Patterns of Evolution in Ischyromys and Titanotheriomys
(Rodentia: Ischyromyidae) from Oligocene Deposits
of Western North America

A thesis presented

by

Timothy Howard Heaton

to

The Department of Earth and Planetary Sciences
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in the subject of
Geology

Harvard University
Cambridge, Massachusetts

August, 1988

[Total of 165 printed pages]


(c) 1988 by Timothy Howard Heaton
All rights reserved.
ABSTRACT

Patterns of Evolution in Ischyromys and Titanotheriomys
(Rodentia: Ischyromyidae) from Oligocene Deposits
of Western North America

TIMOTHY HOWARD HEATON

Ischyromys and Titanotheriomys make up a distinct group of primitive rodents that lived from the late Eocene to the late Oligocene and have been found in deposits from southwestern Saskatchewan to western Texas. Ischyromys is the most abundant rodent in Orellan (middle Oligocene) deposits of Nebraska, South Dakota, Wyoming, and Colorado. Numerous measurements were made on over 4,000 dentaries and lower cheek teeth and were subjected to many statistical analyses in order to discern relationships and patterns of evolution.

The earliest Ischyromys fossils come from a few late Eocene localities, but their relationships are poorly understood. The most unusual species is a previously undescribed form from West Canyon Creek in central Wyoming. In the early Chadronian (early Oligocene) Titanotheriomys developed with a suite of skull specializations and radiated into a number of diverse species, several of which are unnamed. Most of these are known from single localities, so relationships are difficult to reconstruct. This genus went extinct at the end of the Chadronian when Ischyromys, of uncertain origin and with a more primitive skull, began to proliferate.

Ischyromys typus (large) and I. parvidens (small) are very similar in morphology and developed separately from a highly variable late Chadronian population. Great numbers of dentaries of both species have been collected with excellent stratigraphic data from localities in western Nebraska and eastern Wyoming. Ischyromys parvidens dominated the early Orellan of the Great Plains (except North Dakota and northern South Dakota) then went extinct, and I. typus dominated the middle and late Orellan of the Great Plains (and all of the Orellan of North Dakota and northern South Dakota) then went extinct in the Whitneyan (late Oligocene). A previous claim of gradual size increase is in actuality the replacement of I. parvidens by I. typus although I. typus does increase very slightly in size thereafter.


TABLE OF CONTENTS
ABSTRACTi
TABLE OF CONTENTSiii
LIST OF FIGURESvi
LIST OF TABLESviii
LIST OF ABBREVIATIONSix
INTRODUCTION1
  • Acknowledgements
  • 4
    TAXONOMIC HISTORY OF THE ISCHYROMYINAE8
  • Early Work: 1856-1922
  • 9
  • Progressive work by Wood, Stout, and Howe: 1937-1966
  • 13
  • Taxonomic Lumping by Black: 1968-1971
  • 17
  • Two More Chadronian Species Erected: 1972-1974
  • 19
  • Taxonomic Reviews by Wood: 1976-1980
  • 20
    LOCALITIES AND SECTIONS23
  • Harrison area, northern Sioux Co., Nebraska
  • 27
    27
    29
    30
  • Lusk area, southern Niobrara Co., Wyoming
  • 30
  • Douglas area, southeastern Converse Co., Wyoming
  • 31
  • Chadron area, northern Dawes Co., Nebraska
  • 32
  • Badlands National Park, Pennington and Shannon Co., South Dakota
  • 33
  • Reva area, eastern Harding Co., South Dakota
  • 34
  • Dickinson area, Stark and Slope counties, North Dakota
  • 35
  • Scottsbluff area, Scotts Bluff Co., Nebraska
  • 36
    36
    36
    37
  • Sterling area, Weld and Logan Counties, Colorado
  • 37
  • Medicine Bow area, Albany and Carbon Co., Wyoming
  • 38
    38
    38
  • Alcova area, southern Natrona Co., Wyoming
  • 38
    38
    40
  • Lost Cabin area, northwestern Natrona Co., Wyoming
  • 40
  • Lander area, Fremont and Natrona Co., Wyoming
  • 40
    40
    41
    41
  • Dillon area, Beaverhead and Madison Co., Montana
  • 42
    42
    42
  • Butte area, southern Jefferson Co., Montana
  • 43
    43
    43
    43
    44
  • Helena area, Broadwater and Lewis & Clark Co., Montana
  • 45
    45
    45
    45
  • Southwestern Saskatchewan Province, Canada
  • 46
    46
    46
  • Big Bend area, Jeff Davis and Presidio Co., Texas
  • 47
    47
    47
    METHODS49
  • Photography
  • 50
  • Digitizing
  • 52
  • Data Manipulation
  • 58
  • Data Management
  • 61
  • Measurements Used
  • 63
  • Plots and Statistics
  • 70
    STATISTICAL ANALYSES71
  • Size vs. Time Plots
  • 71
  • Principal Components Analyses
  • 82
    83
    85
  • Discriminant Analyses
  • 87
    88
    93
    98
  • Middle Orella to Whitney Ischyromys of Northwest Nebraska
  • 101
  • Lower Orellan Ischyromys of Nebraska and Wyoming
  • 111
  • Cluster Analyses and Multidimensional Scalings
  • 113
  • Individual Character Plots
  • 122
    TAXONOMIC ANALYSIS132
  • Ischyromys vs. Titanotheriomys
  • 132
  • Ischyromys typus
  • 135
  • Ischyromys parvidens
  • 136
  • Late Chadron Complex
  • 138
  • Ischyromys pliacus
  • 139
  • Ischyromys blacki
  • 139
  • New Species of Ischyromys
  • 140
    140
  • Titanotheriomys veterior
  • 141
  • Titanotheriomys douglassi
  • 143
  • Titanotheriomys junctus
  • 144
  • New Species of Titanotheriomys
  • 144
    144
    145
    146
  • Phylogenetic Tree
  • 146
    CONCLUSIONS150
    REFERENCES CITED158

    LIST OF FIGURES
    Figure 1. Map showing Chadronian and Orellan fossil localities.24
    Figure 2. Correlation chart of Oligocene fossil localities.25
    Figure 3. Idealized diagram of occlusal view of tooth showing points digitized and positions of accessory cusps.53
    Figure 4. Idealized diagram of lingual view of tooth showing points digitized and position of lingual accessory cusp.57
    Figure 5. Idealized diagram of lingual view of jaw showing points digitized.59
    Figure 6. Sample panels from database.62
    Figure 7. Diagram of jaw measurements in lingual view.64
    Figure 8. Diagram of tooth measurements in occlusal view.67
    Figure 9. Diagram of tooth measurements in lingual view.68
    Figure 10. Scatterplot of 486 M/2's from Toadstool Park.72
    Figure 11. Scatterplot of 717 M/2's from Munson Ranch.73
    Figure 12. Scatterplot of 59 M/2's from Geike Ranch.74
    Figure 13. Scatterplot of 161 M/2's from Lusk area.75
    Figure 14. Scatterplot of 115 M/2's from Douglas area.76
    Figure 15. Scatterplot of 47 M/2's from Chadron area.77
    Figure 16. Scatterplot of 127 M/2's from Slim Buttes.78
    Figure 17. Scatterplot of 59 M/2's from Little Badlands.79
    Figure 18. Scatterplot of 111 M/2's from Flagstaff Rim.80
    Figure 19. Histogram of canonical variable from the output of three pairwise discriminant analyses.99
    Figure 20. Mean tooth area of M/2 for 30 foot stratigraphic intervals at Toadstool Park and Munson Ranch, Sioux County, Nebraska.104
    Figure 21. Mean value of labial accessory cusp for 30 foot stratigraphic intervals at Toadstool Park and Munson Ranch, Sioux County, Nebraska.106
    Figure 22. Mean value of anterior medial accessory cusp for 30 foot stratigraphic intervals at Toadstool Park and Munson Ranch, Sioux County, Nebraska.107
    Figure 23. Mean value of posterior medial accessory cusp for 30 foot stratigraphic intervals at Toadstool Park and Munson Ranch, Sioux County, Nebraska.108
    Figure 24. Mean value of lingual accessory cusp for 30 foot stratigraphic intervals at Toadstool Park and Munson Ranch, Sioux County, Nebraska.109
    Figure 25. Result of Cluster analysis using Ward method on standardized mean values of 27 groups of Ischyromys.117
    Figure 26. Two dimensional output of multidimensional scaling on 27 populations including absolute size.118
    Figure 27. Two dimensional output of multidimensional scaling on 27 populations excluding absolute size.120
    Figure 28. Result of Cluster analysis using Ward method on standardized mean values of 27 groups of Ischyromys after overall size was factored out.121
    Figure 29. Plot of mean values of the anterior and posterior angles between the tooth row and the ventral margin of the jaw.123
    Figure 30. Plot of mean values of the length of M/2 and M/3.125
    Figure 31. Plot of mean values of the length of M/2 and the length from the posterior valley mouth to the posterior end of the tooth on M/3.127
    Figure 32. Plot of mean values of angles made by the posterior and medial walls of the anterior lingual valleys vs. tooth size.129
    Figure 33. Plot of mean values of cusp heights divided by valley heights in lingual view vs. tooth size.130
    Figure 34. Phylogenetic tree showing possible relationships between species of Ischyromys and Titanotheriomys.148

    LIST OF TABLES
    Table 1. List and description of wear stages assigned.54
    Table 2. Number of cheek teeth of each wear stage from the total of 4015 dentaries digitized.55
    Table 3. List and description of subjective size values for accessory cusps.55
    Table 4. List of measurements calculated for each jaw and contained in Jaw Measurements Panel of database.65
    Table 5. List of measurements calculated for each lower cheek tooth and contained in the respective tooth measurements panels of database.66
    Table 6. Correlation matrix for 26 variables on 641 M/2's from the middle and upper Orella of northwestern Nebraska.84
    Table 7. Rotated factor loadings from principle components analysis on 641 M/2's from the middle and upper Orella.86
    Table 8. Means and coefficients of variation for eight variables on lower jaws from three populations.88
    Table 9. Means and coefficients of variation for 26 variables on P/4's from three populations.89
    Table 10. Means and coefficients of variation for 26 variables on M/1's from three populations.90
    Table 11. Means and coefficients of variation for 26 variables on M/2's from three populations.91
    Table 12. Means and coefficients of variation for 26 variables on M/3's from three populations.92
    Table 13. Success rates of classifying fossils by discriminant analysis.94
    Table 14. Coefficients for canonical variables and group means used in four discriminant analyses on jaws.95
    Table 15. Coefficients for canonical variables and group means used in four discriminant analyses on P/4's.95
    Table 16. Coefficients for canonical variables and group means used in four discriminant analyses on M/1's.96
    Table 17. Coefficients for canonical variables and group means used in four discriminant analyses on M/2's.97
    Table 18. Coefficients for canonical variables and group means used in four discriminant analyses on M/3's.98

    LIST OF ABBREVIATIONS
    CMAmherst College Museum
    ALVAnterior Lingual Valley
    AMNHAmerican Museum of Natural History
    ANSPAcademy of Natural Sciences of Philadelphia
    CMCarnegie Museum
    FMNHField Museum of Natural History
    M/1First lower molar
    M/2Second lower molar
    M/3Third lower molar
    MCZMuseum of Comparative Zoology, Harvard University
    MDSMultidimensional scaling
    MUPMUniversity of Montana
    NMCNational Museum of Canada
    P/4Only lower premolar present on Ischyromys
    ROMRoyal Ontario Museum
    SDSMSouth Dakota School of Mines
    SMNHSaskatchewan Museum of Natural History
    TMMTexas Memorial Museum
    UCMUniversity of Colorado at Boulder
    UNSMUniversity of Nebraska State Museum
    USNMU.S. National Museum, Smithsonian Institution
    UWUniversity of Wyoming
    YPMPeabody Museum, Yale University

    INTRODUCTION
    Ischyromys is a primitive squirrel-sized rodent that inhabited the Great Plains and surrounding areas during the Oligocene Epoch. Its fossils were first discovered in the Big Badlands of South Dakota where it is the most abundant rodent in middle Oligocene sediments (Orellan land mammal age). A similar abundance has been found in Orellan sediments of Colorado, Nebraska, and Wyoming. Several genera were erected but later synonymized with Ischyromys. A very similar rodent was found in early Oligocene sediments (Chadronian land mammal age) of Montana and was given the generic name Titanotheriomys. Some workers have honored this name while others have considered it a synonym of Ischyromys.

    There is a general consensus among most of those familiar with these rodents that the generic distinction between Ischyromys and Titanotheriomys is valid, and it is so considered in this work. This leaves a problem when referring to the group as a whole. Some workers consider the Family Ischyromyidae to include only these two genera (Wood 1937, 1980) while others include all paramyid rodents in the family as well (Black 1968; Korth 1984). So both the terms "ischyromyid" and "Ischyromys" are ambiguous as to their inclusive meaning. This is unfortunate since the rodents under study (Ischyromys plus Titanotheriomys) form a unified group and are quite distinct from all other rodents. To avoid confusion, the subfamily name Ischyromyinae will be used to refer to both Ischyromys and Titanotheriomys.

    Ischyromyine fossils are now known from Saskatchewan to Texas and from the latest Eocene (Duchesnean land mammal age) to the late Oligocene (Whitneyan land mammal age), but only in the Orellan of the Great Plains are they abundant. Titanotheriomys is restricted to the Chadronian and comprises a number of distinct forms, most of which are known only from single localities and most of which have not yet been given species names. Ischyromys, in contrast, is best known in the Orellan where its fossils are very abundant. In the Orellan it displays little diversity, and most of its named species are invalid. Its fossils are also found in the late Duchesnean and Chadronian, and the more primitive skull pattern of Ischyromys suggests that it is the ancestor of Titanotheriomys despite the fact it became dominant later in time.

    A number of works have been devoted exclusively to the Ischyromyinae (Troxell 1922; Howe 1956, 1966; Black 1968; Wood 1976; and Flynn 1977), and good taxonomic summaries have been provided by Wood (1937, 1980). A serious problem has plagued the taxonomy of the group, however, and this is the difficulty of correlating characters between skulls and lower jaws (dentaries). Complete skulls are very rare, but they display much diversity of character. The distinction between Ischyromys and Titanotheriomys has been based entirely on characters of the skull. Dentaries are by far the most abundant elements, but they reportedly lack the diversity of the skulls. Skulls and dentaries are rarely found associated, and both have been used as type specimens.

    Thousands of ischyromyine dentaries have been collected, many with excellent stratigraphic data. Howe (1956, 1966) studied changes over time in Orellan Ischyromys dentaries from northwestern Nebraska and reported trends of increasing tooth size and increased incidence of accessory cusps that he considered worthy of three or four successive chronospecies. Flynn (1977) studied changes over time in Chadronian ischyromyines from Flagstaff Rim, Wyoming and found significant changes in several characters. But he was frustrated at finding a dichotomy in the skulls that was not observable in the dentaries, and consequently he could not tell if the changes were due to evolution or replacement.

    These former evolutionary studies of ischyromyine dentaries used only measurements of gross tooth size (tooth lengths and widths) and total number of accessory cusps (of four possible types) to measure change over time. Taxonomic studies noted many specific peculiarities in the configuration of the cusps, valleys, and accessory features, but these were only examined on small samples (sometimes only on type specimens), so their significance for whole populations was unknown. The opportunity was clearly available for examining the large samples of ischyromyine dentaries in terms of every available character and using this increased resolution to both resolve the taxonomic difficulties and study evolutionary changes over time.

    The manner in which new species arise and undergo change in their morphology has been a subject of great interest ever since Darwin (1859) published his theory of natural selection. Darwin believed that species change gradually through a sequence of finely graded intermediate steps, and he was very concerned that the fossil record failed to document such gradual transitions. Instead the characteristic pattern is for changes to occur abruptly, and Darwin resigned himself to the notion that the fossil record is hopelessly imperfect. In recent years Eldredge and Gould (1972) have challenged this view, claiming that it is natural to have long periods of stability punctuated by short periods of rapid diversification. They proposed that the fossil record is an accurate rather than an imperfect history and that this pattern of stasis and punctuation is the natural result of allopatric speciation and of evolutionary rates being an inverse function of population size.

    The controversy sparked by Eldredge and Gould's (1972) theory of "Punctuated Equilibria" has lead to many careful examinations of fossil sequences including mammals. Gingerich (1974, 1976, 1979, 1980) has studied many lineages of mammals and has presented many cases of gradual anagenesis and cladogenesis. Gingerich's work has a serious flaw in that he has only used a single morphological character (log of length * width on M/1), so all he has considered is the overall size of the animals. Though easy to measure, body size alone is of trivial taxonomic importance and has zero resolution for detecting the more important changes in shape. His studies are also limited in geographical extent. Chaline and Laurin (1986) presented a good case for gradual change in the European vole Mimomys which lacked these limitations. Gould (in press) has pointed out the bias that only lineages where gradual change was thought to be seen upon initial examination are normally used as test cases to resolve the controversy. The Ischyromyinae is no exception.

    To familiarize the reader with the Ischyromyinae, this report begins with a review of the taxonomic history of the group and a description of its fossil occurrences at each locality. Next is a description of methods used and results of all statistical analyses employed. Finally the results concerning taxonomic relationships and patterns of evolution are discussed.

    Acknowledgements
    My desire for doing a project such as the one herein contained began several years before coming to Harvard University. After studying all the mammals from a single fauna for a Masters thesis, I wanted to study change in a single lineage over time in detail. This interest was stimulated by studying the evolutionary models presented by Dr. Stephen Jay Gould which I viewed with both fascination and skepticism. I am very grateful to Dr. Gould for serving as my advisor for this project. His brilliance and enthusiasm have influenced me in areas far beyond evolutionary theory. I also appreciate the way he encouraged objectivity in my work and never influenced me to interpret my data from his perspective.

    Many mammalian lineages were considered for study in this project. Because of my interest in the evolution of beavers I came in contact with Prof. Emeritus T. Mylan Stout who suggested the study of Ischyromys and arranged for me to borrow an enormous collection from the University of Nebraska to get started. Dr. Gould and Prof. Stout have opposing views on many aspects of paleontology, and I enjoyed contrasting their opinions and experiences. Prof. Stout and Mr. Lloyd G. Tanner took me to most of the Oligocene localities in Nebraska and helped familiarize me with the somewhat unusual stratigraphic history of the terrestrial deposits of the Great Plains. Dr. C. Bertrand Schultz also met with me during my trips to Nebraska and gave helpful assistance.

    I express great thanks to the many curators and collection managers who spent many hours loaning fossils to me and providing information concerning them. These include Dr. Margery C. Coombs (ACM); Dr. Richard H. Tedford, Dr. Michael J. Novacek, and Mr. John Alexander (AMNH); Dr. Charles L. Smart (ANSP); Drs. Mary R. Dawson, Leonard Krishtalka, and Richard K. Stucky (CM); Ms. Mary Carmen (FMNH); Dr. Farish A. Jenkins, Jr. and Mr. Charles R. Schaff (MCZ); Dr. Robert W. Fields and Mr. Daniel Garcia (MUPM); Drs. Phillip M. Youngman and C. R. Harington (NMC); Dr. Gordon Edmund and Mr. Kevin Seymour (ROM); Ms. Melissa C. Winans (TMM); Dr. John E. Storer and Mr. Tim T. Tokaryk (SMNH); Dr. Peter Robinson, Mr. Donald G. Kron, and Mr. Logan Ivy (UCM); Prof. T. Mylan Stout and Dr. Richard G. Corner (UNSM); Dr. Robert J. Emry and Mr. Robert Purdy (USNM); Dr. Brent H. Breithaupt (UW); and Dr. John H. Ostrom and Ms. Mary Ann Turner (YPM).

    Dr. Donald R. Prothero and Mr. Donald G. Kron sent me long letters with invaluable information about many localities, particularly in eastern Wyoming. I had the privilege of doing a ten week fellowship at the Smithsonian Institution with Dr. Robert J. Emry as my advisor. Dr. Emry provided information on many obscure Oligocene localities and allowed me to use many of his unpublished stratigraphic sections. Mr. Morris F. Skinner, Frick Curator Emeritus (AMNH), provided me with valuable information about his vast collections and allowed me access to his voluminous unpublished material. I also benefited from discussions at the American Museum with Drs. Richard H. Tedford, John J. Flynn, and John H. Walhert. Since my knowledge of the Oligocene and of primitive rodents was very limited when this project began, I owe a great debt to these persons for their generous assistance.

    Many decisions had to be made concerning methodology, both in obtaining measurements and analyzing them. In this area Dr. Peter G. Williamson offered enormous assistance. Without the ideas derived from our brainstorming sessions together, this project would have taken much longer than it did. I also thank Mr. Paul Morris for help with writing the computer programs. The following persons made critical reviews of the manuscript and gave many helpful suggestions: Drs. Stephen Jay Gould, Peter G. Williamson, Andrew H. Knoll, Robert J. Emry, Donald R. Prothero, and Mrs. Julia S. Heaton.

