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Patterns in the Evolution of Nares Size and Secondary Palate Length in Anomodont Therapsids (Synapsida)

Posted on: Wednesday, 28 May 2008, 03:00 CDT

By Angielczyk, Kenneth D Walsh, Melony L

ABSTRACT- Seemingly consistent proportional differences in several palatal structures have been noted between Permian and Triassic anomodont therapsids for nearly a century. These patterns have been cited as evidence in support of a decline in atmospheric oxygen concentrations that may have contributed to end-Permian terrestrial extinctions. However, it is not known whether the observed differences are significant, or whether they stem from continued directional selection. If they are not significant, or if their timing does not match that proposed for the oxygen decline, support for the hypoxia-based extinction scenario would be weakened. We tested whether the internal nares and bony secondary palate, two palatal features proposed to be related to respiratory efficiency, are significantly larger in Triassic anomodonts, and whether the variation can be attributed to a long-term tendency for increase. Results based on raw data indicate that Triassic anomodonts have significantly larger secondary palates than Permian anomodonts. They also have significantly larger internal nares, but only when primitive, morphologically-divergent specimens are not considered. Although nares and palate size are correlated with stratigraphic occurrence, available data reject the hypothesis that the observed differences were the result of a long-term trend. Most of these findings are consistent with the predictions of the hypoxia scenario. However, removing the effects of body size and phylogeny causes some of the differences to break down, indicating that if selection for increased respiratory efficiency affected these characters, it was most likely not the only factor to do so. Therefore, the characters provide only weak evidence in support of the hypoxia scenario, and we recommend against their use for this purpose. Our results emphasize the need for caution when invoking presumed differences between Permian and Triassic vertebrates as support for hypoxia, or other extinction scenarios, without a rigorous study of the character(s) in question.

INTRODUCTION

A NOMODONT THERAPSIDS (sensu Modesto et al., 1999) are a diverse clade of non-mammalian synapsids known from the Middle Permian to the Late Triassic, and their remains have been found on every continent (King, 1988). The dicynodont anomodonts were particularly abundant and widespread, and were among the most important terrestrial vertebrate herbivores of their time (Sues and Reisz, 1998). Recently, there has been increasing interest in anomodont paleobiology, and papers have appeared which consider new and previously-known species (e.g., Modesto et al., 2002, 2003; Angielczyk, 2002, 2007; Ray, 2005; Maisch and Gebauer, 2005; Frobisch, 2007; Botha and Angielczyk, 2007), anomodont phylogeny (e.g., Rybczynski, 2000; Angielczyk, 2001; Maisch, 2001; Angielczyk and Kurkin, 2003; Surkov and Benton, 2004; Vega-Dias et al., 2004; Surkov et al., 2005), bone histology (Botha, 2003; Germain and Laurin, 2005; Ray et al., 2005), feeding system evolution (Renaut, 2001; Angielczyk, 2004), and functional morphology (Ray and Chinsamy, 2003; Frobisch, 2006; Ray, 2006).

During the history of research on anomodonts, a number of authors have commented on apparent trends in the evolution of the palate within the group, particularly noting a relative lengthening of the bony secondary palate, a shortening of the basicranial region, an increase in the size of the internal nares, and a shortening of the interpterygoid vacuity when Triassic dicynodont anomodonts are compared to Permian dicynodonts (Pearson, 1924; Toerien, 1953, 1955; Camp, 1956; Cox, 1965; Cruickshank, 1967, 1968; Keyser, 1974, 1979; Keyser and Cruickshank, 1979; Cox and Li, 1983). Quantitative data were used to recognize these patterns in some cases (e.g., Cruickshank, 1968; Cox and Li, 1983), but to date there have been no statistical tests of whether the differences between Permian and Triassic anomodonts are significant or whether the putative trends are real instances of directional change brought about by continued selection. Although these patterns have played a prominent role in debates about the taxonomy and phylogenetic relationships of Triassic dicynodont anomodonts, they have received little attention in the wider paleontological literature.

This situation changed to some degree when Retallack et al. (2003; also see Retallack, 2004; Huey and Ward, 2005; Retallack et al., 2006) hypothesized that many of the differences between Permian and Triassic anomodonts were related to a rapid decline in atmospheric oxygen concentrations at the end of the Permian, which they suggested may have played an important role in endPermian terrestrial animal and plant extinctions. In particular, they noted that the increasing degree of separation between the mouth and nasal cavities, among other features, observed in Triassic anomodonts may have been caused by selection for increased respiratory efficiency. However, they did not provide any new data to support these hypotheses; instead, they relied on the previous literature, especially Cruickshank (1968). Therefore, it is not known whether the differences they cite between Permian and Triassic anomodonts are significant. If they are not significant, or if they can be shown to be the result of other selective factors, it would weaken support for the hypoxia-based extinction scenario.

In theory, at least a partial resolution of these issues could be attained by re-analyzing Cruickshank's (1968) data, but in practice this is not easily done. Cruickshank (1967, 1968) did not provide any raw measurement data in his papers; instead they are presented in his unpublished Ph.D. thesis (Cruickshank, 1962). Examination of that document shows that many of the measurements were based on published reconstructions, drawings, or photographs of specimens, taxon sampling was limited, and the available sample size was relatively small (n = 39; a facsimile of Cruickshank's Appendix A can be accessed in the supplemental data archive at journalofpaleontology.org). Our purpose here is not to be overly critical of Cruickshank's seminal work, only to note that practical problems prevent it from being a definitive study of the evolution of palate proportions in anomodont therapsids. Moreover, in the time since the publication of Cruickshank's studies, considerable advances in our understanding of anomodont paleobiology have been made, particularly in the areas of phylogeny and taxonomy. When coupled with progress in biostratigraphy, the rise of phylogenetic comparative methods, and an increasing interest in the causes and effects of the end-Permian extinction in the terrestrial realm, it quickly becomes clear that a reappraisal of palate and nares evolution among anomodonts is due.

HYPOXIA AND THE ANOMODONT PALATE

The crux of the extinction scenario put forward by Retallack et al. (2003) and Huey and Ward (2005) is that a rapid drop in atmospheric oxygen concentrations occurred at the end of the Permian. Terrestrial animals subsequently died off either because of the direct physiological effects of hypoxia, or associated factors such as geographic range contraction (because many elevated regions on land would have been rendered essentially uninhabitable). In this scenario, survivors of the extinction might show morphological features associated with survival at low oxygen concentrations, and Retallack et al. (2003) noted several putative similarities between Permo-Triassic vertebrates and extant vertebrates that live at high altitude. Retallack et al. (2006) expanded this hypothesis by suggesting that multiple rapid declines in atmospheric oxygen concentration during the Permian may have played a role in both end- Guadalupian and end-Permian extinctions. They also reiterated that such changes in oxygen levels potentially could have selected for improved respiratory efficiency among survivors.

