Ischyromyidae. Chapter 18 (pp. 373-398) in Prothero, D. R., and Emry, R. J. (eds.) The Terrestrial Eocene-Oligocene Transition in North America. Cambridge Univ. Press. (1996).

Timothy H. Heaton
Department of Earth Sciences
University of South Dakota
Vermillion, SD 57069

ABSTRACT

Ischyromys is known from the early Duchesnean to the early Whitneyan of the Rocky Mountains and Great Plains of North America. Early species are morphologically diverse and are known from small and sometimes fragmentary samples, so the Duchesnean history of the group is hard to unravel. A diverse radiation of species with a derived but variable jaw musculature dominates the Chadronian of the Rocky Mountains. These species have been assigned to Ischyromys by some authors and Titanotheriomys by others. The name Titanotheriomys is recognized herein as a subgenus of Ischyromys. The Orellan of the Great Plains is dominated by two species of Ischyromys that lack the Titanotheriomys specializations. Both these species are also known from the Chadronian of the Great Plains based on a few fragmentary remains. Ischyromys became less abundant in the Rocky Mountains and more abundant in the Great plains at the Chadronian-Orellan (Eocene-Oligocene) boundary, but no new species originated and no existing species underwent measurable change during the transition.

INTRODUCTION
Ischyromys is one of the most common rodents of the Eocene-Oligocene transition in North America, with a history of discovery going back to the early F. V. Hayden expeditions of the 1850s. Clark and Kietzke (1967), in their systematic paleoecological study of the South Dakota badlands, found Ischyromys to be the most common rodent in every environment and to be most abundant in dry plains environments lacking trees. More than five thousand jaws of Ischyromys exist in public museum collections and have been examined for this study.

In the Great Plains, Ischyromys is dominant during the Orellan but is also occasionally found in sediments of Chadronian and Whitneyan age. Farther west, particularly in Montana, Ischyromys is common in the Chadronian but rare during the Duchesnean and Orellan. The most geographically remote populations of Ischyromys come from Duchesnean and Chadronian deposits of Saskatchewan and Texas. The history of Ischyromys is complicated by the fact that Chadronian skulls typically have a more derived musculature than do their later Orellan counterparts (Wood, 1937, 1980). Several authors have used the name Titanotheriomys for Chadronian specimens with this derived condition, as discussed below.

METHODS
This study of Ischyromys has focused on lower dentitions because dentaries are by far the most common elements recovered. Each dentary or partial dentary containing teeth was placed on a special mount and photographed in occlusal and lingual view. These images were projected onto a digitizing tablet where a periphery/area/centroid measurement and 25 point coordinates were made on each available tooth (Figure 1). These data were used to calculate measurements for length and width of the teeth, positions of cusps and valleys, and various angles in order to quantify tooth size and shape (Figure 2). Three point coordinates were also established along the ventral margin of each jaw in lingual view, and jaw depth and shape were determined therefrom (Figure 3). Subjective scores were given for the wear stage of each tooth (Table 1) and for the size of the four accessory cusps (Table 2). Table 3 lists all measurements used in this study.

By far the largest collections of Ischyromys come from Orellan deposits of the Great Plains states, and these show remarkable morphologic uniformity. For this reason they will be discussed first, after which the problem of the Chadronian "Titanotheriomys" complex will be addressed.

ISCHYROMYS OF THE CENTRAL GREAT PLAINS
The following is a list of ischyromyid genera and species named from the Great Plains of the United States, together with the locality of each type specimen:

Ischyromys typusLeidy, 1856, 1869 SW South Dakota
Colotaxis cristatusCope, 1873a NE Colorado
Gymnoptychus chrysodonCope, 1873b NE Colorado
Ischyromys parvidensMiller and Gidley, 1920 SW South Dakota
Ischyromys pliacusTroxell, 1922 SE Wyoming (?)
Ischyromys typus nanusTroxell, 1922 NW Nebraska
Ischyromys typus lloydiTroxell, 1922 NW Nebraska
Ischyromys troxelliWood, 1937 SW South Dakota
Ischyromys sp. (large)Howe, 1966 NW Nebraska

The number of valid species has been disputed, though all were assigned to the genus Ischyromys at an early date. Wood (1937, 1980) accepted four species: I. typus, I. parvidens, I. pliacus, and I. troxelli. Howe (1956, 1966) proposed that I. parvidens, I. typus, I. pliacus, and I. sp. (large) represent chronospecies of a lineage that increased in size during the Orellan and early Whitneyan. Black (1968), on the other hand, accepted only two valid species, one large (I. typus) and one small (either the small Montana species, I. veterior, or I. parvidens). In an unpublished thesis that included much statistical analysis, O'Neill (1979) went so far as to consider all central Great Plains Ischyromys to be a single species.

My recent study of Great Plains Ischyromys has been the most comprehensive to date (Heaton, 1993a). A reevaluation was made of Howe's (1956, 1966) claim of anagenesis using a much larger sample, and it was concluded that two distinct and rather static species coexisted during the late Chadronian and Orellan in the Pine Ridge area (northwestern Nebraska and adjacent Wyoming). The first line of evidence for this conclusion came from the bimodal, or highly skewed, size distributions found in each stratigraphic interval. Figure 4 shows size histograms for the Chadron Formation, the lower portion of the Orella Member of the Brule Formation, and the middle Orella to Whitney interval of the Brule Formation. All of these populations differ significantly from a normal distribution, especially the lower Orella sample which has the smallest mean and is extremely right skewed. Another striking feature of the three populations in Figure 4 is that they all have about the same overall size range (same minimum and maximum) despite having very different means, medians and modes. While the mean size at each stratigraphic level is different, as Howe noted, it is not a case of a shifting normal distribution as would be expected for anagenetic change in a single lineage.

My alternate hypothesis, that two species of different sizes coexisted but varied in proportion, fits the data nicely. Separating a mixed distribution into its constituent normal distributions can be done mathematically using various assumptions, and a tabular approach was presented in Heaton (1993a). Using this method, the two mean values derived from the three stratigraphic populations are remarkably similar. Only the ratio of the small to large species differs, being about 1:1 in the Chadron, 10:1 in the lower Orella, and 1:20 in the middle Orella to Whitney. Based on the priority of type specimens of appropriate size from the Big Badlands of South Dakota, Heaton (1993a) used the names Ischyromys typus and I. parvidens for the large and small species, respectively. Estimated values for the mean and standard deviation of these two Pine Ridge species are given in Figure 4.

The second line of evidence suggesting the presence of two coexisting species is the absence of the smaller form outside the Pine Ridge area, even in lower Orellan strata. Bivariate plots showing size vs. stratigraphic level were presented in Heaton (1993a) for southwestern North Dakota, northwestern South Dakota, and northeastern Colorado, and corresponding histograms (all levels mixed) are shown in Figure 5. Only slight increases in mean size occurred over time, and for each locality the population closely fits a normal distribution. Mean sizes of these populations match well with the calculated mean for Ischyromys typus at Pine Ridge, so they clearly belong to that species. Therefore I. typus had a much wider geographic range than its smaller contemporary.

My previous report only briefly considered the Big Badlands of southwestern South Dakota despite the enormous collections made there. This was in part because most Big Badlands specimens are not zoned, and most of those that are come from the narrow stratigraphic interval known as the "Lower Nodular Zone." Contrary to my initial impression (Heaton, 1993a), the Big Badlands does not seem to contain the small species of Ischyromys found at Pine Ridge despite its close proximity, which brings into question the validity of the name I. parvidens (Heaton, 1993b).

Figure 6 contains histograms of all Big Badlands specimens and those known to come from the "Lower Nodular Zone." Figure 7 is a bivariate plot of the smaller zoned sample. Unfortunately the stratigraphic level for most of these specimens is not precise, and correlation across the Big Badlands is questionable (Prothero, 1985). But since plots made from separate localities look virtually identical, combining them seems justified and provides a reasonable density for the sparser intervals. A small increase in mean size over time is indicated, much like that in the northern Dakotas localities (Heaton, 1993a), but more notable is the near uniformity in size at all levels. Given this uniformity, it is ironic that Clark (1967) used the geographic uniformity of Ischyromys typus in the "Lower Nodular Zone" as evidence for the rapid and geographically synchronous deposition of the unit.

