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Here I test the hypothesis that temporal variation in geographic range size within genera is affected by the expansion and contraction of their preferred environments. Using occurrence data from the Paleobiology Database, I identify genera that have a significant affinity for carbonate or terrigenous clastic depositional environments that transcends the Database's representation of these environments during the stratigraphic range of each genus. These affinity assignments are not a matter of arbitrarily subdividing a continuum in preference; rather, genera form distinct, nonrandom subsets with respect to environmental preference. I tabulate the stage-by-stage transitions in range size within individual genera and the stage-by-stage changes in the extent of each environment. Comparing the two shows that genera with a preference for a given environment are more likely to increase in geographic range, and to show a larger average increase in range, when that environment increases in areal extent, and likewise for decreases in geographic range and environmental area. Similar results obtain for genera with preferences for reefal and non-reef settings. Simulations and subsampling experiments suggest that these results are not artifacts of methodology or sampling bias. Nor are they confined to particular higher taxa. Genera with roughly equal preference for carbonates and clastics do not have substantially broader geographic ranges than those with a distinct affinity, suggesting that, at this scale of analysis, spatial extent of preferred environment outweighs breadth of environmental preference in governing geographic range. These results pertain to changes over actual geologic time within individual genera, not overall average ranges. Recent work has documented a regular expansion and contraction when absolute time is ignored and genera are superimposed to form a composite average. Environmental preference may contribute to this pattern, but its role appears to be minor, limited mainly to the initial expansion and final contraction of relatively short-lived genera.
Geographic ranges of species and genera are highly dynamic on both ecological and geological time scales (Bennett 1997; Gaston 1998, 2008, 2009; Jackson and Overpeck 2000; Jernvall and Fortelius 2004; Jablonski et al. 2006, 2013; Raia et al. 2006; Brett et al. 2007; Foote 2007; Foote et al. 2007, 2008; Hendy and Kamp 2007; Liow and Stenseth 2007; Patzkowsky and Holland 2007; Krug et al. 2008; Hadly et al. 2009; Roy et al. 2009; Liow et al. 2010; Willis and MacDonald 2011). Given the evidence that species often track the locations of their preferred environments (Bennett 1997; Jackson and Overpeck 2000; Holland et al. 2001; Brett et al. 2007; Hendy and Kamp 2007; Holland and Zaffos 2011; Willis and MacDonald 2011), it is natural to ask whether temporal variation in the magnitude of a taxon's geographic range reflects fluctuations in the extent of its preferred habitat. It may seem obvious that the answer must be affirmative. There are reasons to suppose that the expectation may not be so clear, however. For example, barriers to dispersal (Webb 1991, 2006; Holland and Patzkowsky 2007; Patzkowsky and Holland 2007; Lessios 2008) and ecological incumbency (Rosenzweig and McCord 1991; Sheehan 2008; Valentine et al. 2008), as well as biotic interactions more generally (Jablonski 2008), may restrict taxa from areas that they would otherwise be quite capable of inhabiting.
Using data from the Paleobiology Database, I will characterize occurrences of marine animal genera as coming from carbonate versus terrigenous clastic environments, which reflect both substrate composition and consistency and aspects of the broader depositional system such as nutrient levels, turbidity, and temperature (Wilson 1975; Peters 2008; Foote and Miller 2013: Appendix 1), as well as reefal versus non-reef settings. I will demonstrate that changes in the geographic range sizes of genera correlate with changes in the extent of their preferred environment. Subsidiary analyses suggest that these results are not likely to be artifacts of methodology or biased sampling of environments.