The possible relationship between changing atmospheric oxygen concentrations and mass extinctions in general, and the effects of the late Paleozoic decline in oxygen levels on terrestrial vertebrates in particular, have been considered before (e.g., McAlester, 1970; Graham et al., 1995, 1997; Berner et al., 2003), but Retallack et al. (2003) and Retallack (2004) are unique in suggesting that specific patterns in the evolution of the anomodont palate were related to atmospheric hypoxia. In particular, they noted two changes which they proposed would increase respiratory efficiency. First, they suggested that Triassic anomodonts should show a greater degree of separation between the buccal and nasal cavities of the skull, a change that would create a less obstructed airway and that could be accomplished by an increase in the size of the bony secondary palate (BSP). Second, they proposed a change in the dimensions of the internal narial openings (IN), specifically a relative shortening of the openings. Presumably such shortening would occur as the secondary palate expanded posteriorly, covering parts of the former IN.

It is easy to see how the development of a BSP would help to create a less obstructed airway. Through the separation of the buccal and nasal cavities, inspired air no longer has to pass through the mouth to reach the pharynx and the trachea, allowing breathing and oral processing of food to occur simultaneously (e.g., Brink, 1955; Parrington, 1967; McNab, 1978). The BSP of dicynodont anomodonts may be especially important in this regard because it supported a keratinous, turtle-like beak, and therefore was directly involved in oral food processing. As noted above, there also is a widespread perception in the dicynodont literature that the BSPs of Triassic anomodonts are relatively longer than those of Permian forms (Pearson, 1924; Toerien, 1953, 1955; Camp, 1956; Cox, 1965; Cruickshank, 1967, 1968; Keyser, 1974, 1979; Keyser and Cruickshank, 1979; Cox and Li, 1983). Retallack et al.'s (2003) assertions about the IN are more complex. Specifically, they state that "the internal nares of Lystrosaurus and subsequent Triassic dicynodonts are less than 60% of the interpterygoid space, whereas in Dicynodon and other Permian therapsids the internal nares are more than 60% as long as the interpterygoid space" (Retallack et al., 2003: 1148), citing Cruickshank (1968) as the source for the information. However, Cruickshank's (1968) statement regarding changes in IN length differs subtly but significantly from Retallack et al.'s (2003) assertion. Whereas Retallack et al. (2003) stated that the length of the IN of Triassic anomodonts such as Lystrosaurus typically is less than 60% of the length of the interpterygoid space, Cruickshank said the opposite: "... when the lengths of the internal nares and interpterygoid spaces are compared, then in general, the interpterygoid space of the Permian forms is greater than 60% of the length of its internal nares, whereas the value for Triassic forms is always less than 60%" (Cruickshank, 1968: 23; italics added). Thus, Cruickshank is describing the tendency of Triassic anomodonts to shorten the interpterygoid space (or interpterygoid vacuity; Fig. 1), and not a shortening of the IN. Cruickshank goes on to say that the IN of the Triassic anomodonts he examined ranged between 20% to 23% of the length of the skull, as opposed to 13% to 15% in his Permian specimens, an apparent trend towards lengthening the IN in Triassic anomodonts. Although other authors previously noted the shortening of the interpterygoid vacuity in Triassic taxa (e.g., Toerien, 1953; Camp, 1956; Keyser, 1974), Cruickshank's (1968) work is the only to explicitly document the changes in the size of the IN.

FIGURE 1-Internal nares and bony secondary palate of two anomodont specimens. 1, Processed image showing how IN and BSP measurements were taken. Specimen is PIN 4644/1, Delectosaurus arefievi, a dicynodont anomodont from the Late Permian of Russia. 2, Specimen of the Middle Permian non-dicynodont anomodont Ulemica efremovi (PIN 2793/1) displaying the divergent palatal morphology characteristic of non-dicynodont anomodonts. Abbreviations: BSP = bony secondary palate, IN = internal nares, IPTV = interpterygoid vacuity, PIN = Paleontological Institute, Moscow, Russia.

It would seem, then, that the IN of Triassic dicynodonts were increasing in length even as the secondary palate was expanding posteriorly, which implies that there may have been some advantage to retaining relatively large IN in combination with an expanded BSP. This conclusion brought our attention to the fact that the length of the IN may not be an ideal proxy for respiratory efficiency or adaptation to hypoxic conditions. Instead, the area of the IN in the plane in which they open into the pharynx and trachea likely will be more important. Increasing the area of the IN would reduce airflow resistance within the respiratory tract, potentially reducing the metabolic costs of breathing. Hyperventilation is a well-known response to hypoxic conditions (although it may be more specifically characteristic of hypobaric hypoxia, and not the presumably normobaric hypoxia that would have been experienced by end-Permian vertebrates; see Savourney et al., 2003), so reducing the costs of breathing may have been important as oxygen levels dropped throughout the Permian. Although we are unaware of any physiological studies suggesting that large IN are specifically adaptive for survival under hypoxic conditions, we note that dilation of the external nares can improve nasal airflow and reduce airflow resistance in humans (e.g., Lorino et al., 1998, 2001; Meissner et al., 1999), and that altitude has a small but non- significant effect on external nose dimensions in some Andean highlanders (Palomino et al., 1979).

Based on the above reasoning, we predict that if the hypoxia scenario is accurate, then Triassic anomodonts should have larger BSPs and IN than do Permian anomodonts. However, in seeking to establish a causal relationship between atmospheric oxygen concentrations and palate morphology an additional factor that must be considered is the timing of the changes. If alterations in morphology occur over a much longer time period than proposed changes in atmospheric oxygen levels, then it is unlikely that the latter were a cause for the former. Likewise, if a causal relationship does exist, then the rapidity of the decline will shape our expectations about whether changes in morphology should occur abruptly or take the form of a long-term trend.

Different sources considering hypoxia as an extinction mechanism differ in the precise timing and magnitude of the decline in atmospheric oxygen they envision at the end of the Permian. Statements in Retallack et al. (2003) and Retallack (2004) seem to favor a large, rapid decline (up to 18% by volume in less than 1 Myr, perhaps as little as 10 Kyr). The decline proposed by Huey and Ward (2005) is slightly smaller and notably longer, approximately 16% by volume over the Late Permian (approximately 9 Myr). Retallack et al. (2006) not only favor a large, rapid decline at the end of the Permian, they also posit an additional large drop at the end of the Guadalupian as well.