The mean size of Big Badlands Ischyromys is similar to that of I. typus at Pine Ridge and other Great Plains localities, and the sample very closely approximates a normal distribution. No evidence has been found for the presence of the small Pine Ridge species. Fortunately the type specimen of I. parvidens is a dentary with teeth; its size is marked on Figure 6. This appears to be a classic case in which a specimen from the tail end of a normal distribution was set apart as a distinct species when in fact it is not. This taxonomic problem is discussed below.

Wood (1976), Howe (1966), and others have commented on the uniform pattern of Ischyromys skulls from the Great Plains. Attempts to divide the sample into multiple species using my large multivariate dataset on lower dentitions all failed. Even the small and large species from Pine Ridge seem indistinguishable except for their difference in size. The only other possible distinction found was the incidence of accessory cusps on the teeth, but upon further investigation this turned out to be an allometric correlate of size and not a species difference (Heaton, 1993a). Therefore there is no justification for recognizing multiple species of Ischyromys in the central Great Plains beyond I. typus and the smaller Pine Ridge species, and long-used names such as I. pliacus and I. troxelli should be considered synonyms of I. typus.

ISCHYROMYS (TITANOTHERIOMYS) OF THE ROCKY MOUNTAINS
Ischyromyid fossils have been found in the Rocky Mountains and other western localities from Saskatchewan to Texas with a majority coming from basinal deposits of Montana and Wyoming. Nearly all of these predate the more abundant Orellan Ischyromys of the Great Plains, and most collections are small. By far the largest sample is from the Pipestone Springs Local Fauna in southwestern Montana. Pipestone Springs is the type locality for the first species of Ischyromys named from outside the Great Plains and the species most commonly compared to Great Plains Ischyromys.

Matthew (1903) named the Pipestone Springs material Ischyromys veterior and later gave this species the subgeneric name Titanotheriomys (Matthew, 1910). Miller and Gidley (1920), in their paper describing I. parvidens, considered Titanotheriomys to be of full genus rank, and they noted the similar small size of their new species and T. veterior. But Black (1968) dismissed the differences between Titanotheriomys and Ischyromys and considered I. parvidens to be a junior synonym of I. veterior. This synonymy began a dispute that will be a major focus of this paper.

Wood (1937) was the first to do a thorough taxonomic analysis of the ischyromyids, and his influence on the taxonomy of the group has been long and important (Wood, 1976, 1980). Wood (1937) considered Ischyromys and Titanotheriomys to be distinct genera, but he ignored most of the differences noted by Matthew (1903, 1910) and Miller and Gidley (1920) and instead drew up his own list of distinctions based mainly on skull structure. Titanotheriomys was described as having a broader, flatter skull than Ischyromys with a shorter pre-orbital region and more slender snout, zygoma, and braincase. The temporal crests of Titanotheriomys, as noted by Matthew (1910), do not meet to form a sagittal crest as they do in Ischyromys. Wood (1937) also stated that in Titanotheriomys the masseter extends farther onto the zygoma than in Ischyromys with a thin strip that extends farther onto the snout, thus approaching the advanced sciuromorph pattern found in some other rodent families. The infraorbital foramen is visible dorsally in Titanotheriomys but not in Ischyromys. Wood also stated that the mandible and postcranial elements, insofar as known, tend to be more slender in Titanotheriomys.

Black (1965) briefly mentioned Ischyromys and the problems of its taxonomy in his review of the rodents of the Pipestone Springs Local Fauna, and in a later paper he undertook his major revision of the genus. Black (1968) claimed that the distinctive characters used by Wood (1937) to separate Titanotheriomys from Ischyromys were not real and were due only to crushing and distortion of the two Chadronian skulls available to Wood. With better material from Pipestone Springs, Black stated that the skulls were indistinguishable and, therefore, that Titanotheriomys was a junior synonym of Ischyromys. He did recognize that some skulls have a sagittal crest while others do not, but on finding several intermediate configurations in skulls from Pipestone Springs he attributed this difference to individual or sexual variation. Wood (1969) initially conceded that Black's synonymy was correct, but in later publications he persuasively argued for the validity of Titanotheriomys (Wood 1974, 1976, 1980).

Early descriptions of Titanotheriomys mentioned a number of distinctive characters of the lower cheek teeth. Both Matthew (1903) and Wood (1937) claimed that the molars of T. veterior were relatively narrow compared to those of Great Plains Ischyromys, and Wood (1937) even erected a new species, T. wyomingensis, based on a skull similar to that of T. veterior but with "lower teeth [that] are no longer than they are broad." Wood (1937) also asserted that T. veterior was unique in possessing a partial barrier across the median valley of the lower molars, even though a similar feature was seen in some Ischyromys of the Great Plains.

Black (1968) erected the new species Ischyromys douglassi for specimens from the early Chadronian McCarty's Mountain Local Fauna. He described I. douglassi as being similar in size to I. typus but having teeth that are wider in relation to their length. He also listed many minor dental differences.

Russell (1972) reported ten isolated lower cheek teeth from a Chadronian locality in Saskatchewan and erected a new species, Ischyromys junctus, which he described as being intermediate in size between I. typus and I. parvidens. He stated that 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 nearly to the entoconid. Wood (1974) erected the most recently-named new species, Ischyromys blacki, for a specimen from Texas that he described as having a skull similar to that of I. typus but with teeth that have many primitive characters including prominent metaconules and incomplete metalophs, comparable to the condition seen in T. douglassi.

PIPESTONE SPRINGS, MONTANA
This study includes a much larger sample of Pipestone Springs ischyromyids than has previously been used, and multivariate analysis of the many characters measured can be used to evaluate the various claims of earlier authors. First, however, appropriate samples must be chosen for comparison.

As was the case for the Orellan sample from Pine Ridge, the ischyromyid sample from Pipestone Springs seems to be a mixture of two species. Wood (1937) and Black (1965) both recognized the presence of a second species larger than Titanotheriomys veterior which they provisionally assigned to the same species as the largest Great Plains specimens, Ischyromys pliacus. However, both authors ignored these larger specimens in their later publications. Figure 8 shows two histograms of Pipestone Springs specimens. Note the strong skewness to the right caused by the small number of large specimens, especially apparent in the occlusal area measurements. Since the deviation from a normal distribution is highly significant, the presence of two species is clearly indicated, and their means can be estimated mathematically. The estimated mean for T. veterior, the smaller species, is similar to that of the small Pine Ridge species that dominates the lower Orella. These species of similar size make for a useful comparison because they exemplify the Ischyromys and Titanotheriomys conditions and are available in roughly equal numbers. Because each of these populations is contaminated by specimens of a larger species that overlaps it in size but is not readily distinguishable, pure samples cannot be used. My solution was to eliminate all specimens for which the square root of occlusal area of M2 was 3.4 mm or greater in an attempt to reduce the level of contamination to a minimum.

Discriminant analysis is the ideal statistical technique for determining the degree to which two populations can be distinguished based on a suite of measured characters. Figures 1 through 3 show an idealized Ischyromys tooth and jaw along with the measurements made thereon, and the measurements are listed in Table 3. Heaton (1988, 1993c) reported results on five step-wise discriminant analyses attempting to distinguish Pipestone Springs Titanotheriomys from Great Plains Ischyromys: one analysis for each lower cheek tooth and one using only measurements of the dentary. Table 4 shows the success rates of these analyses and the number of variables selected by the step-wise routine in each case. Analyses of the last two molars were the most successful.