Materials and Methods
Occurrence data for marine animal genera, with associated information on stratigraphy, lithology, paleoenvironment, and geography, were downloaded from the Paleobiology Database (paleobiodb.org) on 23 February 2012. Details of the download and vetting procedures are described by Foote and Miller (2013). The data are available at Dryad (doi: 10.5061/dryad.76082). Collections were assigned to a series of stratigraphic intervals, primarily international stages (Foote and Miller 2013); collections that could not be resolved to a single time interval were ignored. Lithologies of each marine collection were categorized as either carbonate or clastic, following Foote (2006), with minor modification, and using only the primary lithology field in the Database. Collections with a mixed (carbonate and clastic) or unrecorded lithology, and those not readily assignable to either category, were ignored. Results are consistent if secondary lithology and mixed lithologies are taken into consideration (Appendix 1). The presence of a genus in a collection was counted as a single occurrence, irrespective of the number of species. Although all resulting occurrences were used in assigning lithologic affinities of genera, the analysis of changes in geographic range focuses on the Ordovician through Pleistocene, mainly because of limited stratigraphic resolution in parts of the Cambrian.
A genus could occur primarily in a given environment simply because that environment is dominant during its brief stay on Earth (Miller and Connolly 2001). To take this into consideration, I tabulated the proportion of all collections within the stratigraphic range of each genus that are assigned to carbonate and clastic lithologies. These proportions were treated as the null expectation for the frequency of occurrence of the genus in either lithology. Any genus that had significantly more occurrences than expected in either lithology, using a one-tailed binomial probability of 0.05, was considered to have an affinity for the corresponding environment. (This is similar to the approach of Kiessling and Aberhan [2007a] except insofar as they used the overall number of fossil occurrences rather than number of collections to set the probabilities for the null expectation; they note [p. 417] that they obtain similar results using collections instead.) In addition, I stipulated an arbitrary minimum of ten occurrences for a genus to be included in this study. Other protocols, such as using a different critical probability, a different minimum number of occurrences, or a null expectation of equal proportions carbonate and clastic (Foote 2006; Miller and Foote 2009) yield comparable results (Appendix 1). The variety of protocols used to assign affinity preferentially select for longer-lived and more abundant genera. Thus, there is little I can say about the determinants of geographic range within rare taxa. The main analyses include about 21% of all genera, accounting for 70% of all occurrences.
Table 1 shows a few examples of the affinity assignments. During the stratigraphic range of the trilobite Acastella, 64% of the collections are from carbonates and 36% from clastics. This genus has 44 occurrences, 30 of which are from clastics. The probability of observing 30 or more clastic occurrences, if the true frequency is 36%, is only about 10−5, so this genus is assigned a clastic affinity. The gastropod Acteonella is assigned a carbonate affinity, even though 52% of its occurrences are from clastics. This is because its 48% occurrence rate in carbonates is significantly greater than the null expectation of 32%. Finally, the cephalopod Acrioceras has 78% of its occurrences in carbonates; it is assigned no affinity, however, because this is not significantly greater than the null expectation of 67%. Assigning affinities in this way helps avoid a forced correlation between the size of the geographic range of a genus and the extent of its preferred environment.
By assigning genera to an affinity class, I am ignoring the possibility of variation in affinity within the history of individual genera (cf. Miller and Connolly 2001, who looked at the evolution of affinity within higher taxa). However, there is reason to think that genera do not generally change their affinities. I took those genera that have a defined affinity in aggregate and that have a range of two or more stages, i.e., those that logically could shift affinities. For each genus, I tabulated the number of stages in which it was sampled at least once; the total over all genera and stages is 25,260. Next, I calculated the affinity of each genus within each stage in which it is sampled, using the same protocol described above. Of the 25,260 tabulations, 18,397 (72.8%) have too few occurrences to assign an affinity; 1851 (7.3%) have the required minimum number of occurrences but do not yield a clear affinity; 4806 (11.1%) yield the same affinity as the aggregate tabulation over the life of the genus; and only 206 (0.8%) yield the opposite affinity as the aggregate value. Thus, one could make a case that genera fluctuate between having a clear affinity and being ambivalent, but there is little reason to think that they shift affinities substantially over time (Foote 2006; Holland and Zaffos 2011; Hopkins et al. 2013).
