0.302 0.302 1.723 111‘“ 61 Nicklesopora and Rhombopora with Nicklesopora Table 14. Comparison of the type species of the genera renzettiae. pcmmmnm mymmmweos coawoh Hanogmfihom op Hwfixm scam Has: Hmflocoou mo mmcwno asaswcw mflpcow coawmh asamsmapm op Hmfixm sch% Haw: HsHomooa mo mmcmno amaswcm mumzm mafia: Hmwxs vopmascmnoco: mHHmz Hwfixm umpmaacoho swooooa mo mcofipocsn pm wmaomonpcsommoe mHomoou some canons mmhomozwcmomhows mo so» 8 mmcwcmmo Hwfiomoou mo mach Henomafiu wmcficcmo Hmfiococm yo mson Hacfivsvfimccfi elegantula N. lepidodendroides x R. renzettiae N. 62 v I .1; mwfippmacoa .z spa: mmgopme amvomawcc kc Honssz mommcw accommxmz Ho Hmcommpcom ova“ vmcfi>wc mfiomoou mwxm Hmavcac scum mcwwusp Hmhfimw manna mafia: Hmfiowoou mo mcficcxofinp Hasvsam mafia: Hafioooou mo wcficoxofizv pmsnna :ofimon Hmaxs cw memsngmmfiv 13 14 63 Table 15. Comparison of Nicklesopora renzettiae n. sp. with all previou§ly described species of the genus Nicklesopora. Ross 1365:. U) U) H 0H (0 U) U“ 3 S E m 6 3 Characters 3 g: g g g g s a a g o a *1 .. :4 .s a 1; a :3 0 HE Q) Q) om 940) mm “HQ. H0) 3 (D U) U) “1 U) .o -O 00 012 00 . 2a: 2.0: 20: 20 233 z 1 Number of character matches ' with N. renzettiae 5 6 4 5 6 2 zooecial openings form ' longitudinal ranges X X X 3 zooecial openings form ° diagonal ranges X X 4 crenulate zooecial walls in ° axial region X X X X 5. non-crenulated axial walls 6. abrupt thickening of walls at base of peripheral zone X X X X 7. superior hemisepta , X 8. inferior hemisepta X 9. diaphragms in axial region X 10. single series of acanthopores surrounding zooecia . . X X X 11. tight spiral budding pattern ? X X 12. meg- and micracanthopores 13. megacanthopores at junction of zooecia X 64 Continued. Table 15. finessflsv kah+mflfisfiu .2 >mcmcaocx¢z mhwcmfimamp .z mrsfiph mmmmmmu .2 scufihy mmemphmmofipmSMCm .z scufine mammcovfisv .z aaasmpaopa wwofiompw .z mfimxuvfionh «Hammxmw .z Acoanfizv mfisvcmmon .z nossmpamnopm mpmnomoxvrmom .z Characters 1O 3. 4. 5. 7. ? 9. 10. 11. 12. 13. 65 15. Continued. Table .>0: .mm omfivwomcmh .z whoaaflsv mvwscmppw .z Ago..asv mfiHHEHwHMm .z zoapapv .91.-me .2 mgofiuaav asopogosr .z “cohaaav mzmfium> .z mnoauasv mama «cow .2 “coaaasv Hewnppoz .z “soapflsv «swamps» .z Characters 4. 5. 10. 11. 12. 13. 66 Table 16. Leptotrypella ellucida Duncan binary Efiaracter frequences for 33 colonies. Frequency of Frequency of Character Character positive char. positive char. (Table 3) states (percent states ( percent of all zoaria) of all zoaria) 1 0.0 19 3.1 2 90.6 20 9.4 3 9.4 21 84.4 4 0.0 22 0.0 5 10.0 23 25.0 6 18.8 25 18.8 7 3.1 26 0.0 8 3.1 27 0.0 9 71.9 28 15.6 10 28.1 29 15.6 11 53.1 30 0.0 12 12.5 31 15.6 13 62.5 32 15.6 14 3.1 33 0.0 15 93.8 34 34.4 16 93.8 35 62.5 17 75.0 36 9.4 18 68.8 37 9.4 “inn. Table 16. Continued. 38 39 40 41 42 43 44 45 0.0 100.0 93.8 3.1 65.6 21.9 9.4 84.4 67 47 48 49 50 51 52 53 68 Table 17. Leptotrypella pellucida quantitative means’data statistics, based on 33 colonies. Character Mean Standard Deviation Minimum Maximum ZRM 0.153 0.019 0.083 0.183 ZWTM 0.080 0.061 0.015 0.283 APZM 2.117 6.329 0.000 27.800 TMRM 0.878 1.096 0.194 6.631 DARM 6.812 2.627 0.567 15.110 ANM 74.132 11.453 53.000 90.0 NDPRM 5.093 2.793 0.00 13.750 NDARM 2.823 0.620 0.850 3.800 DLCM 0.155 0.121 0.061 0.581 DAM 0.002 0.007 0.000 0.024 AREAM 26.241 3.836 14.200 31.400 NNS 0.879 0.122 0.703 1.237 3.- h . 