UNIVfcRSn"v cp ILLINOIS l sRARY AT URBAMA-CHAMPAIGN LZOLOGY & CO CO 0 1 ft 5 FIELDIANA Geology Published by Field Museum of Natural History Volume 39, No. 3 July 31, 1978 Investigation of the Classification of the Rodent Genus Eumys from the Middle Oligocene of the Big Badlands of South Dakota Using Multivariate Statistical Analysis Sue Vilhauer Rosser University of Wisconsin. Madison ABSTRACT The dental morphology of 292 specimens of the cricetid rodent genus Eumys from the Lower Nodular Zone of the Big Badlands of South Dakota was studied. The study was undertaken to determine the number of species present in the genus Eumys during Middle Oligocene time in the area from which the specimens were col- lected. The Eumys specimens were divided qualitatively into three groups: an E. elegans-hke group, an E. obliquidens-hke group, and a group with both E. elegans- like and E. obliquidens-Uke characters. The same quantitative measurements were then taken on all three of these groups. Three methods of statistical analysis were used to quantitatively analyze measurements taken on the Eumys teeth: multiple discriminant, principal compo- nent, and agglomerative analysis. The results of the study clearly indicated that only one group was present in the Eumys specimens. The one group is considered to belong to the one valid species Eumys elegans. ACKNOWLEDGMENTS This study was carried out as part of the research for my Ph.D. in Zoology, received in May, 1973 at the University of Wisconsin, Madison. I would like to thank Dr. John Clark, formerly of Field Museum of Natural History, for lending me the Museum's Eumys collection for this study. I would also like to thank Dr. J. T. Robin- son, Dr. David L. Clark, and Dr. Edward W. Beals of the University of Wisconsin, Madison, as well as Dr. Charles Oxnard of the Univer- Library of Congress Catalog Card No.: 76-56536 SHE LIBRARY OF Tl ISSN 0096-2651 Publication 1284 33 *"' £b 1 9 78 GEOLOGY .yNIVERS,TYOF/LL»NO!? ^NA-CHAMPAT- 34 FIELDIANA: GEOLOGY, VOLUME 39 sity of Chicago and Dr. William Turnbull of Field Museum of Natural History for critically reading the thesis from which this manuscript was taken. Finally, the diagrams, drawn by Miss Cheryl Hughes and the manuscript typing done by Miss Helen Royal were appreciated very much. INTRODUCTION * V ; The cricetid rodent genus Eumys has been somewhat of a puzzle to paleontologists for several decades. Variations in the dental mor- phology of Eumys have led students of the genus to claim as many as 13 separate species within it. Recently some paleontologists have begun to doubt the validity of some of the species of Eumys. This doubt is primarily due to the extensive collections of the genus available for comparative study and to knowledge about individual variation within a species population. Indeed, one student (Alker, 1967) has claimed that nine species should be considered simply as individual variants of one valid species, Eumys elegans. In an at- tempt to resolve this controversy, the dental morphology of the Eumys specimens from the collection at Field Museum of Natural History was studied to determine whether this genus is mono- specific or polyspecific. This is a fairly large collection of over 400 specimens collected from one level, the Lower Nodular Zone, in the Big Badlands of South Dakota. A study of the collection might be expected to yield information as to the individual variation present in a limited geographical range and limited time geologically. Three different methods of quantitative statistical analysis were carried out on the measurements taken on the Eumys teeth: Multi- ple discriminant, principal component, and agglomerative analysis. The results of these three methods were then synthesized to deter- mine the number of valid species of Eumys present in the collection studied. Materials .—The 292 Eumys specimens used in the study con- sisted of fossilized jaws and teeth from the collection of the Depart- ment of Geology of Field Museum of Natural History. All the specimens were collected by Dr. John Clark and his co-workers in the years 1962, 1968, and 1969 from the Lower Nodular Zone of the Brule Formation of the Big Badlands in Pennington County, South Dakota. The geology and paleoecology of this formation from which the specimens were taken have been described by Dr. Clark (Clark et al., 1967). The specimens come from seven separate collections. (The / ROSSER: CLASSIFICATION OF EUMYS 35 raw data concerning number of specimens in each collection, year of collection, and exact site location along with the measurements of the specimens have been listed previously (Rosser, 1973).) Of the 292 Eumys specimens, 56 are maxillae and 236 are man- dibles. This is approximately a 1:4 ratio of maxillae to mandibles, a situation often found in collections of fossil rodent teeth (Wilson, pers. comm.). Although the sample contains two complete palates, no complete mandibles are included. There are also no upper and lower jaws in occlusion. The 292 specimens include edentulous mandible fragments and specimens with one, two, or all three molars present. Only jaws with all three molars present were employed for purposes of statistical analysis. However, measurements were taken on the specimens con- taining one and two molars. These measurements are presented with the data from complete specimens (Rosser, 1973). The incisors were not measured. One problem which always exists when one deals with fragmented fossil material is the correlation of number of individuals with specimen fragments. Compatible specimen fragments, particularly from a small animal such as Eumys, cannot be assumed to belong to the same individual even if found close to each other, since small fragments are easily