Figure 1 shows the difference between expected and observed proportion of carbonate occurrences for genera having carbonate and clastic affinities, as well as those having the minimum number of occurrences but no significant tendency toward either lithology. (The tabulations for clastic occurrences would simply be the mirror images of these.) The three groups of genera seem to form distinct populations, and the combined distribution of all genera is bimodal, but there is always the possibility that the assignment of affinities simply reflects an arbitrary cutoff in a continuum. Although that may be true for some genera, Figure 2 suggests that there really are populations of genera with distinct carbonate and clastic affinities. This figure tabulates the binomial probabilities of having a certain number of occurrences in either lithology. Under the null hypothesis that genera occur with the same frequency as the lithologies present during their lifetimes, these p-values should be uniformly distributed. Instead, there are pronounced spikes at p < 0.05 for genera of both carbonate and clastic affinities. The clarity of these affinity groups helps account for the fact that results do not depend critically on the details of the protocol used to assign affinities (Appendix 1).
For each stratigraphic interval, the globe was divided into 10,000 equal-area cells by using paleolatitude and paleolongitude (Foote and Miller 2013), and the total number of these cells containing at least one collection was tabulated. The range of each genus in each stage was defined as the proportion of these occupied cells in which it occurs. Thus, observed geographic range was expressed relative to the maximum it could be, given the distribution of available outcrop and how it is sampled. Because cells tend to be within single plates, this measure of range is relatively insensitive to the accuracy of paleogeographic coordinates, and results are barely distinguishable if we use modern coordinates instead (Appendix 1). Results are also consistent if we use absolute geographic range rather than scaling it relative to the maximum possible range (Table A1).
Areal Extent of Environment
Using the same equal-area cells, the areal extent of each environment in each stage was defined as the proportion of cells containing at least one collection of the corresponding lithology. Because a given area can contain both lithologies, the carbonate proportion and clastic proportion need not sum to unity (i.e., the alternatives for each proportion are not carbonate versus clastic, but rather presence versus absence of carbonate for one proportion, and presence versus absence of clastic for the other). This allows more freedom in the results. For example, if the geographic ranges of carbonate-loving taxa are positively correlated with the areal extent of carbonates, they need not be negatively correlated with the areal extent of clastics. If, by contrast, we measured environmental extent based on number of collections, which are assigned only to carbonate or clastic categories, the two correlations, as measured herein (see below), would necessarily be equal in magnitude and opposite in sign.
Temporal Changes in Geographic Range Size and Areal Extent of Environment
For each pair of successive stages and for each genus sampled from both stages, I noted the change in geographic range size from one stage to the next, and calculated the mean change for all such genera in the pair of stages. Note that genera present in only one stage or the other were not tabulated. Thus, the focus here is not on the change in mean geographic range, but on the mean change in geographic range. For each pair of stages, I calculated the change in the areal extent of carbonate and clastic environments. The Spearman rank-order correlation coefficient was used to assess the direction and strength of relationship between the change in areal extent of a given environment and the mean change in geographic range size of genera with an affinity for that environment.
Genera and species differ from one another in their characteristic ranges (Jablonski 1987; Jablonski and Hunt 2006; Foote 2007; Hadly et al. 2009); moreover, ranges of individual genera tend to be smaller near their first and last appearances than in between (Foote 2007). For these reasons, it is arguably more appropriate simply to record whether a genus increased or decreased in geographic range. Therefore, in addition to measuring the mean of what could be a very heterogeneous mix of changes in range, I simply scored whether each genus increased or decreased in range from one stage to the next, and whether each environment increased or decreased in areal extent. From these data, I tabulated 2 × 2 contingency tables and calculated the odds ratio expressing the strength of association between changes in environmental extent and changes in individual geographic range; I used the Fisher exact test to assess the statistical significance of this association.
All analyses were carried out in R, version 2.14.1 (R Development Core Team 2011).
Figure 3 shows the time series of areal extent for each environment. Although a given area can contain both environments, there is obviously an inverse correlation between the areal extent of carbonates and clastics. Changes in geographic range for the two affinity classes are shown in Figure 4. The data from Figures 3 and 4 are presented as scatter plots in Figure 5. Evidently, fluctuations in geographic range of carbonate-loving genera follow changes in the areal extent of carbonates, and likewise for clastic-lovers and clastic lithologies. In addition, the correlation between geographic range and areal extent is substantially stronger for carbonates than for clastics. The correlations reported in Figure 5 are consistent with those obtained if we look at proportional change in environmental extent, measured as the logarithm of the ratio between successive values rather than the simple difference between them (for carbonates, rs = 0.59, one-tailed p ≪ 0.001; for clastics, rs = 0.28, p = 0.01). The odds ratios for individual changes in geographic range (Table 2) show the same direction and relative magnitude of association for genera of carbonate and clastic affinities.
