Reprinted from the Journal of Paleontology, 67(2), pp. 297-308 (1993)

THE OLIGOCENE RODENT ISCHYROMYS OF THE GREAT PLAINS:
REPLACEMENT MISTAKEN FOR ANAGENESIS

TIMOTHY H. HEATON
Department of Earth Sciences, University of South Dakota, Vermillion 57069

ABSTRACT

Ischyromys, the most abundant early Oligocene rodent from the Great Plains, has been considered by some workers to represent a single gradually evolving lineage comprising three or more chronospecies. Statistical investigation of large samples suggest instead that two closely related species coexisted, and the shift in mean size that was thought to represent anagenesis actually represents replacement. In Nebraska and eastern Wyoming both I. parvidens (small) and I. typus (large) were rare but of equal abundance in the Chadronian, I. parvidens was more prevalent in the early Orellan, and I. typus was more prevalent in the middle and late Orellan. In northeastern Colorado, northern South Dakota, and North Dakota I. typus is the only species of Ischyromys found in Orellan deposits, thus showing that the two species had differing geographic ranges.

The mean size of I. typus does increase up section at all localities, but this change is minor and not deserving of chronospecies recognition. Much of this change occurred in the latest Orellan and earliest Whitneyan as I. typus approached extinction, and it was accomplished mostly by loss of small individuals rather than a shift of the entire distribution. Rate of evolutionary change in Ischyromys is found to be inversely correlated with population size, and no new species arose during the Orellan when Ischyromys was most abundant.

INTRODUCTION

ISCHYROMYS IS a primitive rodent of about the size and habit of living prairie dogs. Its fossils have been collected in great numbers from badland deposits of Orellan "age" (Oligocene) in Nebraska and surrounding states (Figure 1), and much smaller samples are available from the preceding Chadronian and succeeding Whitneyan land mammal "ages." (The rock units involved are the Chadron Formation and the Orella and Whitney Members of the Brule Formation; these will be referred to simply as Chadron, Orella, and Whitney throughout the text.) Chadronian Ischyromys, despite their small numbers, show a much greater degree of morphologic diversity than Orellan and Whitneyan Ischyromys, and some Chadronian species are assigned by some workers to a second genus, Titanotheriomys. An extensive morphometric study of these genera has recently been completed (Heaton, 1988), and the findings concerning the abundant Orellan Ischyromys of the Great Plains are presented here.

Orellan Ischyromys have been divided into a number of species, but most type specimens come from the Big Badlands of South Dakota and have incomplete stratigraphic data. Stout (1937), studying material from northwestern Nebraska, was the first to evaluate species of Ischyromys in a stratigraphic context. He assigned a very small dentary and isolated tooth from the Chadron to Titanotheriomys, 125 small jaws from the lower Orella to I. cf. I. parvidens, and 401 large jaws from the middle and upper Orella to I. cf. I. typus. He suggested that the latter group might be further subdivided into two or three stratigraphic varieties, and following this proposal Barbour and Stout (1939) and Galbreath (1953) assigned the upper Orella specimens to I. pliacus. Schultz and Stout (1955) subdivided the Orella into four lettered units and considered I. parvidens to be restricted to the lowest and most distinct of these (Orella A).

Howe (1956, 1966) collected 244 additional dentaries from Sioux and Dawes Counties, Nebraska: 73 from Orella A-B, which he considered to be I. parvidens; 124 from Orella C, which he considered to be I. typus; and 47 from Orella D, which he considered to be 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 a single evolving lineage, the teeth having undergone an increase in size, in crown height, and in incidence of accessory cusps. But he recognized that there was considerable overlap between species with respect to these characters, especially between I. typus and I. pliacus. Howe (1966, p. 1200) interpreted these changes according to the classic gradualistic philosophy: "Changes in the lineage occurred with time but appear to have been gradual, and speciation is facilitated by the presence of breaks in the geologic record and unfossiliferous strata."

This study was started with the intention of measuring rates of evolutionary change in a fossil lineage, and Ischyromys was chosen because it seemed well suited for such a project. But after careful evaluation of the data it was concluded that Howe's assumption that Orellan Ischyromys constitutes a single evolving lineage is probably in error; instead the change in mean size appears to represent shifts in the relative abundance of two coexisting species. This paper will present a careful comparison of these two hypotheses.

METHODS

This analysis includes all the material studied by Stout and Howe as well as other large samples not available to them. The largest number of Ischyromys specimens with good stratigraphic data are in the collections of the University of Nebraska State Museum (UNSM), American Museum of Natural History (AMNH), U.S. National Museum (USNM), University of Colorado at Boulder (UCM), and University of Wyoming (UW). These and other collections were thoroughly examined as part of the research on the ischyromyines.