    Perhaps the greatest debt of all I owe to the numerous collectors of the fossils used in this study. Many of them are mentioned above, and many of them I know only as names on specimen labels and field notes. It was their countless hours of fieldwork spanning over a century and encompassing 7 states and a province that made a project of this type possible. I am particularly indebted to those who kept detailed locality and stratigraphic data while collecting.

    This project was funded by fieldwork grants and other funds from Harvard University, a fieldwork grant from the Geological Society of America, a graduate student fellowship at the Smithsonian Institution, and a collection study grant from the American Museum of Natural History. Drs. Stephen Jay Gould and Peter G. Williamson of Harvard University provided funds from their research grants to purchase supplies.

    And finally I would like to express thanks to my family. My parents, Howard and Carolyn Heaton, did much to provide for the logistics of my stay in Massachusetts as well as provided constant encouragement. My wife, Julie, provided constant support and assistance in innumerable ways and also helped with the preparation of the manuscript. I also want to express my love to my three daughters, Christy, Amy, and Holly, who spent countless hours wishing that Daddy would stop sitting at his computer and play with them instead.

    TAXONOMIC HISTORY OF THE ISCHYROMYINAE
    The taxonomy of the Ischyromyinae is very confused. There have long been disagreements over the status of various taxa and what characters should be used to distinguish them. Much of the problem stems from fact that the most abundant elements, dentaries, have only minor interspecific differences while the most mutable elements, skulls, are so rare that it is difficult to access intraspecific variation. Some type specimens are skulls and others are lower jaws, so in many cases no real comparison can be made. Workers disagree over whether the more abundant or the more variable elements should be given the most weight in taxonomic assignment and whether stratigraphic position should also be considered.

    The controversy occurs at several levels: 1) whether the ischyromyines belong in the same family as the paramyid rodents or in a family by themselves, 2) whether Titanotheriomys is a distinct genus or merely a synonym of Ischyromys, and 3) whether few or many species should be recognized and whether they must be distinct as individuals or as populations. Only the latter two levels are addressed here.

    While this study is not primarily taxonomic and does not deal with descriptions of individual fossils, a review of the taxonomic history and its controversies is important groundwork for studying the group. Whenever possible past controversies will be resolved using multivariate statistical techniques on the large data set that is now available. Since this study only deals with dentaries, diagnoses of lower jaws and teeth are given greatest treatment.

    Early Work: 1856-1922
    Ischyromys typus (new genus and species) was named by Leidy (1856:89) with a 10-line description of a skull (type; now ANSP 11015) and two lower jaw fragments (now ANSP 11025 and 11026) collected by Dr. F. V. Hayden at the head of Bear Creek in the Nebraska Territory (now Big Badlands near Scenic, Pennington County, South Dakota). In this initial description Leidy mentioned similarities of this skull to Steneofiber and Arctomys and gave the tooth formula and three measurements from the type specimen, but he included no illustrations. Leidy (1869:335-338) gave a much more detailed description of I. typus based on the original material plus several additional jaw fragments (now ANSP 11016, 11017, 11020, and possibly 14856-14858) obtained by Dr. Hayden in 1866 from elsewhere in the Big Badlands, South Dakota. The type skull and three dentaries were then illustrated (Leidy 1869, pl. 26, figs. 1-6 [Footnote: Illustrated specimens are now cataloged as follows: figs. 1, 2, and 4: ANSP 11015; fig. 3: ANSP 11017; fig. 5: ANSP 11016; and fig. 6: ANSP 11020]).

    Cope (1873a:1) named Colotaxis cristatus (new genus and species) based on three specimens without any illustration and without any reference to Leidy's two articles mentioned above, but he gave five tooth measurements from one specimen. Cope (1873b:5-7) named Gymnoptychus chrysodon, G. nasutus, G. trilophus, and G. minutus (new genus and species), and several measurements were given for each species. Gymnoptychus chrysodon appears to have been described from a single skull. Gymnoptychus nasutus was said to be smaller, and measurements of skull and mandibular characters were included. Gymnoptychus trilophus included only mandibular measurements, and the teeth were said to be distinct. Gymnoptychus minutus was said to be the smallest species, and only mandibular measurements were included. In his synopsis of the new vertebrata from the tertiary of Colorado, Cope (1873c:3) listed Ischyromys chrysodon, I. nasutus, I. trilophus, I. minutus, and Colotaxis cristatus as being present among the rodent fauna and cited Cope (1873a, 1873b) as sources, but he did not explain the reason for the synonymy of Gymnoptychus with Leidy's Ischyromys, nor did he give any description or list of specimens. Cope (1874:477, 1884:833-838) discussed Ischyromys, and he synonymized Colotaxis cristatus and Gymnoptychus chrysodon with I. typus. Cope (1874:476, 1884:819-826) retained Gymnoptychus trilophus and G. minutus (including G. nasutus) in the genus Gymnoptychus without giving any reason for applying them to Ischyromys in Cope (1873c), but they are now considered to belong to the eomyid genera Paradjidaumo and Adjidaumo respectively (Wood 1937, 1980; except the G. nasutus material is assigned to P. trilophus). Cope (1884, pl. 66, fig. 30, pl. 67, figs. 1-12) illustrated some Ischyromys typus material including a skull and five dentaries. The skull and one dentary (pl. 67, figs. 1, 1a, 1b, and 5b) are also illustrated in Cope's (1888, fig. 5) article on the origin of rodent dentition. At this time the genus Ischyromys was considered to be monospecific, and I. typus was the only name assigned to the material under study. All of the fossils discussed above were found in Orellan strata of South Dakota, Nebraska, and Colorado.

    Matthew (1903:211-212), in his report on Chadronian deposits of Pipestone Springs, Montana, reported a partial skull and some forty jaws of Ischyromys. He described these fossils as being substantially smaller than those from the Dakota area and having narrower teeth with higher cusps. He said they were also distinct in that the last lower molar has "a narrow heel with the last crest imperfect internally, while in all the Colorado specimens the heel is as wide as the rest of the tooth, and the third (last) crest perfectly developed." He said that "in the upper teeth a corresponding difference is to be seen in the last molar, and also the valley between the anterior and posterior inner cusps is well marked on all the teeth, distinct nearly to the base of the enamel, while in the specimens from Colorado and from South Dakota it is absolute on P4/ and on the molars does not extend so far down."

    Matthew (1903) named the Pipestone Springs material Ischyromys veterior (new species), and according to American Museum of Natural History records the skull Matthew intended as the type specimen is AMNH 9647. Wood (1937:196-197, fig. 27), however, designated AMNH 9658, a left dentary with P/4-M/3, as the lectoholotype. Matthew (1910:63) erected the subgenus Titanotheriomys for his new species, I. (T.) veterior. Compared to the subgenus Ischyromys he described Titanotheriomys thus: "Incisors narrow, muzzle small, no sagittal crest but an indistinct lyrate area; zygomata slender, superior border of origin of masseter extended forward on muzzle in an indistinct ridge."

    In addition to the Pipestone Springs material Matthew (1910) assigned to I. (T.) veterior a Chadronian skeleton from Beaver Divide in central Wyoming (reported in Granger 1910:240-241). Matthew (1910:62, figs. 16-18) recognized two species in the subgenus Ischyromys: I. (I.) typus from South Dakota having "teeth wider transversely with lower crowns and heavier enamel" and I. (I.) cristatus from Colorado having "teeth narrower transversely than in I. typus, with higher crowns and thinner enamel; skull and teeth usually smaller and sagittal crest sometimes incomplete anteriorly."

    Miller and Gidley (1918:436), in their synopsis of the supergeneric groups of rodents, listed only the genus Ischyromys as part of the Family Ischyromyidae. But in a later paper Miller and Gidley (1920:73-74) considered the Pipestone Springs material as a separate genus (Titanotheriomys) with distinctly more slender jaws and incisors than Ischyromys. But the purpose of their paper was to describe a new smaller species of Ischyromys from the Badlands of South Dakota. Ischyromys parvidens, described from five mandibles, was said to be similar to T. veterior in size but similar to I. typus in proportions. Nothing was said about the stratigraphic relationship of I. typus and I. parvidens in the Big Badlands.

    Of the larger Ischyromys Miller and Gidley (1920) considered Cope's types of Colotaxis cristatus to be I. typus jaws containing deciduous premolars. But they still recognized two large species of Ischyromys: I. typus with a smaller jaw breadth and "area of muscle attachment in front of antero-external root of P/4 an ill defined shallow depression," and I. chrysodon with a greater jaw breadth and "area of muscle attachment in front of antero-external root of P/4 a well defined, rounded pit."

    Troxell (1922) made the next revision of the genus Ischyromys and speculated (quite erroneously) that it is ancestral to the living prairie dog (Cynomys). Troxell (1922:123) considered Cope's Colotaxis cristatus and Gymnoptychus chrysodon to be synonyms of I. typus, a synonymy that has not been challenged since. He also named a new species and two subspecies. Ischyromys pliacus (Troxell 1922:124, fig. 1) was named for a dentary that is much larger than typical I. typus and has many additional tubercles and pits on the cheek teeth. "The posterior cross crests," said Troxell, "do not arise directly from the external tubercle but from its union with the central longitudinal ridge, thus forming a 'Y.' This cross is made up of two distinct minute cusps...." Ischyromys typus nanus was described as being small, having a narrow M/2, and lacking secondary tubercles (Troxell 1922:124-125, figs. 2-3). Later authors synonymized this subspecies with I. parvidens. Troxell (1922:125-127, figs. 4-5, 1923, figs. 19-20) gave the subspecific name I. typus lloydi to an exceptionally well preserved set of skull and jaws from Nebraska (YPM 12521).

    All of the above studies were extremely limited in scope, were based on very small collections, and did not consider the ages or relationships of the species involved in any useful way. Nothing is known of the stratigraphic level from which the type specimens came. While this early work is important for taxonomic reasons, it does more to confuse than to help the work of assigning names to ischyromyine species.

    Progressive work by Wood, Stout, and Howe: 1937-1966
    Wood's (1937) monograph on the rodents of the White River Oligocene is the earliest thorough taxonomic treatment of the Ischyromyinae. Wood put the generic distinction between Ischyromys and Titanotheriomys on an entirely new basis using mostly skull characters involving jaw musculature. Titanotheriomys was described as having a lower, flatter skull than Ischyromys with a shorter pre-orbital region and a more slender snout, zygoma, and braincase. The temporal crests of Titanotheriomys do not meet to form a sagittal crest as they do in Ischyromys. Wood (1937:193-196) also stated that in Titanotheriomys the masseter extends farther onto the zygoma and a thin strip extends farther onto the snout than in Ischyromys, approaching the advanced sciuromorph pattern found in some other rodent families. The infra-orbital foramen is visible dorsally in Titanotheriomys but not in Ischyromys. He also stated that the mandible and postcranial elements, as far as known, tend to be more slender in Titanotheriomys. A number of minor differences in the cheek teeth were also mentioned, particularly that the lower teeth are much narrower in Titanotheriomys than in Ischyromys. Comments on this generic distinction were also made by Stehlin and Schuab (1951) and Schuab (1958).

    Wood (1937) recognized four species of Ischyromys and two species of Titanotheriomys, including a new species he named in each genus. He distinguished I. parvidens (small), I. typus (intermediate), and I. pliacus (large) mainly by size and by I. parvidens having more primitive teeth (Wood 1937:192-193, figs. 23-25). Ischyromys typus was said to be most distinct from Titanotheriomys and was therefore used as the basis for generic comparison (Wood 1937, fig. 21, pl. 23, figs. 6-7, pl. 25, figs. 1-10a, pl. 26). Wood (1937:191-192, pl. 23, fig. 3) described I. troxelli (new species) as being the same size as I. typus but having a narrower skull at the postorbital constriction and having the longest orbit of any species of the genus. It was also said to be distinct from I. typus in having M/1 and M/2 wider than long and having short posterolophids on all lower cheek teeth. Wood (1937:191) mentioned several specimens with skull characters that match I. troxelli in some respects and I. typus in others, and he proposed that they might represent an additional species. He said I. pliacus is most similar to I. troxelli because it has a narrow postorbital constriction and a short posterolophid on all teeth (Wood 1937:188-191, fig. 22).

    Wood (1937) viewed these four species of Ischyromys as long-term, wide ranging, and coexisting lineages rather than chronospecies. To I. parvidens he assigned the small lower Orellan specimens from South Dakota and the Chadronian material from Cypress Hills, Saskatchewan. He considered I. typus to be the dominant form in the Cedar Creek Beds of Colorado and a rare form in the Big Badlands of South Dakota, thus limiting it to the middle Oligocene. Ischyromys troxelli was considered to have the same range as I. typus but to have been more common in South Dakota and rarer in Colorado. Ischyromys pliacus was considered the most long-ranging species, possibly comprising several large forms. To it Wood (1937:190) assigned a large form from the Chadronian of Pipestone Springs (less common than T. veterior), the largest Orellan specimens from South Dakota and Colorado, and a Whitneyan specimen from Colorado.

    Wood (1937:196-197, figs. 26-27, pl. 27, figs. 2-4) described Titanotheriomys veterior from Pipestone Springs as having lower cheek teeth that are distinctly longer than they are wide, and he noted the presence on the holotype of a barrier forming across the median valley of some of the teeth, a condition also sometimes present in Ischyromys (see Friant 1935, Wood 1937:177, Burt and Wood 1960:957-958, fig. 1A). He also said the upper cheek teeth have deep notches in the paracones. Wood (1937:198, pl. 27, figs. 1, 1a-b) also erected a new species, Titanotheriomys wyomingensis, based on the skull and jaws collected at Beaver Divide by Granger (1910). He stated that T. wyomingensis lacks the notches in the paracones and has a deep pit in the skull anterior to P3/. Its lower teeth are as wide as they are long and lack the barrier across the median valley.

    The first attempt to evaluate the stratigraphic relation of ischyromyines from a single region was done by Stout (1937:18-50) along the Pine Ridge exposures of northwestern Nebraska and adjoining parts of Wyoming. He identified Titanotheriomys sp. from the lower Oligocene Chadron Formation based on a small, slender jaw and a small isolated tooth that matched Miller and Gidley's (1920) description of T. veterior. From the lower part of the middle Oligocene Oreodon beds Stout found 125 slightly larger jaws that he called I. cf. parvidens. From the middle and upper Oreodon beds Stout found 401 distinctly larger Ischyromys jaws that he identified as I. typus and I. cf. typus lloydi, and he suggested that this latter group might be further subdivided into two or three distinct stratigraphic varieties. Stout's (1937) study extended the range of Titanotheriomys eastward, put the ischyromyine species in a stratigraphic context, and led to the suggestion that Titanotheriomys and Ischyromys comprise a lineage that increased in size through time.

    Work on Ischyromys continued at the University of Nebraska following Stout's (1937) original work. Barbour and Stout (1939) and Galbreath (1953:57-58) considered the largest specimens from the upper Oreodon beds to be I. pliacus, and Schultz and Stout (1955:43) concluded that I. parvidens is restricted to the lower Orella. Howe (1956, 1966) collected 244 dentaries from Sioux County, Nebraska: 73 from the lower Orella which he considered I. parvidens, 124 from the middle Orella which he considered I. typus, and 47 from the upper Orella which he considered I. pliacus. He also examined a fragmentary skull from the basal Whitney which he proposed to be a distinct species even larger than I. pliacus. Howe considered these species to represent an anagenetic evolutionary transition in which the lineage underwent an increase in size, crown height, and incidence of accessory cusps. He recognized that there was considerable overlap between the species in these characters, especially between I. typus and I. pliacus. Because of the great variability at each level, he believed that many characters previously used for species recognition were unreliable, and he suggested that I. troxelli was a synonym of I. typus despite Burt and Wood's (1960:958, fig. 1B) recognition of that species.

    The conclusions of Howe (1956, 1966) and other Nebraska workers differed from those of Wood (1937) in that they considered Ischyromys to be a single evolving lineage rather than a suite of coexisting species. Howe failed to address the problem of the large Chadronian ischyromyine at Pipestone Springs which Wood (1937) assigned to I. pliacus and from which he implied that the large Orellan form evolved. But to Howe the stately march of a single continuous size distribution through the Nebraska section was very suggestive of a single evolving lineage and made that the most logical conclusion.

    Taxonomic Lumping by Black: 1968-1971
    Black (1965:7-8) briefly mentioned the ischyromyines and the problems of their taxonomy in his report on the rodents of Pipestone Springs, and in a later paper he took up a major revision of the group. Black (1968:279-282, figs. 1-6) claimed that the distinctive characters used by Wood (1937) to separate Titanotheriomys from Ischyromys were not real and were only due to crushing and distortion in the two Chadronian age skulls available to Wood. With better material available from Pipestone Springs, Black said the skulls are indistinguishable and therefore Titanotheriomys is a synonym of Ischyromys. He did recognize that some skulls have a sagittal crest while others do not, but upon finding several intermediate configurations on skulls from Pipestone Springs he attributed this difference to individual or sexual variation.

    Black further synonymized the group by recognizing only two valid species from those previously named: I. typus and I. veterior. He stated that the size and cheek tooth pattern of I. typus and I. troxelli are identical and that the skull characters used by Wood (1937) to distinguish them are either not preserved on the I. troxelli type or fall within the size range of a single population. He also said that the size and cusp pattern of the type of I. pliacus is identical to the mandible of the I. troxelli type. Black (1968:277-278) therefore synonymized I. pliacus and I. troxelli with I. typus. He also claimed that the characters Wood (1937) used to distinguish T. wyomingensis from T. veterior are either unavailable on the T. wyomingensis type due to wear or fall within the range of variation seen in I. veterior at Pipestone Springs. In addition he stated that the large available samples of I. veterior from Montana (Black 1965) and I. parvidens from Nebraska (Howe 1956, 1966) clearly show that the distinguishing characters recognized by Miller and Gidley (1920) represent individual variation. Black (1968:278-283, figs. 1-6, 13-15) therefore synonymized T. wyomingensis and I. parvidens (including I. typus nanus) with I. veterior. He distinguished I. veterior from I. typus by its smaller size, by the presence of conules on the upper molars, and by the frequent absence of a sagittal crest.

    Black (1968:283-287, figs. 7-12, 16-17, 19-20) erected a new species, Ischyromys douglassi, based on new material from the early Oligocene of McCarty's Mountain, Montana. He said the teeth are wider in relation to their length than those of I. typus but are of the same overall size, and he listed many other minor differences in the teeth. He also plotted a number of characters from four ischyromyine populations, some of which mildly suggest a trend to more elongate teeth through time with I. douglassi being the earliest and most primitive form. Black (1971:203-204, figs. 41-45) later found five isolated teeth of ?Ischyromys sp. from late Eocene deposits of Badwater Creek, central Wyoming which he said were most similar to I. douglassi.

    Wood (1969:2-5, 1976:246) initially conceded to all of Black's (1968) synonyms (see also Harris 1967:53). But in later publications he resurrected all the synonymized taxa except T. wyomingensis (Wood 1974, 1976, 1980), and some workers believe it is valid as well (Wahlert 1974:388-393; Donald G. Kron, per. comm.).

    Two More Chadronian Species Erected: 1972-1974
    Lambe (1908:56, pl. 8, fig. 18) described a lower right molar from Cypress Hills, Saskatchewan and assigned it to I. typus. Russell (1934:56) considered this tooth an M/1 and assigned it to I. t. nanus because of its small size. Wood (1937:192, fig. 24) synonymized I. t. nanus with I. parvidens and said the Cypress Hills tooth was indistinguishable from the type of that species.

    Russell (1972:27-30, figs. 7J, 8A-D) reported ten additional isolated lower cheek teeth from Saskatchewan and erected a new species, I. junctus, which he described as being intermediate in size between I. typus and I. parvidens. He said its unique features are the joining of the anterolophid and metalophid to the metaconid, forming a triangular valley, and the curving of the posterolophid around the posterior margin of the crown almost to the entoconid. Storer (1978:4-7, figs. 1A-I) reported 28 additional teeth of this species from the Calf Creek local fauna, Saskatchewan. Storer (1988:90) later reported 9 teeth from the late Eocene Lac Pelletier Lower Fauna which he considered to be a distinct, earlier species from Saskatchewan.

    Russell (1972:30, figs. 8E-G) also considered there to be a smaller species of Ischyromys from Cypress Hills, but Wood (1980:21) considered the material to belong to other families. Russell's (1972:30) study of the ischyromyids led him to the conclusion "that Titanotheriomys is a valid genus, distinguished by elongate molars, in which the cingular crests, especially the posteroloph, are widely separated from the main crests."