It is worth asking whether these relationships are driven by particular clades or are more general. If we look at the few groups with a large enough roster of genera to analyze separately, we see that they differ in the strength of association between geographic range size and areal extent of environment, and in the relative magnitude of the carbonate and clastic associations (Table 3). Most associations are positive, however, even if they are not all statistically significant. There does not seem to be a clear correspondence between the predominant affinity of a clade and the relative magnitude of carbonate and clastic associations. Brachiopods, like the data at large, are fairly evenly split between carbonate- and clastic-lovers, and they also show a stronger range-area association for carbonates. Trilobites are also roughly evenly split, but they show a stronger association for clastics. The overwhelming majority of corals prefer carbonates, and their range-area association is stronger for carbonates than for clastics. Conversely, gastropod genera are predominantly clastic-loving, and their range-area association is stronger for clastics. By contrast, many more bivalves prefer clastics than carbonates, but their association is stronger for carbonates.
Thus, the relative strength of carbonate and clastic associations is idiosyncratic, and which association is stronger cannot be predicted based on the predominant affinities of the group in question. Nonetheless, the existence of such associations would appear to be fairly general, not confined to certain clades.
Figure 6 and Table 4 show similar analyses, comparing reef and non-reef environments rather than carbonates and clastics. I followed Foote and Miller (2013: Appendix 1) in assigning collections to reef environments. Collections with missing environmental information or with environmental assignments such as “Carbonate indet.” were ignored, rather than being assigned to non-reef environments. There is one exception to this: about 0.01% of the occurrences cannot be assigned unambiguously to reef or non-reef environments by using the environment field, but they do have lithologic assignments, for example “bafflestone” and “reef rocks,” that allow them to be classified as reefal. The association between areal extent of reefs and geographic range size of reef-lovers is stronger than for non-reefs. Given the previous results on carbonates and clastics (Table 2, Fig. 5), and the fact that reef-loving taxa are largely a subset of carbonate-loving taxa (83% of reef-lovers being carbonate-lovers), this result is perhaps unsurprising. The odds ratios indicate that the associations between areal extent and geographic range are stronger for reef- and non-reef settings than for carbonates and clastics. This could be because the categories of carbonate and especially clastic are overly generalized, even though informative enough to yield a signal, whereas the distinction between reefal and non-reef settings is more specific.
Discussion and Conclusions
Because affinity, geographic range, and areal extent of environment are all based on different treatments of the same data, it is worth asking whether the results of this study are somehow forced by methodology. There are several reasons to suppose that this is not the case. First, affinities are based on frequency of occurrence whereas geographic range is based on areal extent, so the assignment of affinities and the analysis of geographic ranges and environmental extent are somewhat decoupled. Second, genera need to deviate significantly from the observed frequency of a given lithology in order to be assigned an affinity; a pulse of carbonates in a given stage, for example, will not perforce lead to a number of genera with carbonate affinities. Third, it is not difficult to construct a model in which genera have strong lithologic affinities and the areal extent of each lithology varies considerably over time, but in which geographic ranges of genera nonetheless do not track lithologic extent. When data are simulated with such a model and then subjected to the analytical protocols used here, we do not end up with results like those seen in the empirical data (Appendix 2). But perhaps the most obvious argument that the methods used here do not force strong relationships between environmental extent and geographic range size is that not all subsets of the data show significant associations (Table 3). If associations were a necessary outcome, we would expect carbonate-loving trilobites to track carbonates, for example, but they do not.