A considerable literature exists using geochemical modeling to reconstruct past atmospheric composition, and a decline in oxygen concentrations at the end of the Paleozoic is a consistent feature of the results of these models (e.g., Berner, 1987, 1989, 1999, 2001, 2004; Berner and Canfield, 1989; Lasaga, 1989; Berner et al., 2003; Bergman et al., 2004). The magnitude of the decline, from a Phanerozoic high of about 30% by volume to a low of about 14% by volume, is comparable to that proposed by Retallack et al. (2003) and Huey and Ward (2005). However, the length of this decline generally has been thought to be relatively long, starting in the Late Carboniferous and continuing into the Triassic, a period of over 50 Myr. Recent detailed work focusing on the Middle Permian to Middle Triassic (Berner, 2005) shows that this decrease could have occurred more rapidly (approximately 30 Myr), but the predicted changes during the Late Permian to Early Triassic are somewhat smaller (approximately 11%-12% by volume) than those assumed by Retallack et al. (2003) or Huey and Ward (2005). Moreover, an extremely rapid decline within thousands of years of the Permo- Triassic boundary does not seem likely given currently available geochemical data and models (Berner, 2005). Therefore, our expectation is that if anomodonts did show a morphological response to changing atmospheric oxygen levels, it would likely be a long- term trend stretching across most of their history, which begins in the late Middle Permian and ends in the early Late Triassic (although see Thulborn and Turner, 2003).

Thus, the first step in testing whether anomodont palates show changes consistent with the hypoxia scenario is to test whether the IN and BSPs of Triassic anomodonts are significantly larger than those of Permian anomodonts, and whether any apparent changes are the result of a long term trend stretching across the history of the clade.

METHODS I: EVOLUTIONARY PATTERNS

Taxon Sampling and Stratigraphie Bins.-We collected data from a total of 366 anomodont specimens (Supplementary Material in the supplemental data archive of journalofpaleontology. org), representing at least 62 taxa. We present this minimum estimate because factors such as poor preservation and taxonomic controversy prevented the confident identification of some specimens in the dataset. In most cases specimens were identified to the traditional "genus" level, but in a few instances species within genera were distinguished. Three hundred fifty-eight of the 366 included specimens belong to the clade Dicynodontia (sensu Modesto et al., 1999; Rybczynski, 2000; Angielczyk and Kurkin, 2003). The remaining eight specimens are non-dicynodont anomodonts, members of a paraphyletic assemblage of taxa at the base of the larger clade (Anomodontia) that includes dicynodonts (Fig. 4.1). The specimens used in this study were collected in Africa, Asia, Europe, and South America.

Taxa and specimens were binned into a series of 10 non- overlapping age-ranks (six Permian, four Triassic; Appendix 1, accessed at www.journalofpaleontology.org, Supplemental Archive) modified from Sidor (2000, 2003a). The age-ranks range in age from late Middle Permian (-268 Myr) to early Late Triassic (-220 Myr), and include all of anomodont history. Although the binning scheme produced a single continuous and resolved sequence of stratigraphie bins, it is a simplification for several reasons. Most notably, dicynodont fossils occur in several widelyseparated basins, and correlations between formations and biostratigraphic divisions among these basins often are loosely constrained. The correlations we used in our age-ranks represent one of several possible interpretations. The age-ranks also mask gaps in the anomodont fossil record, and do not represent equal increments of time. Nevertheless, our age-ranks represent a significant increase in resolution over Cruickshank's (1968) division of taxa into one Permian and one Triassic bin. Therefore, if a long-term trend of increasing respiratory efficiency exists, our data should be able to capture it. Taxa were assigned to age-ranks in one of two ways, depending on the details of the data permutation under consideration. In the first scheme, taxa were assigned to age ranks based on their first occurrences, and a taxon was only included in the age-rank in which it first appeared, even though many taxa have known ranges that span several age ranks. For example, although Diictodon occurs in age-ranks 2-6, we assigned it an age-rank of 2, and the 43 individual Diictodon specimens included in the dataset were used to calculate the taxon mean for Diictodon, despite the fact that they were not all collected in strata assigned to age-rank 2. Under the second binning scheme, taxa were assigned to all age ranks in which they are known to occur. Thus, in this scheme the taxon mean calculated from the 43 Diictodon specimens was included in age-ranks 2-6. We used both of these binning schemes in our analyses because the detail of the available stratigraphie and locality data for the included specimens was highly variable, making it impossible to consistently parse individual specimens from long- ranging taxa into age-ranks. First appearance and stratigraphic range data were taken primarily from Kitching (1977), King (1988), Rubidge (1995), and Ivakhnenko et al. (1997), as well as personal observations by one of us (KDA). Specimens that could not be assigned confidently to one of the included taxa were binned according to available museum locality data.

A total of 302 specimens, representing at least 43 taxa, were assigned to Permian age-ranks, and 64 specimens representing at least 19 taxa were assigned to Triassic age-ranks (Supplementary Material in data archive). The disparity in sample size between the Permian and Triassic in part reflects the fact that Triassic anomodonts tend to be rarer and less diverse than their Permian counterparts. It also is related to the availability of specimens appropriate for inclusion in the analysis in the literature and at museums visited by one of us (KDA).

Only one anomodont genus, Lystrosaurus, occurs in both Permian and Triassic age ranks. Recent research has clarified the taxonomy and stratigraphie range of Lystrosaurus, particularly in the Karoo Basin of South Africa (Ray, 2005; Smith and Botha, 2005; Ward et al., 2005; Botha and Smith, 2006, 2007; Grine et al., 2006). Based on these revisions, we recognized four species of Lystrosaurus, two with Permian first occurrences (L. curvatus, L. mccaigi) and two with Triassic first occurrences (L. declivis, L. murrayi). Four of the 31 included Lystrosaurus specimens could not be assigned confidently to a particular species, and all of these specimens were of Triassic age.

Data Collection.-All measurements were made from digital images of the ventral surface of specimens using Scion Image beta 4.0.2 with the following protocol. Each image had a resolution of 3,200 dpi, and was proportionally scaled so that the length from the anterior edge of the snout to the posterior edge of the occipital condyle was 1,200 pixels. In cases where the occipital condyle was not preserved, the distance from the anterior edge of the snout to the posterior surface of the occipital plate was scaled to 1,200 pixels. This process standardized the measurements for differences in the absolute sizes of the specimens, making measurements from all specimens directly comparable. However, it did not remove possible allometric effects, so if large anomodont species possessed relatively larger BSPs, for example, this difference would still be reflected in the standardized measurements.

The length of the premaxilla (in pixels) from the tip of the snout to the anterior edge of the IN was measured to determine the length of the BSP. This measurement is equivalent to measurement a of Cruichskank (1968), and could be made on 364 of the 366 included specimens. The premaxilla of one specimen (NM QR2902; Eodicynodori) was heavily damaged, preventing measurement of palate length. NM QR3000 (the only known specimen of Patranomodon) was not measured because we did not consider Patranomodon to possess a secondary palate.