Table 5 lists several statistics for M2 and M3 measurements for the two populations. Note that the mean tooth length is larger for M2 than for M3 in the Pipestone Springs sample, but that the opposite is true in the Pine Ridge sample. This led me to believe that combining characters from these two teeth would improve the success of the discriminant analysis even further, and this turned out to be the case (Table 4). Figure 9 diagrams the result of a discriminant analysis on 38 characters, 19 from M2 and 19 from M3. Table 6 lists the variables used and shows the factor loadings provided by the routine. The success rate was 98% with only five Pipestone Springs specimens and one Pine Ridge specimen being misclassified.

The magnitude of the factor loadings shows how much they contributed to the discrimination (Table 6). For the factor loadings on whole tooth measurements (1-6), the positive values for M2 and negative values for M3 show that, on average, M2 is the larger tooth at Pipestone Springs while M3 is the larger tooth at Pine Ridge (thus reinforcing the indications in Table 5). Not only does the last tooth tend to be shorter in Titanotheriomys, but the posterior end of each tooth is also relatively shortened, especially in M3, as seen in the strong negative loadings on the factors that measure posterior features (7-11).

Figure 10 shows the results of an attempt to distinguish the two populations using only two characters, total length of M2 and posterior shortening of M3. One length measurement was divided by the other to create these histograms, thus factoring out differences in overall size. While these two characters alone are not diagnostic, the modes of the Pipestone Springs and Pine Ridge distributions are very different. Note that the Pipestone Springs sample has a wider range and is left skewed, but the Pine Ridge sample is not right skewed. Note also in Table 5 the low mean but high coefficient of variation for the posterior end of both M2 and M3 in the Pipestone Springs sample. This higher variability in Titanotheriomys, along with a tendency to mimic the Ischyromys condition, strongly suggests that the posterior shortening seen in the tooth row of the Pipestone Springs species is a derived condition.

Interestingly, the only character other than size that Matthew (1903) used to distinguish his new Montana species was that the last lower molar "has always 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." Wood (1937) claimed to be "entirely unable to find [this] difference," but it now stands out as an important feature in distinguishing Titanotheriomys veterior from Great Plains Ischyromys.

Table 6 shows that Titanotheriomys veterior of Pipestone Springs also tends to have lower-crowned molars than Ischyromys of Pine Ridge as suggested by the consistent negative loadings on the tooth height measurements (14-17), a difference suggested by Wood (1937). Several features of the lingual valleys also show consistent differences on both M2 and M3, though the magnitude of the loadings is low (Table 6). On average the anterior lingual valley is smaller in T. veterior, and it runs at a slightly greater angle from the main tooth axis (measurements 12-13, 18-19). Both the anterior and posterior lingual valleys sometimes contain an accessory cusp that in extreme cases can dam the valleys, though this feature is not consistent in Titanotheriomys and sometimes occurs in Ischyromys as well (Heaton, 1993a; Wood, 1937).

After examining a great many specimens I came to recognize subtle character differences that, unfortunately, do not show up in any of the measurements. The lingual valleys, especially the anterior, commonly make a bend in Titanotheriomys veterior that is never seen in Ischyromys. When this bend is present, a sharp ridge may extend posterolingually off the metaconid which appears as a bump in lingual view. Figure 11 illustrates this condition compared with a typical Great Plains Ischyromys. This condition, like the posterior shortening of the molars, is quite variable in T. veterior, so it cannot be used to distinguish the two forms with perfect accuracy.

My success in distinguishing the tooth rows of the small Pipestone Springs species from the small Pine Ridge species is ironic in that the only thing that Black (1968) and Wood (1980) agreed up on was that the teeth of the two populations were indistinguishable. This might seem a strong argument in favor of generically separating Titanotheriomys from Ischyromys, but one further consideration must be taken into account. The Pipestone Springs and Pine Ridge populations are separated by 750 km and are significantly different in age. Several smaller samples have been collected from the intervening parts of Wyoming. Most of the localities involved are geographically closer to Pine Ridge but closer in age to Pipestone Springs (i.e., Chadronian). The question to be asked is whether the fossils from the intervening localities match Ischyromys, match Titanotheriomys, or fall somewhere between the two.

The teeth will be considered first. Table 7 lists the pertinent localities arranged in order from northwest to southeast. A map showing several of these localities can be found on page ??. Table 7 also shows the classification of the small ischyromyid teeth (M2-3) provided by the discriminant factors of Table 6. By far the largest sample comes from Flagstaff Rim (to be discussed shortly). The Pine Ridge group consists of small dentaries from the Chadron Formation underlying the lower Orella sample. The discriminant analysis tends to classify specimens from the northwestern localities with the Pipestone species and those from the southeastern localities with the Pine Ridge species, but no distinct boundary exists. Figure 12 diagrams the results of the classification on the same scale as Figure 9, with specimens from each locality coded separately. Taken together these specimens form a unimodal distribution centered just to the right of the dividing line between the Montana and Nebraska samples. This clearly demonstrates that the intervening localities contain populations of intermediate character and not simply a mixture of two distinct species. The latter case would produce a broad bimodal curve similar to that in Figure 9.

FLAGSTAFF RIM, WYOMING
Figure 13 is a bivariate plot showing length of M2 and stratigraphic position of ischyromyids from Flagstaff Rim. This section represents most of the Chadronian, and the collections are well zoned thanks to the work of Emry (1973, 1992). Flynn (1977) studied both skulls and dentitions of ischyromyids from Flagstaff Rim and concluded that the sample represented coexisting lineages of Ischyromys and Titanotheriomys that were not distinguishable by size or tooth morphology. He based this conclusion on the fact that each of the 16 available skulls could clearly be classified as either Ischyromys (4) or Titanotheriomys (12) based on the characters outlined by Wood (1976). See Table 8 for a list of Wood's characters and Table 9 for Flynn's classifications. Flynn (1977) also suggested that a small number of larger specimens (seen in the upper portion of Figure 13) might represent a second species of Titanotheriomys at Flagstaff Rim. These larger specimens are not included in Table 7 or Figure 12. Kron (1978) also reported coexisting Ischyromys and Titanotheriomys from the latest Chadronian of the nearby Douglas locality based on skull morphology.

Wood (1976) discussed whether the differences in skull structure listed in Table 8 could be found as individual variation within a single population. No such variation exists in the abundant Orellan Ischyromys of the Great Plains, but the skull structure of Titanotheriomys is much more variable as Wood's character descriptions suggest (Table 8). The discriminant classification shown in Figure 12 strongly suggests that Flagstaff Rim and other Wyoming localities contain a population of intermediate character. Measurements on lower dentitions from Flagstaff Rim were scrutinized using statistical techniques to search for any sign of mixing. The population shows exceptionally low coefficients of variation for most characters, and a principal components analysis showed a good multivariate normal distribution with no evidence of bimodality or skewness on any principal component (Heaton, 1988). The conclusion seems inescapable that the small Flagstaff Rim ischyromyids represent a single species, contra Flynn (1977).

There is one additional piece of evidence to suggest that only one lineage of small ischyromyid exists at Flagstaff Rim. The first four skulls listed in Table 9 (USNM 215394, 215396, 215403, 215404), plus another partial skull (USNM 215402), came from a fossiliferous burrow filling 0.3 m in diameter and 1.2 m long (Robert J. Emry, personal communication). All five skulls represent juveniles at roughly the same stage of development (M2 fully erupted, M3 unerupted). The burrow filling also contained 5 left and 4 right juvenile dentaries and part of a juvenile articulated skeleton as well as two dentaries of older individuals. The excellent preservation and similar developmental stage make it highly likely that these juveniles are siblings that lived in the burrow rather than scavenged remains. However, using Wood's skull characters (Table 8), three of the five match Ischyromys, one matches Titanotheriomys, and one is not complete enough to determine (Table 9). If both skull types are present among siblings, then certainly both can exist in a single species.