A tacit assumption of this study is that the relative extent of different environments as represented in the data agrees with what it was in the geologic past. There are two potential distortions here: the preservation of environments in the stratigraphic record, and how they are sampled. Systematic biases, for example if carbonates are always underrepresented, should have little effect on the results. We would need to be concerned, however, if there were spurious, short-term variation in the representation of a given environment. If, for example, carbonates consistently represented a relatively fixed proportion of the areal extent in the past, but our data showed that they fluctuated abruptly and significantly on stage-to-stage time scales because of biased representation, then both the observed areal extent of carbonates and the observed geographic ranges of carbonate-lovers could fluctuate in concert, creating a spurious correlation.
It is difficult to think of geological processes that would create fluctuating biases on the short time scales necessary to induce such a problem. Sampling could do so, however, at least in principle. In order to investigate the possibility that the results could be biased by temporal variation in sampling, I carried out various subsampling procedures in which the stage-to-stage representation of carbonates and clastics was made more uniform than in the observed data. Here I present the results of the most draconian procedure, in which every stage was forced to have an equal number of carbonate and clastic collections. This unrealistically assumes that none of the observed variation in the proportion of collections with a given lithology, whether short or long term, is real. Subsampling in this way diminishes but does not eliminate the association between environmental extent and geographic range size (Appendix 3). The difference between carbonates and clastics is also reduced, suggesting that the observed difference could be partly exaggerated by variable sampling. However, that an extremely unrealistic and pessimistic sampling scenario is needed to substantially reduce the lithology-range relationship suggests that the empirical results, at least qualitatively, are unlikely to be sampling artifacts.
Reconstructions of shallow-water habitat suggest that the relative extent of tropical versus extratropical habitat has declined over the course of the Phanerozoic (Walker et al. 2002). It has also been argued that superimposed on this real decline is a biased sampling of the tropics during the Paleozoic and of the extratropics during parts of the post-Paleozoic (Allison and Briggs 1993; Jablonski 1993; Jablonski et al. 2006; Vilhena and Smith 2013). The proportion of area sampled in the Paleobiology Database that is reconstructed as tropical is generally higher than the empirical estimate of Walker et al. (2002) (Fig. 7), even though paleolatitude in both cases is based on similar reconstructions (Scotese and Golonka 1992, cited in Walker et al. 2002; C. Scotese personal communication to the Paleobiology Database 2001). To explore the effects of possible latitudinal sampling bias, I subsampled data so that the proportion of equal-area cells in the tropics for each time interval matched the prediction of the regression line through the Walker et al. data (Fig. 7). The results are consistent with those obtained using the raw data (Appendix 1), suggesting that, to the extent that there is a tropical sampling bias, it is not responsible for the documented correlation between geographic range size and areal extent of preferred environment.
In interpreting the difference between carbonate and clastic results, it must be borne in mind that there is a general tendency for carbonates to occur preferentially in tropical latitudes and shallower water (Wilson 1975; Walker et al. 2002). Therefore, what are interpreted here as effects of preference for carbonate environments could partly reflect latitudinal preferences or other environmental correlates. Although estimates of relative depth of deposition are incomplete, we can at least measure the strength of association between paleolatitude and lithology by forming 2 × 2 tables with the number of collections that are tropical versus extratropical and carbonate versus clastic. All but eight of the 71 time intervals used here show a positive association between tropical latitude (≤30°) and carbonate lithology. I therefore carried out an additional analysis to control statistically for this association. For each time interval, I randomly omitted collections from the more common combinations of latitude and lithology—usually carbonate-tropical and clastic-extratropical—until the association between latitude and lithology was eliminated. The results are at least as strong as in the raw data (Table A1), suggesting that we are not merely seeing the effects of latitudinal preference masquerading as carbonate or clastic preference.
If the difference between carbonate and clastic results is robust, it would be another example of major macroevolutionary and macroecological differences between taxa with these respective affinities, as well as other differences in environmental preference (Miller 1988; Miller and Mao 1995; Cope and Babin 1999; Miller and Connolly 2001; Novack-Gottshall and Miller 2003; Foote 2006; Kiessling and Aberhan 2007a). It seems likely that at least one reason for the different strengths of association between environmental extent and geographic range is that areas of carbonate deposition often represent a more specific subset of environmental factors compared with the more generalized environmental correlates of clastic deposition (Wilson 1975).