The definition of the IN used in this analysis follows that of Cruickshank (1968, i.e., the space between the pterygoids and ectopterygoids starting at the end of the BSP and ending at the anterior edge of the interpterygoid vacuity), and we measured the area of this space exposed in ventral view. In theory, the cross- sectional area of the IN may be a more accurate proxy for respiratory efficiency than our measurement because the cross- sectional area is closer to an orthogonal orientation relative to the direction of airflow. However, our measurement is much easier to make, particularly in specimens that are incompletely prepared, and its use provides some degree of continuity between our work and the only other study to collect quantitative data on nares size in anomodonts.

To measure the area of the IN, the choanal space in the scaled images between the posterior edge of the premaxilla and the anterior- most point of the interpterygoid vacuity was filled with a solid color, and Scion Image was used to determine the area represented by this color (in pixels). The area occupied by the midventral vomerine plate in the choanal region was not included in the measurements. Measurements of IN area could be taken on 263 of the 366 specimens; the remaining 103 specimens were excluded because the choanal region of the skull was not prepared or because the preserved size of the internal nares had been affected by damage or deformation. Figure 1 shows examples of processed images used in this analysis. All data were log transformed before analysis.

Statistical Analyses.-Once the data were collected we ran three sets of statistical tests. First, we used two-sample Kolmogorov- Smirnov tests to determine whether Triassic anomodonts had significantly larger IN areas and BSP lengths than Permian anomodonts. These tests were intended to elucidate whether differences in measurements noted by previous authors (e.g., Cruickshank, 1968; Cox and Li, 1983) were significant. However, these tests provided only a coarse assessment of anomodont palate evolution because it is theoretically possible for the evolution of the BSP and IN to have followed significant non-random trends even if there is no significant difference when all Permian and Triassic anomodonts are compared en masse.

The remaining two sets of tests were used to look more closely at changes in ESf area and BSP length over the course of anomodont evolution. We used Spearman's rank order correlation test to examine whether IN area and BSP length were correlated with stratigraphie occurrence, and thus gain a finer scale picture of changes in the features over time. To test for the existence of a long-term trend in IN area increase and BSP length increase, we employed Wald- Wolfowitz runs tests. The runs test essentially is a simple form of time series analysis, and asks whether a temporally-ordered sequence of data likely was generated by a random or directed process.

Data Permutations.-To assess the robustness of our statistical results, we ran our three sets of tests on several different permutations of the data. We first carried out a K-S test on the mean IN values for 54 taxa (39 Permian, 15 Triassic) chosen because IN measurements were available for them and they occurred in phylogenetic trees (see below). A second permutation of the IN data included mean values for the 54 taxa, as well as values for individual specimens from the remaining taxa and all additional specimens with questionable identifications binned according to whether they were collected in Permian or Triassic strata. We used the same two permutations in our K-S tests on the BSP data, except in those cases we used taxon means for 57 taxa (39 Permian, 18 Triassic) chosen because BSP measurements were available for them and they occurred in phylogenetic trees (see below).

The Spearman's rank order correlation tests were first run on a data set consisting of mean IN values for the 54 taxa binned into the 10 stratigraphic divisions based on their first occurrences. We also re-ran this test with the taxa assigned to all of the stratigraphic bins in which they are known to occur. Lystrosaurus curvatus is the only taxon that occurred in both Permian and Triassic bins under this scheme, but other taxa occurred in multiple Permian or Triassic bins (e.g., Dnctodon occurred in bins 2-6). Finally, we ran a third permutation of the IN data in which mean values for the 54 taxa were assigned to all of the stratigraphie bins in which they occurred and values for individual specimens from the remaining taxa and all additional specimens with questionable identifications were assigned to their appropriate stratigraphic bins (e.g., UMZC T1089 was included in bin 6 under this scheme). We used the same three permutations in our rank order correlation tests on the BSP data, except in those cases we used taxon means for 57 taxa chosen because BSP measurements were available for them and they occurred in phylogenetic trees (see below).

We ran the Wald-Wolfowitz runs tests on the same three basic permutations of the IN and BSP data that we used in the rank order correlation tests. However, for these tests we first calculated the mean values for each bin in the different data sets, as well as the difference between the mean for each bin and its preceding bin. We ran the runs tests using these differences between the means, with the cut-off point for the test set at zero (i.e., if the mean of a bin was larger than its predecessor it was counted as positive; if it was less than its predecessor it was counted as negative). All of the data permutations described so far included the five non- dicynodont anomodonts we sampled (Patranomodon, Otsheria, Ulemica, Suminia, Galeops). Non-dicynodont anomodonts occur early in the anomodont fossil record and are characterized by a rudimentary BSP and the presence of relatively large, anteriorly-located IN (Fig. 1.2). This morphology more closely resembles that found in other basal therapsids than that of most dicynodont anomodonts (e.g., King, 1994; Sidor, 2003b). Because one of these features (large IN) is predicted as a possible response to hypoxic conditions, we deemed it necessary to determine what effect the inclusion of these morphologically disparate and stratigraphically early-occurring specimens had on our results. Therefore, we re-ran all of the tests described above with the data for the five non-dicynodont anomodont taxa excluded. Inclusion of non-dicynodont anomodonts should be conservative for the tests on IN area (i.e., it should make Permian and Triassic anomodont IN areas seem more similar and obscure long- term trends), but not for the tests on BSP length (i.e., it may exaggerate long-term trends and the difference in BSP length between Permian and Triassic anomodonts).

TABLE 1-Results of Kolmogorov-Smirnov two-sample tests comparing IN areas and BSP lengths of Permian and Triassic anomodonts. See text for details of different data permutations.

Lystrosaurus.-As noted above, Lystrosaurus is the only anomodont genus to occur on both sides of the Permo-Triassic boundary. Because of this, and the fact that it is limited to the latest Permian and the earliest Triassic, Lystrosaurus has the potential to provide unique insight into whether there were very rapid changes in BSP and IN dimensions near the boundary that would be compatible with the abrupt decline in atmospheric oxygen levels proposed by Retallack et al. (2003). Ideally, we would like to have large, closely-spaced, and stratigraphically well-controlled samples of Lystrosaurus populations across the PermoTriassic boundary that we could use to track changes in IN area, BSP length, and other characters. Unfortunately, despite well over a century of collecting, including recent detailed efforts in the vicinity of the boundary in the Karoo Basin, the available sample of Lystrosaurus material in museum collections generally does not meet these standards. For example, of 451 catalogued Lystrosaurus specimens in the collections of the South African Museum that were assessed in the data collection phase of this project, only 12 were sufficiently well preserved and prepared to be amenable for use, regardless of the quality of their associated stratigraphic occurrence data. Nevertheless, it may be possible to use the available Lystrosaurus material to make a preliminary test of whether this taxon shows morphological changes consistent with the very rapid drop in oxygen levels predicted by Retallack et al. (2003).