69 Table 18. Leptotrypella pellucida quantitative standard deviation data statistics, based on 33 colonies. Character Mean Standard Deviation Minimum Maximum ZRS 0.809 0.206 0.522 1.376 ZWTS 0.027 0.030 0.008 0.157 APZS 0.768 2.260 0.000 10.030 TMRS 0.148 0.148 0.014 0.798 DARS 0.388 0.339 0.038 1.573 ANS 5.613 4.357 0.000 22.890 NDPRS 1.031 0.676 0.000 2.719 NDARS 0.577 0.269 0.000 1.164 DLCS 0.028 0.013 0.010 0.066 DAS 0.001 0.002 0.000 0.008 AREAS 1.506 0.230 1.099 2.038 70 Table 19. Leptotrypella pellucida Fourier Harmonic means data statistics, based on 33 colonies. Character Mean Standard Deviation Minimum Maximum HM2 HM3 HM4 HMS HM6 HM7 HM8 HM9 HM1O HM11 HM12 HM13 HM14 HM15 HM16 HM17 HM18 HM19 HM20 RCM 0.135 0.056 0.048 0.029 0.020 0.014 0.011 0.008 0.006 0.005 0.004 0.003 0.003 0.002 0.002 0.002 0.001 0.001 0.001 3.401 0.030 0.101 0.011 0.007 0.005 0.003 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.030 0.081 0.035 0.018 0.013 0.008 0.006 0.004 0.003 0.002 0.003 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 3.342 0.193 0.074 0.068 0.038 0.031 0.020 0.016 0.012 0.009 0.008 0.006 0.005 0.004 0.004 0.003 0.003 0.002 0.002 0.002 3.475 71 Table 20. Leptotrypella pellucida Fourier Harmonic Standard deviation data statistics, based on 33 colonies. Character Mean Standard DeviatiOn Minimum Maximum H82 0.062 0.015 0.033 0.092 H83 0.029 0.006 0.016 0.042 H84 0.024 0.006 0.010 0.038 H85 0.015 0.004 0.005 0.024 H86 0.010 0.003 0.003 0.015 H37 0.007 0.002 0.003 0.010 H38 0.005 0.002 0.002 0.010 H89 0.004 0.001 0.001 0.007 H810 0.003 0.001 0.001 0.006 H811 0.003 0.001 0.001 0.005 H812 0.002 0.001 0.001 0.003 H813 0.002 0.001 0.001 0.004 HS14 0.001 0.000 0.001 0.003 H815 0.001 0.000 0.001 0.002 H816 0.001 0.000 9.000 0.002 H817 0.001 0.000 0.000 0.001 H818 0.001 0.000 0.000 0.001 H819 0.001 0.000 0.000 0.001 H820 0.001 0.000 0.000 0.001 RCS 0.017 0.004 0.010 0.027 1 ”fl. 72 Table 21. Comparison of Species of the genus Leptotrypglla with Threeforks material. fl 8 d 3 8 3.: 8 .C O H :2 O 0H Characters :5; ,3? 8E g3 53 c as; 21:3 *3 .2 as 18 o «3 Cd 8 lg .0 0 "d c: C H :0 H :3 c Q 'U 0 0 Oz '5: AQ av him r-Jv r-‘Jv Irregular thickening of X 1° mature wall 2. Monticules present X X X X small acanthopores ringing 3. zooecial opening, not X inflecting walls 4w walls thin in mature region X X 5. axial walls crenulated X 6. diaphragms simple well defined X X X X X 7 zalnia diverge sharply from X X X ‘ axis of axial region 8. zooecia sub-polygonal X X X X X 9. walls thick in mature region X X 10. axial walls uncrenulated X X X X X 11 zooecia diverge gently X X X ° from axis of axial region 12 large acanthopores not X ' inflecting zooecial walls 13 large acanthopores inflecting ° zooecial wall X X X 14. diaphragms in axial region X X 15. cystoidal diaphragms, cysts, mural spines 73 napezmpmv mfimcmofino .A casunmom upoosapase .q AzomHosonv maenowdaacos .A cmspusom spoo>0Hm «covmomoa ..H nssppmom mcmvmomms snowmowms .A cmscnmom 850357.35 :H csossn 888055.85. :H was» mammofimmcazx .q nsocsn «3.211%; 335 spwohsm .q 74 Continued. Table 21. Character Amufiosflfimp .qv Hdwhovms wxnommoace cmccsa moan: .g smegma mcwosfiamm .q smoczo J m>pmc .4 4. 7. 11. 12. 13. 14. 15. CONCLUSIONS 1. Standard deviations of characters within colonies provide significant amounts of independent taxonomic information. This astogenetic variation appears diagnostic for each of the two species studied. A measure of the dispersion (standard deviation) of the data may give more information than its associated mean. 2. The Fourier harmonic amplitudes and binary characters provide significant amounts of independent information, leading to a better phenetic classification, than the standardly used quantitative characters measured in previous taxonomic studies of ectoprocts. 