THE CHADRONIAN-ORELLAN "TRANSITION"
The information presented here might seem to suggest that the small ischyromyids from Montana and Nebraska are merely end-members of a cline and that the Wyoming specimens represent an intermediate condition because of their central location within the cline. However, despite the fact that certain populations exhibit unusual variation in skull shape and musculature, the fact still remains that the abundant Ischyromys of the Great Plains shows no such variation but consistently retains the primitive condition. It therefore seems highly unlikely that Great Plains Ischyromys descended from the variable ischyromyids of Flagstaff Rim despite their close proximity. As explained previously and illustrated in Figure 4, Chadronian Ischyromys of Pine Ridge seems to fall into the same two size classes as Orellan Ischyromys, so they are presumably continuous lineages (Heaton, 1993a). Unfortunately, Chadronian ischyromyids are rare in Nebraska, and no skulls are available for comparison. Wood (1976) and Kron (1978) reported several incomplete skulls from the Douglas Chadronian, only one of which shows affinity to Titanotheriomys.

Figure 14 is a dendrogram from cluster analysis based on mean values from 31 populations of ischyromyids (after Heaton, 1993a). It shows a clear distinction between Chadronian and Orellan populations except that Chadronian teeth from Pine Ridge and the nearby Douglas locality cluster with their Orellan counterparts.

There are many striking differences between ischyromyids of the Great Plains and the Rocky Mountains. The vast majority of ischyromyid specimens collected from the Great Plains belong to Ischyromys typus, a species that is widespread, long-lived, shows remarkable morphologic uniformity, and consistently retains the primitive protrogomorphous skull condition. The smaller Great Plains species, though more restricted geographically, is similar to I. typus in its morphologic uniformity and primitive skull structure. Both species were abundant in the Orellan but have a documented Chadronian ancestry. Rocky Mountain ischyromyids, on the other hand, are virtually all Chadronian or older, are generally represented by small samples, exhibit much greater variation within populations and between localities, and show innovations in the skull that are not present in the Great Plains species. Their diversity may result from the more diverse topography and the likely presence of habitat islands in the more mountainous regions.

The ischyromyid populations of the Great Plains and Rocky Mountains are separated by time, space, and regional physiography. It is therefore difficult to assess which of these factors is most important in characterizing their differences. If time alone were considered, then it would appear that a major transition occurred at the Chadronian-Orellan boundary from a diverse and progressive family of rodents to a pair of primitive and stable species. There may be an element of truth to this, but at least part of the apparent transition is an artifact of the location, age, and productivity of fossiliferous sediments. Ischyromyid fossils have been found in the Chadronian of Nebraska and South Dakota and in the Orellan of Montana, but nearly all are isolated teeth, and they are too few in number for adequate statistical evaluation. Because it is highly unlikely that the primitive and morphologically uniform Ischyromys typus descended from a more derived and variable species like Titanotheriomys veterior, geographic factors should must be considered to explain the differences between Chadronian and Orellan populations. While many changes occurred in land mammal communities at the Eocene-Oligocene boundary as documented in this volume, there may not be such a clear demarcation for the ischyromyid rodents.

A purely geographic explanation for the ischyromyid dichotomy would hold that Ischyromys typus (and its smaller sister species) persisted throughout the Chadronian and Orellan of the Great Plains while an adaptive radiation of more variable and shorter-lived ischyromyid species occurred in the Rocky Mountains. The greater environmental uniformity and higher population density in the Great Plains might help explain such long-term stasis. The similarity of late Chadronian and Orellan ischyromyids from Pine Ridge shown in Table 7 and Figures 4, 12, and 14 supports this model, but the paucity of fossiliferous deposits of early Chadronian age in the Great Plains makes a full evaluation impossible. However, because a likely ancestor for Great Plains Ischyromys has not been found in the extensive Chadronian deposits of the Rocky Mountains, the simplest explanation is that such an ancestor lived in the Great Plains.

Stasis in the small ischyromyid species at Flagstaff Rim also supports a model of long-term regional stability. In Figures 12 and 13, specimens from two quarries low in the section exhibit no significant difference from those in the upper part of the section, although the quarry specimens group with those from some earlier localities in the cluster analysis (Figure 14). While I consider the small ischyromyid from Flagstaff Rim to be conspecific with Titanotheriomys veterior from Pipestone Springs, the Flagstaff Rim population of central Wyoming is morphologically much more similar to Ischyromys of the Great Plains than is its Montana counterpart, as is clearly shown by the discriminant analysis in Table 7 and Figure 12. It should also be noted that the Flagstaff Rim section spans a much longer time interval than the Pipestone Springs beds (Emry, 1992; Emry et al., 1987), yet specimens from Flagstaff Rim that both predate and postdate the Pipestone Springs Local Fauna were classified similarly by the discriminant analysis comparing Montana and Nebraska ischyromyids (Table 7, Figure 12).

Although geographic factors seem to hold greater weight in explaining ischyromyid evolution and diversity, time considerations are also important. The relative abundance of ischyromyids compared to other rodents was highest in the Chadronian of the Rocky Mountains but in the Orellan of the Great Plains. Rocky Mountain ischyromyids barely survived the Chadronian-Orellan boundary and are extremely uncommon in Orellan deposits; their Great Plains counterparts barely survived the Orellan-Whitneyan boundary before going extinct.

ISCHYROMYID TAXONOMY
Pending the completion of a detailed study of the skulls and upper dentitions of ischyromyids, I am not prepared to make a final taxonomic analysis or to erect any new species. This will be done in the near future. I will, however, present my tentative conclusions based on my extensive study of lower dentitions and on studies of skulls conducted by Wood (1976) and others.

Population studies such as those I have conducted with Ischyromys provide satisfactory bases for determining the limits of fossil species so that inappropriate lumping or splitting of taxa can be avoided. Such bases are needed in the science of paleontology for resolving taxonomic disputes at the species level. However, defining the statistical means and limits of a species does not always ease the problem of assessing the validity of old type specimens or, for that matter, of assigning any individual specimen to its appropriate species. Even after doing elaborate statistical analyses of large populations, it remains frustratingly difficult to evaluate samples that are small or fragmentary. Taxonomy has been the most problematic and unrewarding aspect of this lengthy paleobiological study.

THE STATUS OF TITANOTHERIOMYS
The fact that Titanotheriomys veterior and related species have specializations in their skulls that are generally considered to be characters of subordinal rank among rodents would suggest that genus recognition is appropriate (Wood, 1976). The multivariate statistical studies presented in Heaton (1993a) and in this paper suggest that the Ischyromys/Titanotheriomys distinction, at least among some populations, can also be made with dentaries. As can be seen in Figure 14, Chadronian populations with Titanotheriomys-type skulls cluster, along with two Duchesnean populations having Ischyromys-type skulls, into a coherent group that diversified and subsequently went extinct (or became exceedingly rare) in the Chadronian. Orellan Ischyromys of the Great Plains did not evolve from this group but retains the primitive skull condition of its Duchesnean ancestors. Titanotheriomys appears to be a monophyletic group with skull specializations that are shared and derived, though rather variable and inconsistent, characters. If Titanotheriomys is granted genus status, then Ischyromys becomes a paraphyletic group sharing the primitive protrogomorphous skull condition.

The status of Titanotheriomys is subjective, and utility should be a prime consideration. There is no single character that consistently separates any element of Ischyromys from that of Titanotheriomys. In both skulls and lower dentitions, some members of the Titanotheriomys group are indistinguishable from Ischyromys. Because of this, and because the Ischyromys/Titanotheriomys group as a whole is so easily distinguished from all other rodents, I prefer Matthew's (1910) original designation of Titanotheriomys as a subgenus of Ischyromys. Such a designation allows the recognition of the species of Titanotheriomys as a coherent adaptive radiation of rodents, but it also allows ambiguous specimens (or even species) to be labeled "Ischyromys sp." rather than "Ischyromys or Titanotheriomys".

The subgenus Ischyromys will apply to I. typus and other species that retain the primitive skull condition of the genus. The subgenus Titanotheriomys will apply to I. (T.) veterior and its relatives which have a more derived skull musculature.