Dentaries are by far the most abundant elements available, outnumbering skulls and upper dentitions by about ten to one, so they form the basis of this study. More than 4,000 dentaries from 17 institutions were photographed in occlusal and lingual view using color slide film. These images were then projected onto a table with a darkroom enlarger, and measurements were made using a two-dimensional digitizer connected to a personal computer. An area-periphery-centroid measurement and 26 point measurements were made on each cheek tooth, and subjective values were assigned for the tooth's wear stage and the size of each of four accessory cusps. Three additional point measurements were made on each jaw, making a total of 127 measurements on each complete jaw with four cheek teeth.

The digitized data were processed with several Basic computer programs to check for errors and calculate measurements therefrom. Twenty-six measurements were created for each cheek tooth plus eight for each jaw (Heaton, 1988). These data, along with information from specimen cards, field notes, museum files, and topographic maps, were entered into a computer database consisting of eight linked panels. Each specimen with adequate data was assigned to a stratigraphic section and was given a value for its level in that section and a value for the error associated with the level. Measurements were extracted from the database for plots and statistical analyses. All statistical routines were performed using SYSTAT software (Wilkinson, 1988).

COMPOSITION OF ORELLAN ISCHYROMYS

Figures 2 through 10 show bivariate plots of tooth size vs. stratigraphic level for Orellan localities with adequately zoned samples. The first six localities occur from east to west along Pine Ridge between Chadron, Nebraska, and Douglas, Wyoming (Figure 1), and they all show a pattern of increasing mean size over time as reported by Stout (1937) and Howe (1966). But the hypothesis of a single gradually evolving lineage is suspect for the following reasons: 1) nearly all the size increase occurs at the Orella A-B boundary where Schultz and Stout (1955) reported no hiatus; 2) Orella A contains a small number of large specimens as well as a large number of small specimens; and 3) Chadron specimens comprise a size range as great as the lower and upper Orella combined.

These observations led me to consider the alternate hypothesis that a large and a small species coexisted during the Chadronian and early Orellan, and that the small species dominated the earliest Orellan and was then replaced by the large species. Confirmation for this hypothesis comes from a locality in northeastern Colorado and two localities in the northern Dakotas (Figures 1, 8-10) where only the large species is known (i.e., no values below 2.9 mm, mean > 3.4 mm, symmetrical distributions), suggesting that the smaller form represents a separate species with a more restricted geographic range. (No bivariate plot is given for the 562 M/2's measured from Orellan deposits of the Big Badlands of South Dakota because very few specimens are zoned, but this sample has a size range of 2.78-4.07 mm, a mean of 3.44 mm, a coefficient of variation of 7.2, and a strongly left-skewed distribution, suggesting that it, like the Pine Ridge samples, is composed of two species.)

The existence of some large specimens of Ischyromys in the Chadron and lower Orella of Pine Ridge has long been recognized. Barbour and Stout (1939) reported a single large specimen from the middle Chadron, but this did not dissuade them from considering large Ischyromys as an index fossil for the upper Orella. Howe (1966) noted the presence of a few large specimens in the lower Orella but offered no explanation. Howe's (1966) table 3 shows range, mean, and mode values of tooth size for the lower, middle, and upper Orella, and these values are very revealing. For the lower Orella the mean is smaller than the middle of the range for 14 of 18 characters, and the mode is smaller than the middle of the range for 14 of 15 characters. This represents a right-skewed distribution. Howe's values for the middle Orella show the opposite condition, suggesting a left-skewed distribution. His upper Orella distribution appears symmetrical. If Orellan Ischyromys represents a single gradually evolving lineage, and if the increase in its mean size between the lower and middle Orella is merely due to a time hiatus, as Howe contended, then one would expect the shape of the size distribution above and below the boundary to be the same. The difference in the shape of these distributions is inconsistent with gradual anagenesis but is consistent with replacement.

Upon finding large Ischyromys fossils reported from Orella A and the Chadron, therefore defying Howe's (1966) interpretation, there was concern about the true age of these fossils since most were collected as surface float. If there was any chance that they merely washed down from the middle or upper Orella and were misidentified by collectors, then they have no significance. This possibility was investigated and rejected. The largest sample of Orella A specimens comes from the Toadstool Park area (Figure 3). Most Orella B-D specimens on this plot were found in the immediate vicinity of Toadstool Park, but nearly all Orella A specimens came from isolated buttes southeast of the park with no overlying sediments. Likewise, most Chadron exposures along Pine Ridge are isolated from Orellan deposits. Clearly large Ischyromys from the Chadron and Orella A were found in place.