transported by natural forces. Thus, each jaw fragment found was marked as a separate specimen. One cannot assume, therefore, that each of the 292 specimens studied represents an individual Eumys. Indeed it is quite possible that a left mandible containing only molars 1 and 2 may have, in fact, belonged to the same individual as a right mandible containing all three molars. This inability to correlate number of specimen fragments with number of individuals may present a serious pro- blem when trying to do a population study of the entire fauna in which one seeks to obtain ratios between various genera. However, since the purpose of this study is to determine the number of species of Eumys present in the collection on the basis of characters of den- tal morphology, the problem of correlation of specimen fragments with number of individuals is not relevant here, although the lump- ing of right and left mandibular rami may result in a lowered vari- ance as a result of some specimens making a double contribution. A second problem, which is of relevance in this study, was caused by tooth wear. Only 45 of the 52 mandibles containing three molars and 1 1 of the 1 3 maxillae containing three molars were usable for Fig. 1. Upper teeth of Eumys. Key to Figures 1 and 2. Cusp or other feature: Lower teeth Upper teeth 1 Anteroconid Anterocone 2 Protoconid Protocone 3 Paracone 4 Metaconid Metacone 5 Entoconid 6 Hypoconid Hypocone 7 Mesoconid Mesocone 8 Posteroconid Posterocone 9 Mure Mure 10 Anterior cingulum Anterior cingulum 11 Posterior cingulum Posterior cingulum 12 Metalophulid I 13 Metalophulid II 14 Hypolophulid I 15 Hypolophulid II 16 Mesolophid Mesoloph 17 Posterior arm of protoconid 18 Protolophid Protoloph 19 Paraloph 20 Transverse metaloph 36 ROSSER: CLASSIFICATION OF EUMYS 37 Fig. 2. Lower teeth of Eumys. the final statistical analysis; the other nine specimens were too bad- ly worn to allow complete measurements to be taken on them. Wear greatly influences dental patterns in cricetids, as in most other rodents. With wear the cusp heights and relative relation of cusps may be altered, thus changing the details of the original pat- tern. Reconstruction of the original pattern is almost impossible when greatly advanced wear is present. Wear may or may not influence tooth dimensions. It obviously in- fluences height, which has been used (Fahlbusch, 1967) for diagnosis of European cricetids. Although the brachydont cricetid tooth is always somewhat smaller when greatly worn, moderate wear does not appreciably change the length and width dimensions of the tooth. All 45 mandibular and all 1 1 maxillary specimens used for statistical analysis were in stage D as designated by Alker (1968): D. Full maturity: MJ lophs and lophids with occlusal surfaces less than 50% enamel-covered; M! and M2 worn but dental pattern still showing original ar- rangement; and cusps not basined. METHODS Measurements.— Figures 1 and 2 of Eumys specimens show the terminology used in this study for upper (fig. 1) and lower (fig. 2) teeth. The terminology employed here is essentially that suggested by Wood and Wilson (1936) with minor modifications (see key to Figures 1 and 2). Tables 1 and 2 list the points of measurement taken on the lower (1) and upper (2) Eumys teeth. Since the purpose of this study is to determine the number of species of the genus Eumys present in the collection of Field Museum, measurements were chosen that might best elucidate the possible differences between the Eumyine 38 FIELDIANA: GEOLOGY, VOLUME 39 TABLE 1 1. Anterior-posterior tooth row length 2. Anterior-posterior length of M, 3. Width of M, at anteroconid 4. Width of M, at protoconid 5. Width of M, at hypoconid 6. Length of posterior arm of protoconid on M, 7. Length of mesolophid on M, 8. Anterior-posterior length of M2 9. Width of M2 at protoconid 10. Width of M2 at hypoconid 1 1 . Length of posterior arm of protoconid on M2 12. Distance between lingual end of posterior arm of protoconid and entoconid on M2 13. Length of mesolophid on M2 14. Anterior-posterior length of M3 15. Width of M3 at protoconid 16. Width of M3 at hypoconid 17. Length of posterior arm of protoconid on M3 18. Distance between lingual end of posterior arm of protoconid and entoconid on M3 TABLE 2 1. Anterior-posterior tooth row length 2. Anterior-posterior length of M' 3. Width of M' at anterocone 4. Width of M' at protocone 5. Width of M1 at hypocone 6. Length of mesoloph of M' 7. Anterior-posterior length of M2 8. Width of M2 at protocone 9. Width of M2 at hypocone 10. Length of mesoloph on M2 11. Anterior-posterior length of M1 12. Width of M! at protocone 13. Width of M1 at hypocone species. After studying all of the specimens carefully under a stereo dissecting microscope and comparing them with descriptions and diagrams of the various Eumys species described, it became clear that the lower molars of some individuals in the collection appeared to look like E. elegans Leidy. Some appeared to look like E. obli- quidens, and some appeared to have characters of both of these species. None of the individuals in the collections seemed to resem- ble the description or diagrams of any of the other 10 Eumys species that have been described. A possible exception might have been E. parvidens, which can only be separated from E. elegans on the basis ROSSER: CLASSIFICATION OF EUMYS 39 of size, since E. parvidens is about 15 per cent smaller than E. elegans and has a primitive E. elegans pattern (Wood, 1937). Preliminary studies, in which anterior-posterior tooth row length and width of M2 were compared for all specimens, indicated that the specimens fit a normal distribution curve with respect to these two characters. The coefficients of variation of the measurements were approximately 5 per cent and the tests for goodness of fit gave a Chi-square that was not significant. Therefore it was concluded that no E. parvidens specimens were present in the sample. A logical step thus seemed to be to choose the measurements of the molars of Eumys that would not only yield the usual informa- tion about tooth width and length, but that would also best take in- to account known differences between E. elegans and£. obliquidens as described by Leidy (1856), Cope (1884), Wood (1937), and Galbreath (1953). Although each measurement was taken on every specimen, the measurements were chosen with particular considera- tion for the following four characters which Galbreath (1953) used to distinguish E. obliquidens from E. elegans. 