To implement this test we carried out a series of pair-wise comparisons of BSP length and IN area for the four Lystrosaurus species in our data set using two-sample Kolmogorov-Smirnov tests. If strong selection for increased respiratory efficiency was operating near the Permo-Triassic boundary, we predict that the Lystrosaurus species that first appeared in the Permian should have significantly smaller BSPs and IN than the Triassic species. Because our sample sizes for the different species were small (n ranged from four to nine), we also ran two additional Kolmogorov-Smirnov tests comparing the BSPs and IN of all of the Permian Lystrosaurus specimens to all of the Triassic Lystrosaurus specimens. It is important to note that ongoing collecting in the Karoo Basin of South Africa is rapidly increasing the number of Lystrosaurus specimens identified to the species level that also are associated with precise stratigraphie occurrence data (J. Botha, personal commun. 2007). Therefore, it will be possible to undertake additional tests of our preliminary results for Lystrosaurus in the future.

RESULTS 1

Komogorov-Smirnov Tests.-Results from the K-S tests are summarized in Table 1. When the K-S tests were run using the IN data using only taxon means, the IN areas of Permian and Triassic anomodonts were not significantly different. However, if non- dicynodont anomodonts were excluded from the analysis, the IN areas of Triassic anomodonts were significantly larger, on average, than those of Permian anomodonts. When the additional specimens were added, the IN areas of Triassic anomodonts were significantly larger than those of Permian forms regardless of whether the non- dicynodont anomodonts were included in the analysis.

The results for the K-S tests on the BSP length data were simpler than those for the IN data. Triassic anomodonts had significantly longer BSPs, on average, than Permian anomodonts regardless of which permutation of the data was considered.

Rank Order Correlation Tests.-Results from the rank order correlation tests are summarized in Table 2 and an example of one data permutation is plotted in Figure 2. When the tests were run on the IN data using only taxon means, and taxa were assigned only to the bins in which they first occur, IN area was not correlated significantly with stratigraphie occurrence. A significant positive correlation between IN area and stratigraphie occurrence did exist if the same test was run with the non-dicynodont anomodonts excluded. The same pattern of results was obtained for the data sets in which taxa were assigned to all of the bins in which they occur, not just the first. When the additional specimens were included, and all taxa were assigned to all of the stratigraphic bins in which they occur, a significant positive correlation between IN size and stratigraphic occurrence existed regardless of whether the non- dicynodont anomodonts were included.

As was the case for the K-S tests, the results for the rank order correlation tests on the BSP data were simpler than those for the IN data. A significant positive correlation existed between BSP length and stratigraphic occurrence regardless of which permutation of the data was considered.

Runs Tests.-Results for the runs tests are summarized in Table 3 and an example of one data permutation is plotted in Figure 2. The runs tests could not reject the null hypothesis that the observed IN and BSP data were generated by a random process, regardless of which permutation of the data was considered.

Lystrosaurus.-Results for the pair-wise comparisons of BSP length and IN area for the various Lystrosaurus species are presented in Table 4. No significant differences in IN area existed between the Lystrosaurus species at the Bonferroni-corrected alpha of 0.008. Even if the level of significance is relaxed to 0.05 or 0.10 to account for our small sample sizes, and the corresponding low power of the tests, only one comparison (L. mccaigi and L. declivis) yielded a significant result. Similarly, the IN areas of all of the Permian specimens did not differ significantly from those of the Triassic specimens. None of the pair-wise comparisons between the species found a significant difference in BSP length, even at reduced levels of significance. Likewise, a significant difference did not exist when the BSP lengths of the pooled Permian and Triassic specimens were compared.

TABLE 2-Results of Spearman's rank-order correlation tests comparing IN areas and BSP lengths to patterns of stratigraphie occurrence. See text for details of different data permutations.

IMPLICATIONS

The results of our statistical tests generally are congruent with previous studies of anomodont IN and BSP evolution. As noted above, many workers have suggested that the BSPs of Triassic anomodonts are larger on average than those of their Permian relatives, and our K- S tests confirmed that this pattern is significant. BSP length also was significantly positively correlated with stratigraphic occurrence, suggesting that the difference between Permian and Triassic taxa may be the result of a long-term tendency for increase. Nevertheless, the runs test could not reject the hypothesis that the BSP data were generated by a random process for any of the data permutations, despite the somewhat trend-like appearance of Figure 2b. When we focused only on Lystrosaurus, essentially no difference in BSP length between Permian and Triassic species was apparent, although this could stem from the very small sample sizes available for some of the tests. A similar pattern of non-significance was apparent when all of the Permian and Triassic Lystrosaurus specimens were compared.

The anomodont IN have received less attention in the literature. Only Cruickshank (1968) considered them in detail, and he concluded that Triassic anomodonts have larger IN than their Permian relatives. However, a number of additional authors noted a tendency for the interpterygoid vacuity of Triassic anomodonts to be shorter than those of Permian anomodonts (e.g., Pearson, 1924; Toerien, 1953; Camp, 1956; Keyser, 1974, 1979). Because Cruickshank's definition of the IN used the anterior edge of the interpterygoid vacuity as a landmark, the extension of the IN he observed doubtlessly was correlated with a shortening of the interpterygoid vacuity (he himself also noted that the interpterygoid vacuities of Triassic anomodonts tended to be shorter than those of Permian anomodonts).

In this light, the significant results we obtained for some of the K-S tests on IN area are not surprising. Moreover, the non- significant results for some of the data permutations seem likely to stem from our inclusion of the non-dicynodont anomodonts in the data sets in question. These taxa, which were not considered in previous studies, have divergent narial morphologies compared to the dicynodont anomodonts and may be obscuring an otherwise clear pattern for the dicynodonts. The same holds true for the correlation between IN area and stratigraphic occurrence: a significant positive correlation existed between nares area and stratigraphic occurrence when the non-dicynodont anomodonts were excluded from consideration, but generally not when they were included. Despite the possible difference in IN area between Permian and Triassic anomodonts, and the possible correlation between IN area and stratigraphic occurrence, the runs tests could not reject the null hypothesis that the IN data were generated by a random process. When the scope of the analysis was limited to just Lystrosaurus, there was almost no evidence indicative of the Triassic species having larger IN areas on average than the Permian species. As was the case for the BSP, the lack of significant differences for IN area may stem from the very small sample sizes available. Taken together, the statistical results match some, but not all, of our expectations if changes in anomodont palate morphology were being driven by a decline in atmospheric oxygen concentrations. The K-S tests suggest that these characters differ in size between Permian and Triassic anomodonts (particularly between Permian and Triassic dicynodont anomodonts), as predicted by the hypoxia scenario. The correlation tests imply that the size of the characters may be related to stratigraphic occurrence, but these patterns are most apparent when the whole of anomodont evolution is considered, not just Lystrosaurus species in the immediate vicinity of the Permo-Triassic boundary. These results better fit Berner's (2005) prediction that the oxygen decline stretched across a considerable portion of the Permian and Triassic than Retallack et al.'s (2003, 2006) abrupt scenarios. Nevertheless, our runs tests favor the null hypothesis that the observed patterns of change in BSP length and IN area were driven by a random process, not the long-term directional selection that would be expected if an extended decline in oxygen concentrations was the cause of the differences.