    The ischyromyine fossils found farthest from the rich localities of Nebraska and South Dakota come from two sites in western Texas. Harris (1967:51-73, figs. 9A-B, 10A-B) reported T. veterior and a new smaller species of Titanotheriomys from the Chadronian Ash Spring local fauna, but Wood (1974:27-29, figs. 11-12) considered all seven specimens from that site to be variations of T. veterior. Wood (1974:22-26, figs. 8-10) erected a new species, I. blacki, for a skull and dentary from the earliest Chadronian Porvenir local fauna. He described the skull as being similar to I. typus but the teeth having many primitive characters like T. douglassi such as prominent metaconules and incomplete metalophs. The lower molars have an incomplete metalophid and a distinct intermediate cusp in the hypolophid which is also sometimes present in T. douglassi (Black 1968:286, Wood 1974:26).

    Taxonomic Reviews by Wood: 1976-1980
    Wood (1976:247-264, figs. 2-8) wrote a revision on the Ischyromyidae in which he detailed at great length the differences between Ischyromys and Titanotheriomys. These differences consist almost exclusively of skull characters having to do with jaw musculature and are an expansion of Wood's (1937) earlier list. Wood (1976:264-265) excused the lack of differences in the more abundant elements: "Nor should the difficulty or impossibility of assigning isolated cheek-teeth or lower jaws of ischyromyids to the correct genus, without association of at least skull fragments, be considered any more of a real problem than the comparable difficulty with respect to isolated vertebrae or toe bones." He did not agree with Black (1968) that the teeth are indistinguishable or with Russell (1972) that Titanotheriomys has more elongate cheek teeth than Ischyromys.

    Because Titanotheriomys has a more derived jaw muscle configuration than Ischyromys, Wood (1976:268) considered Ischyromys to be the probable ancestor of the group, and he believed that both genera coexisted during the entire Chadronian but not at the same localities at the same time. He considered material from the Porvenir (earliest Chadronian, Texas), Cypress Hills (early Chadronian, Saskatchewan), lower Bates Hole (early Chadronian, Wyoming), and Douglas (late Chadronian, Wyoming) to belong to Ischyromys and material from McCarty Mountain (early Chadronian, Montana), Pipestone Springs (middle Chadronian, Montana), Beaver Divide (middle Chadronian, Wyoming), Ash Spring (middle Chadronian, Texas), and upper Bates Hole (middle Chadronian, Wyoming) to be Titanotheriomys.

    Flynn's (1977:15-16) detailed study of ischyromyines from Flagstaff Rim (Bates Hole) lead him to believe that lineages of Ischyromys and Titanotheriomys coexisted there throughout much of the Chadronian. He based this conclusion on a clearly bimodal distribution in skull musculature arrangement (based on Wood 1976) with no intermediates among a group of small ischyromyines with identical cheek teeth. He also suggested that a small sample of larger specimens represent a second coexistent species of Titanotheriomys. Although the smaller lineages are indistinguishable on tooth morphology, the combined group increases in size, increases in incidence of accessory cusps, and may change slightly in tooth proportions through time. Kron (1978:94-95) reported coexisting Ischyromys and Titanotheriomys from the latest Chadronian of the nearby Douglas locality.

    Flynn (1977:20), noting a marked difference in tooth proportions between the Flagstaff Rim material and equivalent age Titanotheriomys from Montana, suggested that ischyromyines from different regions may have evolved in isolation from one another. He also stated that the Chadronian ischyromyines from Flagstaff Rim are distinct from the lower Orellan I. parvidens of Nebraska in having an accessory ridge between the protoconid and hypoconid (Flynn 1977:19).

    The latest taxonomic review of ischyromyids is in Wood's (1980:17-22) monograph on Oligocene rodents. It is a good summary of previous research. He recognized six species of Ischyromys (I. typus, I. pliacus, I. troxelli, I. blacki, I. parvidens, and I. junctus) and two species of Titanotheriomys (T. veterior and T. douglassi). He noted, however, that the taxonomic status of I. pliacus, I. troxelli, I. parvidens, and I. junctus is not certain.

    Disagreements concerning ischyromyine taxonomy have lead to considerable confusion, and many generic and specific identifications in the literature must be regarded with extreme doubt. The problem is even worse in museum collections where the basis of taxonomic assignments is rarely stated, and most such identifications have no value whatsoever. To rectify this situation it must first be learned which fossil elements are recognizable at the genus and species level and which populations are conspecific. It is hoped that this study will make a significant step toward that goal.

    LOCALITIES AND SECTIONS
    Orellan localities containing Ischyromys occur mainly in a narrow band extending from southwestern North Dakota to northeastern Colorado (Figure 1). Ischyromys is the most abundant rodent at all of these localities. Sections with the best stratigraphy occur along Pine Ridge between Chadron, Nebraska and Douglas, Wyoming. Some of localities are exceptional in their stratigraphic continuity and abundance of specimens, especially Toadstool Park and Munson Ranch in northwestern Nebraska.

    Chadronian ischyromyine fossils come from widespread localities from Saskatchewan on the north to Texas on the south with a majority coming from numerous localities in central Wyoming and southwestern Montana (Figure 1). Ischyromyines are rare in the Chadronian, and most localities have little stratigraphic range. The notable exception is the Flagstaff Rim section in Wyoming which probably covers all of Chadronian time and where fossils have been collected with excellent stratigraphic data. The many widespread localities are significant because many have unique species. Correlating these localities and understanding the evolutionary relations of the species is nearly impossible, however, because of the small sample sizes, age uncertainties, and the possibility that distant populations were evolving in isolation from each other. The largest Chadronian sample comes from Pipestone Springs, Montana.

    Emry et al. (1987) provide an excellent review of the terminology, stratigraphy, and correlation of the Chadronian, Orellan, and Whitneyan land mammal ages which includes all localities containing ischyromyines (Figure 2), and no attempt will be made to reproduce their work here. Prothero (1982, 1984, 1985a, 1985b) has combined biostratigraphy with magnetic reversal data to aid in correlating many of the sections. The purpose of detailing the localities here is to state their accepted time spans, give a description of what levels contain ischyromyines and where collections reside, and to cite the stratigraphic work (if any) used to study change over time.

    The primarily Orellan localities will be detailed first, followed by the primarily Chadronian localities. Much has been published on some of these, while others are known only from museum records.

    Harrison area, northern Sioux Co., Nebraska
    Toadstool Park
    Extending south-southwest for 5 miles (8 km) from Toadstool Park is a linear outcrop of badlands that make up the type locality for the Orella (lower) and Whitney (upper) Members of the Brule Formation. To the north and east are many outcrops of the underlying Chadron Formation. Schultz and Stout (1955) subdivided these stratigraphic units into lettered subunits based on marker beds in that region: Chadron A through C, Orella A through D, and Whitney A through C. Chadron C and Orella A are separated by the top of the Upper Purplish White layer which is widespread in the region (also called the Persistent White Layer). Orella A and B meet at the base of the Lower Nodular Zone, and Orella B and C meet at the base of the Upper Nodular Zone. Orella C and D are separated by a prominent bench layer, and Orella D and Whitney A are separated by a white bed and some channels. The Chadron and Orella are highly bedded and have a number of channels within them, while the Whitney is extremely massive and is interrupted only by a few ash beds. The Chadron is about 209 feet thick in the region, the Orella 205 feet, and the Whitney 278 feet (Schultz and Stout 1955).

    Ischyromys are abundant throughout the Orella section but are particularly numerous in Orella A and D. Most of the Orella D material comes from the bench-forming layer separating Orella C and D and just above it (Diplolophus zone) in the immediate vicinity of Toadstool Park. Most of the Orella A material comes from the southern end of the linear outcrop (around Arner Ranch) and farther southeast in a large area containing only Orella A exposures (around Everson Ranch).

    Schultz and Stout's (1955) section is used to correlate all the collecting localities in the Toadstool Park area. The vast majority of specimens (300 dentaries measured) were collected in the Orella by UNSM and use Schultz and Stout's (1955) stratigraphic terminology, and nearly all of them have excellent stratigraphic data. UCM has a large collection (106 dentaries measured) all from the Diplolophus zone (Hirsch Small Jaw locality). USNM has a small collection from this area (75 dentaries measured), most of which lack good data. Four Orella A dentaries were collected by the author.

    Some other localities which lie west of Toadstool Park (but east of Munson Ranch) have been correlated with this section (Harrison, Meng, Coffee, and Eberspecher Ranches). Of the 161 Ischyromys dentaries measured (146 UNSM, 13 USNM, 1 AMNH, 1 UW) the UNSM collection has the best data.

    In addition to the Orella material listed above, 16 ischyromyine dentaries (7 UNSM, 6 FMNH, 3 AMNH) have been found in Chadron sediments of the area, mostly east of Toadstool Park (including Chadronia Pocket; Wood 1969). Ostrander (1980:76-78) reported 80 isolated teeth of I. veterior and 4 of I. douglassi from north of Toadstool Park (Raben Ranch) which have not been examined. Hough and Alf (1956) reported finding 81 ischyromyine teeth from ant hills on Chadron sediments near Orella, but Guthrie and Allen (1974) showed that this was a mixed fauna. Hough and Alf (1956) also reported finding two dentaries of I. pliacus and one maxilla of Titanotheriomys cf. wyomingensis in place in the Chadron Formation, but no specimen numbers are given. A single UNSM dentary was found high in the Whitney.

    Munson Ranch
    Munson Ranch (Formerly called Parsons Ranch, Plunkett Place, and Hall Ranch) and surrounding localities (Roberts Draw, Zerbst Ranch, and Grim Ranch) have produced the largest and most continuous sequence of Ischyromys fossils by far. Ischyromys fossils are particularly abundant in the middle Orella but range from the lower Orella to the Lower Whitney. Measured dentaries include 465 UNSM, 264 AMNH, 264 USNM, 2 ACM, and 2 UCM, and the stratigraphic zonation of most UNSM, AMNH, and USNM specimens is known to within a few feet.

    The stratigraphy for Munson Ranch is based on an unpublished section by Morris F. Skinner which was used for most of the AMNH specimens. Robert Emry created a modified version of this section that was used for the 151 USNM dentaries that have good data. The UNSM specimens were zoned with Schultz and Stout's (1955) section at Toadstool Park although correlation is difficult between the upper parts of the sections. The UNSM zonation was converted as accurately as possible to the Skinner section. According to the Skinner section the Orella is 180 feet thick and is separated from the Whitney by a large channel.

    A single Chadronian ischyromyine dentary was found 3 miles (5 km) northwest of the main Munson Ranch locality and is zoned with that section. Despite the extensive Chadronian exposures in the area, no other ischyromyines have been reported.

    Geike Ranch
    Just west of Munson Ranch are Geike, Warbonnet, and Dout Ranches from which large collections of Ischyromys have been collected. Unfortunately most of these lack enough stratigraphic data to be of any value to this study. Some 56 AMNH, 4 USNM, and 3 UNSM dentaries are zoned and are tied into an unpublished section made at Geike Ranch by Morris F. Skinner.

    Despite their close proximity, correlation between the Geike and Munson Ranches is difficult above the lower Orella. The lower Orella is 30 feet thick and bounded, as at the previously described localities, by the Persistent White Layer on the bottom and a band of nodules on the top. Zoned Ischyromys come from the lower and middle Orella but become less frequent higher in the section. They have almost exactly the same distribution as at Munson Ranch.

    Lusk area, southern Niobrara Co., Wyoming
    A large area of Oligocene sediments are exposed northeast of Lusk, especially in the areas of Indian Creek and Seaman Hills. The only easily correlatable bed between Lusk and the Nebraska localities described above is the Persistent White Layer that separates the Chadron from the Orella. Correlation between some localities within the Lusk area, except for the white layer, is also difficult. Morris F. Skinner has made several unpublished sections on which some of the AMNH specimens are zoned. Most collections simply give the level in feet above or below the Persistent White Layer. The Orella is less than 140 feet thick in this area

    Because the total number of zoned ischyromyines is not large, all localities in the Lusk area are zoned together although there may be discrepancies in the upper part of the section. This includes 124 AMNH, 17 USNM, 12 ROM, and 2 UW dentaries. The largest numbers come from the lower Orella, but some are from higher in the Orella and some are from the Chadron just beneath the Orella.

    Douglas area, southeastern Converse Co., Wyoming
    Another widespread Oligocene exposure occurs southeast of Douglas. A white layer runs through the section which has been used as the primary reference for zoning fossils, and Prothero (1982, 1985a) has shown by magnetostratigraphic studies that it is equivalent to the Persistent White Layer (Upper Purplish White layer) of Nebraska which marks the Chadron-Orella boundary. The faunal change at this boundary is much more gradual than in Nebraska, however, and characteristic Chadronian fossils are found up to 30 feet above the Persistent White Layer (Kron 1978).

    Measured ischyromyines from the Douglas area with good data include 52 UCM, 48 AMNH, 24 UW, 9 USNM, and 1 ACM dentaries. The UCM and UW material is zoned into local faunas. The AMNH and USNM material is zoned in distance from marker beds, some from the Persistent White Layer and some from a black ash layer 50 to 90 feet higher in the section (according to unpublished sections by Morris F. Skinner).

    A composite section was constructed for all the material with the Persistent White Layer at 0 feet and the black ash at 60 feet. The Orella is about 100 feet thick according to this section. As in the Lusk and Geike Ranch sections, the bulk of the material comes from the lower Orella. A few come from the upper Orella and lower Whitney. There is also a sizable collection from the Chadron, separated by a barren zone from the lowest Orella material.

    Wood (1976:272) considered all the skull material from the Douglas area, Chadronian and Orellan, to be of the Ischyromys type. Kron (1978:94-95) referred Chadronian material both to I. cf. typus and Titanotheriomys cf. veterior, and he has since found material that he considers to be T. wyomingensis because of its small size (pers. comm.). In the Orellan the material from the lower 130 feet is considered I. parvidens because of its small size, and what little material available above that is considered I. typus because of its larger size (Prothero 1982; Kron, pers. comm.).

    Chadron area, northern Dawes Co., Nebraska
    East of Toadstool Park and surrounding Chadron are a number of Oligocene exposures which contain a few ischyromyines. Measured dentaries with stratigraphic data include 39 AMNH and 17 UNSM. The UNSM and most of the AMNH Orellan specimens are zoned with reference to a white zone believed to be the Upper Purplish White layer of Toadstool Park. Some AMNH specimens from localities north of Chadron are zoned with reference to a thin blue ash that occurs 35 feet above the white layer, and a few are referenced to unpublished sections by Morris F. Skinner. The Orella is about 140 feet thick in the area. Ischyromyine fossils are concentrated in the lower 40 feet, but a few are found in the upper Orella and Lower Whitney. Most of the Chadron specimens are from UNSM and have no information other than Chadron Formation.

    Badlands National Park, Pennington and Shannon Co., South Dakota
    Although Ischyromys fossils have been recovered from the Big Badlands area in great abundance including several important type specimens, little work has been done on stratigraphic zonation. This is partly due to the early date of many of the collections. Even for those Ischyromys that are zoned, nearly all of them come from the Lower Nodular Zone (equivalent to the Orella A-B boundary at Toadstool Park but shown to be time transgressive in the Big Badlands), and the Chadron-Orella contact is marked by a significant hiatus in the region (Prothero 1985a). Because of these handicaps compared to other Orellan localities, Big Badlands specimens have not been given much attention in the analysis part of this study.

    Ischyromyine dentaries measured include 288 AMNH, 191 FMNH, 57 MCZ, 54 UCM, 15 ACM, 10 ANSP, 8 USNM, 7 SDSM, 3 TMM, and 2 UNSM. As far as stratigraphic information is available, all of these are Orellan in age except a possible early Whitneyan specimen from near Interior (AMNH) and two possible Chadronian specimens from near Scenic (MCZ). Clark and Beerbower (1967:27) also reported a single dentary from the Chadron (CM 9493), and Harksen and Macdonald (1969:15) listed Ischyromys sp. as a Chadron species. In addition to the material from the Big Badlands proper, one dentary was found at the Chadron-Orella contact near Kodoka, Jackson County; one was found in the middle Orella near Oglala, Shannon County; and two were found in the middle Chadron near Oelrichs, Fall River County (all AMNH). Two Orellan dentaries have also been recovered from the northern Black Hills, Lawrence County (USNM).

    Ischyromys typus was reported from the middle Oligocene (Orellan) in the Big Badlands by Leidy (1856, 1869; type description), O'Harra (1910:87), and Harksen and Macdonald (1969:17). Ischyromys parvidens was named for five small dentaries from the Orellan of the Big Badlands (Miller and Gidley 1920). Ischyromys was reported by Wilson (1971). Harksen and Macdonald (1969:20) also reported I. typus as a late Oligocene (Whitneyan) species in the Big Badlands.

    Of the Ischyromys dentaries measured, 176 FMNH and all 54 UCM dentaries measured are part of an ecological study of the Lower Nodular Zone by Clark and Kietzke (1967:124-125). They found Ischyromys to be the most abundant rodent in every environment, but it was particularly abundant in drier plains environments which lacked trees. Clark (1967:99) used the uniformity of I. typus and several other taxa throughout the Scenic Member (Orella equivalent) as evidence for its rapid deposition.

    Reva area, eastern Harding Co., South Dakota
    A significant Oligocene exposure occurs at Slim Buttes in northwestern South Dakota. Lillegraven (1970) has published a section where he divides the Brule formation into eight lettered units (A: Chadronian-Orellan transition; B-E: Orellan; F-H: Whitneyan). The Orellan is 265 feet thick (including Chadron-Orella transition) and the Whitneyan 175 feet thick suggesting a fast accumulation rate (Prothero 1985a:267). The largest ischyromyine collection is at the SDSM (103 dentaries measured) and is zoned to Lillegraven's section. They ranged from zones A through F with the vast majority coming from zones B and D. Unfortunately they are not zoned within Lillegraven's units which are up to 110 feet thick (Unit B).

    AMNH has a smaller collection (52 dentaries measured), some zoned to an unpublished section by Morris F. Skinner and some zoned only to lower, middle, or upper part of the Oligocene exposure. Where possible these were correlated to Lillegraven's (1970) section and included. Southwest of Slim Buttes (north of East Short Pine Hills) is a locality of Chadron sediments from which 6 FMNH ischyromyine dentaries were measured.

    Ischyromys material from Slim Buttes and from the North Dakota localities described below tends to be quite large. For this reason the material has generally been assigned to I. typus and I. pliacus (Prothero 1982). Burt and Wood (1960) assigned a fragmentary maxilla from Slim Buttes (ACM 10604) to I. troxelli.

    Dickinson area, Stark and Slope counties, North Dakota
    North of Slim Buttes in southwestern North Dakota are several more Oligocene exposures including the Little Badlands (Fitterer and Herauf Ranches) in Stark County and Chalky Buttes in Slope County. Skinner (1951) has published a composite section and has made several unpublished sections with greater detail and with which most of the 94 AMNH and 2 USNM Ischyromys dentaries measured can be correlated.

    Scottsbluff area, Scotts Bluff Co., Nebraska
    Lyman Beaver Site
    East of Lyman and south of Morrill are some low badland exposures dubbed Lyman Beaver Site by T. Mylan Stout because of the abundance of beaver fossils found there. Twenty five UNSM dentaries from this locality were measured as well as one collected by the author. These beds are biostratigraphically Orellan, but the level has not been exactly correlated (Stout, pers. comm.).

    Despite a number of significant Oligocene exposures in western Scotts Bluff County (Schultz and Stout 1955), no ischyromyines are known except at Lyman Beaver Site. The same applies to a continuation of these exposures into Goshen County, Wyoming, where the only specimen reported is a dentary of Titanotheriomys sp. from near Lingle (Stout 1937:18) which apparently is lost from the UNSM collection.

    Scotts Bluff National Monument
    The impressive Orella and Whitney exposures at Scotts Bluff have produced disappointingly few ischyromyine fossils. Schultz and Stout (1955) provided a correlated set of sections from this and other Oligocene exposures in the area, and Morris F. Skinner has also made several unpublished sections. But only 16 UNSM, 2 AMNH, and 1 USNM ischyromyine dentaries are available from the area, and some of these have very poor data. The Orella is about 180 feet thick at Scotts Bluff, and all the ischyromyines appear to come from that member.

    Weitzel Ranch
    Just north of Scotts Bluff County at Weitzel Ranch (6 miles north of Mitchell), Sioux County, is a Whitney exposure from which two AMNH Ischyromys dentaries have been collected. It appears that this exposure can be correlated with Schultz and Stout's (1955) section. These specimens are significant since no ischyromyines have been found at the major Whitney exposures at Scotts Bluff and Chimney Rock.