STATISTICAL TESTS

To demonstrate the presence of two coexisting species, the size distributions had to be tested to see if their deviations from normality were statistically significant. The hypothesis put forward here holds that the underlying structure of the Orella A and Chadron distributions is bimodal. This bimodal pattern is not visually obvious in Figures 2-7 because the two species have overlapping size distributions, because they are represented in vastly unequal numbers in Orella A, and because both species are very sparse in the Chadron. Figure 11 shows histograms and statistics for three populations: 1) Chadron; 2) Orella A; and 3) Orella B through Whitney. The two Orellan populations comprise all zoned dentaries from Toadstool Park and Munson Ranch (Figures 3, 4); the Chadron population comprises all Chadronian dentaries from Pine Ridge and Douglas (Figures 2-7). Reliable marker beds separate the Chadron from the Orella at all localities and Orella A from Orella B at Toadstool Park and Munson Ranch.

The skewness (G1) and kurtosis (G2) statistics are of particular interest (Figure 11). The upper distribution is mildly left-skewed and mildly leptokurtic, the Orella A distribution is strongly right-skewed and strongly leptokurtic, and the Chadron distribution is nearly symmetrical but strongly platykurtic (lacks a modal cluster in the center of its distribution). Both G1 and G2 are zero for normally distributed populations, and studies of living populations of mammals show this ideal to be nearly realized. (For example, right cheek tooth rows were measured on 207 USNM skulls of Sciurus carolinensis from the eastern United States. G1=-0.11 [tG1=0.63] and G2=0.05 [tG2=0.15]. Since the critical value is t.05[]=1.96, neither statistic differs significantly from zero at the 5% level. The coefficient of variation for this sample is 4%.) The hypothesis GX=0 can be tested using the formula (Sokal and Rohlf, 1981, p. 139, 174-175):

tS=GX/SGx
with
SG1=[6N(N-1)/(N-2)(N+1)(N+3 )]1/2,
SG2=[24N(N-1)2/(N-3)(N-2)(N+3)(N +5)]1/2,
and
df=

Skewness and kurtosis values were tested for significance for each of the three populations in Figure 11, and the results are shown in Table 1. Both statistics for the upper population are significant to about the 0.001 level, and this suggests that even this sample is a mixture of two species. For Orella A both statistics are highly significant, far above even the 0.001 level. Neither statistic is significant for the Chadron population because of the small sample size, but the G2 value is large and strongly suggestive of bimodality. Since all three populations appear to represent mixed samples, the next question is whether they can all be interpreted as representing different ratios of the same two species.

COMPUTER SIMULATIONS

To facilitate the interpretation of these distributions, pairs of normally distributed populations were generated and mixed by computer using various ratios and separations, and the skewness and kurtosis values of the combined distributions are presented in Table 2. Each cell has a unique pair of G values, so any pair of G values represents a unique ratio and separation. When this is applied to real samples it is assumed that there are no more than two species mixed together, that each is normally distributed, and that they have the same standard deviation. There is no reason to believe that species of Ischyromys deviate significantly from these assumptions.

Table 3 shows the results when G values of the three samples in Figure 11 are extrapolated on Table 2. According to the hypothesis presented here, each of these three samples contains the same two species, so the mean size of each species (and therefore their separation) should be equivalent for each sample. This is nearly realized, especially when it is taken into account that the large species is expected to have a slightly larger standard deviation than the small species (variation being proportional to size). The lower Orella sample has the highest SD separation because it is dominated by the small species, and the upper sample has the lowest SD separation because it is dominated by the large species. Table 3 also gives a calculated mean for each of the two species for each population based on the best estimates of true standard deviations, and these values are very similar for all three populations. The best estimate for the true mean and standard deviation of each species is shown at the bottom of Figure 11. This gives each species a coefficient of variation of just under 5 percent.

I therefore conclude that two species of Ischyromys coexisted in Nebraska during the Chadronian and Orellan. Using priority type specimens of equivalent size and morphology from the Big Badlands of South Dakota (Figure 1), the large species can be called I. typus and the small species I. parvidens. Both of these species were rare during the Chadronian. During the earliest Orellan, I. parvidens became very abundant while I. typus remained rare. At the end of the earliest Orellan, I. parvidens became extremely rare and eventually went extinct, and I. typus became the dominant rodent and remained so until the end of the Orellan. There is no evidence that either species changed appreciably from the Chadronian to the middle Orellan, but any minor changes would be masked by the mixing.

ANAGENETIC CHANGES

Most of the increase in mean size of Orellan Ischyromys has now been accounted for by the replacement of I. parvidens by I. typus as the dominant species at the end of the earliest Orellan. Both Stout (1937) and Howe (1966) reported additional size increase in the middle to upper Orella and Whitney. Such an increase is apparent in some of the bivariate plots (Figures 2-10). Table 4 shows mean tooth size for successive stratigraphic intervals at four sections: Toadstool Park, Munson Ranch, Slim Buttes, and Little Badlands. Toadstool Park and Munson Ranch are the only sections along Pine Ridge with adequate samples above Orella A. The lower two intervals at each of these sections represent the Chadron and Orella A, which are contaminated by I. parvidens, but the levels above these are assumed to be almost exclusively I. typus. The northern sections have smaller samples, but they have the advantage of lacking I. parvidens entirely. The main hindrance for all sections is the small sample size at some levels, and all the sections except Slim Buttes show reversals in mean size rather than a consistent increase. Nevertheless, all four sections show an overall trend toward increased size.