An important question to consider at this point is whether the runs test may be overly conservative given our data, and thus prone to erroneously accept the null hypothesis of a random walk as the source of our data (Type II error). In other words, our runs tests only have nine data points to work with (the nine differences between the ten stratigraphic bins) for each character, and this small sample size makes it relatively difficult to obtain a significant result. One possible solution to this problem would be to more finely subdivide our stratigraphic bins to create additional data points. However we do not think this is advisable. Although our correlations between faunal assemblages containing anomodonts vary slightly in some cases from other recent works (e.g., Lucas, 1998, 2002; Golubev, 2005; Rubidge, 2005), the faunas themselves are essentially the same as those recognized by these authors (with the possible exception of faunas assigned to bin 8). Therefore, further subdivision does not seem warranted given currently available data.

If the runs test is assumed to be overly conservative given the available data, our statistical results seem to match the predictions of the hypoxia scenario well, and a qualitative examination of plots of mean IN area or BSP length versus stratigraphic occurrence suggests that these differences are the result of a long-term increase. However, this does not necessarily mean that a decline in atmospheric oxygen concentrations was the cause of the observed changes, and establishing a definitive causal link is difficult given the resolution of our data and the available atmospheric reconstructions. A potential way to circumvent this problem is to test whether other, more easily-examined factors could have caused the observed differences in Permian and Triassic anomodonts. If such factors can be identified, then it would be unnecessary to invoke hypoxia as a cause for the differences; if such factors cannot be found then the hypoxia scenario would receive additional corroboration.

FIGURE 2-Plots of IN area and BSP length versus age rank. 1, Plot of IN area data against age ranks. The data used in this plot are average values for the 54 taxa (including non-dicynodont anomodonts) used in the K-S tests. Taxa are included in all of the age ranks in which they are known to occur. 2, Plot of BSP length data against age ranks. The data used in this plot are average values for the 57 taxa (including non-dicynodont anomodonts) used in the K-S tests. Taxa are included in all of the age ranks in which they are known to occur. The line drawn in each plot connects the mean values of the age ranks (filled circles).

METHODS II: CAUSES OF EVOLUTIONARY PATTERNS

Potential Causes

We focused on two potential alternative causes for the observed differences in IN area and BSP length among Permian and Triassic anomodonts. We chose to study these potential causes in detail because they are relatively obvious and methods exist for attempting to control for their effects in statistical analyses.

The first potential cause we considered was increasing body size. A cursory comparison of body size ranges in Permian and Triassic anomodont faunas (Fig. 3) showed that the smaller size classes of anomodonts which were present in the Permian largely were missing in the Triassic. This rarity of small anomodonts in the Triassic most likely is the result of the complete or near-complete extinction of the robertiid and emydopid lineages of dicynodont anomodonts, which dominated this size class during the Permian history of the group, at the Permo-Triassic boundary (Frobisch, 2007). Although our BSP and IN measurements were size standardized to make the values for all specimens directly comparable, this process did not remove possible allometric effects. Therefore, if IN area or BSP length show a positive allometric relationship among the anomodonts, for example, then Triassic anomodonts would have larger IN and BSPs than their Permian relatives simply because, on average, they were larger animals and not necessarily because selection was working directly to increase the size of these features.

The second potential cause we examined was phylogeny. As can be seen from Figure 4.1, the majority of Triassic dicynodonts are members of a single large clade. It has been recognized for some time that the possible influence of phylogeny should be taken into account in comparative studies because the hierarchical phylogenetic relationships which exist between sampled taxa preclude them from being independent data points (e.g., Felsenstein, 1985; Brooks and McLennan, 1991; Harvey and Pagel, 1991; Gittleman and Luh, 1992; Miles and Dunham, 1993; MacLeod, 2001; Garland et al., 2005). Therefore, it is possible that the IN areas and BSP lengths of Triassic anomodonts were significantly different from those of Permian forms because most of the Triassic taxa inherited large BSPs and IN from a recent common ancestor, and not because of widespread selection for increased respiratory efficiency.

The first step in determining whether body size and phylogeny are responsible for the differences in IN area and BSP length observed for Permian and Triassic anomodonts is to determine whether the anatomical characters are correlated with the potential causes. If no correlation exists, a causal relationship is unlikely, and removing the effects of the potential cause from the statistical analyses likely will have little effect on the results.

Body Size

We used the length between the tip of the snout and the posterior surface of the occipital condyle (measured along the ventral surface of the skull) as a proxy for body size. When the occipital condyle was damaged or missing, we used the length between the tip of the snout and the occipital plate as a substitute (the difference between the measurements ranges from a few millimeters for small specimens to a few centimeters for very large specimens). We chose this metric because many anomodont specimens consist only of skulls, and using a skull measurement ensured that we could collect body size information from all of our specimens. Furthermore, the relationship between linear measurements (particularly for the postcranial skeleton) and body size or mass have not been examined in detail for anomodonts, meaning that there was no known advantage or disadvantage to using ventral skull length over other potential measurements. Measurements were made in millimeters using digital calipers or a measuring tape (depending on the size of the specimen), and were taken directly from the specimens, except in the few cases where data were collected from published photographs (Supplementary Material). Measurements were log transformed before subsequent analyses.

TABLE 3-Results of Wald-Wolfowitz runs tests on IN areas and BSP lengths. See text for details of different data permutations.

Once the skull length data had been collected we used Pearson product-moment correlation tests to determine whether skull length was correlated with IN area or BSP length. The tests were run using all of the individual specimens for which a particular measurement was available (263 specimens for IN area, 364 specimens for BSP length), as well as with the eight non-dicynodont anomodont specimens excluded.