    Sterling area, Weld and Logan Counties, Colorado
    Galbreath (1953:57-58), in his extensive report on the Vertebrata of northeastern Colorado, reported finding more than 100 Ischyromys typus fossils in the Cedar Creek beds (early and middle Orellan), and he referred a small number of fossils from underlying Chadronian deposits to I. troxelli, Titanotheriomys cf. veterior, and Titanotheriomys? sp. He also noted a trend toward increasing size in the I. typus lineage similar to the one in Sioux County, Nebraska. Unfortunately inquiries to the University of Kansas to borrow Galbreath's material went unanswered.

    From other collections a few ischyromyine dentaries were obtained from various localities in Weld and Logan Counties, Colorado: 25 AMNH, 9 UCM, 5 YPM, 4 FMNH, 3 ACM, 1 UNSM, and 1 ROM. Most have little data. Three additional YPM dentaries comprise the material Troxell (1922) used as types for I. pliacus, and Wood (1937:190) said these came from the Cedar Creek beds of Colorado. Galbreath (1953:58) showed that this is probably in error, and the type of I. pliacus probably comes from somewhere in southeastern Wyoming (and is therefore of uncertain age). Barbour and Stout (1939) suggested that the I. pliacus type came from the same locality as the type of Diplolophus insolens, an upper Orellan index fossil, because O. C. Marsh apparently collected them on the same day (August 22, 1870).

    Medicine Bow area, Albany and Carbon Co., Wyoming
    Little Medicine
    A single UW ischyromyine dentary found in an arkose matrix comes from a locality in northwestern Albany County. According to UW catalogs, the age is believed to be early Chadronian.

    Harshman Quarry
    An ischyromyine dentary and maxilla, Chadronian in age, come from one of the quarries shown on Harshman's (1968) map. These quarries are in northeastern Carbon County.

    Alcova area, southern Natrona Co., Wyoming
    Flagstaff Rim
    The section at Flagstaff Rim is 750 feet thick and covers virtually all of Chadronian time (about 6 million years). As such it is the one exception to the generally discontinuous nature of Chadronian deposits. A number of continuous ash beds are present in the section which allow easily correlation between the various canyons. Emry (1970, 1973) has studied the stratigraphy in detail and has supervised most of the fossil collecting in the area. Fortunately a sizable collection of ischyromyines has been recovered, almost all of which can be zoned to Emry's section (70 UNSM, 52 AMNH, 1 UW, 1 FMNH). These fossils are found continuously through the middle part of the section but are very rare in the upper part. In the lower part of the section they are concentrated in two small pockets.

    Wood (1976) was the first to study the material in question. He concluded that all 14 skulls available to him from the middle part of the section were of Titanotheriomys, but a single skull from the bottom of the section he identified as Ischyromys.

    Flynn (1977) did a more detailed analysis and tried to determine the number of coexisting lineages and the patterns of change through time. From 16 skulls with snout features exposed he concluded that Ischyromys and Titanotheriomys coexisted through the section. Most of the upper teeth associated with these skulls could not be distinguished between the genera, but a few of the Titanotheriomys skulls had larger teeth, suggesting the possibility that two species of that genus coexisted. Flynn (1977) took length, anterior width, and posterior width measurements on all the lower cheek teeth available to him and also noted the presence or absence of accessory cusps and ridges. From lumped samples at each level Flynn noted statistically significant increases in tooth size and incidence of accessory cusps through time. He also noted a marginally significant increase in the ratio of length to average width of M/2 over time. A few additional fossils are included in my study that were not available to Flynn (1977).

    Ledge Creek
    Thirteen miles (21 km) southeast of Flagstaff Rim is another extensive Chadronian outcrop on the tributaries of Ledge Creek. Morris F. Skinner has made an unpublished section of the locality. Prothero (1985b) showed by magnetostratigraphic techniques that it correlates with the lower half of the Flagstaff Rim section. Only five ischyromyine dentaries (3 AMNH and 2 USNM) have been recovered from Ledge Creek.

    Lost Cabin area, northwestern Natrona Co., Wyoming
    Black (1971:203-204), using screening techniques, recovered five isolated cheek teeth of ?Ischyromys sp. from the late Eocene Tepee Trail Formation at Badwater Creek. Only one of these, a left M/1 or M/2, is from a dentary. If the taxonomic assignment is correct, these are the oldest known ischyromyines. Black (1971) stated that they bear resemblance to molars of I. [Titanotheriomys] douglassi (Black believed that Ischyromys and Titanotheriomys to be synonymous). Wood (1976:273) predicted, based on his assumption that Ischyromys predates Titanotheriomys, that these specimens will prove to be Ischyromys if diagnostic skull material is ever found. This material has not been examined by the author.

    Lander area, Fremont and Natrona Co., Wyoming
    Western Beaver Divide
    Beaver Divide (also called Beaver Rim) is a long east-west trending exposure in the Gas Hills area of central Wyoming between Lander and Casper. Here a sequence of Eocene through Miocene rocks is exposed including up to 650 feet of White River Formation (Van Houten 1964). Emry (1975) cleared up some biostratigraphic problems in western Beaver Divide and stated that all the fossils from the White River Formation indicate a Chadronian age.

    Granger (1910:240-241) recovered a skull and jaws from Devil's Gap at the western end of the divide which he said was identical with Ischyromys veterior from Pipestone Springs and which Matthew (1910:63) used as a paratype for that species. Wood (1937:198) made this material the type for Titanotheriomys wyomingensis. Van Houten (1964:68-69) lists additional Titanotheriomys material collected near Green Cove, Devil's Gap, and Dishpan Butte, all in south central Fremont County. Five AMNH dentaries are included in the present study.

    Cameron Spring
    Teacup Butte, near Cameron Spring, is a fossiliferous White River outcrop just north of the eastern end of Beaver Divide. It is part of the Oligocene fill of a channel that cuts about 680 feet into Eocene beds (Van Houten 1964:64). Hough (1956:531) reported Titanotheriomys sp. from the locality and noted the similarity of the Cameron Spring fauna to that at Pipestone Springs. Van Houten (1964:70) reported T. cf. veterior and Love (1970:67) reported Ischyromys sp. from the same site. A total of 28 dentaries were measured for this study (21 USNM, 3 AMNH, 2 CM, 2 UCM).

    West Canyon Creek
    Three miles east of the Cameron Spring locality and straddling the Fremont-Natrona county line are the exposures of West Canyon Creek. Van Houten (1964:70) reported I. cf. typus from this locality. Robert J. Emry (pers. comm.) has done extensive fossil collecting and stratigraphic work on these sediments (yet to be published), and he has concluded that they are part of a channel fill that is larger and considerably older than the one at Cameron Spring. The ischyromyines (16 USNM dentaries measured) are larger than those from Cameron Spring and have a much higher incidence of accessory cusps in the lingual valleys of the molars.

    Dillon area, Beaverhead and Madison Co., Montana
    Diamond O Ranch
    Northeast of Dillon on the south side of the Big Hole River, Beaverhead County, is a locality from which a single ischyromyine M/1 (MUPM 2586) has been recovered. The locality is possibly late Duchesnean in age (Fields et al. 1985:33).

    McCarty's Mountain
    On the north side of the Big Hole River in Madison County are the local deposits of McCarty's Mountain. Fields et al. (1985) considered these sediments to be early Oligocene while Emry et al. (1987) believed them to be middle Chadronian (but older than the Pipestone Springs beds). Black (1968) assigned all the ischyromyine material from this locality to his new species, I. douglassi (considered Titanotheriomys by Wood 1976). Twenty dentaries (13 CM, 6 MUPM, 1 AMNH) were measured for this study.

    Butte area, southern Jefferson Co., Montana
    Haxby Ranch
    Southeast of Butte and just south of Little Pipestone Creek are some small exposures from which a few ischyromyines have been recovered (2 MUPM dentaries measured). According to the MUPM catalogs these sediments are late Chadronian in age. Kuenzi and Fields (1971) reported Titanotheriomys veterior and ?Ischyromys pliacus from this locality.

    Little Pipestone Creek
    East of Haxby Ranch are some rather extensive exposures known as Little Pipestone or Little Pipestone Creek. Kuenzi and Fields (1971) reported Titanotheriomys veterior and ?Ischyromys pliacus from this locality, and Fields et al. (1985) considered it to be middle to late (?) Chadronian). Twenty two dentaries were measured for this study (9 MUPM, 5 FMNH, 4 USNM, 3 CM, 1 AMNH). Kuenzi and Fields (1971) also reported possible occurrences of T. veterior from two localities and ?Ischyromys sp. from one locality in the same area but north of Little Pipestone Creek.

    Pipestone Springs
    Just west of Pipestone Hot Springs, east of Butte, are the classic beds of the Pipestone Springs local fauna. Prothero (1984) has shown using magnetostratigraphic and biostratigraphic data that this fauna is early middle Chadronian in age (see also Fields et al. 1985). Prothero's (1984) work suggests that the Pipestone Springs beds cover about one million years of time (as long as the entire Orellan age), but very few ischyromyine fossils have been collected with reference to their location in the section.

    Matthew (1903:211-212, 1910:63) named Ischyromys (Titanotheriomys) veterior for a skull from Pipestone Springs. In addition to T. veterior, Wood (1937) recognized a larger form that he assigned to I. pliacus (as did Black 1965:8), but he later considered it to be a form of Titanotheriomys (Wood 1976, 1980). Black (1968) and Kuenzi and Fields (1971) recognized only T. veterior, but Tabrum and Fields (1980) recognized T. veterior and ?Ischyromys sp., and they showed T. veterior as being present at more sublocalities at Pipestone Springs than the second (larger) form. A total of 195 dentaries were measured from the main Pipestone Springs locality (69 USNM, 63 AMNH, 46 MUPM, 15 FMNH, and 2 CM). In addition, 4 MUPM dentaries come from the smaller Fence Patch locality 3/4 mile southeast of the Pipestone Springs locality.

    Easter Lily
    Just north of Pipestone Springs are some rather extensive exposures of Orellan sediments below the Easter Lily Mine. Kuenzi and Fields (1971) reported ?Ischyromys sp. from this area. One dentary with only a premolar was measured for this study (MUPM 7843).

    The rarity of ischyromyines from Orellan sediments in Montana is quite a contrast to their abundance in Nebraska and surrounding states. Except for the single specimen listed above and one from Canyon Ferry (listed below), no Orellan ischyromyines are known from Montana. In that state they seem to have been much more numerous during the Chadronian.

    Helena area, Broadwater and Lewis & Clark Co., Montana
    Thompson Creek
    A few ischyromyines have been recovered from localities south of Toston in southern Broadwater County. These sediments are considered to be early middle Chadronian like the Pipestone Springs beds (Emry et al. 1987). Freeman et al. (1958:509-510) reported Ischyromys troxelli and Titanotheriomys cf. veterior, and Klepper et al. (1971:13) reported T. cf. veterior and Titanotheriomys sp. Four USNM dentaries were measured from this area.

    Southern Canyon Ferry
    On the western shore of Canyon Ferry Lake, northern Broadwater County, is a locality from which one USNM dentary was recovered and which was measured for this study. White (1954) described this locality and reported it as Chadronian in age.

    Northern Canyon Ferry
    Around the Canyon Ferry dam in southern Lewis and Clark County are several Chadronian and Orellan localities. White (1954) reported Ischyromys cf. pliacus and Titanotheriomys veterior (3 specimens each) from a Chadronian bluff south of the Canyon Ferry Lake offices. Three USNM dentaries from this locality have been measured. Five MUPM dentaries from a locality to the northeast were also measured, and the MUPM catalogs list this locality as ?Late Chadronian. One USNM dentary comes from an island in Canyon Ferry Lake (formerly Cemetery Hill), and White (1954) and Fields et al. (1985) list this locality as Orellan in age.

    Southwestern Saskatchewan Province, Canada
    Cypress Hills
    The Cypress Hills in southwestern Saskatchewan have produced a number of ischyromyine fossils, all isolated teeth. According to Emry et al. (1987) the Cypress Hills Formation from which they come covers possibly all of Chadronian time, but the largest number of specimens come from the Calf Creek local fauna which is late early Chadronian in age (Storer 1978).

    Lambe (1908:56) reported a single molar from Cypress Hills which he assigned to I. typus, but Russell (1934:56) reassigned it to I. typus nanus which Wood (1937) synonymized with I. parvidens. Russell (1972:28-30) erected the species I. junctus to cover all ischyromyines from Saskatchewan, and Storer (1978) concurred with this. A total of 29 lower cheek teeth were measured for this study (14 SMNH, 12 ROM, and 3 NMC). Of these, all 14 SMNH and 4 of the ROM teeth are from the Calf Creek local fauna.

    Swift Current
    Two faunas in the lower Cypress Hills Formation of Eocene age have produced isolated teeth that are similar to Ischyromys. The earlier of these is the Swift Current local fauna (Uintan). Storer (1984:96-99) named the material of interest from this locality Microparamys solidus, and he has suggested the possibility that this species is an ancestor of Ischyromys (Storer, per. comm.). Five SMNH lower cheek teeth were measured for this study, but their relationship to ischyromyines have not yet been investigated in detail.

    Of slightly younger age (Duchesnean) is the Lac Pelletier Lower Fauna. Storer (1988:90) reported 9 isolated teeth which he believes to be an undescribed and very primitive species of Ischyromys.

    Big Bend area, Jeff Davis and Presidio Co., Texas
    Ash Spring
    In western Jeff Davis County, 2 miles from the Mexican border, is the Ash Spring local fauna. The fauna appears to be middle Chadronian and slightly older than the Pipestone Springs local fauna (Emry et al. 1987). Wilson (1978) believed it to be the youngest of the Oligocene faunas of Trans-Pecos Texas.

    Harris (1967) did a detailed paleontologic study of the Ash Spring fauna and reported three ischyromyine dentaries with teeth, all of which were measured for this study. Two of these (from the same individual) he considered to be Titanotheriomys veterior and the other he considered to be a new, smaller species of Titanotheriomys. Wood (1974:29) felt that the size difference did not warrant taxonomic distinction, and he considered T. veterior to be the only species of the group at Ash Spring.

    Porvenir local fauna
    The Porvenir local fauna of Presidio County, Texas, is the southernmost ischyromyine locality and also one of the earliest. Radiometric dates place the Porvenir local fauna at approximately the Duchesnean-Chadronian boundary (Wilson 1978). Wood (1974) created the new species I. blacki for the skull and single dentary found there, and the dentary (TMM 41211-8) was measured for this study.

    The absence of ischyromyines from Texan localities with ages intermediate between the Porvenir and Ash Spring deserves notice. Since ischyromyines from the two localities are vastly different there is no reason to assume the presence of a continuous lineage from one to the other. On the other hand the ischyromyine sample is so small from the localities where it is present that it is very possible that a similar presence in another locality could have gone unnoticed.

    METHODS
    The initial purpose of this project was to study in detail the patterns of evolution in a lineage of fossil mammals. The ischyromyines were chosen because there were many large collections available with good stratigraphic data and because there were claims that Ischyromys had undergone measurable evolutionary change. The objective was to take a large number of measurements on a large sample of fossil specimens and use plots and multivariate statistical techniques to study the variation within species, the relationship between species, and the patterns of change in individual lineages.

    For rodents such as Ischyromys the only elements that are usually identified are skulls and jaws, and lower jaws outnumber skulls and upper jaws by nearly ten to one. Each complete jaw half contains one ever-growing incisor and four rooted cheek teeth (three molars [M1-3] and one molariform premolar [P4]) separated from the incisor by a diastema. Upper jaws also contain a rudimentary peg-like premolar [P3]. Since cheek teeth have the most complexity and are easiest to make consistent measurements on, they form the basis of this study. I originally intended to measure both upper and lower cheek teeth, but only lower jaws are included in this study. Results of my study on skulls and upper cheek teeth will appear subsequently.

    Collections of ischyromyines from many institutions were used in this study. Of 4015 dentaries (or isolated lower cheek teeth; 2042 left and 1973 right) that were photographed and digitized, 1237 were from the American Museum of Natural History (AMNH [232] and F:AMNH [1005]), 1035 from the University of Nebraska State Museum (UNSM), 652 from the U.S. National Museum (USNM), 429 from the Field Museum of Natural History (FMNH), 227 from the University of Colorado at Boulder (UCM), 113 from the South Dakota School of Mines (SDSM), 78 from the University of Montana (MUPM), 64 from Harvard University's Museum of Comparative Zoology (MCZ), 31 from the Royal Ontario Museum (ROM), 31 from the University of Wyoming (UW), 29 from the Amherst College Museum (ACM), 22 from the Academy of Natural Sciences of Philadelphia (ANSP), 21 from Carnegie Museum (CM), 19 from the Saskatchewan Museum of Natural History (SMNH), 10 from Yale University's Peabody Museum (YPM), 9 from Texas Memorial Museum (TMM), and 3 from the National Museum of Canada (NMC). In addition I collected 5 dentaries myself. Of these, the F:AMNH, UNSM, USNM, UCM, and SDSM collections have the best stratigraphic data. The TMM, CM, FMNH, SMNH, ROM, and NMC collections provided valuable fossils, especially for Chadronian localities where this rodent was very rare.

    Photography
    I decided that the best way to take measurements on the small (2-4 mm length) cheek teeth was to take a closeup photograph of each dentary in occlusal and lingual view and use a computer digitizer to take measurements from the photographs. A labial view of the teeth was partially blocked by the ascending ramus of the jaw (when preserved).

    To make photography quick and consistent, I constructed a cubical wood block with 11 cm sides to hold ischyromyine dentaries for photographing. A wide slot in the top of the block was filled with foam rubber which was cut to conform to the shape of the dentaries. The dentaries were placed between the foam and a band of fine, taut fishing line around the upper edge of the block. One side of the block holds right dentaries and the other side left dentaries. Each dentary was inserted so that the occlusal surface was at the level of the top of the block and the lingual surface was even with the side of the block. Using this block an occlusal photograph could be taken, the block turned on its side, and a lingual photograph taken, all without having to adjust the fossil or the camera. A measuring grid was glued to the foam on the top and side of the block so that a scale would automatically be included in each photograph. With this system it took approximately 5 minutes per specimen to photograph it and copy the data included with it. All dentaries were photographed at Harvard University (MCZ) except the AMNH (including F:AMNH and SDSM) and USNM collections which were photographed at the American Museum and National Museum respectively using the same equipment.

    For all photography a Canon FTb camera was used with a Canon FD 50 mm macro lens and extension tube and with the focus always fully extended for minimum focal distance. With this setup the image on the film is exactly the same size as the object photographed (ratio 1:1). For ease in viewing the subtle details of the teeth, Kodak Ektachrome (EPY404 Tungsten 50 ASA) slide film was used to give a positive color image. Two tungsten floodlamps were used for illumination. Film was bulk loaded from 100 foot rolls and developed in the lab but not mounted. Developed rolls of film, with photos of about 20 dentaries each, were numbered, wound, and stored in film cans. Rolls shot at MCZ are numbered 001 through 106, those shot at AMNH are numbered 193 through 261, and those shot at USNM are numbered 351 through 384.

    Digitizing
    The job of choosing characters to measure was a difficult one since it was uncertain what measurements would prove most valuable. Former numerical studies were based mainly on tooth lengths and widths. All the lower cheek teeth, including the deciduous and adult fourth premolar, have the same basic pattern of cusps and valleys, so homologous measurements could be made on all four teeth. I decided to make an area-periphery-centroid measurement on the occlusal surface of each tooth even though this added significantly to the digitizing time. All other data were obtained by taking X-Y coordinates of various features of the cheek teeth and jaws and calculating measurements therefrom. Nine measurements were taken around the periphery of each tooth (Figure 3). Three of these are at valley mouths (3, 6, and 8), two are at the anteroposterior extremes of the tooth (1 and 5), and four are at the lateral extremes of various lobes (2, 4, 7, and 9). These points remain consistent and recognizable from the time the teeth erupt until they are quite heavily worn.

    Measurements within the teeth's occlusal surface are complicated by wear patterns. Erupting teeth have five major cusps connected by ridges, but by old age the teeth are worn down to a nearly flat, featureless surface. Cusp peaks are initially rounded and are the first features to wear, so marking their location is impractical. Valley walls and valley bottoms are linear rather than point features, but they can be used to help measure tooth proportions. The labial and anterior lingual valleys are deep and have essentially vertical posterior walls, so a measurement was made on each of these at the most lateral point where the wall was perpendicular to the anteroposterior tooth axis (10 and 14 on Figure 3). Points were also digitized at the top of each valley although these points are known to migrate in later wear stages (11, 12, 15, and 16). Two measurements were made at the top of the anterior lingual valley because it is rather square in shape. In some specimens a cusp or ridge (anterior medial accessory cusp) is present on the anterior side of the anterior lingual valley, so a measurement was taken at the most posterior extension of that cusp when present (13). This measurement is meaningless for teeth lacking the accessory cusp, which is usually the case.