1. Mesolophid of M, should be as long or longer than the posterior arm of the protoconid in E. obliquidens. In E. elegans the mesolophid of M, should be shorter than the posterior arm of the protoconid. 2. Posterior arms of the protoconid on M2 and/or M3 extend postero-mesiad to unite with the entoconids on either or both teeth in E. obliquidens. In E. elegans, the posterior arm of the protoconid on M2 and/or M3 should turn forward and be reduced on either or both teeth. 3. In E. obliquidens the protoconid on M, is united to the antero- conid and and the metaconid remains free. In E. elegans, the pro- toconid on M, is united to the anteroconid and the arm from the metaconid is united to the protoconid crest. 4. In E. obliquidens the anterior lingual cingulum on M, is not reduced. In £. elegans, the anterior lingual cingulum on M, is reduced. It should be noticed that the characters distinguishing/?, elegans from E. obliquidens are in general relevant only to the lower teeth since the upper teeth have no equivalent of the posterior protoconid arm. 40 FIELDIANA: GEOLOGY, VOLUME 39 The measurements on all the Eumys specimens were taken using an optical micrometer on a binocular dissecting microscope. The specimens were placed on a piece of plasticene on the stage of the microscope. Each specimen was placed as nearly as possible in the center of the field of vision through the microscope. Each specimen was placed so that the anterior end of M, and the posterior end of M3 were in focus when the measurements for anterior-posterior tooth row length were taken. The two rows of maxillary molars are further apart than the two rows of molars in the mandible. Thus the tooth row of the maxilla slants inward and downward and runs diagonally so that the left M1 and the right M1 of the upper jaw are closer together than are the left and right M3. In the lower jaw, the tooth row slants outward and upward, also run- ning diagonally to match the corresponding maxillary row. Thus, it was impossible to have the entire tooth row in focus at one time. All length measurements of individual teeth and entire tooth rows were measured on a line parallel to the line of the tooth row from posterior to anterior, regardless of whether it was left, right, upper, or lower jaw. All width measurements were taken on a line perpendi- cular to the tooth row line from the lateral to medial side of the tooth. All measurements were taken to the nearest tenth of an op- tical micrometer unit. The magnification under which the measurements were taken was such that the anterior-to-posterior-tooth-row length of Eumys was magnified 10 times, with 12.8 optical micrometer units equalling 1 mm. Measurements on individual Eumys teeth were magnified 20 times with 30.3 optical micrometer units equalling 1 mm. Each specimen was completely measured once. Several months later all specimens were again measured without looking at the original measurements. If the two measurements of a particular character disagreed by more than 0.01 mm., the character was again measured until two measurements that were the same were obtained. Statistical Analysis.— Three basic methods of statistical analysis were used to analyze the data obtained from measuring Eumys specimens. The three techniques are multiple discriminant, prin- cipal component, and agglomerative analysis. These methods were chosen primarily because they all are methods of multivariate analysis. All three methods allow one to assess the relationships of multiple measurements within multiple populations. The primary ROSSER: CLASSIFICATION OF EUMYS 41 restriction on these populations is that they must be assumed to be multivariate normal. If each population under consideration may be described by a series of q dimensions, then each individual within a population may be represented by a point in q-dimensional hyper- space, where each axis is equivalent to one univariate dimension. In- dividuals within the populations that are similar to each other with respect to many measurements will tend to group together around particular co-ordinates in the q-dimensional hyperspace and will have a characteristic dispersion around those co-ordinates. Thus a characteristic dispersion around those individuals clustering to- gether around the same co-ordinates may be thought of as belong- ing to the same group, or in this case, species. Although all three methods of analysis are multivariate, ag- glomerative analysis differs from the other two methods. Ag- glomerative analysis starts with individuals as separate entities and unites them according to their affinities. Multiple discriminant and principal component analysis both are divisive techniques which separate individuals and groups according to their dif- ferences. Several other basic differences exist among the three techniques, both in mathematical theory and practical application. For a theoretical and complete discussion of discriminant and ag- glomerative analysis see Sokal and Sneath (1963). For a discussion of principal components analysis and its association with the ap- proach of numerical taxonomy see Gittins (1968). DATA Selection of Eumys groups.