It is tempting to ask whether the expansion of preferred environments is a factor that contributes to survival beyond the stage of first appearance of a genus (Heim and Peters 2011; Foote and Miller 2013; Nürnberg and Aberhan 2013). For genera having a defined affinity, I calculated the odds ratio showing the association between whether preferred environments expanded from the stage of first appearance to the subsequent stage, and whether the genera survived to the next stage. There is a statistically significant association (combined carbonate and clastic odds ratio: 1.53; p ≪ 0.001). However, this may not be very significant biologically, because the chances of survival are so high regardless of whether preferred environment expands (proportion surviving is 84.4% for genera whose preferred environment shrinks and 89.2% for those whose environment expands). Any genus that occurs frequently enough to show a distinct environmental affinity is generally sufficiently abundant and widespread that it is almost certain to survive past its stage of first appearance. Genera that meet the minimum of ten occurrences throughout their duration have odds of survival beyond their stage of first appearance that are 16.5 times higher than those of genera that fall short of this minimum. Statistically, this effect swamps the expansion of preferred environments.
For many clades, the average geographic ranges of species and genera are initially small, expand over time, and contract leading up to the time of extinction (Jernvall and Fortelius 2004; Raia et al. 2006; Foote 2007; Foote et al. 2007; Liow and Stenseth 2007; Tietje and Kiessling 2013), although of course many other general patterns have been discussed as well (Jablonski 1987; Kiessling and Aberhan 2007b; Gaston 2008). Given the results of this study, could the rise and fall be explained by genera tracking the expansion and contraction of their preferred environments (Holland and Zaffos 2011)? One reason to suppose a priori this is not the explanation is that the regular averages that have been documented are based on aggregates of genera with staggered first and last appearances and variable durations. Also, a symmetrical average rise and fall is the expected outcome of a bounded random walk process (Foote 2007: Appendix; Pigot et al. 2012), so it is possible that no overriding factor is needed to drive the average expansion and contraction, even if, as shown here, areal extent of preferred environments influences range fluctuations of individual genera.
To explore the relationship between environment and the rise-and-fall pattern, I segregated genera into duration classes (number of stages), calculated the average geographic range of each group of genera in each stage of its duration, and compared this with the mean areal extent of the preferred environment of these genera in these stages (Fig. 8). For genera with durations of three stages, the initial average expansion in range from the first to the second stage corresponds to an increase in the extent of their preferred lithology (Fig. 8A). Similarly, the contraction in average range from the second to the final stage is matched by a decrease in extent of preferred lithology. Note, however, that the change in the average extent of preferred lithology is small compared to the changes documented with respect to real geologic time (Fig. 5). When removed from the context of actual time, three-stage genera show a considerable expansion and contraction, but the small corresponding change in the average areal extent of carbonates and clastics suggests that these average aggregates tend to change largely irrespective of how environmental extent changes.
Moreover, the relationship between environment and geographic range largely breaks down for genera with durations of more than three stages (Fig. 8B–F). Genera with longer durations expand and contract on average, but the only clear relationship to preferred environment seems to be a decline in the areal extent of clastics from the penultimate to the ultimate stage. Moreover, when genera are separated into duration classes rather than superimposed as a single aggregate, there is little systematic variation in average range other than the initial expansion and final retreat. In light of these results, we should ask whether the overall correlation between geographic range and areal extent of lithology (Table 2) reflects anything other than the initial expansion and final contraction of individual genera. It does: If we ignore transitions involving the stages of first and last appearance, we see that the association between individual changes in range and changes in environmental extent is just as strong (Table 5).
Another factor that influences genus geographic range is breadth of environmental tolerance, whether this is because individual species are broadly tolerant (Bozinovic et al. 2011; Slatyer et al. 2013) or because congeneric species vary in their preferences. Against this backdrop, the results presented here agree with the notion that widespread taxa do not necessarily have the broadest tolerances, but instead track environmental factors that are more broadly distributed, as Jablonski et al. (2013) recently reported for temperature preferences of living bivalve species. A rough look at the role of environmental breadth is possible by comparing genera with distinct carbonate or clastic affinities to those that have no clear affinity. Although the test is quite crude, given the coarse environmental categories, it suggests that eurytopic genera, operationalized as those that occur nearly as frequently in carbonates as in clastics, are at most about 10% more widely distributed on average than genera with clear carbonate or clastic affinities (Appendix 4).