    Several subjective integer values were also given for various tooth features. A value was given for the wear stage of each tooth ranging from 0 for unerupted teeth to 9 for extremely worn teeth. Table 1 describes the basis for these values, and Table 2 shows the number of teeth with each value. The anterior medial accessory cusp discussed above, when present, can vary in size from a tiny knob or ridge to a large structure that spans the entire valley. Less frequently the posterior lingual valley also contains such a cusp or ridge (posterior medial accessory cusp). In addition, cusps also sometimes occur at the mouths of the labial and anterior lingual valleys (labial and lingual accessory cusps). A value was given to the size of each of these four accessory cusps ranging from 0 for absent cusps to 4 for unusually large and well-developed cusps or ridges that span the entire valley (Table 3). Three of these cusps were judged in occlusal view (18, 19, and 20 on Figure 3) and the forth in lingual view (10 on Figure 4). This gives a total of 20 measurements per tooth in occlusal view in addition to the area-periphery-centroid measurements.

    In lingual view a measurement was taken at the top of each of the two lingual cusps (although the height of these cusps is heavily influenced by wear; 1 and 4 on Figure 4). Measurements were also made in the two lingual valleys (2, 3, and 5). When a cusp was present at the mouth of the anterior lingual valley, a measurement was taken on each side of it; when it was absent the two measurements were both made at the bottom of the valley. Three measurements were also made along the boundary between the enamel and the dentine at the base of each tooth: one at the anterior end, one at the posterior end, and one in the middle (6, 7, and 8). A measurement was also taken where the middle of the tooth meets the top of the jaw (9). The last measurement (10) was the subjective value for the size of the lingual accessory cusp discussed above, making ten total measurements on each tooth in lingual view.

    In addition to the 31 measurements on each tooth, three measurements were made along the ventral margin of the jaw in lingual view: one directly under the P/4-M/1 boundary (1), one directly under the M/1-M/2 boundary (2), and one under M/3 in the center of the curve where the ventral jaw margin most closely approaches the tooth row (3; Figure 5). The measurements calculated from the digitized data and used as the basis of this study are described below (page 63).

    To get measurements from the photographs, a Simon Omega darkroom enlarger was used to project the images onto a table with 10.4X magnification. A Numonics 1224 digitizer was used to take measurements (in cm) and input them into data files on a Leading Edge Model D computer. A total of 127 measurements were made on each dentary. The first four were made by circumscribing each of the four cheek teeth in occlusal view, and output consisted of four numbers: occlusal area, periphery, and X and Y coordinates of the centroid. The digitizer allowed this to be done in a single operation with automatic loop closure. The other 123 measurements consisted of X and Y coordinates of various points. The twenty occlusal point measurements were made on each tooth, the film was advanced one frame, and the 10 lingual point measurements were made on each tooth. The last three point measurements were made along the ventral margin of the jaw in lingual view as described above. Following the digitizing of each specimen the film was advanced one frame to the occlusal view of the next dentary, the digitizer was reprogrammed for doing loops, and the number of the next specimen was entered into the computer. Digitizing took approximately seven minutes per dentary.

    Missing values were entered as follows when a tooth or part thereof was not available for measuring. For the area-periphery-centroid measurements the digitizer arm was held stationary while the measurement was taken, resulting in a zero being entered for the area and periphery values. For missing point measurements, wear stages, and cusp size values the digitizer arm was positioned so as to enter a negative value for the Y coordinate. The COMPRESS.BAS program described below converted all missing measurements to "-9" for all entries.

    Data Manipulation
    To facilitate entering and checking the data and calculating measurements from them, I wrote three computer programs: DIGITIZE.BAS, COMPRESS.BAS, and MEASURE.BAS. These were written in Microsoft GW Basic and run on an IBM PC/XT computer. DIGITIZE.BAS was written as a general software interface between the Numonics 1224 digitizer and the IBM PC, and it accepts measurements from the digitizer and enters them into a data file on the computer. Each set of measurements (2 for X-Y point coordinates, 4 for area-periphery-centroid measurements) is entered on a line along with a group number, specimen number, and measurement number.

    Data files produced by DIGITIZE.BAS are quite large and sometimes contain incorrect values due to digitizer or operator error, so COMPRESS.BAS was written to check for errors and put the data into a compact format with only one index number per specimen (888.99 where 888 is the film roll number and 99 is the specimen number on the roll). The digitizer occasionally gives erroneous values (either zero or a ridiculously large number) for the area or periphery, so COMPRESS.BAS checks for unusual values for these measurements. It also checks for non-consecutive measurement numbers and for tooth wear and accessory cusp size values that are too large. This scheme easily exposes measurements that are out of sequence. When errors were found, the problematic specimens were redigitized and the data files updated.

    MEASURE.BAS takes compressed files and calculates a set of 8 measurements for each jaw and 26 measurements for each tooth (112 total measurements for each dentary; see page 63 below). It also multiplies all values by 0.96 so that measurements represent true mm values on the original fossils. The program uses a number of techniques to calculate these measurements. It first establishes an axis for both the occlusal and lingual views of each tooth, and most of the length and width measurements are calculated relative to the axes. In many cases this gives more meaningful values than mere point to point distances. Several angles are calculated as well. The measurements are printed into five output files: one for each cheek tooth and one for jaw measurements. The output files are formatted for easy input into the database program described below.

    Data Management
    I designed a relational database structure to give maximum flexibility to the use of the data. This was done on an IBM PC/XT computer using WordPerfect Corporation's database program, DataPerfect 2.0. The structure contains eight linked panels, five for measurements from COMPRESS.BAS and three for catalog, locality, and stratigraphic data derived from specimen and locality cards, field notes, maps, stratigraphic columns, published materials, etc. The three latter panels are hierarchical. Each "specimen" belongs to a "locality" and each "locality" belongs to a "section." Each "locality" contains all the specimens from a specific collecting locality in a particular museum collection. Each "section" contains all the localities from a specific region (for all museum collections) that can be correlated on a single stratigraphic column. Each dentary has one unique record in each of the following panels: Specimens, Jaw Measurements, P/4 Measurements, M/1 measurements, M/2 Measurements, and M/3 Measurements. Figure 6 shows an sample of each type of panel.

    Each specimen belongs to a section and (when possible) is assigned a stratigraphic level value for that section. Values are measured in feet above or below the Chadronian-Orellan boundary or from the base of the section and are based on information provided by collectors (specimen labels, field notes, etc.). An error value is also assigned to each specimen indicating (as far as possible) the accuracy of the level value. When a fossil is assigned to a stratigraphic range, the middle value is used as the level and half the range is used for the error (20 to 30 feet above base of section = 25 +/- 5). When a fossil is assigned to a stratigraphic unit, the level used is the middle of the unit and the error is half the thickness of the unit. When a single value is given relative to a marker bed, an error is concocted based on the assumed precision of the number (if fossils are assigned in 10 foot increments, the error is 5). When no stratigraphic data is available, an error value of 99 is assigned and the level value is considered meaningless.

    The relational database provides the user with unsurpassed flexibility with the data. Data can be easily accessed and modified, and searches can be conducted based on any combination of fields. Calculated fields can hold values created from formulas using other fields as variables. Any combination of field values can be exported from any or all panels and can be selected based on templates or ranges of one or many fields and can be sorted according to several indexes. These exported data files can be used for making plots, doing statistical analyses, etc.

    Measurements Used
    The MEASURE.BAS program calculates 9 measurements for each jaw and 26 measurements for each tooth for input into the database. Jaw measurements are listed in Table 4 and diagramed in Figure 7. The first three represent the depth of the three points along the ventral margin of the jaw from the tooth row as defined by a line between the base of M/1 and M/2. The fourth is the distance between the posterior point on the ventral jaw margin and the base of M/3. Measurements 5 and 6 are distances between the points on the ventral jaw margin along a line parallel to the one established above. Measurements 7 and 8 are the angles (in degrees) made between pairs of these points and that line. The program adds 30 to each angle to insure a positive value. The last measurement is an indicator of whether the jaw is a right or left dentary. This was used for error checking only.

    Tooth measurements are listed in Table 5 and diagrammed in Figures 8 and 9. The first two measurements are the area and periphery. The square root of the area is used to make it more comparable to the linear measures. Most of the measurements are based on an axis system, the axis being defined by a line from the mouth of the anterior lingual valley to the mouth of the labial valley. Measurement 3 is the tooth length, and measurements 4, 5, and 6 are the anterior, medial, and posterior widths, all based on this axis grid. Measurements 7 through 11 are the grid measurements from various tooth features to the posterior end of the tooth. Measurements 12 and 13 are simple point to point distances measuring the dimensions of the anterior lingual valley.

    The lingual measurements are also based on an axis system, the axis being defined by a line between the anterior and posterior margins of the tooth where the enamel and dentine meet. Measurements 14 through 17 are the heights of the lingual peaks and valleys above this axis. As stated above, the cusp heights are heavily influenced by wear. Measurement 18 is the width of the cusp at the mouth of the anterior lingual valley, also based on the axis grid.

    Measurements 19, 20, and 21 are angles (in degrees) calculated by the MEASURE.BAS program from the occlusal view data. Measurement 19 is the angle between the posterior wall of the anterior lingual valley and the grid axis. The program adds 45 to the angle to insure that it is positive. Measurements 20 and 21 are angles made between three points in the anterior lingual valley. The latter one only has meaning if an accessory cusp or ridge is present in the valley (see page 54). Measurements 22 through 26 are the wear stage and cusp size values described in Tables 1 and 3.

    The database calculates a number of additional measurements from the input measurements. Only one is calculated for the jaw (Table 4). It is measurement 7 minus measurement 8 (plus 30 to insure that it is positive), and it is a measure of the curvature of the ventral margin of the jaw. Many additional measurements are calculated for each tooth (Table 5). Measurement 27 is the maximum of the three tooth widths. Measurement 28 is the square root of the occlusal area divided by the periphery, and it is a measure of the roundness (smoothness) of the tooth. Measurements 29 through 36 (except 32) are lengths of various tooth features divided by the tooth length, giving a proportional size for these features. Measurement 32 compares the anterior width with the posterior width. Measurement 37 is the width of the anterior lingual valley multiplied by the angle between its posterior and labial walls. It was noticed that specimens of Titanotheriomys from Pipestone Springs tend to have a large value for both of these variables, so their product gives an even more distinctive character. Measurements 38 and 39 are the ratios of the anterior cusp height and valley height and the posterior cusp height and valley height, respectively, in lingual view, and they give proportional measures of cusp height and valley depth.

    Plots and Statistics
    Variables were exported from the database for the various analyses described in the next section. Plots and summary statistics were made using WordPerfect Corporation's spreadsheet program, PlanPerfect 3.0. Factor analyses, discriminant analyses, and regressions were run on an IBM PC/XT computer using BMDP Statistical Software. Cluster analyses and multidimensional scalings were run on a VAX/VMS mainframe computer using SPSS-X version 3 statistical software.

    This thesis was written using WordPerfect version 5.0 word processing software and takes advantage of this program's text integrated graphics features. Plots were imported as graphics files from PlanPerfect to WordPerfect. The thesis was printed on a Hewlett-Packard Laserjet Series II printer with Dutch typeface from Bitstream Fontware.

    STATISTICAL ANALYSES
    Size vs. Time Plots
    To get an initial idea of how ischyromyines changed over time, a number of scatter plots are shown with size of M/2 (the most commonly preserved tooth) vs. level in the section for the major localities with good stratigraphic control (Figures 10 to 18) [Footnote: Tooth size on these plots is the sum of the square root of occlusal area, occlusal periphery divided by three, length, anterior width divided by two, medial width divided by two, and posterior width divided by two. This sum of measurements was found to reduce the coefficient of variation and make bimodal distributions more visible compared to using any single measurement.]. The Toadstool Park and Munson Ranch sections of northwestern Nebraska cover the entire Orellan and have by far the most data points (Figures 10 and 11). Very few fossils have been found above or below the Orella in the region. In both these sections a distinct change can be seen between the lower Orella (0 to 33 feet) and the middle and upper Orella above (33 to 200 feet). In the lower Orella, shown best in Figure 10, the mean tooth length is quite small and the distribution appears right skewed or bimodal. The mean is larger and the distribution more symmetric for the upper Orella, and this pattern remains similar through 170 feet of section with the possibility of a slight size increase over time.

    The obvious question to ask is whether the transition from the lower Orellan species to the upper Orellan species represents phyletic evolution or replacement. The skewed distribution of lower Orellan specimens (compared to a symmetrical upper Orellan distribution) suggests that more than a single species is represented there. The long right tail of the distribution corresponds well with the distribution of the upper Orellan specimens, so perhaps the abrupt change at the top of the lower Orella represents the extinction of a smaller species and the proliferation of a larger species that exists in smaller numbers below the boundary. It will be shown below that this lower Orella distribution is not the result of sloppy collecting (page 111).

    Ischyromyines from other sections in northwestern Nebraska and eastern Wyoming show a pattern similar to Toadstool Park and Munson Ranch, but with much less data (Figures 12 to 15). The increase in mean size from the lower to the middle Orella can be seen at all these localities, but the right skewed distribution in the lower Orella is only obvious in the Douglas section (Figure 14).

    The northern sections at Slim Buttes and Little Badlands (Figures 16 and 17) are distinct from the others in their total lack of a small form in the early Orellan. The entire population from these sections corresponds well with the large population of the middle and upper Orella of Nebraska. A gradual increase in mean tooth size is noticeable, and some of the highest specimens in both sections are larger than any along Pine Ridge.

    The Flagstaff Rim section (Figure 18) is the only complete Chadronian section, and the plot shows a very strong suggestion of multiple species. Flynn (1977) concluded that three concurrent species are represented in this section, two small ones (based on skull differences) and one large one. Figure 18 shows a large population with an even smaller mean size than the lower Orella population extending from 50 to 450 feet in the section. A larger but rarer form extends from 300 to 700 feet. The rarity of specimens from the upper part of the section leaves some uncertainty as to the fate of these lineages. Late Chadronian specimens have been found at the Douglas localities 140 km away, which display a bigger size range than all the Flagstaff Rim material combined (Figure 14), but skull differences cast doubt on the relationship between the Flagstaff Rim and Douglas populations.

    Although some inferences can be made from these simple size vs. time plots, they leave considerable ambiguity and show the limitations of studying size alone. They do, however, lay some groundwork for further investigation by suggesting which groups of fossils might be considered as single species in order to evaluate correlation between the many shape characters measured.

    Principal Components Analyses
    The best case for a large population of a single species among the above plots is the upper Orellan specimens from northwestern Nebraska. A number of species have been named from this population, but all are either chronospecies distinguished by size (which seem precluded by the above plots) or are based on single specimens and probably represent individual variation (which has never been studied in the material involved, mainly skulls). A principal components analysis with Varimax rotation was run on 641 M/2's from Toadstool Park and Munson Ranch with wear stages of 2 to 4 and from levels 50 to 185 feet with level errors of 0 to 20 feet. The analysis includes 27 variables: the 26 standard variables contained in the database for each tooth, plus the product of the posterior angle and the width of the anterior lingual valley (measurement 37; Table 5). The correlation matrix is shown in Table 6 and the factor loadings in Table 7.

    Correlation Matrix
    As can be seen in the correlation matrix, all the characters that measure gross tooth size in occlusal view (1-6) are strongly correlated. The three tooth width measurements (4-6) are much more correlated with each other than with tooth length (3). Tooth length is strongly correlated with distances between various tooth features and the posterior end of the tooth (7-11), especially the mouths of the labial and anterior lingual valleys (7). This character, in turn, is the measurement to which the distance between the mouth of the posterior lingual valley and the end of the tooth (8) is most correlated (
    Figure 8 and Table 5). Another group of strongly correlated characters consist of the heights of the cusps and valleys in lingual view (14-17) since these are all in part measuring crown height. Wear stage has a strong correlation only with the height of the cusps in lingual view since these are the only wear-dependent characters in the analysis. Since only teeth that are fully erupted and mildly worn (wear stages 2-4) were included, few characters are correlated with wear stage. If later wear stages were included, it would affect other characters as well.

    Correlations between presence (and size) of accessory cusps and other characters are of particular interest since there is little supposition as to the result. While there are no strong correlations, the size of each accessory cusp is positively correlated with all the gross tooth size measurements (1-6) and cusp heights (14, 16). These accessory cusp size measurements, while subjective, were made relative to tooth size and are therefore not size dependent. If these correlations are significant and not due to any type of methodological bias, they suggest an allometric relation between tooth size and presence of accessory cusps.

    Size of the lingual cusp (26) is strongly correlated with the width of that cusp (18), but this is expected since they are measuring the same feature and since both are zero when the cusp is absent. There is significant correlation between the anterior and posterior medial cusps (24, 25), mainly because the latter is rarely present without the former even though it is the rarest cusp of all. The labial and lingual accessory cusps (23, 26) also display some correlation with each other but not with the medial cusps.

    Factor Loadings
    Several principal components analyses were run on this data set using different numbers of factors. Eight factors had eigenvalues above one, and the analysis with eight factors was the most interpretable (
    Table 7). Factors 1, 2, and 3 clearly represent tooth length, width, and height respectively. All the variables that measure the distance between tooth features and the posterior end of the tooth (3, 7-11) load on factor 1. The three tooth widths load on factor 2. Occlusal area and periphery load on both factors 1 and 2 since they measure tooth length and width. All the cusp and valley height measurements in lingual view (14-17) load on factor 3.

    Factors 4 and 5 deal with the shape of the anterior lingual valley. Measurements loading most strongly on factor 4 are the width of the valley (13) and this width multiplied by the posterior angle of the valley (37). The anterior angle of the valley (21) loads negatively on this factor, and the posterior angle of the valley (20) and the size of the anterior medial cusp (24, found in the valley) load on it with smaller positive values. So factor 4 deals with the anteroposterior width of the valley and with the size and position of the anterior medial cusp which it contains. Measurements loading most strongly on factor 5 are the orientation of the posterior wall of the valley (19), the negative of the posterior angle of the valley (20), and the labial-lingual length of the valley (12). So factor 5 deals with mainly with the orientation and length of the valley's posterior wall.

    Factors 6, 7, and 8 deal with sizes of the accessory cusps. These cusps are rare in all the large samples, so species are unlikely to be distinguished by their presence or absence but may differ in their relative abundance. The size and width of the lingual cusp (26, 18) load on factor 6. The negative of the size of the labial cusp (23) loads on factor 7. For some reason wear stage (22) and the height of the cusps in lingual view associated with it (14, 16) also load on this factor. It may be that this cusp was easier to see while digitizing on specimens with less wear, but this seems unlikely since the part of the tooth where this cusp appears is not affected by early stages of wear. The size of the medial cusps (24-25) load on factor 8, as does the negative of the anterior angle of the anterior lingual valley (21) which is also an inverse measure of the size of the anterior medial cusp.

    Principal components analyses were run on much smaller samples of M/2's (described below) from the lower Orella of northwestern Nebraska and from the Chadronian of Pipestone Springs, Montana, and also on the M/3's of all three populations. These gave similar but less easily interpreted results. In none of the analyses were any unexpected correlations noted. Correlated variables generally measure the same gross aspect or particular feature of a tooth.

    Discriminant Analyses
    To further determine which characters are most valuable in distinguishing ischyromyine species, discriminant analyses were run on multiple populations. Analyses were run comparing three populations: the middle and upper Orella of northwestern Nebraska (hereafter called Orella C), the lower Orella of northwestern Nebraska (hereafter called Orella A), and the Chadronian of Pipestone Springs, Montana (hereafter called Pipestone). The Orella samples are thought to represent two distinct species of Ischyromys while the Pipestone sample is the type population of Titanotheriomys. The Orella C form is large in size while the Orella A and Pipestone forms are small. Each pair and the trio of populations were discriminated five times using jaw measurements and measurements on each of the four lower cheek teeth, making a total of 20 analyses. Using each tooth separately allows for larger sample sizes since few jaws contain all four teeth. All samples were exclusively of jaws or teeth with no missing values, and only teeth with wear stages 2 through 4 were used (see Table 1).

    Means and Coefficients of Variation
    Tables 8 through 12 list the mean values and coefficients of variation for all variables on each of the three populations. For all the gross tooth size measurements in occlusal view (1-6) the Orella C sample has by far the largest means. The Orella A and Pipestone samples are similar in size but rather different in mean proportions. The Pipestone sample has the smallest mean values for all of the jaw measurements and all the gross tooth measurements (1-6) on M/3. But the Orella A sample has the lowest mean values on P/4, M/1, and M/2 except the anterior width of P/4 (which is only slightly larger). These gross tooth measurements (1-6) have the lowest coefficients of variation, being as low as 4% and rarely exceeding 10%. The variation is generally lowest in the Orella C sample.