3. The nearest neighbor statistic and interzooecial surface area statistic are shown to carry significant independent information. 4. Characters carry varying amounts of independent information. The reduction of the work involved in future data collection, and the in-depth understanding of character interaction and information content make the inclusion of R-mode analysis in future numerical taxonomic studies desirable. 5. Leptotrypella pellucida and Nicklesopora renzettiae n. sp. dominate the fauna of the Threefbrks Formation. 75 ELL-.1 - 76 One specimen belonging to the genus Fistulipora was found, and one Specimen belonging to the Family Phylloporinidae, previously unreported from the Devonian. 6. Spasmodic deposition of terrigenous muds prevented the development of fully mature bryozoan zoaria. LIS T OF REFERENCES LIST OF REFERENCES Anstey, R. L. and Delmet, D.A. 1972. Genetic Meaning of Zooecial Chamber Shapes in Fossil Bryozoans: Fourier Analysis. Science, v. 177, p. 1000-1002. , and Delmet, D. A. 1973. Fourier Analysis of Zooecial Chamber Shapes in Fossil Tubular ‘3 Bryozoans. Geol. Soc. of America Bulletin, ‘ v0 84, p0 1753-17640 , and Pachut, J. F. 1974. Size, Shape, and Surface Area Variation of Zooecia and Monticular Mosaics within Zoaria of Paleozoic Tubular Bryozoans. AAPG Abstract national meeting 1974, p. 2. Blackith, R. E. and Reyment, R. A. 1971. Multivariate * Morphometrics. Academic Press, New York. p. 412. Bonham-Carter, G. F. 1967. FORTRAN IV Program for Q-mode Cluster Analysis of Nonquantitative Data Using IBM 7090/7094 Computers. Computer Contribution 17, Kansas Geological Survey. Clark, C. J. and Evans, F. C. 1954. Distance to Nearest Neighbor as a Measure of Spatial Relationships in Populations. Ecology., vol. 35 no. 4, p. 445-453. Cuffey, R. J. 1973. An Improved Classification, Based upon Numerical-Taxonomic Analysis, for the Higher Taxa of Entoproct and Ectoproct Bryozoans. Proceedings of the International Bryozoology Assoc. Conference, Living and Fossil Bryozoa. p0 549-5640 Davis, J. C. 1973. Statistics and Data Analysis in Geology. John Wiley and Sons Inc., New York. 550 pp. Delmet, D. A. and Anstey, R. L. 1974. Fourier Analysis of Morphological Plasticity within an Ordovician Bryozoan Colony. Paleontol., V. 48, pp. 217-226. Eftaxiadis, T. 1973. Numerical Taxonomy and Phylogeny of Paleozoic Fasciculate Bryozoans (Ectoprocta). Michigan State University, Unpub. M.S. Thesis, 103 p. 77 78 Ehrlich, R., and Weinberg, B. 1970. An Exact Method for Characterization of Grain Shape. Journal Sed. Petrol. V0 90, p0 205-2120 Klapper, 0., Sandberg, C. A., Collinson, C., Huddle, J.W., Orr, R. W.. Rickard, L. V., Schumacher, D., Seddon, 0., and Uyeno, T.T. 1970. North American Devonian Con0d0nt Biostratigraphy. Geological Society of America Memoir v. 127, p. 285-316. Michener, C. D. and Sokal, R. R. 1966. Two Tests of the Nonspecificity in the Hoplitis Complex (Hymenopterax Megachilidae) Ann. Entomological Society of Americas, 370.59, p. 1211-1217. Nie, N. H.,Bent, D. H., and Hull, C. H. 1970. SPSS: Statistical Package for the Social Sciences. McGraw-Hill Book Co., New York. 343 p. Oxnard, C. E. 1969. Mathematics, Shape and Function: A Study in Primate Anatomy. American Scientist, V. 57,119 p. 75-960 Parks, J. M. 1970. FORTRAN IV Program for Q-mode Cluster Analysis on Distance Function with Prhted Dendrogram. Computor Contribution 46., Kansas Geological Survey, 32pp. Renzetti, P. 1961. Fauna of the Threeforks Shale (Devonian) of Southwestern Montana. Indiana University, unpub. Ph. D. Thesis, 342 pp. Siegel, S. 1956. Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill Book Co., New York. 301 pp. Sneath, P.H.A. and Sokal, 8.8. 1973. Numerical Taxonomy. W. H. Freeman and Company, San Francisco. 573 Pp. Sokal, B. S. and Sneath, P. H. A. 1963 Principles of Numerical Taxonomy. N. H. Freeman and Co., San Fracisco. 359 pp. Throckmorton, L. H. 1968. Concordance and Discordance of Taxanomic Characters in Drosophili Classification. Systematic Zoology., V. p. 355-387. Underwood, E. E. 1970. Quantitative Stereology. Addison- Wesley Publishing Co., 279 pp. Wittick, R. I. 1973. GEOSYS, and Information System for the Description and Analysis of Spatial Data (Version 2) Michigan State University Computor for Social Science Research, Technical Report. 73-6. 42 pp. APPENDIX I Listing of program DMAT, with Fisher's exact probability option. (1CFOC3CMOC1CPOC1CJO (MO 79 PROGRAM DMAT (INPUT,00TPUT,PUNCH) 00050 IN FORTRAN xv FOR CDC 6500 BY 9; ANSTEY AND J. NRAKOVICH. DEPARTMENT OF GEOLOGY-USU. FALL 1972. PRQGRAH DMAT CALCULATES A DISTANCE HATiIA IN EUCLIDEAN SPA a {on xwpur to cLusr. 3 ANALYSIS PROGRAM; OUTPUT r34 ’RnGRAN DMAT IS CONTAINED IN MATRIX DIST. DATA IS NORMALIZED AND RANGES [V VALUE FRDH 1.0 TD 0.0 WITH 1,0 MEANING THE GREATEST SIMILARITY AND 0,0 tHE LEAST: FIRST DATA CARD nJST CONTAIN THE FOLLOWING INFORMATION IN 414 FORHAI .I.~F 13 NUMBER OF FEATJR953...NS IS ”UNDER 0F SAMPLES....NOR=0 IF G-NODE,=1 IE R- MODE. NFH=1 CALLS FISHERS 5XACT PROBABILITY NFM=O FISHERS EXACT PROa IS SKIPPED SECOND DATA CARD IS FURnAT 0F INPUT IN 13A8 FORMAT, THIS CARD gs FOLLONED THIRD DATA CARD CAN BE UsED FOR EXTENDED FOBHATES IF NOT NEED USE BLANK CABD BY INPUT DATA dHlCH IS READ INTO MATRIX HRHSPL. DIMENSION H4N§PL1100.1001oRHEAN<100).FH1120’.DIST(100.1001 DIMENSION FACI(9),NFACT(9) DOUBLE PRECISION FACT.FNUH.FDEN READ5}NF,NS.NUR,NFH,FHT READ FHT,(¢4RHSPL(I.J).I=1.NFI.J=1.NSI TOTAL ROHS AND CALCULATE MEANS IF (NFN1150.150.151 150 CONTINUE 0015I=1.NF SUM=0.0 DO13J=10NS D: 10 SUH=SUH.HNNSPL(I,J) 15 RHEANII):SU“/N$ NORMALIZE HRHSPL ARRAY 3v DIVIDIVG EACH RON av :15 RESPECTIVE MEAN D020I=1.NF DOZOJ‘loNS 20 HRHSPLII.J)'("R”5PL1IoJI/RHEAV(II) CALCULATE DISTANCE MATRIX HITH VALUES RANGING FRON ZERO TO ONE SPECIFY 0 OR RoHUDE 151 IFINOR)70:25090 7O CONTINUE 25 NH=NS$N52NFINL§NH 30 DO4CI:1,NF H=I*1 IPIHZGT.NF)301039 DO40K=H.NV DISTII.K)=0.D 1r (NFH)133.193.154 153 CONTINUE IFcNORIBE.85.§4 60 CONTINUE 85 DO9DJ:1.NS 9O DIST:I,K)8DISL(I,K)o(NRHSPL¢J.K)-HRMSPL(J,IIIolz so To 34 34 0035J=1.Ns IF(NOR) 35.35.37 35 DISTIIoKI'DISIIII“1*(HRHSPLIK0JI'HRH5PLIIaJ)I"2 36 DISTII.K135381191571IcK’I Go TO 37 154 CONTINUE 83000 93000 c3000 D3000 NSUMsNS DO 105 JJ‘ION§ IF (NOR) 600.900.601 601 CONTINUE IF (HRHSPLI‘.JJI-2) 202.201.201 80 202 IF (HRMSPLII,JJ)-2) 200.2J1.201 201 NSUHENSUH'1 GO TO 150 200 0=HRMSPL(I.JJI¢HRHSPL(K,JJ) lr(0'2)2g102 1 A=A*1 on T0 1cb IFIOI 4:304 D=D*1 GO TO 100 00=HRHS°LTloJ9)“HRH5PL(K0JJI IV (00) 8'20107 8:801 GO TO 100 8 C=C¢1 GO TO 126 DMAT u‘um 600 CONTINUE IFIHRH59LIJJ,K)52)502.502.551 502 IFIHRHSPLIJJ.II*2) 500.501.501 501 NSUMaNsun-1 GO TO 100 500 0=HRHSPL¢JJa12*HRNSPLTJJ.K) If (0-2)511o512.511 511 A=Ao1 so To 136 512 IF(0)51‘.513c?14 513 080*1 60 TO 166 514 ooaHRHSPLcJJ.T)IHRHSPLIJJ.K) IF (00) 51895010517 517 88801 GO To 106 518 080.1 no To 106 100 CONTINUE NFACTI1)3N$UH NFACTIZIsA NFACT(3)§B NFACTI4)§C NPACTI5330 NFACTI6)aAoB NEACTI7):C¢D NFACTIBIsAOC NFACTI9):BOO D0 800 L8109 800 FACTIL)=1yo D0 801 L3119 NENDvNFAcTILI'I IF (NEND) 80108010303 803 DO 802 LL'1uN5ND LLL=LL¢1 802 FACTIL):FACT(C)§LLL 801 CONTINUE FNUH§1.0 FnEn'ioo