Phylogeny

Although the phylogenetic relationships of anomodonts have been the subject of much scrutiny (e.g., Cluver and King, 1983; King, 1988; Cox, 1998; Modesto et al., 1999, 2003; Modesto and Rybczynski, 2000; Rybczynski, 2000; Angielczyk, 2001, 2002, 2004, 2007; Angielczyk and Kurkin, 2003; Maisch, 2001, 2002; Surkov and Benton, 2004; Vega-Dias et al., 2004; Maisch and Gebauer, 2005; Surkov et al., 2005; Ray, 2006; Frobisch, 2007), a general consensus has yet to be reached and no recent analysis has included a large sample of both Permian and Triassic taxa. To accommodate these uncertainties we used three composite cladograms as the foundation for our phylogenetic framework (Fig. 4). The topology for the Permian anomodonts in these cladograms was modified primarily from Angielczyk (2001, 2002, 2004, 2007) and Angielczyk and Kurkin (2003). The topologies for the Triassic taxa were based on the results of Maisch (2001), Vega-Dias et al. (2004), and Surkov et al. (2005), respectively. Taxon sampling varied from cladogram to cladogram because different authors included different Triassic anomodonts in their analyses. Moreover, none of the three cladograms are completely resolved. Because the included polytomies represent uncertainty (i.e., they are "soft" polytomies), we generated 50 random, fullyresolved cladograms that were compatible with each of the three cladograms shown in Figure 4 (also see Supplementary Material). We then analyzed our data in the context of each of these 150 cladograms to ascertain how different hypotheses of relationship might affect our results. TABLE 4-Results of Kolmogorov-Smirnov two- sample tests comparing IN areas and BSP lengths of different species of Lystrosaurus, as well as comparisons between pooled Permian and Triassic Lystrosaurus specimens. The significance of differences between species should be judged at a Bonferroni-corrected alpha of 0.008.

We endeavored to estimate the strength of the effect of phylogeny on IN area and BSP length using the method described by Laurin (2004). First, BSP length and IN area were optimized on the three consensus cladograms portrayed in Figure 4 using squared-change parsimony (Maddison, 1991) and equal branch lengths in Mesquite 1.05 (Maddison and Maddison, 2004), and the observed tree-lengths were noted (Table 6). Then the tip taxa and their IN area and BSP length values were randomly permuted 10,000 times across the trees while holding the tree topologies constant. This process generates a distribution of tree length values for data with no phylogenetic signal that can be compared to the observed tree lengths. If the observed tree lengths fall outside the 95% confidence interval of the random distribution, we can conclude that the observed set of measurements has more phylogenetic signal (i.e., phylogeny has a great effect of the character values) than we would expect by chance.

FIGURE 3-Plot of snout-occipital condyle length (a proxy for body size) versus age rank. The data used in this plot are average values for the 58 taxa (including non-dicynodont anomodonts) that were included in statistical tests on IN area and/or BSP length. Taxa are included in all of the age ranks in which they are known to occur. Open triangles represent emydopid dicynodonts, +'s represent robertiid dicynodonts, x 's represent non-dicynodont anomodonts, and filled circles represent other dicynodont anomodonts that are not robertiids or emydopids. Note that the robertiids and emydopids dominate the smaller size range in the Permian, and that their rarity in the Triassic corresponds to a general scarcity of small anomodonts during that time period.

FIGURE 4-Composite cladograms used in the phylogenetic generalized least squares regression analyses. 1, Composite cladogram based on the analyses of Angielczyk (2001, 2002, 2004, 2007) and Angielczyk and Kurkin (2003) for Permian anomodonts, and Maisch (2001) for Triassic anomodonts. Triassic taxa are shown in bold type. 2, Composite topology for Triassic anomodonts based on the analysis of Vega-Dias et al. (2004). This section of the tree should be grafted onto the tree in 1 at the star. 3, Composite topology for Triassic anomodonts based on the analysis of Surkov et al. (2005). This section of the tree should be grafted onto the tree in 1 at the star. See Supplementary Information for the topologies of the 150 fully resolved trees described in the text.

Removing the Effects of Size and Phylogeny

Results of the product-moment correlation tests and the randomization tests suggest that BSP length is correlated with both body size and phylogeny (see below). Surprisingly, the results for IN area suggest that this character is not strongly correlated with body size, but strongly correlated with phylogeny. Nevertheless, we endeavored to remove the effects of phylogeny and body size from both characters, although we expected that doing so might affect the BSP data more strongly.

TABLE 5-Results of product-moment correlation tests examining the relationship between body size (skull length) and IN area, and body size (skull length) and BSP length. See text for details of different data permutations.

TABLE 6-Results of permutation tests for the presence of phylogenetic signal in the IN area and BSP length data, using the three phylogenetic topologies described in the text.

We used phylogenetic generalized least squares regression (PGLS; e.g., Grafen, 1989; Martins and Hansen, 1997; Garland and Ives, 2000; Rohlf, 2001; Martins et al., 2002) to attempt to remove the effects of body size and phylogeny for the IN and BSP data. PGLS is similar in most respects to traditional generalized least squares regression, but differs in the fact that the error term has been modified to take the phylogenetic distance between taxa, as well as variation within individual taxa, into account (Martins and Hansen, 1997). In the context of our analysis, it allowed us to examine the relationship between body size and IN area, and body size and BSP length, while accounting for the possible influence of the phylogenetic relationships between taxa. Furthermore, we could use residuals from the PGLS analyses to examine whether Permian and Triassic anomodonts differed in IN area and BSP length, after the variance attributed to body size and phylogeny by the PGLS model had been removed.

The PGLS analyses were carried out on the three sets of 50 cladograms (both with and without non-dicynodont anomodonts included) using Compare 4.6b (Martins, 2005). Because the implementation of PGLS in COMPARE can take within-taxon variation into account, we calculated standard errors for IN area, BSP length, and ventral skull length for the taxa included in the various cladograms that were known from multiple specimens. However, several included taxa are known only from single specimens (e.g., Patranomodon, Otsheria, Colobodectes), and therefore do not have standard errors for their measurements. To resolve this problem, we calculated the mean standard errors for IN area, BSP length, and ventral skull length for all included taxa and used these means as the standard error for taxa known from only one specimen or for which only one measurement was available. The PGLS model used in COMPARE also takes into account the mode of evolution postulated to be responsible for generating the observed data by incorporating a parameter (alpha; Martins and Hansen, 1997) in the phylogenetic error term which describes whether the data are expected to follow a Brownian motion model or to deviate from it (e.g., if stabilizing selection is occurring). This parameter can either be set in advance or estimated using maximum likelihood, and we took the latter approach in our analyses. Starting branch lengths were assumed to be equal for the PGLS analyses.