— After measurement and careful study of the Eumys specimens, they were divided into groups for statistical analysis. The divisions were based upon species as defin- ed by the descriptions of the type specimens (Cope, 1884; Wood, 1937). Three groupings were made from the lower jaw specimens: Group 1 included 21 individuals fitting the description of Eumys elegans (Cope, 1884). Group 2 included nine individuals fitting the description of Eumys obliquidens (Wood, 1937). Group 3 included 15 individuals which could not be placed with certainty into either group 1 or group 2. The individuals in group 3 seemed to possess some characters of the E. elegans type and some characters of the E. obliquidens type. A group 3 individual might have a combination of characters such as the following: Posterior arm of protoconid of M2 extends postero- 42 FIELDIANA: GEOLOGY, VOLUME 39 mesiad to unite with entoconid (E. obliquidens character). Mesolophid on M, is shorter than posterior arm of protoconid (E. elegans character). Protoconid of M, is united to anteroconid and arm from metaconid is united to protoconid crest (E. elegans character). The anterior cingulum is not reduced (E. obliquidens character). It would be impossible to classify the above individual as either E. elegans or E. obliquidens. The 1 1 complete Eumys maxillae all seemed to fit the criteria for E. elegans. Thus, they were randomly divided into two groups so that the statistical tests could be run. However, it should be noted that all the criteria that have been used to separate E. elegans and E. obliquidens are characters of the mandibular teeth alone. For ex- ample, the upper teeth do not even have a posterior protoconid arm. Furthermore, in the literature there are no examples of upper jaws belonging to E. obliquidens. Even though upper jaws are only one- third to one-fourth as common as lower jaws, it seems strange that no maxillae have been described. One may question whether the type specimens of E. elegans and E. obliquidens could be distin- guished from each other on the basis of upper teeth. Only a specimen of E. obliquidens with upper and lower jaws in occlusion could answer this question with certainty. Data Analysis.— The multiple discriminant computer program us- ed for analysis in this study was a tape called Muldis written by Robert Avery of the University of Wisconsin Department of Economics. A few points about this program should be mentioned. Some of these are unique to the Muldis program; others are common in multiple discriminant analysis. As with other multiple discriminant programs, the variance- covariance matrices of the groups are assumed to be equal in Muldis. Although this assumption may not always be true, Rao (1970) suggests that this is robust and probably will not affect the results even if the assumption is occasionally violated. Like other multiple discriminant programs, Muldis requires that any individual considered must include all of the measurements be- ing used. Thus, specimens for which a complete series of measure- ments are not available cannot be used. A feature unique to Muldis is a stepwise procedure which permits evaluation of the importance to the overall discrimination of each variable when combined with other variables. This differs from the univariate ranking of the variable which may be obtained also. The ROSSER: CLASSIFICATION OF EUMYS 43 univarate ranking indicates how well each variable would discri- minate if used alone. Another feature unique to Muldis is the classification section. During the first part of Muldis, individuals with complete measure- ments are put into the program as predetermined groups. The cen- troids (co-ordinates of points in space), dispersion (variance), and various group statistics are calculated as a function of the discrimi- nant analysis. The second part of Muldis has a classification sec- tion. Individuals are entered without being placed in groups. Muldis groups them on the basis of the criteria set up for each group in the multiple discriminant section of the program. A priori probabilities of particular group membership may be assigned. In this study the a priori probabilities of all groups were assumed to be equal. Thus, individual 28, which may have been entered with group 2 in the multiple discriminant part of the program, may be classified as belonging to group 3 by the classification section of Muldis because it has more features in common with the other members of group 3 than with those of group 2. Individuals not entered in the multiple discriminant section of Muldis may be entered in the classification section of the program and be assigned to one of the groups. The program then graphs the individuals entered as groups in the multi- ple discriminant section of Muldis in reduced space; it also graphs the individuals after classification in reduced space. Thus, the two graphs before and after classification can be compared. Data sets on which multiple discriminant analysis was run. — A. Forty-five complete Eumys mandibles with 18 variables each. They were entered as 30 individuals in two groups of nine and 21 in- dividuals each in the multiple discriminant section. They were entered as 45 individuals in the classification section. B. Eleven complete Eumys maxillae with 13 variables each. They were entered as 11 individuals in two groups of five and six in- dividuals each in the multiple discriminant section. The classifica- tion section could not be run because the sample size was too small. Data sets on which principal component analysis was run.