The rate of anagenetic change can be approximated by dividing the natural log of proportional change in size by the time interval (Haldane, 1949). From the four sections in Table 4, it is estimated that Ischyromys typus increased in mean size from 3.4 mm to 3.8 mm over the Orellan, which lasted approximately 1.8 million years (Swisher and Prothero, 1990; Emry et al., 1987). This gives an evolutionary rate of 0.06 darwins, which is a very slow rate of change even considering the time interval involved (Gingerich, 1983). The total shift in mean size is also small compared to the range at each level, and most of this apparent shift occurs at the upper and lower ends of the sections where sample sizes and ranges of variation are small.

It is apparent from Figures 2-10 that I. typus cannot be broken conveniently into chronospecies based on size. The levels in Table 4 with the highest and lowest mean size values do not exhibit a shift in the entire size range, but merely a preponderance of either large or small specimens, and in most cases the largest specimens do not occur at the highest level. Particularly in the Munson Ranch section (Figure 4), which has far more I. typus specimens than any other section, it is evident that the size range does not change appreciably, if at all, from the middle Orella to the Whitney. So there is no justification for separating this lineage based on size into I. typus for the middle Orella and I. pliacus for the upper Orella as proposed by Howe (1966), and there is certainly no biostratigraphic utility in such a separation as employed by Prothero (1982a, 1982b).

MULTIVARIATE ANALYSIS

So far only data representing the overall size of the animals have been presented. Numerous factor and discriminant analyses were employed in an attempt to identify differences in shape between I. parvidens and I. typus and between samples of I. typus at different stratigraphic levels. The results show an extraordinary level of uniformity between all these groups, and no shape characters were able to discriminate any of them. Overall size is therefore the only reliable character for distinguishing individual fossils. The only other difference found was in the relative frequency of accessory cusps. These occur in a minority of specimens at all levels, but they occur with different frequencies in the two species.

Accessory cusps.--There are four different accessory cusps that occur on the molars (Table 4). The labial and lingual accessory cusps are conical in shape and occur where the labial and anterior lingual valleys meet the tooth margin, and they tend to occur together. The two medial accessory cusps occur high in the anterior and posterior lingual valleys, and when well developed they form anteroposterior ridges that dam off these valleys. The posterior medial cusp is very rare and almost never occurs without the anterior medial cusp also being present. Howe (1966) reported significant increases in the incidence of these cusps from the lower to middle and middle to upper Orella, and this was his justification (besides size differences) for separating the lineage into I. parvidens, I. typus, and I. pliacus.

When measuring the teeth a subjective value was assigned to each accessory cusp ranging from zero (no cusp) to four (exceptionally large cusp). Most Orellan Ischyromys molars lack accessory cusps, and the frequency of each successive size value is lower than the last. This makes their size distribution extremely right-skewed, so mean values for populations are only meaningful for large samples (100+ teeth). All four accessory cusps occur more commonly in I. typus than I. parvidens as can be seen in Table 4 by comparing the Orella A samples (0-9 m) at Toadstool Park and Munson Ranch with the other large samples (particularly 19-27 and 28-36 m at Munson Ranch). Above Orella A the accessory cusp frequencies are inconsistent and not very suggestive of the trend claimed by Howe (1966). Table 5 shows mean values on four size classes of I. typus from Orella B-D of Toadstool Park and Munson Ranch. The frequency of occurrence of each cusp is correlated with tooth size, so the difference in this character between I. typus and I. parvidens appears to be nothing but an allometric corollary of their size difference.

Whitney specimens.--The largest mean values for accessory cusps occur high in the sections (Table 4), but always for very small samples. They are particularly frequent on the few available Ischyromys from the Whitney, probably because of their large size. In addition to the two Whitney dentaries from Pine Ridge, two dentaries were found at a Whitney locality (AMNH) in southern Sioux County on Weitzel Ranch. Also of interest in this context is the very large type specimen of I. pliacus and some associated teeth. Unfortunately, the locality and age of this material is uncertain, but the best guess is late Orellan (Barbour and Stout, 1939; Galbreath, 1953). All the teeth of these dentaries are large and have prominent accessory cusps.