DO 804 ”H'los ao4 FDEN=FDEN0FACEINHI DO 505 ”H‘619 805 FNUMkadH'FACTIHMI C C C 81 DISTIIOKI‘FVU"/FDEN GO TO 37 37 DISTIKoII‘DISIIIoK) IF(NFH)7O2.7OZ.701 701 DIST(131)'100 GO TO 40 702 DIST(III):OQO 40 CONTINUE DIST(TpII'OoO 39 DISTITaTIgovO SCAN DIST FOR VAX AND DIVIDE INTO ALL VALUES AND SUBTBACT EACH FROM 1:0 IF (NFHI160,100.161 160 CONTINUE DHAX:fi.c NT=NF91 0045I=10NI H=I*1 DO4SK=M0NF IF(DHAX-DIST(I.K))43,45.43 43 DHAXSDIST(’.K? 45 CONTINUE DIVIDE DMAX INTO EACH VALUE AND SUBTRACT FBQN 1.6 DOSOX‘IINT "31*1 DDSOK=H0NF DIST(IoKI'loO’(DIST(IOK’IDHAXI DISTII,K)=DISIII¢K)7DHAX 50 DISTIKo II‘DISTIIIK’ 161 0055J=19NF PRINT 611.com” J). mmgm 55 PUNCHOOoIDISTIIc J’o ISJONF’ 5 FORMATI4I‘IIOGB/10A8) 611 FORMATI. '0 1?F533, 60 FORMAT(16f503I ' ‘ ) '37.! APPENDIX II Listing of program FOURIER. OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 82 PROGRAM FOURIER (INPUT,OUTPUT,PUNCH) EXPLANATION OF METHOD GIVEN BY EHRLICH + HEINBERG. 1970. JOUR. SE00 PETROLOGY, V0 “0’ Po 205-2120 REVISIONS TO ORIGINAL PROGRAM BY ROBERT L. ANSTEY. NOV. 20. 1972 DECK STRUCTURE... 1. CONTROL CARD - NUMBER OF HARMONIC COEFFICIENTS DESIRED. COLS. 1-2. IF DATA IS FROM AN OPEN CURVE. PUNCH 1 IN COL. A. 2. TITLE CARD (FOR SAMPLE GROUP) - ANY ALPHANUMERIC SYMBOLS. LIMITED TO ONE CARD 3. DATA CARDS ALL VALUES MUST BE RECORDED AS A DIGIT INTEGER NUMBERS, 20 TO A CARD. VALUES FROM A CLOSED SHAPE MUST BE RECORDED AS X, Y IN A COUNTERCLOCKHISE SEQUENCE STARTING FROM THE POINT X=XMAX. VALUES FROM AN CFEN CURVE MUST BE RECORDED AS X, Y IN ORDER OF DECEASING X STARTING FROM THE POINT X=XMAX. Y AT X=XMAX MUST EQUAL Y AT X=XMIN. IN A CLOSED SHAPE. N0 VALUE OF THETA SHOULD HAVE MORE THAN ONE VALUE OF R. IN AN OPEN CURVE. NO VALUE OF X SHOULD HAVE MORE THAN ONE VALUE OF Y. (ALL VALUES MUST BE LESS THAN 9999) LAST 8 COLUMNS OF LAST CARD FOR EACH SAMPLE MUST BE BLANK OR ZERO-FILLED (OTHERWISE A BLANK CARD MUST BE INSERTED) A. FLAG CARD - 9999 IN COLS. 1-h (SIGNALS END OF EACH SAMPLE GROUP) 5. CONTINUATION CARD - CONT OR FINI IN COLS. 1-h IF CONT, NEXT SAMPLE GROUP IS EXECUTED IF FINI. PROGRAM TERMINATES 6. REPEAT DECK STRUCTURE. STEPS Z-S. FOR EACH SAMPLE GROUP SIZE LIMITATIONS AND RESTRICTIONS... 1. LESS THAN 150 POINTS PER SAMPLE 2. LESS THAN #05 SAMPLES PER SAMPLE GROUP 3. NUMBER OF SAMPLE GROUPS IS UNLIMITED 6. ONLY THE FIRST 20 HARMONICS CAN BE CALCULATED. ALL HARMONICS ARE DIVIOED BY THE VALUE OF THE ZEROTH HARMONIC, MAKING ITS VALUE UNITY. AMPLITUOES OF THE FIRST HARMONIC ARE NEITHER PRINTED NOR PUNCHED. BECAUSE THE FOURIER SERIES IS GENERATED FROM THE CALCULATED CENTER OF GRAVITY OF EACH SHAPE. TO OBTAIN MORE THAN 20 HARMONICS. INCREASE THE DIMENSIONS OF A, B. C, AMP, AND ARRAY. 5. PHASE ANGLES ARE NOT PRINTED 6. STATISTICAL ESTIMATES HILL NOT BE CALCULATED. NOR MILL DATA BE NORMALIZED FOR SAMPLE SIZES SMALLER THAN 20. NORMALIZEO VALUES ARE THOSE DIVIDED BY THE MEAN OF THE SAMPLE GROUP. 7. NORMALITY IS TESTED ONLY FOR SAMPLE SIZES GREATER THAN 35 8. PROGRAM REQUIRES 100000 OCTAL NORDS OF CENTRAL MEMORY 9. PROGRAM REQUIRES 1.3 SECONDS (CDC 6580) PER SAMPLE 10. PROGRAM PUNCHES 2N + 7 CARDS FOR N SAMPLES IN EACH SAMPLE GROUP. AND PRINTS APPROXIMATELY 20 PAGES PER SAMPLE GROUP. COMMON NUMIZDOOT,NN,KV.FVAR,FMED,FMEAN,FKS DIMENSION XIISD), Y(150), RAD(156). THETA(1SC) DIMENSION A(20), 8(2)), C(20), AMP(ZD). NAME(10) DIMENSION ARRAY(AOD,ZD). ARAD(AODI DIMENSION IX(1SO). IY(150) EQUIVALENCE (X,IX), (Y,IY) 1060 30 A0 50 60 70 72 7A 73 76 75 77 79 78 O1 71 83 LOGICAL TRBL BETA=QHCONT NTEST1=1000 NTESTZ=2000 NTEST3=3000 IFLAG=3999 READ 1330. NHARH. NOPEN READ 1000. NAME 00 