— The data for principal component analysis was run on a computer program written by T. F. Allen, S. M. Bartell, and W. Post of the University of Wisconsin Botany Department. The particular pro- gram used carried out an Orloci transformation of the data, which removes any influence on the analysis of differences in the numbers of attributes in different individuals. Since all the individuals com- 44 FIELDIANA: GEOLOGY, VOLUME 39 pared had the same number of attributes, the transformation should have made no difference. The principal component program was run on the following data: A. Forty-five complete Eumys mandibles with 17 variables each. (Measurement 1 of anterior-posterior tooth row length was deleted because it was known to be very highly correlated with anterior- posterior length of M,, M2, and M3.) B. Eleven complete Eumys maxillae with 12 variables each. (Measurement 1 was again deleted due to known correlation with other measurements.) Data sets on which agglomerative analysis was run. — The data for agglomerative analysis was run on a computer pro- gram written by S. M. Bartell of the University of Wisconsin Botany Department. It is essentially a modification of the Orloci ag- glomerative analysis. The program may be run in two forms, with or without an Orloci relativization of the data. The Eumys data was run using both forms of the program. Without the Orloci transfor- mation absolute distances between the individuals are considered when calculating the D or D2. Absolute distances reflect the dif- ferences among individuals in the absolute number of attributes measured. The Orloci transformation corrects for differences in number of attributes measured. The agglomerative programs were run both with and without Orloci relativization on the following data: A. Forty-five complete Eumys mandibles with 17 variables. (Measurement 1 was deleted because of known high correlation with other variables.) B. Eleven complete Eumys maxillae with 12 variables. (Measure- ment 1 was deleted because of known high correlation with other variables.) It was necessary to test to see whether or not the two groups into which the agglomerative program had placed the Eumys in- dividuals in each case were valid groups statistically. Thus, a t-test had to be run. For the t-test to be performed, it was necessary to know the within-group variance of each of the groups. W. Post of the University of Wisconsin Botany Department wrote a variance program which takes the individuals clustered by a particular pass of the agglomerative program and calculates the within-group variance. The variance program was run on the following data: ROSSER: CLASSIFICATION OF EUMYS 45 1. Two agglomerative groups of 45 complete Eumys mandibles with 17 variables each with Orloci relativization. 2. Two agglomerative groups of 45 complete Eumys mandibles with 17 variables each without Orloci relativization. 3. Two agglomerative groups of 11 complete Eumys maxillae with 12 variables each with Orloci relativization. 4. Two agglomerative groups of 11 complete Eumys maxillae with 12 variables each without Orloci relativization. RESULTS Results of Multiple Discriminant Analysis: A. Multiple discriminant analysis and classification of 45 com- plete Eumys mandibles with 18 variables each.— Figure 3 shows the results of the multiple discriminant analysis of group 1 (A), con- sisting of 21 individuals qualitatively identified as being E. elegans, and group 2 (B), consisting of nine individuals qualitatively iden- tified as E. obliquidens. The centroid of group 1 is at .0393 and that of group 2 at .150; there is no overlap between the two groups. Since the first eigenvalue (axis) accounts for 100 per cent of the discri- mination, the results were graphed in linear space. Using the information from multiple discriminant analysis, it is possible to find the amount each variable contributes to separation of the groups. It is thus possible to rank the variables according to the importance of their contribution to the discrimination of groups. The technique for ranking is analogous to analysis of variance in that the within-group variance from the major diagonal of the pooled within-groups deviation sums-of-squares and cross products matrix is divided by the between-groups variance from the major diagonal of the pooled between-groups deviation sums-of-squares and cross products matrix for each variable. Using this method, the following ranking of variables was obtained; the first one listed is the most important and the last one listed is the least important: * Variable 18— Distance from posterior arm of protoconid to en- toconid on M3 * Variable 12— Distance from posterior arm of protoconid to en- toconid on M2 Variable 13— Length of mesolophid on M2 * Variable 11— Length of posterior protoconid arm on M2 Variable 10— Width of M2 at hypoconid 46 FIELDIANA: GEOLOGY, VOLUME 39 A A_A A AA A A A -.01*18 .0139 .0395 AA A A AAA A A A .0401 .0657 .0*913 BB BBB .0919 .118 .143 B B B B_ .144 .169 .195 Fig. 3. Graph of observations in eigenvector space. A indicates one or more ob- jects in group 1; B indicates one or more objects in group 2; Z indicates an overlap between two groups. ^Variable 6— Length of posterior protoconid arm on M, * Variable 17— Distance from posterior arm of protoconid to en- toconid on M3 Variable 3— Width of M, at anterocone *Variable 7— Length of mesolophid on M, Variable 14— Anterior-posterior length of M3 Variable 5— Width of M, at hypoconid Variable 9— Width of M2 at metaconid Variable 4— Width of M, at metaconid Variable 1— Anterior-posterior tooth row length Variable 15— Width of M, at metaconid Variable 2— Anterior-posterior length of M, Variable 17— Width of M, at hypoconid Variable 8— Anterior-posterior