Comparisons between Permian and Triassic Anomodonts

Once the residuals from the PGLS analyses were in hand, we asked the same questions as we did with the uncorrected data set: did Triassic anomodonts have significantly larger BSPs and IN than Permian anomodonts, are BSP length and IN area correlated with stratigraphie occurrence, and do the apparent patterns of change represent the results of directional trends or random processes? As with our original data set, we used two-sample Kolmogorov-Smirnov tests, Spearman rank order correlation tests, and Wald-Wolfowitz runs tests to answer these questions, and we considered multiple data permutations. The K-S tests and rank order correlation tests were run using the residuals generated from the three sets of 50 phylogenetic trees, both with and without the non-dicynodont anomodonts included in the analyses. The rank order correlation tests were run with taxa counted only in the bin in which they first appear (e.g., Diictodon was included only in bin 2). For the Wald- Wolfowitz runs tests, mean values for the ten stratigraphic bins were calculated using the residuals in two ways. One set of means for each bin was computed using only taxa that have their first appearance in a particular bin. The second set of means was computed using values for all taxa that occurred in a particular bin (i.e., taxa with first appearances in a given bin as well as taxa with earlier first appearances whose stratigraphie range included the bin). As with the other statistics, all of the runs tests were carried out both with and without the non-dicynodont anomodonts included.

To determine whether the results of these tests were significant, we computed the average p-value for each set of 50 trees for all of the different tests that we ran based on the following justification. Ultimately, our goal in running these tests was to determine the probability of obtaining a difference or correlation as large as or larger than could be obtained by chance (i.e., if the null hypothesis is true) for the true phytogeny. We'll denote this probability as P(more extreme). For each of the different trees used to generate the residuals, the probability we calculated is the probability of obtaining the observed results under the null hypothesis and if the tree is the true tree. This can be designated P(more extreme and tree). P(more extreme) is equal to P(more extreme and tree) summed over the distribution of all possible trees. Averaging the observed p-values from our trees gives essentially the same result, except instead of summing over the entire universe of possible trees, we are summing over a presumably representative sub- sample of 50 trees for each of the three main topologies. RESULTS II

Correlations between Size, IN Area, and BSP Length

Results from the product-moment correlation tests are summarized in Table 5. When all 263 specimens with IN area measurements were considered, a significant correlation between body size (skull length) and IN area did not exist. This pattern did not change if the non-dicynodont anomodonts were excluded. In contrast, when the 364 specimens with BSP length measurements were considered, BSP length was significantly positively correlated with body size. The results for BSP length did not change when the non-dicynodont anomodonts were excluded from the data set. Based on these findings we predict that correcting for size-related differences will have a stronger effect on the BSP length data than the IN area data.

Phylogenetic Effects

Results from the randomization tests are summarized in Table 6. For both IN area and BSP length, the observed tree lengths are not only outside the 95% confidence intervals for the randomized data, they are lower than the minimum values obtained from the 10,000 randomizations for each of the three data sets. The fact that both characters require less change than we would expect if they showed random variation implies that the evolutionary histories of the characters correspond quite well with the phylogenetic trees. In other words, both characters display a strong phylogenetic signal, indicating that correction for the possible effects of phytogeny is warranted.

TABLE 7-Results of Kolmogorov-Smirnov two-sample tests comparing PGLS residuals of IN areas and BSP lengths of Permian and Triassic anomodonts. The reported values are means of the values associated with the 50 fully resolved topologies based on a given starting tree. Individual values for each tree that were used in calculating the means can be found in the Supplementary Material. See text for details of different data permutations.

Phylogenetic Generalized Least Squares Regression and Comparison between Permian and Triassic Taxa

Full results for the PGLS analyses are presented in the Supplementary Material. Accounting for the effects of phylogeny tended to weakly to moderately reduce the correlation between IN area and body size, with larger reductions occurring in the data sets that included the non-dicynodont anomodonts. The estimated alpha parameter for the IN area data ranged from 2.04 to 3.18 when the non-dicynodont anomodonts were included, and from 3.50 to 5.78 when they were excluded. This suggests that IN area was not following a strict Brownian motion model of evolution. Instead, some type of constraining force seems to have been limiting the amount the character was able to change.

Correcting for phylogeny also consistently reduced the strong correlation between BSP length and size, regardless of whether the non-dicynodont anomodonts were included or excluded. The magnitude of the reduction always was considerably larger than was the case for the IN area data, although the remaining correlations usually were stronger as well. The estimated alpha parameter for the BSP data ranged from 0.72 to 1.38 when the non-dicynodont anomodonts were included, and from 2.40 to 4.97 when they were excluded. Again, this suggests that BSP length was not following a strict Brownian motion model of evolution, although the BSP data sets with non- dicynodont anomodonts included most closely approximated this model. Moreover, BSP length seems to have been slightly less constrained in its changes than was IN area.

TABLE 8-Results of Spearman's rank-order correlation tests comparing PGLS residuals of IN area and BSP length to patterns of stratigraphie occurrence. The reported values are means of the values associated with the 50 fully resolved topologies based on a given starting tree. Individual values for each tree that were used in calculating the means can be found in the Supplementary Material. See text for details of different data permutations.

Full results of the K-S tests comparing PGLS residuals for IN area and BSP length in Permian and Triassic anomodonts are presented in the Supplementary Material, and are summarized in Table 7. Residual IN areas for Permian and Triassic anomodonts were not significantly different when the non-dicynodont anomodonts were included in the analysis, regardless of which of the three main phylogenetic topologies were considered. However, a significant difference was apparent in two of three cases when the non- dicynodont anomodonts were excluded (tree topologies of Vega-Dias et al. and Surkov et al.), with Triassic taxa possessing significantly larger IN areas. Residual BSP lengths for Permian and Triassic anomodonts were not significantly different in any of the data permutations we investigated.

Residual IN area was not correlated with stratigraphic occurrence for any of the three data sets when non-dicynodont anomodonts were included in the analysis, although a significant correlation did exist for all data sets when the non-dicynodont anomodonts were excluded (Table 8). Residual BSP length was strongly correlated with stratigraphic occurrence for all data sets, regardless of whether non-dicynodont anomodonts were included or excluded (Table 8). The runs tests could not reject the null hypothesis that the residual IN data were generated by a random process, regardless of which permutation of the data was considered (Table 9). The same was true for the residual BSP length data, with one exception, the topology of Maisch (2001) when only first appearances were considered and non- dicynodont anomodonts were included (Table 9).

TABLE 9-Results of WaId-Wolfowitz runs tests on PGLS residuals of IN area and BSP length. The reported values are means of the values associated with the 50 fully resolved topologies based on a given starting tree. Individual values for each tree that were used in calculating the means can be found in the Supplementary Material. See text for details of different data permutations.

IMPLICATIONS

The results from the tests using the PGLS residuals showed a mixture of similarities to and differences from those of the analyses based on the raw data, and they generally did not consistently match the predictions of the hypoxia scenario. As wa

Source: Journal of Paleontology

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