1050 N=1.NHARM AMP(N, 3 Go AMPSUH390 NOGOOO=0 ISEO=0 LTOTAL=0 NN=0 PRINT 960. NAME JL=1 JU=10 TR3L=.FALSEo READ 953. (IX(J).IY(J).J=JL.JU) IF (IXTJL)-IFLAG) 50.810.860 00 6C K=JL.JU KHIT=IX(K)§IY(K) IF (KNIT) 60.70.50 CONTINUE JL=JLR10 JU=JUA10 GO TO #0 L=K-1 IF(NOFEN) 71.71.72 IXMAX=IX(1) DO 73 I=Z.L IFCIXMAX-IX(I)) 7h.73.73 IXNAX=IX(I) CONTINUE IXHIN=IX(1A 00 75 1:2’L IF(IXMIN-IX(I)) 75.75.76 IXMIN=IXTID CONTINUE IXHAX=IXHAX-IXHIN DO 77 1:1,L XTI)=((IX(I)°IXMIN)’6.2832)IIXHAX Y(I)=IY(I) IYMAX=IY(1) 00 78 I=ZgL IF(IYMAX-IY(I)) 79.76.70 IYMAX=IYTIT CONTINUE 00 51 I=1.L _ IXCI)=(Y(I)‘COS(X(I)))+IYHAX IYTI)=(Y(I)‘SIN(X(I)’)+IYHAX L=L'1 ISEO=ISEQR1 LTOTAL=LTOTAL+L 80 100 110 120 13C 150 150 160 170 180 190 200 210 220 230 2&0 25C 26C 270 280 290 300 310 320 330 3&0 350 360 370 380 390 #00 “10 A20 A30 84 DO 560 J=1.L INT=2 LHI=J01 LLO=J-1 IF (LHI-L) 90,90,80 LHI=1 IF (LLQ) 110,100,110 LLO=L LLOO=LLO-1 IF (LL00) 130,120,130 LLOO=L IF (J-2) 1h0,220,300 IF (IY(L-1)) 860,310,150 IF (IY(L-1)-NTEST1) 180,310,160 IF (IY(L-1)-NTEST2) 180,310,170 IF (IY(L-1)-NTEST3) 180,310,180 IF (IX(L-1)) 860,310,190 IF (IX(L-1)-NTEST1) 220,310,200 IF (IX(L-1)-NTEST2) 220,310,210 IF (IX(L-1)—NTEST3) 220,310,220 IF (IY(L)) 860,310,230 IF (IY(L)oNTEST1) 260,310,2A0 IF (IY(L)-NTEST2) 260,310,250 IF (IY(L)-NTEST3) 260,310,260 IF (IX(L)) 860,310,270 IF (IX(L)-NTEST1) 300,310,280 IF (IX(L)-NTEST2) 300,310,290 IF (IX(L)-NTEST3) 300,310,300 LOINTY=IABS(IY(LLO)-IY(LLOO)) LOINTX=IABS1IX£LLO)-IX(LLOO)) JUMPLY=IABS(IY(LLO)-IY(J)) JUMPLX=IABS(IXtLLO)-IX(J)) KICKLY=IABS(JUMPLY-LOINTY) KICKLX=IABS(JUMPLX—LOINTX) LEAP=200 GO TO 320 KICKLX=58 KICKLY=KICKLX IF (IY(J)) 860,370,330 IF (IY(J)-NTEST1) 360.370.3A0 IF (IY(J)-NTEST2) 360,370,350 IF (IY(J)-NTEST3) 360,370,360 IF (KICKLY‘LERP) ““09““0’370 IF (IY(LHI)) 860,A20.380 IF (IY(LHI)-NTEST1) A10,A20.390 IF (IY(LHI)-NTEST2) A10,A20.A00 IF (IY(LHI)-NTEST3) A10,A20,A10 IF (IY(LHI)-IY(J)) A30.h20,h30 LHI=LHI+1 INT=INT+1 IF (LHI.GT.L) LHI=1 GO TO 370 IY(J)=IY(LLO)+((IY(LHI)-IY(LLO))/INT) INT=2 LHI=J+1 1TH? “AC 450 A6C #70 ABC A90 500 51C 520 532 SAC 550 560 570 580 590 600 610 620 630 6h0 650 66C 67C 85 IF (LHI.GT.L) LHI=1 IF (IX(J)) 860,A90.A50 IF (IX(J)‘NTEST1) N80,N909N60 IF (IX(J)-NTEST2) 080,A9C,A70 IF (IX(J)-NTEST3) A80.h90.h80 IF (KICKLX—LEAP) 560,560,A90 IF (IX(LHI)) 860,550,500 IF (IX(LHI)-NTEST1) 530,5A0.510 IF (IX(LHI)-NTEST2) 530.5A0.520 IF (IX(LHI)-NTEST3) 530,5A0,530 IF (IX(LHI)-IX(J)) 550,590,550 LHI=LHI§1 INT=INT+1 IF (LHI.GT.L) LHI=1 GO TO “90 IX(J)=IX(LLO)+((IX(LHI)-IX(LLO))/INT) CONTINUE OO 57J J=1.L X(J)=IX(J) Y(J)=IY(J) MX=0 MY=MX MMY=1 MMX=MMY Y"0H:OO XMOM=YMOM YAREA=XMOM XAREA=YAREA MMX=MMX+1 MX=MXO1 IF (MX-L) 600,590,600 MMX=1 YAREA=YAREA+(X(MMX)-X(MX))‘(Y(MMX)§Y(MX)) YMOM=YMOM+(X(MMX)-X(MX))'((Y(MMX)§Y(MX))"2-Y(MMX)'Y(MX)) IF (MK-L) 580,610,580 MMY=MMY+1 MY=MY§1 IF (MY-L) 630,620,630 MMY=1 XAREA=XAREA+(Y(MMY)-Y(MY))‘(X(MMY)§X(MY)T XMOM=XMDH+(Y(MMY)-Y(MY))’((X(MMY)+X(MY))"2-X(MMY)‘X(MY)) IF (MY-L) 610.6%0.610 YCEN=YMOM/(YAREA'3.) XCEN=XMOM/(XAREA’3.) DO 660 I=1,L THETA(1)=ATAN((Y(I)-YCEN)/(X(I)-XCEN)) IF (X(I)-XCEN) 650,660,660 THETA(I)=THETA(I)+3.1A159 RAO(I)=SQRT((Y(I)-YCEN)"2+(X(I)-XCEN)“2) 00 673 I319NHAR" A(I)=B(I)=0. ‘0300 FL=L AJ=25.IFL DO 760 I=1oL 86 II=I+1 680 II=1 690 ANGLE=THETA(II)-THETA(I) IF (ANGLE) 700,760,710 700 ANGLE=ANGLE+6.28136 710 IF (ANGLE-AJ) 730,720,720 720 TRBL=.TRUE. GO TO 760 730 IF(TRBL) 760.7A0 7A0 AO=A0+ANGLE‘(RAO(II)FRAD(I)) DO 753 N=1.NHARM FN=N COSZ=COS(FN'THETA(II)) COS1=COS(FN’THETA(I)) SIN2=SIN(FN‘THETA(II)) SIN1=SIN(FN‘THETA(I)) A(N)=A(N)t((RAD(II)-RAD(I))‘(COSZ-COS1))/(ANGLE'FN’FN)O(RAD(II)’SI 1N2-RAD(I)’SIN1)IFN 750 8(N)=B(N)+((RAD(II)-RAO(I))‘(SIN2°SIN1))l(ANGLE‘FN'FN)-(RAD(II)’CO 1$2-RAO(I)’COS1)/FN 760 CONTINUE IF(TRBL) 770.700 770 NOGOOD=NOGOOO+1 PRINT 1050. ISEQ GO TO 30 700 00 793 I=1,NHARM 790 A(N)=(SORT(A(N)"2+B(N)"2))’A.IAO NN=NN+1 DO 000 N=1,NHARH 800 ARRAY(NN,N)=A(N) ARAD(NN)=AOIIZ5.663 GO TO 30 810 PRINT 900. NH IF‘NN'10’ 8,101,829,629 029 00 8&0 I=Z,NHARM 00 630 J31’NH F=ARRAY(J,I)'10000. 