length of M2. The nine most important variables include all those measure- ments (*) which are considered to be the criteria by which Wood (1937) and Galbreath (1953) separated E. elegans and E. obli- quidens. These criteria were also used in this study for the qualitative separation of the two groups. ROSSER: CLASSIFICATION OF EUMYS 47 Classification of the 45 complete Eumys mandibles was then car- ried out. The individuals were placed in either group 1 (A) or 2 (B) by the computer on the basis of the criteria set up for separating the two groups in the multiple discriminant section of the program. In addition to the 30 individuals that had been used as the basis for forming the two groups in the multiple discriminant section of the program, 15 individuals of unknown group membership were classi- fied. These 15 individuals could not be placed with certainty into either group on the basis of the descriptions. They seemed to have characteristics of both E. elegans and E. obliquidens . The computer was programmed to put these individuals in either group 1 (A) or 2 (B). Thus, an individual from the unknown group was placed in the one of the two groups with which the individual had the most similar characters. The results of the computer classification are shown in Figure 4. The 30 individuals used for the discriminant part of the program were classified into exactly the same groups as predicted by the group criteria. There were no misclassifications. Of the 15 individuals of unknown group membership (represented by circled letters in Figure 4) 60 per cent were placed in group 1 (A) ®A A A ®A Ajg A A A© -.0118 .0139 .0395 AA A A gM (A) A A ® A © .0401 .0657 .0913 BB© BBB ,0919 .118 .143 B B ® B B_ .1*44 .169 .195 FlG. 4. Graph of observations in eigenvector space. A indicates one or more ob- jects in group 1; B indicates one or more objects in group 2; Z indicates an overlap between two groups. 48 FIELDIANA: GEOLOGY, VOLUME 39 Principal Components Diagram 1. Individual number that each zero represents is known, but was omitted for clarity of diagram. and 40 per cent were placed in group 2 (B). Two individuals were off the graph to the right. Three individuals fell exactly between groups 1 (A) and 2 (B). These results from the 45 Eumys mandibles do not support the idea that there is a clear separation between the E. elegans and E. obliquidens, which should be the case if they are two good species. This is especially clear since the characters used by the computer in- clude those used to define the two species. Although many in- dividuals seem to fit one extreme or the other, several individuals have characters of both groups. One continuous group, rather than two discrete groups, seems to be formed by the 45 individuals. ROSSER: CLASSIFICATION OF EUMYS 49 u o 00 o u Hp X Y Principal Components Diagram 2. Individual number that each zero represents is known, but was omitted for clarity of diagram. B. Multiple discriminant analysis of 11 complete Eumys maxillae with 13 variables each.— Although the program began to run and did calculate some statistics, it was terminated because the sample size was too small compared to the number of variables. Thus, no significant information was obtained from the program. Principal Components Analysis: A. Principal components analysis was run on the 45 complete Eumys mandibles with 17 variables each.— Measurement 1 of anterior-posterior tooth row length was deleted because it was 50 FIELDIANA: GEOLOGY, VOLUME 39 n 1 1 i 1 u 1 i 0 i \ 0 0 % 1 0 0 0 0- X Y Principal Components Diagram 3. Individual number that each zero represents is known, but was omitted for clarity of diagram. known to be very highly correlated with anterior-posterior length of M„ M2, and M3. Principal components diagrams 1 and 2 show the results of the analysis. The X axis accounts for 74.4 per cent of the variance. The Y axis accounts for 4.8 per cent of the variance, and the Z axis ac- counts for 3.9 per cent of the variance. Diagram 1 shows the in- dividuals graphed on the X and Z axes; diagram 2 shows the same individuals graphed on the X and Y axes. The three-dimensional diagrams show that the mandibles are essentially one continuous group with an almost normal distribu- ROSSER: CLASSIFICATION OF EUMYS 51 Principal Components Diagram 4. Individual number that each zero represents is known, but was omitted for clarity of diagram. tion. The small break in the center is not considered to be signifi- cant. The individuals were numbered so that numbers 1-21 fit the E. elegans description; numbers 22-30 fit the E. obliquidens descrip- tion; numbers 31-45 had characters of both E. elegans and E. obli- quidens. The slight separation in the middle of the three- dimensional diagram does not separate the individuals correspon- ding to the E. elegans type and E. obliquidens type. Numbers 2, 26, 13, 21, 29, etc. are on the same side of the break. Thus, the principal components analysis yields one group for all the Eumys mandibles. 52 FIELDIANA: GEOLOGY, VOLUME 39 B. Principal components analysis was run on the 11 complete Eumys maxillae with 12 variables each.