A cluster analysis (Figure 12; discussed below) grouped the I. pliacus type material with the Whitney samples from Pine Ridge and Weitzel Ranch, and this cluster appears distinct from Orellan Ischyromys. All this might suggest that I. pliacus is a valid and distinct species, and it might also suggest a Whitneyan age for the type specimen. To test this a discriminant analysis was run using 24 characters on M/2 for two groups: 1) Whitneyan material from Pine Ridge and Weitzel Ranch and the I. pliacus type material; and 2) Orella B-D material from Toadstool Park and Munson Ranch (Table 6). In addition to this material, four populations containing only large Ischyromys from North and South Dakota were also classified in the analysis. The Little Badlands and Slim Buttes samples are of particular interest since they show large mean sizes like the Whitney samples (Figures 9, 10). The analysis was not able to discriminate the groups well, and many specimens from the Orellan samples were classified with the Whitney group. This is not surprising since there are specimens even in Orella B that are larger and have accessory cusps as prominent as those in the Whitney. It can be concluded, therefore, that the Whitney and I. pliacus type specimens are just large I. typus and not a distinct species. Ischyromys pliacus is a junior synonym of I. typus.

SPECIES RELATIONSHIPS

One last issue that needs addressing is how Orellan Ischyromys relate to their Chadronian predecessors. Although considered in greater depth elsewhere (Heaton, 1988), the subject will be treated briefly here in order to put I. typus and I. parvidens in their proper context. Wood (1937, 1976) has shown from skull material that the ischyromyines split into two genera early in the Chadronian. Prior to my study, dentaries of the two genera were thought to be indistinguishable (Black, 1968; Wood, 1980). Both the earliest (late Duchesnean, earliest Chadronian) and the latest (Orellan, Whitneyan) ischyromyine skulls have primitive musculature similar to Paramys, so these retain the original name Ischyromys. Most ischyromyine skulls from Chadronian deposits have a highly derived jaw musculature that parallels the sciuromorphs and myomorphs, and these forms are referred to Titanotheriomys.

Figure 12 shows the result of a cluster analysis comparing important fossil populations. Several of these populations have been subdivided by stratigraphy and size. The Toadstool Park and Munson Ranch specimens have been divided into seven stratigraphic categories, and the Chadron and Orella A samples have been further subdivided by size into I. parvidens and I. typus. The Flagstaff Rim specimens have been divided into two stratigraphic categories, and the younger sample has been separated by size because a small and a large species are known to coexist there (Flynn, 1977; Heaton, 1988). The Pipestone Springs specimens have been separated by size since a small and a large species are known to coexist there as well (Wood, 1937; Black, 1965; Heaton, 1988). Some of these size divisions are imperfect because of overlapping size ranges. Before the cluster analysis was run, overall size was factored out, so similarities are based solely on shape. But size classes are listed in Figure 12 for comparison.

This analysis separated populations primarily by locality and age. The early Ischyromys populations and the entire Titanotheriomys radiation cluster together at the bottom. The only Chadronian populations not included in this group are the large and small Chadron samples from Pine Ridge, which cluster with Orellan Ischyromys. This reinforces the claim that they are I. typus and I. parvidens, and are the ancestors of the large Orellan populations of those species.

Among Orellan Ischyromys, the small Orella A form clusters closely with the Douglas and Lusk samples, since they are dominated by I. parvidens. Theoretically, the small Chadron form should also cluster with these, and with some cluster algorithms it does. Its proximity instead to the large Chadron form may represent a closer morphologic similarity between I. parvidens and I. typus in the Chadronian than in the Orellan, or it may represent an inadequate job of separating the Chadronian specimens into the two species. In any case, when size is taken into account the small Chadron form is clearly most similar to the other I. parvidens populations. As discussed above, it is considered that the Whitneyan samples are I. typus in spite of their distant clustering from other I. typus populations.

Paleobiogeography.--The biogeographic relationship between Ischyromys and Titanotheriomys during the Chadronian is not entirely clear. The only certain sympatric occurrence of the two genera is in the Chadron Formation at Douglas, Wyoming. West of Douglas, at Flagstaff Rim, is the thickest and most complete Chadronian section. It contains only Titanotheriomys, but it does not extend to the uppermost Chadronian. The Chadron thins considerably to the east into Nebraska where Ischyromys is found, and it is not certain which stages of the Chadronian are represented. It may be that Chadronian Ischyromys in Nebraska merely postdate Titanotheriomys in Wyoming, or it may be that Ischyromys maintained a more eastern range than Titanotheriomys after their divergence. The geographic and chronologic limits of outcrop leave ambiguity, but the latter hypothesis fits most harmoniously with the data. The reason that Titanotheriomys seems to dominate the Chadronian and Ischyromys the Orellan, under this model, is that the most extensive Chadronian outcrops are in central Wyoming and Montana while the best Orellan outcrops are in the Dakotas, Nebraska, eastern Wyoming, and northeastern Colorado. The proliferation of Ischyromys during the Orellan seems restricted to the Great Plains since ischyromyines are virtually unknown from Orellan deposits in Montana. If the two genera were allopatric after their divergence, it further weakens the value of ischyromyines as biostratigraphic indicators.