    Table 8 not only shows that Pipestone specimens tend to have smaller jaws, but it also documents a difference in jaw proportion. The angle measurements (7-8) indicate the slope of the bottom of the jaw relative to the tooth row. In both Orella samples the slope is quite steep, and the posterior angle (8) is significantly larger than the anterior one (7) which means the ventral jaw margin is highly curved. But the Pipestone jaws have a flatter ventral margin that is more parallel to the tooth row as shown by the smaller and more similar angles.

    Differences can also be seen in mean tooth proportions, especially between the Pipestone and Orella samples. The distance from the mouth of the posterior lingual valley to the end of the tooth (8) has a smaller mean value in the Pipestone sample than in the Orella samples for every tooth even though the Orella A sample has the smallest gross size for three of the four teeth. The variables that measure tooth height (14-17) generally have the smallest means in the Pipestone sample in spite of their larger occlusal area, and the lowness of the crowns is particularly noteworthy on M/3. On M/1, M/2, and M/3 the Pipestone sample has the largest value for the posterior angle of the anterior lingual valley (20) while the Orella C sample has the smallest value.

    The accessory cusp size measurements (18, 23-26) have enormous coefficients of variation because the distributions are so skewed, most specimens having a value of zero. The Orella C sample has the highest mean for nearly all of the accessory cusps. For both the Orella samples the anterior medial cusp is the most common, the labial and lingual cusps are less common, and the posterior medial cusp is very rare. The same pattern exists in the Pipestone sample except the labial cusp is very rare.

    In summary, the Orella C sample differs from the Orella A and Pipestone samples in its larger size, greater frequency of accessory cusps, and smaller posterior angle of the anterior lingual valley. The Pipestone sample differs from the Orella A sample in having a larger P/4-M/2 but smaller jaw and M/3, lower crowned teeth, more compressed posterior end of teeth, rarer labial cusp, and larger posterior angle of the anterior lingual valley. The question now is how well these differences serve to discern the identity of individual fossils.

    Success of Discriminant Analyses
    Table 13 shows the success rates of the 20 discriminant analyses in separating the groups. A success rate of 100% would represent a complete separation with no overlap whatever. The jaw is least successful, and the teeth tend to become more successful from front to rear. M/3 is the most useful in separating every pair and trio of groups. This is noteworthy since population studies of ischyromyines have generally ignored the M/3's in favor of the more abundant M/1's and M/2's (see tables and graphs in Flynn 1977 and Howe 1966).

    The BMDP discriminant analysis program uses a stepwise algorithm to select the most useful set of variables from those available. It adds or eliminates variables, one by one, in accordance with their F-statistic. At each step the variable with the highest F to add value is added to the analysis until there are no variables with an F to add value higher than four. However, if there are any variables in the analysis with an F to remove value of under four, then the variable with the lowest F to remove value is eliminated. This continues until all of the included variables and none of the excluded variables have F values over four. Variables with an F to add value under four are considered to add so little to the discriminant analysis that they are not worth including. Tables 14 through 18 list the measurements selected by each analysis and their canonical variables as well as the canonical variables for the mean of each group.

    On the discriminant analyses involving the jaws (Table 14) measurements 1 through 6 measure different aspects of jaw size, and several of these are useful in distinguishing the larger Orella C specimens from the smaller groups. Because of the flatter ventral margin of the jaw in the Pipestone sample, the posterior angle of the jaw (8) is important in distinguishing it from both Orella groups. This latter character is the reason for the superior success rate in distinguishing Pipestone jaws from Orella jaws compared to distinguishing the Orella groups from each other (Table 13), so in this case shape is of much more important significance than size.

    In all the tooth analyses (Tables 15 to 18) one or more of the gross tooth measurements in occlusal view (1-6) are important in distinguishing the Orella C sample from the other groups. The distances from the labial and anterior lingual valley mouths to the end of the tooth (7) are very significant in discriminating Pipestone specimens from both Orella samples on M/2 and M/3--this because the Pipestone teeth have a proportionally shorter posterior end. The distance from the posterior lingual valley mouth to the end of the tooth also shows up on P/4-M/2 comparing Pipestone with Orella A for the same reason. Differences in tooth height (14-17) are most important on M/3 which is one important reason for the usefulness of that tooth. This is because the anterior cusp height (14) and the posterior valley height (17) are small (albeit variable) compared to the height of the valley and cusp between them (15-16) on the Pipestone sample.

    In summary, the Orella C group is distinguished by its large size and the Pipestone group by its peculiar shape. The program had the most success in discriminating Orella C from Pipestone since they differ in both size and shape. Of the other two comparisons the Orella A-Pipestone comparison had a slightly better success rate overall than the Orella C-Orella A comparison, suggesting again that shape is more important than size overall.

    Composition of the Three Groups
    The three groups used for discriminant analysis were chosen because they each comprised a large sample of what was thought to be a single species (or at least dominated by a single species). The output from the discriminant analyses can be used to help confirm or reject this premise.
    Figure 19 shows histograms of canonical variables to illustrate graphically the success of the analyses and the distribution of misclassified specimens. Since the greatest success occurred with M/3, only the outputs of the pairwise analyses on that tooth are shown. Outputs from the jaw and other teeth are similar but have more overlap of the two groups being discriminated.

    In the top two histograms it can be seen that very few Orella C specimens are misclassified, and those that are tend not to stray far from their group. This is particularly evident in the middle histogram where there is a distinct break between the Pipestone and Orella C groups. In contrast, there are many Orella A and Pipestone specimens scattered along the Orella C group in the top and middle histograms respectively, and many Pipestone specimens are misclassified as Orella A in the bottom histogram. Overall the Orella C group has the cleanest and most symmetrical distribution, so it is the best case for a single species. This is further confirmed by the fact that the Orella C group tends to have the lowest coefficients of variation, being as low as 4% for the area and periphery variables on M/3 which is the most distinctive tooth (see Tables 8 through 12).

    The Orella A group has very little overlap with the Pipestone group, but a number of Orella A specimens fall throughout the Orella C distribution (Figure 19). This is clearly showing the same phenomenon as the right skewed distribution of the lower Orella specimens shown in the Toadstool Park scatterplot (Figure 10). If the Orella A and Orella C species are coexisting lineages, then these large specimens in Orella A may represent a small population of the Orella C species. If the Orella C species is a derivative of the Orella A species, then these large specimens may represent a subset of individuals trending in the direction of the Orella C species, or they may represent fossils from the upper Orella that have been washed down slope and were mistakenly identified as being from the lower Orella by collectors (see page 111).

    Many Pipestone specimens fall within the region of the Orella C and Orella A samples in Figure 19 and in such a way that both the Pipestone distributions are strongly right skewed and probably bimodal. This problem appears to be the primary reason why the analyses were not more successful than they were in discriminating the various groups since most of the "misclassified" specimens are from the Pipestone group. Wood (1937:190) first recognized that there is a large ischyromyine form at Pipestone Springs that is distinct from the more abundant smaller form, and this seems to be what these aberrant specimens represent.

    While the Orella A and Orella C populations are closely allied geographically and stratigraphically, the Pipestone Springs population differs from them in many ways. It is separated by 700 km, belongs to sediments of an earlier land mammal age, and may represent a separate genus that only paralleled Ischyromys. To discover which of these factors or combination thereof is the basis for this difference, it is necessary to examine other Chadronian populations. But first the Orella populations will be examined in greater detail.

    Middle Orella to Whitney Ischyromys of Northwest Nebraska
    As discussed on page 100, the middle to upper Orella section is the best case for a single species of the three populations on which analyses were run. It has the lowest coefficients of variation for most of the tooth variables (Tables 9 to 12) and the most symmetrical distribution in the histograms from the discriminant analyses (Figure 19). This is particularly significant since these specimens come from a much thicker section than the other two populations and also comprise a much larger sample. To further test for multiple species, the plots of factor scores from principal components analyses on each tooth and the jaw were carefully examined to look for any hint of deviation from normality. The plots for the four cheek teeth look like good normal distributions, much more so than the same plots for Orella A and Pipestone.

    There is one mildly skewed distribution in the Orella C sample that needs to be addressed. This is the factor from a principal components analysis on the jaws which the two jaw angles and the anterior and medial jaw depths load on (variables 7, 8, 1, and 2 of Table 8). This is also reflected in the coefficients of variation being highest for the Orella C sample for these variables (Table 8, in contrast to the tooth variables on Tables 9 to 12). The jaw variables were plotted in various combinations to determine the source of the variation. About 30 of the 553 jaws used in the Orella C sample have an unusually low value for the anterior jaw depth which in turn gives them a small value for the anterior jaw angle. Less commonly the medial jaw depth and posterior jaw angle are similarly affected. These unusual specimens are randomly distributed with respect to stratigraphic level and wear on the cheek teeth of the jaws, suggesting that it is neither a phylogenetic nor an ontogenetic variation. Photographs of these unusual jaws were examined and were all found to have a common feature that is unrelated to their true morphology. All of them happen to be broken near where the anterior jaw depth is measured or are heavily worn on their ventral surface. Their morphology does not appear to differ from that of "normal" specimens as the digitized numbers suggest. It is therefore concluded that the skewed distribution is due to measurement error on a normal distribution. There is a similar bias in the Orella A and Pipestone groups, but it is less pronounced. Therefore no evidence is found for multiple coexisting species in the middle and upper Orella of northwestern Nebraska.

    With the conclusion that the middle Orella to Whitney Ischyromys represent a single lineage, it can easily be determined if and how much the lineage changed over time and whether the change might justify recognizing multiple chronospecies. Howe (1956, 1966) thought two or three chronospecies were warranted from this group based on increases in mean size and accessory cusp incidence. Several attempts at multiple linear regression were made on the middle Orella to Whitney samples from Toadstool Park and Munson Ranch (and the two combined) using level in the section as the dependent variable. In every case the correlation was so weak that the results were spurious (intercept values from 100 feet above to 120 feet below Chadron-Orella contact). The main source of the problem appears to be the concentration of most of the fossils in a narrow stratigraphic interval.

    Figure 20 shows mean values of M/2 occlusal area for 30 foot stratigraphic intervals at Toadstool Park and Munson Ranch. Values are also given for the Chadron and Orella A populations although they represent an average of multiple species. Middle to upper Orella specimens show a mild tendency toward larger size through time. But fluctuations, possibly caused by small sample sizes at some intervals, make the magnitude and significance of this trend hard to test.

    The standard deviation of M/2 occlusal area for the whole population is 0.24 mm, and the increase in mean size from the base of the middle Orella to the Whitney does not appear to exceed this value. An increase of 0.24 mm centered on the mean of 3.42 mm over the interval of about one million years that this part of the section represents gives an evolutionary rate of 0.07 Darwins [Footnote: ln(3.54/3.30)/(1 million years) = 0.07 Darwins]. This is an exceeding low rate of change, and the "trend" seems insignificant when one considers the relatively short time interval over which it was measured (Gingerich 1983). Since the overall shift in the mean is only a small fraction of the range of variation at each level, the division of the lineage into chronospecies is totally unjustified.

    Accessory cusps are absent on the majority of teeth at every stratigraphic level, so they are useless taxonomically. But Howe (1956, 1966) claimed to see an increase in their occurrence up section at Toadstool Park and Munson Ranch. The heavily skewed distributions caused regression analyses to give spurious results. Figures 21 to 24 show mean values (and sample sizes) for 30 foot intervals of section. These are means for the qualitative values given to each accessory cusp and described in Table 3. Separate plots are shown for each of the four accessory cusps since factor analyses showed that they are not well correlated with each other. It was noticed during digitizing that M/1 and M/2 (and to a lesser extent M/3) tend to have the same pattern of accessory cusps. To increase sample size, values for M/1 and M/2 are combined, but separate plots are given for M/3 since this tooth is the most distinct between species. To further increase the sample the Toadstool Park and Munson Ranch sections are combined. These sections are almost identical, with differences in thickness occurring only in the uppermost parts. This lumping is necessary because the highly skewed distribution of cusp sizes gives erratic mean values for small samples.

    The lower two points in each plot represent the Chadron and Orella A populations which may comprise multiple species. The highest point represents a few rare specimens from the uppermost Orella and Whitney (when available), but the small sample size makes the value for these points erratic. Although the Orella A specimens (0-30 feet) have a lesser incidence than most other intervals for all accessory cusps, no consistent increase in incidence or size can be seen through the middle and upper Orella. There is a suggestion that accessory cusp incidence increases then decreases again in levels 30 through 180, but zig-zag patterns seem to preclude this from being a meaningful trend. So while Howe (1956, 1966) is correct in saying that there is an increase in accessory cusps from Orella A to Orella B, no real trend is observed in the sole lineage of the middle and upper Orella and Whitney.

    The difference in cusp frequency between the small and large Orellan species raises the question of whether the size of accessory cusps is allometrically related to overall tooth size. The method used to measure accessory cusps prohibits automatic correlation with tooth size, yet the correlation matrix for the Orella C M/2 population shows the frequency of all accessory cusps to be positively correlated with the measurements of gross tooth size with values ranging from 0.04 to 0.20 (Table 6). To further test for allometric correlation all the jaws from a single level (150 feet at Toadstool Park) were divided into three size groups, and mean values for each accessory cusp were calculated for each group. Results varied between different cusps and different teeth, but on average the smallest size group had the lowest frequency of accessory cusps, and the medial group had the highest. So although there appears to be some correlation between tooth size and accessory cusp incidence, there is no evidence that very large specimens tend to have the very largest accessory cusps. This is important in examining some exceptionally large dentaries from Colorado (discussed below) which all have very large accessory cusps.

    Lower Orellan Ischyromys of Nebraska and Wyoming
    As discussed above, the best plots showing sizes of Ischyromys from Orella A have a right skewed or bimodal distribution [Footnote: Skewness: G1 = 1.1; Kurtosis: G2 = 1.7.]. The sample seems to comprise a large population of small specimens and a small population of large specimens. This is most clearly observed at Toadstool Park (Figure 10) because of its large sample from Orella A. It is also evident in the top histogram of Figure 19 where a number of Orella A specimens were grouped with the larger Orella C sample.

    It seems beyond doubt that two distinct species are represented in the lower Orella of Nebraska and Wyoming. Presumably the two forms coexisted. But because the larger form is so similar to that found in great numbers in the overlying sediments, the possibility has to be addressed that these large specimens were merely washed down slope and mistakenly assigned to Orella A sediments by collectors. If such stratigraphic mixing has occurred, it is a great detriment to this study.

    The logical test case for the stratigraphic validity of the large Orella A Ischyromys specimens is a locality where nothing overlies Orella A. Fortunately such localities do exist, and they confirm the coexistence of small and large forms. In the Toadstool Park and Munson Ranch area alone there are 27 collecting localities (24 UNSM and 3 USNM) from which Orella A specimens have been collected with good stratigraphic data. Of these 13 have only small specimens, 9 have both small and large specimens, and 5 have distributions that are ambiguous. The lack of large specimens at some localities is not a problem since the large form is always uncommon compared to the small form, and all these localities have small sample sizes (1 to 7 specimens). At six of the nine localities with small and large forms, no specimens were reported from higher in the section. All six may be local areas with no overlying sediments. But three of these collecting localities are in the area of Everson Ranch, six miles southeast of Toadstool Park, where the hills are capped by Orella A, and no other stratigraphic levels are available for mixing. The UNSM localities (Sx-29 and Sx-32) are separated by a mile, and the USNM locality (Everson Ranch) is not as specific. These three localities have small to large specimen ratios of 6:1, 5:2, and 23:2 respectively. The largest collection of Orella A specimens comes from a UNSM locality (Sx-26) between Toadstool Park and Everson Ranch, and most of the Orella A exposures at that locality are isolated hills with no overlying sediments. There the ratio of small to large specimens is 85:6. So clearly there were coexistent small and large forms of Ischyromys in northwestern Nebraska during the early Orellan.

    Stout (1937) and Howe (1956, 1966) considered the lower Orella to contain a single lineage of Ischyromys, a small form that subsequently evolved into the larger form of the middle Orella. It now appears that the two forms coexisted during the early Orellan and may have been derived from different Chadronian species. Although rare, Chadronian ischyromyines from Nebraska show an enormous range in size--a range nearly as large as all the Orellan specimens. So the origin of multiple species in the early Orella is not a problem. The connection between the late Chadronian and the early Orellan is discussed below (page 119).

    While a large collection of Orella A specimens exists, few have data on their stratigraphic position within that 33 foot thick layer. In particular it is uncertain whether the large form is present in the lowest part of Orella A.

    Cluster Analyses and Multidimensional Scalings
    Chadronian ischyromyines are rare, very diverse in form, and can usually not be studied in any stratigraphic context. Most deposits are widely spaced local faunas which contain unique forms, and tying them together into an evolutionary sequence is nearly impossible. It is also difficult to determine which, if any, of the known early Chadronian forms is the ancestor of the abundant species of the Orellan.

    In order to determine similarities between various forms, numerous discriminant analyses, cluster analyses, and multidimensional scalings (MDS) were run comparing lower jaws and teeth from various localities. For cluster analyses and MDS's, 27 groups were selected and mean values were calculated for all measurements (except wear) on jaws, M/2's, and M/3's, giving a total of 58 variables. Special formulas were used in a spreadsheet to derive each mean value from the maximum number of specimens with that character available. While gross tooth measurements can be taken on almost any specimen, most characters are only valid on teeth with little wear. So for each measurement, all teeth were included with wear stages for which the character was considered valid. This method especially added to the accuracy of variables dealing with accessory cusps, which are plagued with heavily skewed distributions because of their rarity. The biggest problem with this analysis is differing sample sizes, some localities being represented by hundreds of specimens and others by only one or a few.

    Ischyromyine jaws from each locality were studied to look for evidence of multiple, coexisting species. This was done by examining the coefficients of variation for each variable and by running principal components analyses to look for skewed or bimodal distributions on the principal components. Most Chadronian localities seem to contain a single species, but there are three important exceptions: Pipestone Springs, Flagstaff Rim, and the Chadronian deposits of Pine Ridge.

    The presence of a second less abundant and larger species at Pipestone Springs has long been recognized and is strongly confirmed by the discriminant analyses discussed above. Separating these species was easily done on size alone, and only one specimen was difficult to classify because of its intermediate character. The large form comprises less than 7% of the total sample. The two forms are herein labeled "small Pipestone" and "large Pipestone."

    Flagstaff Rim represents by far the best stratigraphic sequence of any of the Chadronian ischyromyine localities. From the plot of tooth size vs. level in the section (Figure 18) the Flagstaff Rim specimens were divided into three groups: "early Flagstaff," "small Flagstaff," and "large Flagstaff." The "early" group includes the specimens below 200 feet in the section while the other groups include those above 200 feet. The "small" group includes specimens with tooth sizes below 15.2 mm while the "large" group includes those above 15.2 mm (Figure 18). Each group shows homogeneity within itself. The "small Flagstaff" group in particular was examined for bimodality because Flynn (1977) concluded from his studies of skull structure that this population represents combined forms of Ischyromys and Titanotheriomys. I could find no evidence whatever for such mixing. This group has exceptionally low coefficients of variation for most characters, and a principal components analysis showed that this population has a good multivariate normal distribution with no evidence of bimodality or skewing on any principal component. Considering the significant variation between other Chadronian ischyromyine forms, it seems virtually impossible that two combined lineages could exhibit the uniformity that this population does.

    A handful of ischyromyine jaws have been found in the Chadron Formation underlying the big Orellan localities along Pine Ridge (Figures 10 to 15). When combined these make a respectable sample. Correlation between sections is difficult, however, and in no section does there seem to be noticeable change over time. This group exhibits an enormous size range, a range about as large as all the Orellan material from Pine Ridge. It seems logical that two or more distinct species are represented in this sample, but no basis could be found for separating them. A principal components analysis showed uniform distributions, and except for size variation the group shows considerable uniformity. So this sample is kept as a single group called the "Late Chadron Complex."

    A number of Orellan localities are also included for cluster analysis and MDS. The big Orellan sample from Toadstool Park and Munson Ranch discussed above was divided into three groups: "small Orella A," "large Orella A," and "Orella C." The Orella A groups were segregated on a tooth measurement of 16.3 (Figure 10). Presumably the "Orella C" group is the continuation of the "large Orella A" group. Orellan samples with fewer specimens or without stratigraphic control are harder to divide although some probably contain both the small and large form found at Toadstool Park. The Big Badlands, Lusk, Douglas, and Scotts Bluff localities fall in this category. The Lyman sample comes from a narrow but uncertain stratigraphic interval and has very small coefficients of variation, so it probably represents a single species. The Colorado sample contains a few exceptionally large specimens (including the type of I. pliacus) which are very similar to each other and are set off from the rest of the group. These were separated as "large Colorado" and the rest as "small Colorado" although their relationship is unclear because of the small overall sample size. The northern Orellan localities at Little Badlands and Slim Buttes contain what seems to be a single large species that increases slightly in size over time.