— (Measurement 1 of anterior-posterior tooth row length was deleted because it was highly correlated with anterior-posterior length of M1, M2, and M3.) Principal components diagrams 3 and 4 show the results of the analysis. The X axis accounted for 43.0 per cent of the variance. The Y and Z axes accounted respectively for 27.0 per cent and 10.5 per cent of the variance. Diagram 3 shows the individuals graphed on the X and Y axes; diagram 4 shows the individuals graphed on the X and Z axes. Although the three-dimensional graphs seem to show the in- dividuals separated into three groups, the sample size is so small that this grouping is more likely to be due to lack of data rather than a representation of actual groups. AGGLOMERATIVE ANALYSIS: A. Agglomerative analysis was run on the 45 complete Eumys mandibles with 17 variables each. — (Measurement 1 was again eliminated.) The analysis was run both with and without the Orloci transformation. Theoretically, there should be no difference in results between the two methods, since all 45 individuals had all 17 attributes. The Orloci transformation corrects for differences in numbers of attributes in different individuals. Figure 5 is a dendrogram showing the results of analysis with the Orloci transformation; the dendrogram in Figure 6 shows the results of analysis without the Orloci transformation. In Figure 5 -♦«»-«l-t« NN-* MlOCVilO lOlOWOJPlKl*K)^-flJ-N- INOIVIOUALS Fig. 5. Dendrogram showing the results of analysis with the Orloci transforma- tion on the 45 complete Eumys mandibles with 17 variables each. ROSSER: CLASSIFICATION OF EUMYS 53 .I960 .1760 - .1560 J 360 J 1 60 J0960 .0760 .0160 — K> IO — CM INDIVIDUALS Fig. 6. Dendrogram showing the results of analysis without the Orloci transfor- mation on the 45 complete Eumys mandibles with 17 variables each. the final two groups are of sizes 30 and 15; in Figure 6 the final two groups are of sizes 31 and 14. Although group 1 in both dendro- grams has 20 individuals in common and group 2 in both dendro- grams has four individuals in common, the other 10 or 11 individu- als in both groups differ in the two dendrograms. When one examines the data, a possible reason for the differences in the two dendrograms becomes apparent. The absolute size of every measurement for the individuals that are in group 1 in both dendrograms is larger than the absolute size of every measurement for the individuals that are in group 2 in both dendrograms. The individuals that fall into different groups in the two dendrograms have some measurements that are large in absolute size and some that are small in absolute size. Thus, these individuals fall into one 54 FIELDIANA: GEOLOGY, VOLUME 39 26 r- 22 18 O 14 X oeh 10 I II 8 4 2 10 3 7 6 INDIVIDUALS Fig. 7. Dendrogram showing the results of analysis with the Orloci transforma- tion on the 11 complete Eumys maxillae with 12 variables each. group with the Orloci transformation and another group without the Orloci transformation. The appearance of the dendrograms, with the so-called "chaining effect," indicates that the individuals are probably all members of a single group, rather than two or three groups. The t-tests for dif- ference of means run on the two-group-level of both dendrograms confirm this. The t value for the difference between means for dendrogram 1 (fig. 5) with the Orloci transformation was 0.0099 with 43 df. This value certainly indicates that there is no significant difference be- tween the means of the two groups. ROSSER: CLASSIFICATION OF EUMYS 55 .I60r- .140 .120 .100 cfH 080 .060 .040 .020 .000 6 10 5 8 INDIVIDUALS Fig. 8. Dendrogram showing the results of analysis with the Orloci transforma- tion on the 11 complete Eumys maxillae with 12 variables each. B. Agglomerative analysis was run on the 11 complete Eumys maxillae with 12 variables each.— (Measurement 1 was eliminated.) The analysis was run both with and without the Orloci transforma- tion. Dendrogram 3 (fig. 7) shows the results of analysis with the Orloci transformation. Dendrogram 4 (fig. 8) shows the results of analysis without the Orloci transformation. In dendrogram 3, the final two groups are of sizes 9 and 2; in dendrogram 4, the final two groups are of sizes 8 and 3. Although the larger groups in both dendro- grams have six individuals in common, the other two or three indi- viduals differ in the two dendrograms. Differences in absolute size of measurements are probably responsible again for the apparent discrepancy caused by the Orloci transformation. 56 FIELDIANA: GEOLOGY, VOLUME 39 The t-test for the difference between means for dendrogram 3 with the Orloci transformation was 0.017 for 9 df. This indicates that there is no significant difference between the means of the two groups. The t-test for the difference between means of dendrogram 4 without the Orloci transformation was 0.272 for 9 df. This value indicates that there is no significant difference between the means of the two groups. DISCUSSION The results of all analyses when considered separately and together indicate that the teeth of the 45 complete Eumys man- dibles all fall into one group, rather than two or three separate groups. Using qualitative-type descriptions that purport to describe two different species, the specimens could be partially divided on the basis of simple observation. This division yielded three categor- ies: an E. elegans-like group, an E. obliquidens-like group, and an intermediate group between the first two which contained individuals with some E. elegans-like characters and some E. obliquidens-like characters. The individuals of the intermediate group, which obliterated the gap between the other two, could not be placed with certainty into either of the first two groups. Multiple discriminant analysis separated the E. elegans-like group from the E. obliquidens-like group. However, when the intermediate group was added, the program classified some of the individuals belonging to it as being within both groups and some individuals as falling between the two groups. Thus a continuum was formed among all of the groups. It has been suggested that multiple discriminant analysis should show the best separation between groups if any separation is pre- sent. If one assumes that correlated variables might be controlled by the same genetic factors, then the fact that multiple discriminant analysis weights