CONCLUSIONS

Orellan Ischyromys of the Great Plains comprise two coexisting species, I. typus (large) and I. parvidens (small), which diverged in the Chadronian. Of the two, I. parvidens appears to have had a more restricted range since only I. typus is found in North Dakota, northern South Dakota, and Colorado. The stratigraphically zoned collections from Pine Ridge show that I. parvidens dominated the earliest Orellan while I. typus dominated the middle and late Orellan. The two species differ mainly in size and have overlapping size ranges, thus making it difficult to classify some specimens or to study subtle changes in either species where they are found together. This is a particular problem for I. parvidens because its entire geographic and stratigraphic range is subsumed by I. typus. In addition, most I. parvidens fossils were collected from Orella A but were not zoned within that unit.

Patterns of change in I. typus are more easily studied, although the Pine Ridge sections are confused by mixing with I. parvidens and the northern localities by small and unevenly zoned samples. In all sections I. typus undergoes a slight increase in mean size, usually with some size reversals, but it is not always clear that there is a shift in the entire range of variation. The enormous sample of I. typus from Munson Ranch (Figure 4) shows only stasis during the entire period that this species was abundant, and the increase in mean size at the top of the section is accomplished only by the loss of small individuals. At the northern Dakota localities (Figures 9, 10) I. typus exhibits a more classic gradualistic size increase. In both cases, the increase in mean size is so small compared to the range of variation at each level that the division of the lineage into chronospecies is definitely not warranted.

The interpretations of Oligocene Ischyromys put forward here differ markedly from those of Howe (1956, 1966) both in terms of the number of lineages and their pattern of change. The notion that changes occurred gradually is admitted by Howe to be an assumption rather than a conclusion: "This treatment assumes that a regular increase in size continued at approximately the same rate throughout Orellan time" (1956, p. 74). Howe found the biggest changes to occur at the two paleosols that separate Orella B-C and C-D, so he concluded that these represent time hiatuses. The much larger dataset used in my study shows that Howe's conclusions were premature: Ischyromys shows mainly stasis from Orella B through Orella D, and virtually all the change occurs at the Orella A-B boundary (Figures 3, 4). This is the level at which nodules begin, but no paleosol is present (Schultz and Stout, 1955). Since there is no stratigraphic evidence of a time hiatus, the change may have occurred rapidly. As discussed above, several lines of evidence show that the change is the result of replacement rather than evolution, and the shift in lithology at the boundary suggests the possibility that an environmental change was responsible.

The conclusion that I. parvidens and I. typus are sympatric species rather than chronospecies was anticipated by some taxonomic workers. Wood (1937) and Black (1965, 1968) concluded that a small and a large species coexisted during the Eocene and Oligocene because of the presence of both small and large specimens at Pipestone Springs (Chadronian) and the Great Plains (Orellan). (However, Wood, 1976, and Heaton, 1988, have shown that the two Pipestone species are part of the Titanotheriomys radiation, as can be seen in Figure 12, and therefore are not ancestral to Ischyromys of the Great Plains.) Wood's (1976, 1980) assignment of some large Chadronian skulls from Douglas to I. typus fits the conclusions of this paper perfectly. This author disagrees with Wood (1937, 1976, 1980), however, in his assertion that there is more than one large Orellan species of Ischyromys. Ischyromys pliacus and I. troxelli are here considered junior synonyms of I. typus.

Howe's (1956, 1966) conclusion that Orellan Ischyromys can be separated into three chronospecies has led to the notion that Ischyromys is a good biostratigraphic indicator (Prothero, 1982a, 1982b). Since I. pliacus is a synonym of I. typus, since I. typus ranges from the Chadron to the Whitney without significant modification, and since I. parvidens ranges from the Chadron to at least the lower Orella, Ischyromys does not make a good index fossil as far as individual specimens go. But as a result of drastic shifts in species abundance, the genus is still useful where large samples can be obtained. In the Great Plains Ischyromys is a rare element in the Chadronian and Whitneyan, I. parvidens is the most abundant rodent in the early Orellan (except at northern localities), and I. typus is the most abundant rodent in the middle and late Orellan. The possibly restricted range of Ischyromys after its split with Titanotheriomys in the early Chadronian makes its biostratigraphic usefulness outside the Great Plains doubtful.

It was intended that this study would provide a test case for Eldredge and Gould's (1972) theory of punctuated equilibria. Since reported cases of speciation were all refuted, the theory could not be tested directly. But the results do offer some interesting insights. Most notable is the morphologic stability of the two Ischyromys lineages during their periods of abundance. The only measurable change is a slight increase in size in I. typus, and this is most pronounced at the northern localities where it is the only species represented. Ischyromys typus and I. parvidens split during the Chadronian when this genus was very rare. The morphologic similarity of the two species suggests that they diverged after the split with Titanotheriomys in the early Chadronian (Figure 12), yet they seem to be fully diverged in the lower part of Chadron Formation at Toadstool Park and Douglas (Figures 3, 7). This suggests that cladogenesis occurred rapidly in terms of the lifetime of the lineages it produced, thus supporting the punctuated equilibria model. So Ischyromys displays features of both "punctuated equilibria" and "phyletic gradualism" as defined by Eldredge and Gould (1972). But the primary revelation of this study is that what was thought to be a single gradually evolving lineage must now be seen as the replacement of one stable species by another.