    Figure 25 shows the results of a cluster analysis using the Ward method on the 27 groups discussed above using 58 standardized variables from jaws, M/2's, and M/3's. Other cluster methods gave a similar result. The first order separation is on the basis of size. Among the large forms the Orellan groups cluster closely together while the Chadronian groups are more distinct. Among the small forms the two Orellan groups are very closely tied but are nestled within the numerous Chadronian groups. Several Chadronian groups appear to be closely related: small Flagstaff, Cameron Spring, Beaver Divide, and small Pipestone. Oddly enough the early Flagstaff and small Flagstaff groups seem quite distinct in spite of their similar size and sequential stratigraphic position. A two dimensional MDS separates forms almost exclusively on size, but it does show the early Flagstaff group being closer to the small Pipestone and small Flagstaff groups than is suggested in the cluster analysis (Figure 26).

    Since size dominates the above analyses, another analysis was done in which overall size was eliminated before the variables were standardized. This was accomplished by dividing all size-dependant variables by the sum of the area and periphery of M/2 and M/3, these being the best measures of overall size. An MDS on this data set shows the Orellan and Flagstaff Rim groups tightly clustered at the center and the other Chadronian forms widely spaced (Figure 27). Most cluster methods merely separated off individual Chadronian groups until they got to the Orellan groups which were shown to all be very similar. This makes the groups very hard to classify. The only exception is the result of the Ward method, shown in Figure 28. It is more interpretable.

    All the Orellan Ischyromys cluster very closely together at the top of the diagram with the small and large forms being distinct but closely related. The mixed samples cluster according to the form that dominates them: the large Orellan form for Big Badlands, Scotts Bluff, and Colorado; and the small Orellan form for Lusk and Douglas. Although the type of I. parvidens is from the Big Badlands, it is a small form similar to small Orella A. A more distant member of this top cluster is the very early Chadronian form from the Porvenir fauna of Texas, considered by Wood (1974) to be the most primitive Ischyromys.

    A large cluster at the bottom of the diagram includes the forms usually assigned to Titanotheriomys veterior. Of these the most geographically isolated locality, Ash Spring, is the most distinct. Fossils from the northernmost locality, Cypress Hills, also fall in this group. Between these two large groups is a third group containing primitive forms such as early Flagstaff, West Canyon Creek, and McCarty's Mountain and the odd large forms from Flagstaff Rim, Pipestone Springs, and Colorado.

    In both cluster analyses, the Late Chadron Complex clusters with the Orellan Ischyromys rather than with other Chadronian forms. This group's morphology, geographic and stratigraphic position, and size diversity strongly suggest that it gave rise to the small and large species that dominate the Orellan. The origin of the Late Chadron Complex is difficult to determine. Figure 27 shows the Flagstaff Rim forms being most similar to the Orellan groups, especially the large Flagstaff form that extended into the late Chadronian. The close morphologic similarity and geographic proximity suggest a relationship. However Flynn (1977) identified skulls of the large Flagstaff species as Titanotheriomys, which Wood (1976) considered to be a specialized derivative of Ischyromys rather than its ancestor. Wood (1974) considered the Porvenir species to be the most primitive Ischyromys, and Figure 28 shows it to be the closest form to the Orellan species and the Late Chadron Complex.

    Individual Character Plots
    The above analyses were based on 58 variables, and the cluster and MDS techniques were used in an attempt to simplify the data so all groups could be evaluated on all characters. The same groups are now plotted using pairs of variables in order to illustrate some of the important differences. This also shows the difficulty of determining relationships since different characters show radically different groupings. In general the Orellan groups always cluster closely together (except in size where they form two distinct groups) while the Chadronian groups are widely spaced (except a group of small forms that tend to always cluster together).

    Figure 29 is a plot of the angles of the ventral margin of the jaw, measurements that are not size-dependent. The difference between the anterior and posterior angles indicates whether the jaw margin is flat, concave, or convex, and the magnitude of the values indicates how steep the jaw margin is relative to the tooth row. This illustrates the difference between the Orella and Pipestone jaws that allowed them to be separated by discriminant analysis. The small Pipestone form, like most of the small Chadronian populations, has anterior and posterior angles that are equivalent. This is because the ventral jaw margin is very flat. All the Orellan populations have a higher posterior angle than anterior angle, meaning that the jaws margins are convex. Three populations have jaws that are concave: early Flagstaff, large Flagstaff, and large Pipestone.

    The tight clustering of the Orellan populations (all Ischyromys) in the upper left of the plot and of the Chadronian populations (all Titanotheriomys) to the bottom and right strongly suggest that this is an important character. Since the two genera are distinguished by skull characters rather than tooth characters, the shape of the jaw is perhaps the most related feature that can be found on a dentary. Unfortunately the jaw features of the single Porvenir dentary (identified as Ischyromys by Wood 1974) could not be measured because it is imbedded in matrix. Since the Cypress Hills form is known only from isolated teeth, it could not be included either. But from the information available, this seems to be a character of generic importance. The plot also illustrates the extensive diversity among some of the Chadronian forms. Some forms that stand out in other ways, such as McCarty's Mountain, are not unusual in this respect, however.

    Little can be said about evolutionary relationships from this plot because it is not known which condition is primitive. The cluster of small Chadronian forms is much closer to the cluster of Orellan forms than are larger Chadronian forms such as large Flagstaff and large Pipestone, and this strongly suggests that these large Chadronian forms are dead end specializations rather than ancestors to the large Orellan forms.

    Figure 30 is a plot of M/2 length vs. M/3 length. The two are highly correlated, so the large forms are all at the upper right while the small forms are at the lower left. While the small Pipestone form is distinct from the small Orella A form in having M/3 shorter than M/2, that is not the case for all small Chadronian forms. Nevertheless, the Chadronian forms do tend to have a relatively shorter M/3 compared to the Orellan forms, and this may be a generic distinction. The single Porvenir dentary has a very elongate M/3, so it fits (in an extreme way) the pattern of the Orellan Ischyromys despite its very early age. At the other end of the spectrum is the Cypress Hills form. It is based on a small sample of isolated teeth (11 M/2's and 6 M/3's) with high coefficients of variation, but on average the M/3's are much shorter than the M/2's.

    Figure 31 compares the posterior end of M/3, from the mouth of the posterior lingual valley to the posterior end of the tooth, to the length of M/2. This is to further measure compression at the posterior end of the tooth row.

    In this respect the small Chadronian forms are quite varied. The extreme shortness of the posterior end of M/3 in the small Pipestone form, which helped greatly in distinguishing it from the Orella A form with discriminant analysis, is seen to be more of a specialization for that population rather than a general feature for all the small Chadronian forms. In fact the small Chadronian forms nearly divide into two groups based on the posterior length of M/3. The small Flagstaff, Cameron Spring, and Beaver Divide populations, which are similar in location and age, clump closely and are somewhat close to the small Pipestone, Ash Spring, and Cypress Hills populations. Much higher on the plot are the early Flagstaff, Ledge Creek, Harshman Quarry, and West Canyon Creek populations from earlier in the Chadronian. This pattern suggests that the later small Chadronian forms are a specialized offshoot from the earlier group, with the small Pipestone population being the most highly specialized. The large Chadronian forms (large Flagstaff, large Pipestone, and McCarty's Mountain) retain a long posterior end on M/3, as do all the Orellan populations.

    It appears that the primitive condition for the group is an M/3 that is similar in shape to M/1 and M/2, and that the compressed posterior end of M/3 is only a specialization in a terminal lineage. The only contrary evidence is that the single Porvenir dentary is very low on the plot. But M/3 on that dentary is quite worn and the character is ambiguous, so little weight should be placed on its position.

    Figure 32 shows the shape of the anterior lingual valley plotted against tooth area (sum of M/2 and M/3 for both axes). Forms with high values for this character have anterior lingual valleys that are longer (extend farther labial) anteriorly than posteriorly and tend to be square with respect to the tooth margins rather than extending posteriorly as they extend labially. The forms that Wood (1974) considers to be the most primitive, McCarty's Mountain and Porvenir, have unusually high values. Other early forms such as West Canyon Creek, Ledge Creek, and early Flagstaff also tend to be to the right. This might suggest that the condition seen in the McCarty's Mountain form represents the primitive condition. This needs to be viewed with skepticism, however, because the McCarty's Mountain population is specialized and unusual in many ways and therefore doesn't make a good ancestor. Despite its early date, its unusual condition may be derived. The Porvenir form is represented by only a single dentary, so its position on this plot needs to be regarded with a large zone of error.

    Figure 33 shows cusp height as seen in lingual view plotted against tooth area (sum of M/2 and M/3 for both axes). Cusp height is here calculated as the quotient of cusp height divided by valley height (both from the base of the tooth enamel). These are calculated for both the anterior and posterior cusp and valley, and the total shown on the plot is the sum of the two quotients from each tooth. Populations to the right have high cusps and deep valleys while those to the left have low cusps and shallow valleys.

    The oldest populations tend to be on the left of the diagram. Unfortunately the single Porvenir dentary could not be measured in lingual view, so its condition is unknown. The only Chadronian forms on the right of the diagram are large Pipestone and Ash Spring, and of course the Late Chadron Complex which always clusters with the Orellan forms. All the large Orellan forms are clustered together in the upper right of the diagram, and the small Orellan forms are also close together but occur closer to the Chadronian groups. The McCarty's Mountain and large Flagstaff forms are unusual in being large in size but retaining low cusps. To summarize this plot, Ischyromys populations have relatively higher cusps than Titanotheriomys populations although there is some overlap, but some Titanotheriomys populations have also developed high cusps.

    TAXONOMIC ANALYSIS
    The purpose of this study is not to revise ischyromyine taxonomy. Skull material on which many species diagnoses are based has not been studied. But to facilitate further work, an attempt is made to summarize the results of this study in a taxonomic framework. In particular this study helps discern which populations are conspecific. While a study of skulls will be necessary to work out the taxonomy, this study of the much more numerous lower jaws suggests that some named species are clearly valid, others are probably invalid, and many are ambiguous. It also appears that several unnamed morphotypes clearly deserve recognition as new species.

    Ischyromys vs. Titanotheriomys
    This study provides neither strong support nor opposition to the generic distinction favored by Wood (1976) and Flynn (1977). This is not surprising, however, since these workers stated that lower jaws are not diagnostic. Black (1968) has been the strongest opponent of the generic distinction, and this study clearly demonstrates that his cross-generic synonymy of Titanotheriomys veterior and Ischyromys parvidens is erroneous. The tooth characters that distinguish these two species are not useful in distinguishing all populations of the two genera, however.

    The best evidence from dentaries for the generic distinction is the shape of the ventral margin of the jaw (Figure 29). The population means for the Ischyromys groups show a higher value for the posterior jaw angle relative to the anterior jaw angle compared to the Titanotheriomys groups. In other words Ischyromys have convex ventral jaw margins while Titanotheriomys have flat or concave ventral jaw margins. The second best distinction between genera is cusp height (Figure 33). Ischyromys tend to have high cusps and deep valleys while Titanotheriomys tend to have low cusps and shallow valleys. A third and less reliable distinction is the relative lengths of M/2 and M/3 (Figure 30). Ischyromys tend to have longer M/3's than M/2's while Titanotheriomys tend to have M/3's that are shorter than or equal in length to M/2. All these characters are useful in distinguishing population means, but they are less useful in distinguishing single dentaries because of individual variation.

    All the Orellan material seems to fall into two closely related species (I. typus and I. parvidens) whose skull material clearly allies them with Ischyromys. Ischyromys-type skulls are rare in the Chadronian. Several have been found in the Douglas area in the Chadron Formation immediately underlying the Orellan (Wood 1976:271; Kron 1978). These are part of the highly variable Late Chadron Complex that is more closely allied with the Orellan forms than with any other Chadronian group. Wood (1976:271) reported an Ischyromys-type skull from the lower levels of Flagstaff Rim, and Flynn (1977) reported several more from the smaller material of the middle levels of the same locality. My study suggests that the corresponding jaws from these localities are quite distinct from Ischyromys of the Orellan and are more closely allied with groups having Titanotheriomys-type skulls. The earliest known skull is the one from Porvenir (type of I. blacki) which Wood (1974, 1976, 1980) considers without question to be Ischyromys. The single jaw from that locality is distinct from all other forms, but a cluster analysis did group it with the Ischyromys forms of the Orellan (Figure 28).

    All skull material of the Titanotheriomys-type comes from the Chadronian, and it occurs in forms with very diverse tooth morphology. In spite of this Wood (1980) recognized only two species of Titanotheriomys, both of whose types are from Montana. Titanotheriomys douglassi appears to be unique to McCarty's Mountain and is the only form known from that locality. The name T. veterior has been applied to small forms throughout Wyoming and as far south as Texas as well as to the type material at Pipestone Springs, and Wood (1976) has confirmed the generic assignment on skull material from most of these localities. Flynn (1977) demonstrated that the large form from the middle and upper levels of Flagstaff Rim has the Titanotheriomys-type skull, and Wood (1976:271, 1980:19) at least suggests that the same applies to the large form at Pipestone Springs.

    It appears that Titanotheriomys-type rodents were very diverse and widespread during six and a half million years of Chadronian time while Ischyromys-type rodents remained very rare until they flourished during one million years of the Orellan. If Wood is correct in asserting that the two forms are generically distinct and have a common ancestor no younger than the earliest Chadronian, then the groups seem to have closely paralleled if not converged on each other; for the cheek teeth of the two groups are most similar in some of their youngest specimens. More work is needed to resolve the taxonomic significance of skull morphotypes. Particular attention needs to be given to the small Flagstaff Rim form where there is conflicting evidence as to whether one or two lineages are represented.

    Ischyromys typus
    The type specimen of Ischyromys and its first-named species, I. typus, is a skull from the Big Badlands with poor geographic and no stratigraphic data. Yet its similarity to numerous other Orellan fossils makes it clear that it belongs to the large Orellan form of Ischyromys that is so common in the middle and upper Orellan sediments of Pine Ridge and numerous other localities.

    Howe (1956, 1966) considered I. typus to have arisen from the smaller form of the lower Orellan of Nebraska and therefore to have not existed during early Orellan. But this study shows that it coexisted with the smaller form as a distinct lineage during most or all of the early Orellan of Nebraska as shown by bimodal size distributions (Figures 10 and 11). This interpretation is further strengthened by the fact that some late Chadronian material is identical to I. typus of the upper Orellan. In fact the Late Chadron Complex (discussed below), when taken as a whole, tends to cluster with the large Orellan form in every respect (Figures 25 to 28). This conclusion is further substantiated by the Slim Buttes and Little Badlands sections where the small Orellan form has never been recovered and where I. typus seems to have been the sole species of the group throughout the entire Orellan (Figures 16 and 17).

    This species did increase in size through time as asserted by Howe (1956, 1966), but the mean change is so inconsequential compared to the range of variation at any level that it certainly does not deserve the taxonomic recognition that Howe gave it. Even at the Slim Buttes and Little Badlands localities where this species became exceptionally large, the overlap between the lowest and highest levels precludes any hope of taxonomic distinction. Howe (1956, 1966) considered the upper Orellan material to be I. pliacus, descended from I. typus, and a lower Whitneyan specimen to possibly belong to another distinct species, descended from I. pliacus. My study shows that all the middle Orellan through Whitneyan material (of Toadstool Park and Munson Ranch) combined has a uniform distribution with low variance despite the gradualistic evolutionary trends. With the taxonomic uncertainty of I. pliacus (discussed below) and the lack of need for a distinct upper Orellan or Whitneyan species, this name should not be applied to material from Pine Ridge or any more northerly localities.

    This study also provides no support for I. troxelli as a large species of Ischyromys coexisting with I. typus as asserted by Wood (1937, 1980). This is because of the uniformity of the group as discussed above. The type of I. troxelli includes a skull and jaws, and measurements on the lower jaws and teeth fall near the mean of I. typus for most characters and well within its range of variation for all characters. Wood's (1937) main diagnostic features for I. troxelli refer to the skull, but no one has yet studied the range of variation of those features on enough specimens to assess their significance.

    Ischyromys typus is the most abundant rodent in middle and upper Orellan sediments of the Great Plains. It is also found in the late Chadronian (as part of the Late Chadron Complex discussed below), the early Orellan, and the lower Whitneyan but in much smaller numbers.

    Ischyromys parvidens
    The type of I. parvidens is a dentary from the Big Badlands with poor field data. It is smaller than the mean but well within the range of variation of the small Orella A form of Nebraska that is usually given its name. This species is very similar to I. typus, the latter being distinguished mainly by its larger size (especially M/3) and higher incidence of accessory cusps. There appears to be a slight overlap between these two species that even a discriminant analysis using many characters cannot resolve, but the portion of ambiguous specimens is small (about 10% in one analysis, some of which are due to actual mixing rather than intermediacy). Since I. parvidens and I. typus coexisted during the early Orellan as shown by a bimodal distribution, they should definitely be recognized as separate species.

    Black's (1968) synonymy of I. parvidens with T. veterior and his claim that their cheek teeth are indistinguishable is erroneous, as discriminant analyses were able to separate them with over 90% accuracy on either M/2 or M/3 and with over 80% accuracy on jaw, P/4, or M/1 measurements (comparison of Orella A sample with Pipestone Springs sample, Table 13). Titanotheriomys veterior is the more specialized of the two, and it differs from I. parvidens in having a flatter ventral margin of its jaw, larger M/2 but smaller M/3, teeth with proportionally shorter posterior ends, lower crowned teeth (especially M/3), and a larger posterior angle of the anterior lingual valley (especially on M/3).

    Ischyromys parvidens is the most abundant rodent in the lower Orellan of Pine Ridge. A discriminant analysis suggests that it also makes up 15% of the Big Badlands ischyromyines and 41% of the Colorado ischyromyines (I. typus making up the remainder). It is apparently absent from the more northern localities of Slim Buttes and Little Badlands. One of the only two known Orellan ischyromyine fossils from Montana (Easter Lily locality just north of Pipestone Springs) is a P/4 that is similar in size to I. parvidens, although the taxonomic relationship is questionable.

    Ischyromys parvidens appears to have gone extinct at the end of the lower Orellan when I. typus became abundant. A few small specimens from the middle and upper Orellan may represent remnants of I. parvidens but are probably just small individuals of I. typus. The Late Chadron Complex contains specimens that are identical to I. parvidens, so this species could be considered late Chadronian as well as early Orellan.

    Late Chadron Complex
    The ischyromyine specimens found in the Chadron Formation underlying the productive Orellan beds of Pine Ridge illustrate a typical problem in taxonomy. These fossils are very rare compared to their Orellan counterparts, so they must be combined from all levels at all localities to get a sample of about 40 jaws. They exhibit a range of variation equivalent to I. typus and I. parvidens combined, but their distribution is so continuous that no way could be found to split them into multiple groups. At Douglas and Toadstool Park there is a hint of bimodality, but the Lusk sample fills in the gap (Figures 14, 10, and 13).

    This Complex is clearly a precursor to both I. typus and I. parvidens. In every analysis it clusters with the Orellan Ischyromys rather than any of the other Chadronian forms. According to Wood (1976:272), all Chadronian skull material from the Douglas area is clearly Ischyromys. Kron (1978, pers. comm.) considered some of it to be Titanotheriomys, however. The high degree of variability in the Complex may merely be the result of two coexistent species with overlapping characters. It may be, however, that it represents a highly variable population from which a large and a small form emerged. With such a small sample it is difficult to draw conclusions. Should the latter hypothesis be substantiated, this group could be named as a distinct species.

    Ischyromys pliacus
    The small group of large specimens that was separated off as "large Colorado" and which includes the type of I. pliacus is very unusual in many respects, and its status is riddled with uncertainty. In tooth structure it clusters closest to the Orellan Ischyromys, but in jaw structure it falls among the Titanotheriomys populations (Figures 29 to 33). It has the highest incidence of any population for the labial accessory cusp, and it also has a very high incidence for the lingual accessory cusp.

    Galbreath (1953) showed that the collection locality, and therefore the age, of the I. pliacus type is uncertain. It is also uncertain whether these exceptionally large specimens represent average members of a population or whether they are merely the upper tail of a distribution. For these reasons status of this species should be considered in dispute. It definitely seems unwise to apply the name I. pliacus to large individuals of I. typus or to the large Pipestone form, as has often been done.