ISCHYROMYS (ISCHYROMYS) TYPUS OF THE GREAT PLAINS
Range: Late Chadronian (or earlier) to early Whitneyan.
Ischyromys typus is the latest surviving ischyromyid species, one of the most wide ranging geographically, and by far the most common in museum collections. It is unusually uniform in the structure of its skull and teeth, although it increased slightly in mean size between the Chadronian and early Whitneyan (Heaton, 1993a). Ischyromys typus is most abundant at Orellan localities of the Great Plains from Colorado to North Dakota.

As the genotype, the type specimen of Ischyromys typus (ANSP 11015) from the Big Badlands of South Dakota has absolute priority. Fortunately the specimen is a fairly complete skull with the typical protrogomorphous condition. As shown earlier in this paper, only one species of Ischyromys is indicated by the large sample of lower dentitions from South Dakota, so this species is I. typus.

The following taxa are synonyms of Ischyromys typus Leidy (1856, 1869): Colotaxis cristatus (Cope 1873a), Gymnoptychus chrysodon (Cope 1873b), I. pliacus (Troxell 1922), I. typus lloydi (Troxell 1922), and I. troxelli (Wood 1937). The types of I. parvidens (Miller and Gidley 1920) and I. typus nanus (Troxell 1922) are small jaws that may belong to I. typus or may instead belong to the smaller ischyromyid of the Great Plains discussed below.

ISCHYROMYS (ISCHYROMYS) (SMALL) OF THE GREAT PLAINS
Range: Late Chadronian (or earlier) and Orellan.
As originally proposed by Miller and Gidley (1920) and demonstrated by Heaton (1993a), there exists a second, smaller species of Ischyromys in the central Great Plains. This species has usually been called I. parvidens. As shown above, it is distinct from I. veterior of Pipestone Springs and does not belong to that species, contra Black (1968). Also, it did not give rise to I. typus during the Orellan as proposed by Stout (1937) and Howe (1956, 1966). Both species coexisted in the Orellan and for an undetermined portion of the Chadronian (Heaton, 1993a).

The decision as to the proper name for this small species has been one of the biggest dilemmas faced in this study. The type of Ischyromys parvidens is a small, unzoned dentary (USNM 9134) from the Big Badlands of South Dakota (Miller and Gidley, 1920). As can be seen in Figure 6, the Big Badlands appears to have only a single species of which this specimen is but a small member at the tail end of the size distribution. As such I. parvidens would be a junior synonym of I. typus. However, this specimen is smaller than the mean size of the small species at Pine Ridge just 100 km to the southwest, and it is conceivable that the small Pine Ridge species could have ranged north into the Big Badlands. All that can be stated with certainty is that the small species does not appear in the Big Badlands in statistically significant numbers, and therefore the probability that such a specimen belongs to the small Pine Ridge species is exceedingly low.

Second in priority to Ischyromys parvidens is I. typus nanus named by Troxell (1922) for a dentary from Pine Ridge north of Harrison, Nebraska. The type specimen (YPM 12519) is slightly larger than the type of I. parvidens but is still smaller than the mean of the small Pine Ridge species. While there are clearly two coexisting species at Pine Ridge, only the very largest and smallest specimens can be assigned to one species or the other with any degree of confidence because the only features that distinguish the two are size and characters allometrically correlated with size (Heaton, 1993a). Most specimens from the ranches north of Harrison are I. typus from the middle and late Orellan, so the type of I. typus nanus may be nothing more than a small specimen of I. typus as proposed by Troxell (1922).

The resolution of this problem must await a careful study of the skulls and upper dentitions. If a new type must be designated, there is a nearly complete skeleton with skull and dentaries (UNSM 68129) from the early Orellan which almost certainly belongs to this species.

ISCHYROMYS (TITANOTHERIOMYS) VETERIOR OF THE ROCKY MOUNTAINS
Range: Early to late (but not latest) Chadronian.
This species was named by Matthew (1903) who mentioned "the anterior part of a skull and some forty jaws or parts of jaws, upper and lower" from Pipestone Springs but provided no illustrations or museum catalog numbers. Records at the American Museum of Natural History list a skull (AMNH 9647) as Matthew's intended type specimen, but Wood (1937) designated a dentary (AMNH 9658) as the lectoholotype. The material available to Matthew adequately characterizes this small Pipestone Springs species, so Ischyromys (Titanotheriomys) veterior is the valid name. Wood (1937) named the species T. wyomingensis for a skull and associated dentaries (AMNH 14579) from Beaver Divide, central Wyoming, but this has since been considered a synonym of I. veterior (Black, 1968; Wood, 1980).

As shown in Figures 9 and 10 and Tables 5 and 6, Ischyromys veterior from Pipestone Springs is distinct from the small Orellan species of Pine Ridge in having a short M3 relative to the other teeth and in having a shortening of the posterior region of all the lower cheek teeth. This appears to be a derived character that is most distinctive in the Montana specimens; teeth referred to I. veterior from Wyoming localities are more similar to those from Pine Ridge (Figure 12, Table 7). While the Montana and Wyoming populations show measurable differences, the overlap is so great that the two should be regarded as the same species. The Montana population could be considered a more derived subspecies or variety.

The study of Ischyromys veterior from Wyoming provides some of the clearest insights into ischyromyid evolution. Figure 13 shows that this species underwent a minor decrease in size during the Chadronian. The cluster analysis in Figure 14 grouped the specimens from the upper part of the Flagstaff Rim section with the Pipestone Springs population and with other populations of similar age from Wyoming, but it grouped the quarry samples from low in the section with several early Chadronian populations, one of which (West Canyon Creek) has the Ischyromys-type skull. This suggests that I. veterior might have been the stem species that first developed the Titanotheriomys-type skull and subsequently gave rise to the other, more distinctive members of the subgenus (Heaton, 1988). The fact that Flagstaff Rim I. veterior dentaries, regardless of stratigraphic level, lack the specializations of the Pipestone Springs population (Figures 11 and 12, Table ) suggests that Titanotheriomys may have originated in a region closer to Wyoming than to Montana.

The probable descendants of Ischyromys veterior are discussed below, together with some populations that may prove to be conspecific. As can be seen in Figure 13, I. veterior may not have survived to the end of the Chadronian or even survived as long as the larger Flagstaff Rim species, although the Flagstaff Rim section becomes less fossiliferous toward the top and makes the available evidence inconclusive.

ISCHYROMYS (TITANOTHERIOMYS) (LARGE) OF FLAGSTAFF RIM, WYOMING
Range: Middle to late Chadronian.
A second, larger species of Ischyromys (Titanotheriomys) first appears near the middle of the Flagstaff Rim section as noted by Flynn (1977) and Emry (1992) and shown in Figure 13. Its teeth are nearly identical in shape to those from the lower quarries at Flagstaff Rim, as indicated by the cluster analysis in Figure 14. The appearance of this species may represent a case of sympatric speciation in I. veterior, although such an assertion is impossible to prove. The only distinguishing feature of this species is its large size, but this alone, following cladogenesis, warrants its recognition as a new species.

There is a striking similarity in evolutionary pattern between the ischyromyids and the leptomerycids at Flagstaff Rim (Emry, 1973; Heaton and Emry, this volume). In both cases an ancestral species seems to have split into two: one that became slightly smaller and underwent a change in shape and another that became much larger but retained the ancestral morphology.

ISCHYROMYS (TITANOTHERIOMYS) (LARGE) OF PIPESTONE SPRINGS, MONTANA
Range: Middle Chadronian.
As discussed above and illustrated in Figure 8, a large ischyromyid occurs in small numbers at Pipestone Springs along with Ischyromys veterior. This species was erroneously identified as I. pliacus by Wood (1937) and Black (1965) but was later recognized as a new species of Titanotheriomys based on skull characters (Wood, 1976, 1980). This species clusters with the middle Chadronian populations of I. veterior (Figure 14) and probably arose from that species later than did the large Flagstaff Rim species. It differs from the later species and from I. veterior in having dental characters that are convergent with I. typus of the Great Plains (Heaton, 1988). It is a distinct but as yet unnamed species.