ACKNOWLEDGMENTS

This project is an extension of a Ph.D. thesis that I completed at Harvard University under S. J. Gould. I thank him for his insight and encouragement as I undertook the detailed study of a fossil lineage. P. G. Williamson provided much help with the logistics of measuring and evaluating the specimens. T. M. Stout suggested the study of Ischyromys and took me to many fossil localities to familiarize me with the stratigraphy. R. J. Emry, D. G. Kron, and D. R. Prothero also provided valuable information about Oligocene paleontology. I also thank the many curators and collection managers who loaned or allowed access to fossils in their care. Funding was provided by Harvard University, the Smithsonian Institution, the Geological Society of America, and the American Museum of Natural History. I thank S. J. Gould, R. J. Emry, D. R. Prothero, J. A. Howe, W. W. Korth, and J. S. Heaton for reading the manuscript and offering many helpful suggestions.
REFERENCES

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BLACK, C. C. 1965. Fossil mammals from Montana, Part 2. Rodents from the Early Oligocene Pipestone Springs local fauna. Annals of Carnegie Museum, 38:1-48.

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ELDREDGE, N., AND S. J. GOULD. 1972. Punctuated Equilibria: an alternative to phyletic gradualism, p. 82-115. In T. J. M. Schopf (ed.), Models in Paleobiology. Freeman, Cooper and Company, San Francisco.

EMRY, R. J., P. R. BJORK, AND L. S. RUSSELL. 1987. The Chadronian, Orellan, and Whitneyan Land Mammal Ages, p. 119-152. In M. O. Woodburne (ed.), Cenozoic Mammals of North America: Geochronology and Biostratigraphy. University of California Press, Berkeley.

FLYNN, J. J. 1977. Morphological variation in the Oligocene Ischyromyidae (Rodentia) from Flagstaff Rim, Wyoming. Unpubl. B.S. thesis, Yale University, New Haven, Connecticut, 46 p.

GALBREATH, E. C. 1953. A contribution to the Tertiary geology and paleontology of northeastern Colorado. University of Kansas Paleontological Contributions: Vertebrata, 4:1-120.

GINGERICH, P. D. 1983. Rates of evolution: effects of time and temporal scaling. Science, 222:159-161.

HALDANE, J. B. S. 1949. Suggestions as to quantitative measurement of rates of evolution. Evolution, 3:51-56.

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

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

--------. 1966. The Oligocene rodent Ischyromys in Nebraska. Journal of Paleontology, 40:1200-1210.

LILLEGRAVEN, J. A. 1970. Stratigraphy, structure, and vertebrate fossils of the Oligocene Brule Formation, Slim Buttes, Northwestern South Dakota. Geological Society of America Bulletin, 81:831-850.

PROTHERO, D. R. 1982a. Medial Oligocene magnetostratigraphy and mammalian biostratigraphy: testing the isochroneity of mammalian biostratigraphic events. Unpubl. Ph.D. dissertation, Columbia University, New York, 284 p.

--------. 1982b. How isochronous are mammalian biostratigraphic events? Third North American Paleontological Convention Proceedings, 2:405-409.

SCHULTZ, C. B., AND T. M. STOUT. 1955. Classification of Oligocene sediments in Nebraska. Bulletin of the University of Nebraska State Museum, 4:17-52.

SKINNER, M. F. 1951. The Oligocene of western North Dakota, p. 51-58. In J. D. Bump (ed.), Guide Book, Fifth Field Conference of the Society of Vertebrate Paleontology in Western South Dakota. Museum of Geology, South Dakota School of Mines and Technology, Rapid City, South Dakota.

SOKAL, R. R., AND F. J. ROHLF. 1981. Biometry, 2nd ed. W. H. Freeman and Company, San Francisco, 859 p.

STOUT, T. M. 1937. A stratigraphic study of the Oligocene rodents in the Nebraska State Museum. Unpubl. M.S. thesis, University of Nebraska, Lincoln, 138 p.

SWISHER, C. C., III, AND D. R. PROTHERO. 1990. Single-crystal 40Ar/39Ar dating of the Eocene-Oligocene transition in North America. Science, 259:760-762.

WARD, J. H., Jr. 1963. Hierarchical grouping to optimize an objective function. Journal of the American Statistics Association, 58:236-244.

WILKINSON, L. 1988. SYSTAT: The System for Statistics. SYSTAT Inc., Evanston, Illinois, 822 p.

WOOD, A. E. 1937. The mammalian fauna of the White River Oligocene, part II: Rodentia. Transactions of the American Philosophical Society, N.S., 28:155-269.