    Ischyromys blacki
    Although based on only a single skull and dentary, I. blacki has features that make it a distinct species. Those of the skull are discussed by Wood (1974, 1976). The most unusual feature of the dentary is the long M/3 but short M/2, and this allies it (although in an extreme way) with Ischyromys rather than Titanotheriomys. The cluster and MDS analyses in this study show I. blacki as being distinct from all other forms but generally closest to species of Ischyromys. The early age and distinct geographic location of this form also argue for its separation as a distinct species.

    New Species of Ischyromys
    West Canyon Creek
    The small collection of dentaries from West Canyon Creek at the east end of Beaver Divide, Wyoming, illustrates well the difficulties involved in unraveling the relationships between Chadronian ischyromyines. They appear to be of a single species that is average in most respects, but this species has a unique feature that separates it from all other groups. This unique feature is an exceptionally high incidence of both medial and the lingual accessory cusps. Its incidence of the anterior and posterior medial cusps is higher than any other population on both M/2 and M/3. An exceptionally low value for the anterior angle of the anterior lingual valley also reflects the exceptional size of the of the anterior medial cusp, which often dams off the valley entirely. Also, the posterior lingual valley extends unusually far anteriorly as it extends medially. These characters give quite a distinct look to the molars.

    It is difficult to determine if this species is a likely ancestor or whether it is a unique, terminal lineage. It is of medium size and is quite average in most respects, and it tends to cluster among the Titanotheriomys populations (Figures 25 to 28). The skulls have not been studied in detail, but they have some features in common with Ischyromys such as sagittal crests. In these respects it makes a good ancestor. The high incidence of accessory cusps is most easily seen as a derived character, but this may not be the case. Since these cusps show up sporadically and only rarely in later species and show little or no evidence of being selected for, they might be atavisms of a formerly important character trait.

    The relationship of the West Canyon Creek ischyromyine to other early ischyromyines such as I. blacki of Texas and ?Ischyromys sp. of Badwater Creek, Wyoming is very uncertain, mostly because of the limited material of the latter forms. The West Canyon Creek dentaries do not have the elongate M/3 of the I. blacki dentary, and only one of the two lower molars on the I. blacki jaw has an accessory cusp--a medium sized anterior medial cusp on M/3. The one preserved M3/ on the type skull of I. blacki has the peculiar look of the West Canyon Creek molars, but the other teeth lack it. None of the teeth of ?Ischyromys sp. illustrated by Black (1971:204) show this pattern. So although there are some hints of similarity, nothing very conclusive can yet be said about their relationships. But the morphological differences and geographic distance between I. blacki and the West Canyon Creek fossils clearly warrant the erection of a new species, the genus of which (Ischyromys or Titanotheriomys) is still to be determined from a study of the skulls.

    Titanotheriomys veterior
    The genus Titanotheriomys and the species T. veterior were erected for the small Pipestone species from Montana and have since been applied to many other widely distributed Chadronian populations. This species is clearly valid, but it is somewhat of a judgement call as to how widely it should be applied.

    The small Flagstaff and Cameron Spring populations of Wyoming are almost identical to each other in every respect, and they are also very similar to the small Pipestone population (Figures 25 to 28). All three are the same age, but the Pipestone Springs locality is the most distinct geographically. The small Pipestone population is also the most derived of the three because the posterior end of M/3 is more compressed than in any other population (Figure 31). There is enormous overlap between these three populations in this character, however, so it is not worthy of species recognition. The Pipestone population also has the largest mean size of the three, but the overlap again is enormous. The small Flagstaff and Cameron Springs populations are clearly T. veterior.

    Somewhat more distinct are the populations of small Titanotheriomys from earlier in the Chadronian of Wyoming. The Beaver Divide fossils are geographically close to and probably slightly older than those from Cameron Spring, and they are the most similar to the trio discussed above. Titanotheriomys wyomingensis was named for this population (Wood 1937), but because of its very close similarity to the Cameron Spring and small Flagstaff populations Black (1968) and Wood (1980) were clearly justified in synonymizing it with T. veterior. The Ledge Creek and Harshman Quarry fossils are also very similar to all the forms discussed above, and their seeming distinctions may be due to small sample size. They are therefore assigned to T. veterior.

    Of greater interest is the early Flagstaff population. When size is factored out the early Flagstaff form is more similar to the large Flagstaff form than the small Flagstaff form, and it probably gave rise to both. All the cluster and MDS analyses group it differently, and the MDS plots tend to place it in an intermediate position between some of the major groups (Figures 25 to 28). These facts strongly suggest that it represents a primitive condition from which others were derived, so it may well be ancestral to many of the later groups. It almost certainly gave rise to the small Pipestone form, and the two are probably close enough to be considered conspecific despite the specializations of the latter. Yet it is awkward to say that T. veterior was an ancestral species when the type specimen is from its most derived and dead end population!

    The Ash Spring and Cypress Hills forms are small and somewhat similar to the small Pipestone form, but they are more distinct than any of the forms discussed above and are also more isolated geographically. They could for convenience be called T. veterior, but since the Cypress Hills has been given its own name (I. junctus) they will here be considered separate species that are closely related to T. veterior. Although they both have unique features, they tend to group with Titanotheriomys rather than Ischyromys. They will each be discussed below.

    Titanotheriomys douglassi
    The McCarty's Mountain form is definitely distinct enough to be considered a valid species as proposed by Black (1968). It's present occurrence is restricted to McCarty's Mountain, and none have been found in similar age sediments of Wyoming. Ostrander's (1980:78) assignment to this species of two isolated teeth from the late Chadronian of Nebraska is certainly in error since he used Black's (1968) synonymy as his taxonomic basis and since the measurements he gives fall well within the size range of the Late Chadron Complex.

    Titanotheriomys douglassi is distinct in being the largest species with low cusps and shallow valleys (Figure 33), and its anterior lingual valleys are deeper anteriorly than posteriorly and do not extend posteriorly as they extend labially (Figure 32). The M/3 of T. douglassi has not undergone the posterior shortening seen in T. veterior; in fact it has the longest mean posterior M/3 of all the populations studied (Figure 31).

    Titanotheriomys junctus
    Only isolated teeth are known from Cypress Hills, so Wood (1980) considered the generic affinity of I. junctus (Russell 1972) to be uncertain. This study allies it with forms that Black assigned to Titanotheriomys. It is smaller than any known Ischyromys but similar in size to T. veterior. Its most distinct feature is its short M/3 relative to M/2, and this specialization is seen to a lesser degree in many populations of small Titanotheriomys but never in Ischyromys (Figure 30). In all other respects it clusters closely with populations of T. veterior.

    New Species of Titanotheriomys
    A number of Chadronian populations are so distinct from all named species that they deserve recognition as new species. All these except West Canyon Creek (described above) are known from skull material to be Titanotheriomys rather than Ischyromys.

    Ash Spring
    In most respects the Ash Spring population is similar to Titanotheriomys veterior from Wyoming and Montana, but it has unique features. The most significant is that the cusps have become very high, converging on the large Ischyromys of the Orellan (
    Figure 33). This and other lesser differences caused the cluster and MDS analyses to set this population apart from all others, especially when mean size was excluded (Figures 25 to 28). But because of the small sample size and similarity to T. veterior, this is the most tenuous of the new species.

    Large Flagstaff
    This is a primitive species, being almost identical in shape to the early Flagstaff population (primitive Titanotheriomys veterior) but being substantially larger. The cluster analyses are particularly instructive because the one that includes mean size groups this species with the other large Titanotheriomys and not at all close to the early Flagstaff form, but the one that excludes mean size links the early and large Flagstaff forms very closely together (
    Figures 25 and 28). Like the early Flagstaff population it has a very concave jaw and relatively low cusps (Figures 29 and 33), features which are found only in some of the earliest Titanotheriomys populations. The mean length of its M/3 is shorter than that of its M/2 as in many of the smaller Titanotheriomys, and it is the largest form studied with this arrangement (Figure 30).

    For some reason the MDS plots place the large Flagstaff species very close to the Orellan Ischyromys (Figures 26 and 27), and this in connection with their close geographic and stratigraphic proximity might suggest an evolutionary relationship. But in the most generically distinct characters (listed above, plus skull characters listed by Wood 1976 and Flynn 1977) the large Flagstaff and Orellan forms exhibit configurations at the opposite ends of the spectrum, so a genealogical relationship seems most unlikely.

    Large Pipestone
    The larger and less common of the two forms of Titanotheriomys at Pipestone Springs is another distinct species with a unique suite of characters. Like the early and large Flagstaff populations it has a very concave jaw, but the angle with respect to the tooth row is much lower than in those populations (
    Figure 29). In this character it seems primitive and somewhat unique, and it is vastly different from the highly convex jaws of the Orellan populations. But in most dental characters this species is very convergent on the Orellan Ischyromys. It has a longer M/3 than M/2, a long posterior end on M/3, and high cusps (Figures 30, 31, and 33). This species resembles the West Canyon Creek form (described below) in having a very high incidence of the medial accessory cusps, but it lacks the high incidence of the lingual cusp found in the latter species.

    Phylogenetic Tree
    In summary, Chadronian ischyromyines have been over-lumped while Orellan ischyromyines have been over-split. Species names seem to have been generated more in accordance with the number of fossils collected than the morphologic diversity they displayed. In spite of the scarcity of fossils, Chadronian ischyromyines display an incredible amount of morphological diversity, vastly more than the plentiful fossils of Orellan Ischyromys.

    Relationships between the numerous Chadronian species are difficult to work out, especially for the more peculiar forms. Orellan ischyromyines are not as taxonomically complex as previously thought, so their relationships are simple. The origin of the Orellan ischyromyines from among the Chadronian species is still one of the greatest mysteries, however. Figure 34 is a phylogenetic tree showing the most likely relationships between species based on morphology, age, and geography. Relationships between late Duchesnean and early Chadronian species are the most tenuous. The West Canyon Creek species has the most unique-looking teeth in overall appearance, but its relationship to other species is still unclear.

    With the advent of Titanotheriomys veterior there is more continuity between species, so the scheme presented is more reliable. There are three distinct forms or subspecies within T. veterior as here proposed. The first is the early Flagstaff form. It is very generalized and could have given rise to all the middle and late Chadronian forms of Titanotheriomys. The second form is slightly smaller and comprises the small Flagstaff, Cameron Spring, and Beaver Divide populations. The third form is the type population from Pipestone Springs which is the largest in size and the most derived morphologically. In addition, T. junctus and the Ash Spring populations are quite similar to early T. veterior, yet they each have unique specializations.

    There are three larger forms of Titanotheriomys. The large Flagstaff species is an enlarged version of the early Flagstaff form of T. veterior and is very primitive and unspecialized. The two larger Montana forms, T. douglassi and the large Pipestone species, are primitive in some respects and unique and specialized in others. Their isolation makes their origin elusive.

    In the Orellan there are two species, Ischyromys typus and I. parvidens, which are nearly identical except for their size. They are obviously closely related, and they appear to have arisen separately from a diverse late Chadronian population herein called the Late Chadron Complex. The origin of this complex is uncertain, but skull features and some tooth features suggest that it did not arise from any of the derived species of Titanotheriomys. Instead it is most similar to the late Duchesnean and early Chadronian species whose relationships are poorly understood. The Ischyromys lineage remained very elusive throughout most of the Chadronian, and perhaps it populated regions where no fossils are known. Since a majority of Chadronian and Duchesnean species are known from single localities, this does not seem at all unlikely.

    CONCLUSIONS
    Through detailed analysis of many characters on many fossil specimens, much has been learned about the diversity and relationships between ischyromyine species. Yet, despite the completeness of many stratigraphic sections and the abundance of fossils examined, the nature of the change from one species to another remains obscure, and not a single speciation event has actually been documented.

    The only complete section for the Chadronian is at Flagstaff Rim, and only two of the many Chadronian species are represented there. Morphological similarities strongly suggest that one species branched into two, but the event of interest occurs in a barren stratigraphic interval (Figure 18). Most Chadronian and Duchesnean species are only known from single localities and are not zoned within those localities, so nothing can be said concerning the rates or patterns of their origins. The only Chadronian species with temporal continuity is Titanotheriomys veterior which is composed of three populations or subspecies, but nothing is known about the transition from one subspecies to another. The shift from the primitive, early Wyoming form to the later, smaller Wyoming form occurs in the barren stratigraphic interval at Flagstaff Rim mentioned above. The most derived, type population is only known from Pipestone Springs and other nearby localities in Montana.

    There are many complete Orellan sections from which Ischyromys have been collected at virtually every level. Ischyromys from these sections were previously thought to display a gradual increase in size and incidence of accessory cusps. But nearly all of that change occurs at the boundary of the lower and middle Orella (Figures 10 to 15), and it is clearly the result of the replacement of I. parvidens by I. typus rather than an evolutionary transition. Specimens identical to both species occur in the underlying Chadron Formation, and lower Orella Ischyromys display a bimodal size distribution showing that I. typus was present there in small numbers (Figure 10). But perhaps the best evidence for this conclusion comes from the Slim Buttes and Little Badlands sections where I. typus was the sole species throughout the entire Orellan (Figures 16 and 17).

    The replacement of I. parvidens by I. typus as the dominant Orellan species can be studied in some detail in the Toadstool Park and Munson Ranch sections where the sample size is large (Figures 10 and 11). Although these sections differ in the stratigraphic distribution of specimens, both show a very sparse interval following the disappearance of I. parvidens before I. typus becomes abundant. In fact the only sections containing I. parvidens that don't show this sparse interval are the Lusk and Douglas sections of Wyoming where I. typus never did become as abundant as I. parvidens was (Figures 13 and 14). This shows that the replacement was not due to I. typus outcompeting I. parvidens, although the disappearance of I. parvidens may have given I. typus the ecological opportunity it needed to proliferate.

    The only species found to exhibit any evolutionary change is I. typus. From the middle Orella to lower Whitney it increases in mean size by approximately one standard deviation of its overall diversity, and this amounts to an evolutionary rate of 0.07 Darwins. This is an exceeding slow rate of change, and there is no evidence that it involves anything besides overall size. This change is certainly not worthy of taxonomic recognition because the variation at any level far exceeds the change in mean. Other ischyromyine species might show a similar pattern of gradual change if they were represented by more zoned fossils or over a larger stratigraphic interval.

    The gradual size increase exhibited by I. typus is a minor change compared to the greater changes in size and shape that occurred at speciation. But for some reason, all substantial morphologic changes occur in poorly documented intervals. This cannot be attributed simply to gaps in the stratigraphic record because the Oligocene formations of Wyoming and Nebraska are known to be exceptionally continuous. It also cannot be attributed to poor preservation because fossils of other mammals are found in abundance even where ischyromyines are rare or absent. Instead the record seems to reflect the actual abundance of ischyromyines. Because of this, a comparison can be made between population size and other factors.

    An overall comparison between ischyromyines of the Chadronian and Orellan is instructive. In the Chadronian ischyromyines are scarce both in absolute numbers and in comparison to other rodents. Yet they are extremely diverse in number of species and in the differences that distinguish them. In Orellan sediments Ischyromys is the most abundant rodent and has an enormous population size, but not a single species appears to have arisen there. After originating in the Chadronian I. parvidens and I. typus display considerable uniformity until they go extinct. This suggests an inverse relationship between population size and speciation rate.

    There is also a correlation between population size and geographic range. Species that are well represented at one locality are more likely to be represented at other localities. In the Chadronian Titanotheriomys veterior is by far the most abundant ischyromyine species at every locality where it is found, and it is a very widespread species. It is found throughout Wyoming and Montana, and closely related species are found in Texas and Saskatchewan. All other species are known from single localities or very small regions. In the Orellan I. typus and I. parvidens are both abundant and widespread. This is particularly true of I. typus which is found in abundance at localities from North Dakota to Colorado.

    Eldredge and Gould (1972:89) named the classical Darwinian view of evolutionary change "phyletic gradualism" and described it as follows:

    1. New species arise by the transformation of an ancestral population into its modified descendants.
    2. The transformation is even and slow.
    3. The transformation involves large numbers, usually the entire ancestral population.
    4. The transformation occurs over all or a large part of the ancestral species' geographic range.
    Deviations from this pattern were classically attributed to imperfections in the fossil record by Darwin (1859) and later workers. Eldredge and Gould (1972) proposed an alternative model of evolutionary change called "punctuated equilibria" that takes the fossils record at face value. They described it as follows:
    1. New species arise by the splitting of lineages.
    2. New species develop rapidly.
    3. A small sub-population of the ancestral form gives rise to the new species.
    4. The new species originates in a very small part of the ancestral species' geographic extent--in an isolated area at the periphery of the range.
    Much controversy has arisen regarding the validity of this dichotomy, but many paleontologists accept it as a valid and testable alternative to the classical view, and numerous studies have been devised to test it (see reviews in Gould and Eldredge 1977; Gingerich 1985; Barnosky 1987).

    The patterns of change seen in ischyromyines display some features of both phyletic gradualism and punctuated equilibria. The gradual trend of increasing size seen in I. typus fits all the tenets of phyletic gradualism except that it doesn't continue long enough to produce a new species. Although this is the best documented case of change in the group, the very slow rate of this trend and the fact that it involves nothing but overall size makes this type of transition wholly inadequate to explain the speciation events and morphologic changes that occurred in Chadronian ischyromyines.

    Although the actual rates of speciation cannot be measured, the patterns fit the punctuated equilibria model quite well. The only logical ancestor for all Chadronian species of Titanotheriomys is T. veterior, and it persists (although with minor modifications) throughout most of the Chadronian. All species appear to have originated by the splitting of lineages and none by anagenesis. The endemic nature of Chadronian species also suggests that they arose allopatrically from small, isolated populations rather than sympatrically from large populations of ancestors, especially with so many localities containing only a single species. It seems beyond question that most new species originated in a very small part of their ancestor's geographic range.

    The inverse correlation between population size and rate of speciation in ischyromyines also supports the punctuated equilibria model. Gould and Eldredge (1977) emphasized that small populations are able to evolve much more rapidly than large ones because new innovations can become more quickly incorporated. If evolutionary rates were not a function of population size, then one would expect to find a representative amount of morphologic change in the most prolific fossil sequences, and this is not the case with ischyromyines.

    The combination of gradual and sudden change seen in ischyromyines could be considered a case of what Malmgren et al. (1983) termed "punctuated gradualism," or as Gould (1985:10) has more appropriately called "punctuated anagenesis." The dichotomy both in rates of change and population size seem much greater in ischyromyines than in the foraminifera studied by Malmgren et al. (1983), and anagenesis in the Ischyromyinae is only documented in one terminal lineage. Barnosky (1987) has shown that many lineages of Quaternary mammals show elements of both phyletic gradualism and punctuated equilibria.

    The results of this study differ markedly from the those of Gingerich (1974, 1976, 1979, 1980) whose numerous plots of tooth size vs. stratigraphic level for Eocene mammals show many cases of gradual anagenesis and cladogenesis. His use of only one size variable masks the more important changes in shape, however, and one can always challenge his phylogeny because size alone does little to establish ancestor-descendent relationships. Cheetham (1987) has shown that trends in single morphologic characters can be very misleading when compared to multivariate studies, so this is a serious criticism of Gingerich's work.

    The importance of studying many morphological characters together cannot be overemphasized. If overall size were the only variable studied in ischyromyines, the diversity of the Chadronian compared to the Orellan would never be recognized, the true relationships between populations would be totally obscured, and the gradual increase in the size of I. typus would be thought to be of much greater import to the group than it actually is. In this study the determination of relationships was in some cases actually enhanced by eliminating overall size from the analysis.

    While a detailed study of ischyromyine skulls and upper dentitions will be necessary to completely work out their taxonomy, the multivariate study of over 4,000 dentaries has made a significant step toward discovering the elusive relationships and patterns of evolutionary change within this group of primitive rodents. Although dentaries and lower dentitions remain quite stable throughout the life of the group, they are not useless as has sometimes been claimed, and when studied in large numbers and with numerous characters they do an excellent job of discriminating species. Because of their large numbers they also provide considerably more information about diversity and the details of change over time than do the rarer skulls and upper dentitions.

    In summary, this study has shown four important things about the Ischyromyinae: 1) There is a great wealth of diversity in the Chadronian that has gone largely unrecognized, apparently because of the rarity of specimens, 2) There is very little diversity in the Orellan, in spite of the enormous numbers of fossils, and it is very likely that no new species arose during that age, 3) The reported anagenetic shift of the Orellan is really due to the proliferation of a large species after the extinction of a small one, and 4) A minor increase in mean does occur in I. typus during the Orellan, but it is small compared to the diversity at each level and seems to involve nothing but overall size, so it is of trivial taxonomic importance compared to the differences in shape between species.

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