ISCHYROMYS (TITANOTHERIOMYS) DOUGLASSI OF McCARTY'S MOUNTAIN, MONTANA
Range: Early Chadronian.
Ischyromys douglassi is sufficiently distinct to be considered a valid species as proposed by Black (1968). It has the snout musculature of Titanotheriomys but has a sagittal crest in all known specimens (Wood, 1976, 1980; see Table 8). It is unique in being the largest species of Ischyromys with low cusps and shallow valleys, and the anterior lingual valleys of the teeth have a distinctive shape (Heaton, 1988). The M3 of I. douglassi has not undergone the posterior shortening seen in I. veterior; in fact it has the longest mean posterior M3 length of all the populations studied. This species is known only from McCarty's Mountain, Montana; it has not been found in sediments of similar age in Wyoming.

ISCHYROMYS (TITANOTHERIOMYS) JUNCTUS OF CYPRESS HILLS, SASKATCHEWAN
Range: Early and/or middle Chadronian.
Russell (1972) named Ischyromys junctus for a small number of isolated teeth from the Cypress Hills in western Saskatchewan. The cluster analysis of Figure 14 groups it with Titanotheriomys, but the skull is unknown. When mean values for various populations are compared, I. junctus has the shortest length for M3 of any ischyromyid (Heaton, 1988). This suggests that it may have taken the relative shortening of M3 to an even greater extreme than did I. veterior of Pipestone Springs, but with the present small sample of isolated teeth it is impossible to prove this conjecture. The cusps of the teeth are very low and rounded and the valleys shallow, so they are distinct from I. veterior despite their similar size. Storer (1978) mentioned this and listed several other distinguishing characters. Ischyromys junctus appears to be a valid species, but without more complete material it is difficult to establish its relationship to other ischyromyids.

ISCHYROMYS (TITANOTHERIOMYS) OF ASH SPRING, TEXAS
Range: Middle Chadronian.
Dentaries of two small individuals of Ischyromys were found in the Big Bend region of Texas (Harris, 1967) and were considered by Wood (1974) to belong to Ischyromys (Titanotheriomys) veterior. The cluster analysis of Figure 14 groups this population with I. junctus from the Cypress Hills despite the 2200 km that separates the two localities. The Ash Spring species, however, lacks the low, rounded cusps of I. junctus. In fact the cusps would be unusually high for I. veterior, so the Ash Spring form may represent a distinct species (Heaton, 1988). Morphological differences of small magnitude in such a small sample do not warrant species recognition, but the distant geographic locality may make such a distinction useful.

ISCHYROMYS (ISCHYROMYS) BLACKI OF PORVENIR, TEXAS
Range: Latest Duchesnean and/or early Chadronian
The Porvenir Local Fauna of Texas is the southernmost Ischyromys locality as well as one of the earliest. Wood (1974) erected the new species I. blacki for a skull and dentary from the Porvenir Local Fauna. Like the other early species discussed below, I. blacki lacks the skull specializations of Titanotheriomys (Wood, 1976).

The single known dentary of Ischyromys blacki has an M3 that is exceedingly long compared to M2, a trend opposite that seen in I. veterior. The cluster analysis of Figure 14 groups this species with other early populations (mostly Titanotheriomys), though as a very distinct member of that group. Both its early age and distinctive suite of characters make it a valid species.

ISCHYROMYS (ISCHYROMYS) OF WEST CANYON CREEK, WYOMING
Range: Late Duchesnean
A channel fill in central Wyoming has produced a late Duchesnean fauna that is currently under study by Robert J. Emry. Several well-preserved skulls and jaws of Ischyromys have been found there which, like I. blacki, lack the skull specializations of Titanotheriomys. The West Canyon Creek specimens comprise a new species that is typical in most respects but which has a unique dental feature that separates it from all other species of Ischyromys and gives the molars a distinctive appearance. This unique feature is the exceptionally high incidence of medial and lingual accessory cusps (Figures 1 and 2, Tables 2 and 3), higher than in any other Ischyromys population on both M2 and M3. These accessory cusps are so strongly developed that they completely dam the lingual valleys in most cases. In addition, the posterior lingual valley extends unusually far anteriorly (Heaton, 1988).

It is difficult to determine whether this species represents a likely ancestor for later species of Ischyromys or whether it is a unique, terminal lineage. The species is of medium size and is quite average in most respects. Like I. blacki, it tends to cluster with the Titanotheriomys populations (Figure 14) in spite of having an Ischyromys-type skull. However, the West Canyon Creek form lacks the elongate M3 of I. blacki. In these respects it makes a likely ancestor for all later species. The high incidence of accessory cusps might most easily be explained as a derived character, but an alternative explanation is available. Since these cusps show up sporadically in all later species of Ischyromys for which large samples are available, they may represent atavisms of a former, more consistent character trait. The M3 on the type skull of I. blacki has the peculiar look of the West Canyon Creek molars, but the other teeth lack it. Of these two known late Duchesnean species, it is difficult to say which, if either, would make a good ancestor for Chadronian and Orellan Ischyromys.

ISCHYROMYS OF BADWATER CREEK, WYOMING
Range: Early Duchesnean
Black (1971), using screening techniques, recovered four upper and one lower cheek teeth from the Hendry Ranch Member of the Wagonbed Formation in central Wyoming which he called ?Ischyromys sp. These appear to be the oldest known Ischyromys specimens. Despite the close proximity of this site to West Canyon Creek, none of these teeth have accessory cusps. Even the major cusps appear weakly developed and the valleys shallow as in I. junctus. Without better specimens it is difficult to evaluate this material, but it may represent a new species.

ISCHYROMYS OF LAC PELLETIER, SASKATCHEWAN
Range: Early or middle Duchesnean.
Storer (1988) recovered five upper and four lower isolated cheek teeth of a small form of Ischyromys from the Lac Pelletier Lower Fauna which he believes to represent a new species. Some of these teeth have very low and indistinct cusps like those of I. junctus; others are similar to I. veterior of the lower Flagstaff Rim section.

As with the Badwater Creek specimens, the lack of large samples, associated teeth, and skull remains from the Lac Pelletier Lower Fauna makes evaluation of this material impossible using the methods employed in this study. At present it is not even possible to determine how many species might be represented.

CONCLUSIONS
Working out the early evolution of Ischyromys is difficult because most of the available populations are small and seem to represent local species. Early Duchesnean samples consist of only a few isolated teeth, while late Duchesnean samples are difficult to interpret because they possess unique characters. All known Duchesnean skulls are of the Ischyromys type and lack the specializations seen later in the Titanotheriomys radiation (Table 8). Ischyromys douglassi of the early Chadronian is intermediate in this respect.

The Chadronian of the Rocky Mountains and Canadian Great Plains hosted an adaptive radiation of species that possess the skull specializations of Titanotheriomys. Ischyromys (T.) veterior of the lower Flagstaff Rim section is the most generalized member of the group and may be ancestral to the others. Populations from the upper part of the Flagstaff Rim section, Pipestone Springs and other Montana localities, and at Ash Spring, Texas, all have more derived characters. Figure 15 shows possible relationships among Ischyromys species and among geographic populations of I. veterior. The Titanotheriomys radiation dominates the Chadronian, but this subgenus is not known from the Orellan, with the possible exception of a few isolated teeth from Montana.

Orellan Ischyromys of the central Great Plains is not derived from Titanotheriomys but had a separate, as yet unknown ancestry from some Duchesnean species that lacked the Titanotheriomys skull specializations. Ischyromys typus is by far the most common ischyromyid fossil and is known from the late Chadronian to early Whitneyan at localities from Colorado to North Dakota. Its smaller sister species is known only from the late Chadronian and Orellan of Pine Ridge, Nebraska, to Douglas, Wyoming, where it dominated over I. typus during the early Orellan at all localities in its range (Heaton, 1993a).