--------. 1976. The Oligocene Rodents Ischyromys and Titanotheriomys and the content of the family Ischyromyidae, p. 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, Totonto.

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Accepted 27 March 1992


TABLE 1--Student's t values for the G1 and G2 statistics of three populations of Ischyromys testing the hypothesis that GX=0. Critical values are t.05[]=1.96, t.01[]=2.58, and t.001[]=3.29.

TABLE 2--Skewness (G1) and kurtosis (G2) values for simulated mixed pairs of normal distributions with the same standard deviation. Each row contains populations with the indicated sample size ratio. Each column contains populations with the indicated separation (in standard deviations) between the means of the two constituent distributions. All populations shown in this table are symmetrical (G1=0) or right-skewed (G1>0); for left-skewed distributions, reverse the sign of G1.

TABLE 3--Ratios and separations for three populations of Ischyromys using the simulated mixed populations of Table 2, and the best estimate for the mean of each species.

TABLE 4--Mean values and sample sizes for tooth and accessory cusp size measurements for successive stratigraphic intervals at four localities. Tooth size measurements are based on the square root of M/2 occlusal area. Accessory cusp measurements are averages for all lower molars (M/1-3) on which the characters are determinable. The majority of teeth lack the accessory cusps and therefore have a zero value.

TABLE 5--Mean values of accessory cusp size measurements for four size classes of molars from Orella B-D at Toadstool Park and Munson Ranch. Size classes are based on occlusal area. Sample size is approximately 240 for each M/1 and M/2 class and 150 for each M/3 class.

TABLE 6--Classification of large Ischyromys into "Orella" and "Whitney" groups by discriminant analysis of 24 characters on M/2. The Orella group is based on Orella B-D specimens from Toadstool Park and Munson Ranch. The Whitney group is based on Whitney specimens from Toadstool Park, Munson Ranch, Weitzel Ranch, and the type specimens of I. pliacus.

FIGURE 1--Index map showing the location of Orellan age deposits where large samples of fossil Ischyromys have been recovered.

FIGURE 2--Bivariate plot of 48 M/2's from Chadron area, Dawes County, Nebraska (range 2.72-3.97 mm, mean 3.16 mm, CV 8.5%). Section is based on unpublished data by M. F. Skinner (AMNH).

FIGURE 3--Bivariate plot of 540 M/2's from Toadstool Park, Sioux County, Nebraska (range 2.66-3.99 mm, mean 3.25 mm, CV 8.6%). Section is based on Schultz and Stout (1955).

FIGURE 4--Bivariate plot of 753 M/2's from Munson Ranch, Sioux County, Nebraska (range 2.70-3.96 mm, mean 3.39 mm, CV 5.8%). Section is based on unpublished data by M. F. Skinner (AMNH) and R. J. Emry (USNM).

FIGURE 5--Bivariate plot of 60 M/2's from Geike Ranch, Sioux County, Nebraska (range 2.70-3.70 mm, mean 3.21 mm, CV 8.2%). Section is based on unpublished data by M. F. Skinner (AMNH).

FIGURE 6--Bivariate plot of 147 M/2's from Lusk area, Niobrara County, Wyoming (range 2.65-3.63 mm, mean 3.15 mm, CV 6.5%). Section is based on unpublished data by M. F. Skinner (AMNH).

FIGURE 7--Bivariate plot of 116 M/2's from Douglas area, Converse County, Wyoming (range 2.57-3.76 mm, mean 3.06 mm, CV 7.7%). Section is based on unpublished data by D. G. Kron (UCM) and M. F. Skinner (AMNH).

FIGURE 8--Bivariate plot of 95 M/2's from Logan County, northeastern Colorado (range 3.00-3.96 mm, mean 3.44 mm, CV 5.3%). Section is based on Galbreath (1953); accuracy of stratigraphic data is inferior compared to the other eight localities.

FIGURE 9--Bivariate plot of 134 M/2's from Slim Buttes, Harding County, South Dakota (range 2.90-4.24 mm, mean 3.65 mm, CV 6.1%). Section is based on Lillegraven (1970).

FIGURE 10--Bivariate plot of 60 M/2's from Little Badlands and Fitterer Ranch, Stark and Slope Counties, North Dakota (range 2.96-4.17 mm, mean 3.52 mm, CV 7.1%). Section is based on Skinner (1951) and unpublished data by M. F. Skinner (AMNH).

FIGURE 11--Histograms of tooth size values for three stratigraphic samples of Ischyromys. Tooth size is calculated as the square root of M/2 occlusal area. The upper two histograms include all appropriate specimens from Toadstool Park and Munson Ranch. The lower histogram includes Chadronian specimens from all Pine Ridge and Douglas localities. Below the histograms are the concocted statistics for the two species that are thought to make up these samples.

FIGURE 12--Dendrogram from cluster analysis on 31 populations using the Ward (1963) method. 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 M/2. "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. 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.