030 NUH(J)=FO1 PRINT 1060. IgNAHE CALL STA! A(I)=(KVI100.)"Z B(I)=FVAR C(I)=FMED AMP(I)=FREAN RAD(I)3FKS IX(I)=KV 0A0 CONTINUE PUNCH 1000, NAME FUNCH 99$, (ANPIN),N=Z'NHARH, PUNCH 99C,(RAO(N),N=2.NHARM) PRINT 1003 DO 100“ I=ZoNHARM 100“ PRINT 1005,I,AMP(I).C(I).RAO(I),IX(I) 8A1 PRINT 970 87 PRINT 980. (N,N=2.NHARH) DO 658 HzleN ARAO(H)=ARAO(HTI362.6 PRINT 960, H,(ARRAY(H,N),N=2,NHARH).ARAO(H) 850 CONTINUE DO 858 N=1,NN F=ARAO(N)'10000. 858 NUH(N)=F61 CALL STAT PRINT 878, FHEAN,FKS PUNCH 990, FHEAN,FKS IF(NN'10’ 855,856,856 856 8VAR=J.0 VAR=UOU 00 851 I=Z,NHARH VAR=VAR+A(I’ 851 8VAR=3VAROB(I) DO 852 I32.NHARH IY(I)=(8(I)/8VAR)‘100. 852 IX(I)3(A(I)/VAR)‘1000 PRINT 871, OVAR PRINT 872, (N,N=2,NHARH) PRINT 873, (17(N). N32,NHARH) PRINT 876. VAR PRINT 872, (N,N=2,NHARN) PRINT 873. (IX(N). N32,NHARH) PRINT 876 PRINT 980, (N. N=2,NHARNT 00 853 H31,NN ARAO(N)30.0 DO 85“ N=2,NHARH ARRAY(H,l)=ARRAY(H,N)/AHP(N) 85h ARAO(N)=ARAO(H)+(ARRAY(H,N)“2) ARAO(H)8SORTTARAO(H)I20) PRINT 968, H. (ARRAY(H,N), N32,NHARH), ARAO(H) PUNCH 991. ARAO(N) 853 CONTINUE DO 857 N81,NN FSARAO(N)’IOOOb 857 NUH(N)=F+1 CALL STAT FHEAN=FHE‘N‘1.0 FKS‘FKS’IOO PRINT 875, FHEAN PRINT 877. FKS . PUNCH 990, FHEAN.FK$ 855 READ 10189 ALPHA IF (ALPHA‘BET‘A 8609209860 860 CONTINUE 871 FORNAT(1H0,2X,17HTOTAL VARIANCE IS, F9o5) 872 FORMAT(1H8,b2X.25HPERCENT OF TOTAL VARIANCE/3X,19(I2,4X)) 873 FORMAT(II,1981A,2X)I 87A FORMAT(1HO,BZX,30HNORNALIZEO HARMONIC AHPLITUOES,QAX,15HNORNALIZEC * R.C.) ' 875 FORMAT(1N8,2X,AOHHEAN NORMALIZEO ROUGHNESS COEFFICIENT IS,F9.5’ (T 88 876 FORMAT(1H0,2X,28HTOTAL NORMALIZEO VARIANCE IS,F9.5) 877 FORMAT(1H0,2X,7HS.O. IS,F9.5) 678 FOQHAT(1H0,2X,7HHEAN IS,F9.5,2X,7HS.D. IS,F9.S) 905 FORMAT(22H USABLE SAMPLE SIZE IS,IA) 9&0 FOQNAT(1H1,10(1H&),10A8,10(1H+)/37H THE FOLLOWING SAMPLES CANNOT B +E USED) 950 FORMAT (201A) 960 FORMATT1H ,I3,19F6.h,F8.h/) 97: FORMAT(1H0,53X,19HHARNONIC AHFLITUOES,ASX,10HRADIUS(HH)) 980 FORMAT(6X,19(I2,QX)I) 990 FORMAT (10F7.h) 991 FORMAT (F8.h) 1000 FORHAT(10A5) 1001 FORMAT(16HHEOIAN HARMONICS) 1002 FORflATt1hHHEAN HARMONICS) - 1003 FORMAT(9HOHARHONIC,QX,hHHEAN,hX,6HNEUIAN,AX,8HSTD.OEV.,hX,10HOOEFF +0 VAR.) 1005 FORMAT¢1H0,2X,IZ,7X,F6.R,3X,F6.R,SX,F6.R,8X,I#) 1010 FORMAT (Ab) 103C FORMATTZIZD 10u0 FORMAT(1X.3(1H‘),1SHHARHONIC NUMBER,I3,3(1H‘),10A0) 1050 FORMAT (21X.6HNUHBER,IS) END 00000 89 SUBROUTINE STAT CALCULATIONS ARE VALID FOR “ SIGNIFICANT FIGURES NORMALITV IS TESTED 87 THE KOLHOGOROV’SHIRNOV VALUE 0F 0 AT THE .05 LEVEL OF SIGNIFICANCE. FOR OTHER PROBABILITY LEVELS OF 0, CONSULT TABLE E OF SIEGEL, 1956, NONFARAHETRIC STATISTICS FOR THE BEHAVIORAL SCIENCES, HCGRAN-HILL. COHHON NUH‘ZGOO),NNgKVgFVARgFHE09FHEANgFKS DIMENSION NBR(10000),NHIST(ZO),KHISTTZO,100),IO(ZO) EQUIVALENCE (NUHgKHIST) OO 10 I=1y10000 1C NBRTI)=O 00 20 I313NN 20 NBR‘NUH‘I))=N8R(NUH(I)’01 DO 35 131910000 IF (NBR‘I)) 33,30,90 3O CONTINUE no HIN=I . OO 50 131910008 J=10081'I IF (NBRTJ’) 58950960 50 CONTINUE 6O HAX‘J KR=HAX-NIN HH88 DO 65 I=HIN9HAX H=TNN/28§1 HH=HH+CNBRTI39 IF‘HH'H) 65,65,66 65 CONTINUE 66 HEO=I INTSTKRIZOTOI HF=HIN+(INT'19) DO 67 HSHINgflFgINT I=((H'HIN)/INT’91 NHIST(I)88 L=N01NT IOCI)‘H OO 68 JPHgL '68 NHISTTI’SNHIST(IT§NBR(JT 67 CONTINUE NSUH=8 DO 70 ISHINgflAX TO NSUN=NSUHOTI.NBR(ITT HEAN=NSUHINN HHxNN-I KVAR’O ' DO 90 I310NN 9O KVAR=KVAROTCHEAN-NUHTI)"’Z) KVAR=KVARIHH FVARSKVAR K5350RTCFVAR) IF (HEAN’ 110,118,100 108 KVSKKS‘1OO)/HEAN FHEAN=NEANI100000 FHEOSHEoltooooo 101 103 105 10“ 106 102 107 6 7 110 8 9 180 90 FHIN=NINI10000. FHAX=NAXI100000 FKR=KRI10000u FKS=KSI10000. FVAR=FKS"Z 00 101 I=1920 DO 101 J=1,100 KHISTTI,J)=1H DO 102 I=1,20 IF(NHIST(I)) 102,102,103 K=NHIST(I) IFTK-100) 10h,10h,105 K=99 KHIST‘I,IUUT:IH§ DO 106 J=1,K KHIST(I,J)=1H’ CONTINUE FINT=INT110000o PRINT 1h0,FINT DO 107 I=1120 FIO=IO(I)I10000. PRINT 150, FIO,NHIST(I),(KHISTTI:J),J=1,100) IFCNN-35) 110311095 00 1 I31’28 J=(INT/2)+1 NUHTI)8HINO(I‘INT)-J N8RTI)=(INT’100)I(KS‘SQRTT6,2832)T FS-(T(NUHTI)-HEAN)IKS)"2)IZ. NBRCI)8NBRTI)‘(2o7183"F) IOT1’31ABSTNBR(1)-((NHIST‘1)’100)INN)) DO 2 I32920 J'I'1 NORTIT=NBR(I)+NBR(J) NHIST(I)8NHIST(I)+NHIST(J, IO(I)8IABS(NBR(I)‘((NHIST‘I)‘100)INN)’ IOHAX8I001) DO 3 I82,28 IF(IONAX'IOTI)) 6,3,3 IONAxslolID CONTINUE DNAX=IONAXI1000 FNN=NN OTEST=1c36ISQRTTFNN) IFCOHAX-OTEST’ 6,7,7 PRINT 8, DNA! 60 TO 110 PRINT 9, DHAX PRINT 160 RETURN ‘ FORHAT(32H OATA FIT A NORHAL OISTRIBUTION.,ZBH KOLHOGOROV-SHIRNOV #0 IS’F503’ FORMAT039H OATA DO NOT FIT A NORNAL OISTRIEUTION.,2BH KOLHOGOROV-S +HIRN°V D 159F503’ FORMATT101H HISTOGRAH OF DATA FREQUENCIES IN 20 EQUAL SIZE CLASSES + RANGING FRON THE NINIHUH TO THE NAXINUH VALUE/25H SIZE CLASS IN 91 +TERVAL IS,F6.‘9) 150 FORMATUXJFGJT,I5,2X,100A1) 160 FORNAT(1X,100(1H+H END APPENDIX III Listing of means and standard deviations of the 20 repetitive measures for each character on a single 1,, ._ _g specimen. 150 binary characters coded O for negative response, 1 for positive, and 2 for unable to determine, characters taken from Eftaxiadis (1973). Data listed in the following format; Title of specimen Harmonic Means 2-11 Harmonic; Means 12-20 Harmonic Standard deviations 2-11 Harmonic Standard deviations 12-20 Mean radius and its standard deviation Roughness coefficient and its standard deviation ZRM, ZRS , ZWTM, zw'rs , APZM,APZS , TMRM, TMRS ,DARM,DARS ,ANM,ANS , NDPRM,N‘DPRS,NDARH,‘NDARS DLCM,DLCS,DAM,DAS,MDM,MDS,AREAM,AREAS,NNS 150 binary characters listed in order in last two rows. 92 --...-- L... . - .- ...-....--—---—--~- . ..- - TITLj_ (1’ -° 01’ 0 0"79 099?:- 09991 0"AQ ofiIlfi ofinfll ,007n .nna1 0999: ‘99?“ 099-99 0991.9” I999" ' 0'91“" 0991”“ 09.939" 00’711 04799 0‘319 0“”70 onPflfi ,fllfifl 0W‘h7 .nnez .anR .0035 .nnp3 onfifil 0“”1” 00“!” 099"“ 099”” 0"““9 _0“OO6 can 5 0000? ' C .1He*.017?.9667.n100 o.n G..."077.0171“049500911760?" 4. 25 306504803 P.2.4721 0116?,fi1fifi fi.h O.fi I.“ fi.'"m.pn 1010 .OHn Elfin-W hnfinn1oofl1“““1ffiPflPOAP”Athnho“oh1P1blfin~n1111Ann]fi“nnnanafinnhnnnnnnonannnann«an ¢flnhfiann1finn1nnnnnnl1hpaq1nnnnn11n11A1AnnfifinnanohfifihpaohfififlOAAAAAAAOOA filnA—Q TITL” 61”?-30 ,0171'J 05472 007‘9..00234..0”14P -0:116.~L0C33-110Q62__N.00>3“-qooflfiimu.ml- _.w 0fl0?4 09599 0’n13 .nle 99916 09914 0091] 00011 00908 00999 09?73 '915 00119 09589 0“C7100032 00039 0903: 00026 00014 09990 :CQOQ ofihréi 09938 19:55 -SOOOQ- ..30006-H00004 .H ..-. 01”}? 0:194 . . ago-sap, 01919091’f0 91991005 f! 909306940477900340:0?99011349907310118'y000 ‘000 2.7.47“' “(SAGQ'T‘IAA .r‘ln?.n"';f ’9.“ a.“ ?£;.nl.7’7"s .()44 (‘1.fip-fi" :‘nf‘fiq1qanl(tf‘njfififififlfinfihflhhflfiHOAAAIfiInfifinhnl 19999919 lfiflmflfihhflnfiflflfiAAOI‘q annnpnAAa, 9IOIFO1!““1999”“O"O"I19199199CF'11100199*“fiOfixfifiafiKaxfixo‘fiofiofifi“DOOOOOO “ £159“? 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