correlated variables less heavily might lead to less emphasis being placed on characters controlled by the same gene. Principal components analysis yielded no separation into groups of the Eumys individuals. The E. elegans-like individuals were mix- ed with those of the E. obliquidens-like and intermediate types along the axes. Agglomerative analysis differs from the above two types of analysis in that it groups individuals according to their affinities, rather than separating them according to their differences. Thus, agglomerative analysis has a different method of forming groups of ROSSER: CLASSIFICATION OF EUMYS 57 individuals. Nevertheless, there was no significant difference be- tween the means of the two groups formed by agglomerative analysis. Furthermore, both groups formed had E. elegans-hke, E. obliquidensAike, and intermediate - type individuals. Thus, the results of all methods of analysis used treated the 45 complete mandibles as belonging to a single group. The group of 1 1 complete Eumys maxillae was really too small in sample size for significant statistical analysis. However, the quan- titative tests that were run indicated that the maxillae also formed only one group. By qualitative observation it was also impossible to find more than one group. Furthermore, in the literature no upper teeth of E. obliquidens have ever been mentioned or described. Although it is usually the case that the upper teeth are more conser- vative evolutionary, it seems unlikely that the upper teeth of the E. elegans-like and E. obliquidens -like forms would not show some difference, if the two forms are really separate species. Since all the upper teeth look like the E. elegans form, a specimen in which upper and lower teeth of the E. obliquidens form are in occulsion would be necessary to finally prove this point. Although the results showing that the Eumys specimens all are members of one group are fairly conclusive, the taxonomic inter- pretation of these results is not so clear-cut. The literature indicates that it is often not possible to separate living cricetid rodents solely on the basis of dental morphology (Hooper, 1968; Lindsay, 1972; Rosser, 1973), although the work of Schmidly (1973) on Peromyscus boylei offers some hope. Many characters other than dental morphology are used to separate extant species. Characters such as pelt color, hind-foot length, tail length, and features of the male reproductive tract are used for separation. Furthermore, many geographic clines, sym- patric species, and sibling species are found among modern cricetid rodents. Sibling species can never be distinguished as fossils. None of the characters such as'pelt color are ever fossilized either. Most of the other characters such as hind-foot length are not usually preserved. The paleontologist primarily has tooth material with which to work. Since it seems that dental morphology is not a reliable indicator of species separation in cricetid rodents, the paleontologist is left in a very ambiguous position with respect to defining taxa at the species level. 58 FIELDIANA: GEOLOGY, VOLUME 39 Solely on the basis of dental morphology, it seems a bit extreme to go as far as Alker (1967) did and suggest that nine of the 13 species of Eumys are invalid and that those nine should all be placed in E. elegans. On the other hand, most of the Eumys species were named using a typological approach without taking into account individual variation within populations. Without consideration of individual variation within a population, undoubtedly too many species were named. Wood (1937), who originally named many of the Eumys species, has recently suggested (Wood, 1969) that there are too many species, and that many are, in fact, variants of E. elegans. CONCLUSIONS In evaluating the results in this study, it may be said that the in- dividuals all fall into one group. However, when one considers the taxonomic question of whether or not this means that the E. elegans-like forms and the E. obliquidens-\ike forms represent in- dividual variation within the one E. elegans species, one must recommend with reservation. The quantitative statistical results and the qualitative fact that there are intermediate types that have both characters indicate one species. The literature indicates that species cannot always be distinguished from each other on the basis of dental morphology. Thus, the 22. elegans-hke form andE. obliquidens-hke form and their intermediates might represent separate sympatric species or sibling species. However, the kind of behavioral evidence necessary for deter- mination of sibling species is never fossilized. Nor will the characters such as pelt color that are used to separate extant species ever be fossilized. But, the taxa made with the fossil material must be based on the sort of evidence that is preserved and must be distinguishable objectively so that specimens can be assigned to the correct taxa with reasonable certainty. The evidence from this study indicates that there was only one group of Eumys present in the Lower Nodular Zone of Sage Creek in the Big Badlands of South Dakota in Middle Oligocene time. Thus, this study suggests that all individuals in this group should be con- sidered to be variants of the one species E. elegans and that there was no such species as E. obliquidens in that area during Middle Oligocene time. The decision to eliminate the species E. obliquidens and consider all the individuals to be members of E. elegans is made solely on the ROSSER: CLASSIFICATION OF EUMYS 59 basis of the fossil evidence of dental morphology. Dental mor- phology may not be the best indicator of species differences in cricetid rodents. 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