The Rocky Mountains hosted many localized species and populations of Ischyromys throughout the Duchesnean and Chadronian. The Great Plains, in contrast, hosted only two very conservative, similar, static species, one of which had a wide geographic range. While this difference may be due in part to the later (Orellan) age of most Great Plains specimens, it seems largely related to geographic differences between the Rocky Mountains and Great Plains physiographic provinces. For instance, the isolated basins of the Rocky Mountains might promote the formation of isolated populations capable of speciation while the environmental uniformity of the Great Plains might inhibit this. Some of the apparent differences between Chadronian and Orellan ischyromyids may, therefore, be artifacts of the location of fossiliferous sediments. However, the Chadronian-Orellan transition is marked by the decline and extinction (or extreme rarity) of Titanotheriomys in the Rocky Mountains and by the increasing dominance of Ischyromys in the Great Plains.

ACKNOWLEDGEMENTS
This project began as a doctoral dissertation under the direction of Stephen Jay Gould at Harvard University. The study of Ischyromys was proposed by T. Mylan Stout, who also introduced me to the Nebraska Oligocene. Robert J. Emry and Donald R. Prothero provided extensive help and encouragement throughout the duration of the project. Alan R. Tabrum and John E. Storer read the manuscript and made many helpful comments. To these individuals, and many others who helped in numerous ways, I offer my warmest thanks.

This study included nearly every Ischyromys jaw available in a public museum. I therefore owe the greatest debt to the hundreds of collectors and curators over the last 150 years who made a study such as this possible by preserving these fossils, along with pertinent data, and making them available for study.

This research was supported by fellowships and grants from Harvard University, the University of South Dakota, the Geological Society of America, the Smithsonian Institution, and the American Museum of Natural History.

LITERATURE CITED

Black, C. C. 1965. Fossil mammals from Montana. Pt. 2. Rodents from the early Oligocene Pipestone Springs local fauna. Annals of Carnegie Museum, 38(1):1-48.

Black, C. C. 1968. The Oligocene rodent Ischyromys and discussion of the Family Ischyromyidae. Annals of Carnegie Museum 39(18):273-305.

Black, C. C. 1971. Paleontology and geology of the Badwater Creek area, central Wyoming. Part 7. Rodents of the family Ischyromyidae. Annals of Carnegie Museum, 43(6):179-217.

Clark, J. 1967. Paleoecology of the Scenic Member of the Brule Formation. Pp. 75-110 in Clark, J., J. R. Beerbower, and K. K. Kietzke (eds.), Oligocene Sedimentation, Stratigraphy, Paleoecology and Paleoclimatology of the Big Badlands of South Dakota. Fieldiana: Geology Memoirs, 5:1-158.

Clark, J., and K. K. Kietzke. 1967. Paleoecology of the Lower Nodular Zone, Brule Formation, in the Big Badlands of South Dakota. Pp. 111-137 in Clark, J., J. R. Beerbower, and K. K. Kietzke (eds.), Oligocene Sedimentation, Stratigraphy, Paleoecology and Paleoclimatology of the Big Badlands of South Dakota. Fieldiana: Geology Memoirs, 5:1-158.

Cope, E. D. 1873a. Second notice of extinct vertebrates from the Tertiary of the plains. Paleontological Bulletin, 15:1-8.

Cope, E. D. 1873b. Third notice of extinct vertebrates from the Tertiary of the plains. Paleontological Bulletin, 16:1-8.

Emry, R. J. 1973. Stratigraphy and preliminary biostratigraphy of the Flagstaff Rim area, Natrona County, Wyoming. Smithsonian Contributions to Paleobiology, 18:1-43.

Emry, R. J. 1992. Mammalian range zones in the Chadronian White River Formation at Flagstaff Rim, Wyoming. Pp. 106-115 in D. R. Prothero and W. A. Berggren (eds.), Eocene-Oligocene Climatic and Biotic Evolution. Princeton University Press, 568 p.

Emry, R. J., P. R. Bjork, and L. S. Russell. 1987. The Chadronian, Orellan, and Whitneyan Land Mammal Ages. Pp. 119-152 in M. O. Woodburne (ed.), Cenozoic Mammals of North America: Geochronology and Biostratigraphy. University of California Press, Berkeley, 336 p.

Flynn, J. J. 1977. Morphological variation in the Oligocene Ischyromyidae (Rodentia) from Flagstaff Rim, Wyoming. Unpublished ms., Yale University, Department of Geology and Geophysics, Senior Paper Series, 46 p.

Harris, J. M. 1967. Oligocene vertebrates from western Jeff Davis County, Trans-Pecos Texas. Unpublished M.A. thesis, University of Texas, Austin, 165 p.

Heaton, T. H. 1988. Patterns of evolution in Ischyromys and Titanotheriomys (Rodentia: Ischyromyidae) from Oligocene deposits of western North America. Unpublished Ph.D. thesis, Harvard University, 165 p.

Heaton, T. H. 1993a. The Oligocene rodent Ischyromys of the Great Plains: replacement mistaken for anagenesis. Journal of Paleontology, 67(2):297-308.

Heaton, T. H. 1993b. The fossil rodent Ischyromys in Badlands National Park, South Dakota (Abstract). Proceedings of the South Dakota Academy of Sciences, 72:332-333.

Heaton, T. H. 1993c. Dentaries of Ischyromys and Titanotheriomys (Oligocene, Rodentia) can be distinguished by discriminant analysis, cluster analysis, and multidimensional scaling (Abstract). Journal of Vertebrate Paleontology, 13(3):41A.

Howe, J. A. 1956. The Oligocene rodent Ischyromys in relationship to the paleosols of the Brule Formation. Unpublished M.S. thesis, University of Nebraska, Lincoln, 89 p.

Howe, J. A. 1966. The Oligocene rodent Ischyromys in Nebraska. Journal of Paleontology, 40(5):1200-1210.

Kron, D. G. 1978. Oligocene vertebrate paleontology of the Dilts Ranch area, Converse County, Wyoming. Unpublished M.S. thesis, University of Wyoming, Laramie, 185 p.

Leidy, J. 1856. Notices of remains of extinct Mammalia discovered by Dr. F. V. Hayden in Nebraska Territory. Proceedings of the Academy of Natural Sciences of Philadelphia, 8:88-90.

Leidy, J. 1869. The extinct mammalian fauna of Dakota and Nebraska, including an account of some allied forms from other localities, together with a synopsis of the mammalian remains of North America. Journal of the Academy of Natural Sciences of Philadelphia, Series 2, 7:23-472.

Matthew, W. D. 1903. The fauna of the Titanotherium beds at Pipestone Springs, Montana. Bulletin of the American Museum of Natural History, 19:197-226.

Matthew, W. D. 1910. On the osteology and relationships of Paramys, and the affinities of the Ischyromyidae. Bulletin of the American Museum of Natural History, 28:43-71.

Miller, G. S., Jr., and J. W. Gidley. 1920. A new fossil rodent from the Oligocene of South Dakota. Journal of Mammalogy, 1(2):73-74.

O'Neill, K. E. 1979. Taxonomic study of middle Oligocene specimens of the genus Ischyromys: multivariate analysis of the cheek tooth dentition. Unpublished M.A. thesis, University of Wisconsin, 358 p.

Prothero, D. R. 1985. Correlation of the White River Group by magnetostratigraphy. Dakoterra, Museum of Geology, South Dakota School of Mines, 2(2):265-276.

Russell, L. S. 1972. Tertiary mammals of Saskatchewan. Part II: The Oligocene fauna, non-ungulate orders. Life Science Contributions of the Royal Ontario Museum, 84:1-63.

Storer, J. E. 1978. Rodents of the Calf Creek Local Fauna (Cypress Hills Formation, Oligocene, Chadronian), Saskatchewan. Contributions of the Saskatchewan Museum of Natural History, 1:1-54.

Storer, J. E. 1988. The rodents of the Lac Pelletier Lower Fauna, late Eocene (Duchesnean) of Saskatchewan. Journal of Vertebrate Paleontology, 8(1):84-101.

Stout, T. M. 1937. A stratigraphic study of the Oligocene rodents in the Nebraska State Museum. Unpublished M.S. thesis, University of Nebraska, Lincoln, 83 p.

Troxell, E. L. 1922. Oligocene rodents of the Genus Ischyromys. American Journal of Science, Series 5, 3(8):123-130.

Wood, A. E. 1937. The mammalian fauna of the White River Oligocene. Part II. Rodentia. Transactions of the American Philosophical Society, New Series, 28(2):155-269.

Wood, A. E. 1969. Rodents and lagomorphs from the 'Chadronia Pocket', Early Oligocene of Nebraska. American Museum Novitates, 2366:1-8.

Wood, A. E. 1974. Early Tertiary vertebrate faunas, Vieja Group, Trans-Pecos Texas: Rodentia. Bulletin of the Texas Memorial Museum 21:1-112.

Wood, A. E. 1976. The Oligocene rodents Ischyromys and Titanotheriomys and the content of the Family Ischyromyidae. Pp. 244-277 in C. S. Churcher (ed.), Athlon: Essays on Paleontology in Honor of Loris Shano Russell. Royal Ontario Museum Life Science Miscellaneous Publication, University of Toronto Press.

Wood, A. E. 1980. The Oligocene rodents of North America. Transactions of the American Philosophical Society, 70(5):1-68.


Figure 1. Diagram of an idealized lower molar of Ischyromys in occlusal and lingual view showing points digitized and positions of accessory cusps (after Heaton, 1988).

Figure 2. Diagram of an idealized lower molar of Ischyromys in occlusal and lingual view showing measurements generated for this study (after Heaton, 1988).

Figure 3. Diagram of an idealized dentary of Ischyromys in lingual view showing points digitized and measurements generated for this study (after Heaton, 1988).

Figure 4. Histograms of M2 length values for three stratigraphic samples of Ischyromys at Pine Ridge, Nebraska. The upper two histograms include all appropriate specimens from the Toadstool Park and Munson Ranch localities (see Heaton, 1993a). The lower histogram also includes Chadronian specimens from all Pine Ridge and Douglas localities (see map on page ??). The bar and parentheses below each histogram show graphically the mean and standard deviation of each sample. Below the histograms are the estimated statistics for the two species that are thought to make up these three samples.

Figure 5. Histograms of M2 length values for three geographic populations of Ischyromys: southwestern North Dakota, northwestern South Dakota, and northeastern Colorado (see map on page ??). Each of these populations closely approximates a normal distribution whose mean and standard deviation closely matches the larger species from Pine Ridge (I. typus) shown in Figure 4. Note the paucity of specimens in the 3.0-3.3 mm range where the small Pine Ridge species has its mode. The skewness of the Slim Buttes sample is a result of stratigraphic mixing and anagenesis, not coexisting species (Heaton, 1993a).

Figure 6. Histograms of M2 length values for Ischyromys from the Big Badlands, southwestern South Dakota (see map on page ??). The lower histogram contains only specimens known to have come from the "Lower Nodular Zone" (the most fossiliferous stratigraphic interval). Like the localities in Figure 5, this population closely fits a normal distribution and is therefore interpreted to contain only I. typus. The type specimen of I. parvidens falls in the extreme left tail of the size distribution.

Figure 7. Bivariate plot of 605 zoned Ischyromys from the Big Badlands of South Dakota, a subset of the sample shown in the upper histogram of Figure 6. Stratigraphic levels are shown with reference to the Chadron/Brule boundary. Most specimens are from the "Lower Nodular Zone."

Figure 8. Histograms of M2 length and square root of occlusal area values for Ischyromys (Titanotheriomys) from Pipestone Springs, Montana. Like the lower Orella sample in Figure 4, this population is clearly a mixed sample containing a small number of specimens from a large species as well as a large sample of I. (T.) veterior.

Figure 9. Histogram showing results of discriminant analysis on Pine Ridge lower Orella and Pipestone Springs populations based on 38 characters of M2 and M3. Only dentaries for which both molars are present and fall in wear classes 2 through 5 are included (see Table 1). Table 6 lists the characters used and their corresponding factor loadings. Only 5 of the Pipestone Springs and one of the lower Orella specimens were misclassified, giving the analysis a 98% classification success rate.

Figure 10. Histograms for Pipestone Springs and Pine Ridge lower Orella populations showing values generated by dividing the length of the posterior end of M3 by the total length of M2. This calculated variable combines the effects of the shortening of M3 relative to M2 and the relative shortening of the posterior end of M3 in Ischyromys (Titanotheriomys) veterior. Note that there is still considerable overlap, mainly because the posterior shortening in I. veterior is a highly variable character (see Table 5).

Figure 11. Idealized diagram showing differences between Ischyromys (Ischyromys) from Pine Ridge, Nebraska, and I. (Titanotheriomys) veterior from Pipestone Springs, Montana.

Figure 12. Histogram showing classification of specimens from Wyoming localities using the factor loadings from the discriminant analysis shown in Figure 9. The Wyoming specimens do not match either the Pipestone Springs or the Pine Ridge samples but form a single population of intermediate character.

Figure 13. Bivariate plot of 120 zoned Ischyromys from Flagstaff Rim, Natrona County, Wyoming (see map on page ??). The entire section is Chadronian in age.

Figure 14. Dendrogram from cluster analysis on 31 populations using the Ward method (after Heaton, 1993a). Analysis is based on mean population values for 83 characters: 25 on each molar and 8 on the jaw. Overall size has been factored out so that similarities are based on shape alone. Size is given for comparison, with values representing tenths of a mm over 3.0 mm for mean length of M2. "T-M" groups are combined samples from Toadstool Park and Munson Ranch. "T-M Chadron" groups also include specimens from other Pine Ridge and Douglas localities. "Orella A" refers to the lower Orella, and the other lettered units refer to higher intervals in the section. The "T-M Orella C-D" group comes from a very productive level at the Orella C-D boundary. Groups cluster primarily by location and age with Chadronian populations forming a more diverse group than Orellan populations. The separation of Whitneyan populations from Orellan populations is an artifact as explained in Heaton (1993a).

Figure 15. Proposed evolutionary tree of the species of Ischyromys. The species in the Chadronian radiation on the right belong to the subgenus Titanotheriomys.

Table 1. Subjective scores for wear stage assigned to each cheek tooth.

Table 2. Subjective size scores assigned to each of the four possible accessory cusps on each cheek tooth.

Table 3. List of measurements made on each molar (Figure 2) and dentary (Figure 3).

Table 4. Success rates of discriminant analyses at distinguishing Ischyromys from Pipestone Springs, Montana, and from the lower Orella, Pine Ridge, Nebraska. The first four are stepwise discriminant analyses done with BMDP (Heaton, 1988). The last one was done with SYSTAT and includes previously unmeasured Pipestone Springs material.

Table 5. Selected measurements on M2 and M3 for populations of Ischyromys from the lower Orella, Pine Ridge, Nebraska and Pipestone Springs, Montana.

Table 6. Factor loadings from discriminant analysis on Ischyromys using 38 characters on M2 and M3. Positive values indicate features that tend to be larger on Pipestone Springs specimens; negative values indicate features that tend to be larger on lower Orella specimens from Pine Ridge.

Table 7. Classification ischyromyids based on the discriminant factor loadings listed in Table 6. In addition to the Pipestone Springs and lower Orella samples on which the discriminant analysis is based, Chadronian specimens from Wyoming localities and Pine Ridge are also classified. The mean value of the canonical variable for each population is also given (see scale in Figures 9 and 12).

Table 8. List of skull characters used by Wood (1976) to distinguish Titanotheriomys of Pipestone Springs from Ischyromys of the Great Plains.

Table 9. Classification by Flynn (1977) of ischyromyid skulls from Flagstaff Rim, Wyoming, using selected characters from Table 8. "I" = Ischyromys, "T" = Titanotheriomys, "-" = not observable. USNM = U.S. National Museum, Smithsonian Institution, Washington, D.C.; AMNH = Frick Collection, American Museum of Natural History, New York.


Timothy H. Heaton: E-mail, Home page, Phone (605) 677-6122, FAX (605) 677-6121