In summary, the results presented here illustrate two ways in which the properties of species—their tendency to track preferred environments and to be more widespread when their preferred environments are more widespread—mesh with the larger-scale observation that changes in geographic range of genera over millions of years are correlated with, and presumably influenced by, the expansion and contraction of their preferred habitat. These in turn mirror patterns at even larger taxonomic scales, in which diversification and prevalence of preferred habitat are related (Miller and Connolly 2001).
I am grateful to the many people who have contributed to the Paleobiology Database. Major contributors for the data used herein include M. Aberhan, J. Alroy, A. Miller, D. Bottjer, M. Clapham, F. Fürsich, N. Heim, A. Hendy, S. Holland, L. Ivany, W. Kiessling, B. Kröger, A. McGowan, T. Olszewski, P. Novack-Gottshall, M. Patzkowsky, M. Uhen, L. Villier, and P. Wagner. I thank D. Jablonski, A. I. Miller, M. F. Przeworski, S. E. Peters, and D. B. Rowley for discussion and advice. S. Finnegan, A. I. Miller, M. Powell, and an anonymous referee kindly reviewed the manuscript. Supported by NASA Exobiology (NNX10AQ44G). This is Paleobiology Database publication number 194.
I explored several alternative protocols to assess the robustness of results, in addition to those briefly mentioned in the main text. In all cases, the alternative results show a positive association between changes in areal extent of a given environment and changes in the geographic ranges of genera with an affinity for that environment (Table A1). In most cases the measures of association are also quantitatively rather close to the baseline analysis.
Coding of Lithology
Secondary lithology was ignored in the standard analysis, and occurrences with a mixed carbonate-clastic lithology were omitted. In an alternative analysis, collections from mixed settings were retained and the secondary lithology was included in assigning a collection. A collection is considered to come from a mixed setting if the primary and/or secondary lithology field indicates mixed carbonate-clastic lithology, or if the primary lithology is carbonate and the secondary lithology clastic (or vice versa) (Foote 2006: Table 3). Such collections, which account for 14% of the total, were randomly and equiprobably assigned to the carbonate and clastic categories. The association between environmental extent and geographic range weakens somewhat for carbonates, but the results are consistent with the baseline analysis (Table A1).
Convention for Stratigraphic Gaps
In the analyses presented in the main text, a change in geographic range was recorded only if a genus is sampled in two successive stages. Stages in which a genus is known to be extant but is not sampled were ignored. As an alternative, I conducted an analysis in which I credited a genus with a geographic range of zero during a stage in which it is extant but not sampled (Table A1).
Accounting for Cases in Which Absolute Geographic Range Does Not Change
Geographic range is measured as the ratio between the number of equal-area cells occupied and the maximum that could be occupied given the spatial extent of data. It is therefore possible for geographic range to change from one stage to the next because of changes in the spatial extent of data rather than the number of cells occupied. I therefore carried out a separate analysis in which changes in proportional cell occupancy were included only if absolute cell occupancy also changed. In this analysis, the correlation between environmental extent and geographic range is still stronger for carbonate-lovers, but the difference between carbonate- and clastic-lovers in the strength of association for individual changes vanishes (Table A1).
The main analysis included all marine animal genera, including those that are planktonic and nektonic. The rationale is that lithology reflects not just substrate but also the overall depositional system, which is relevant to pelagic organisms. I performed a separate analysis (Table A1) including only the major, principally benthic, classes with at least 1000 occurrences (Anthozoa, Bivalvia, Crinoidea, Demospongea, Echinoidea, Gastropoda, Gymnolaemata, Hexactinellida, Lingulata, Ostracoda, Polychaeta, Rhynchonellata, Scaphopoda, Stenolaemata, Stromatoporoidea, Strophomenata, and Trilobita). These collectively account for about 84% of all occurrences.
Protocol for Assigning Affinity
Three alternative protocols were used (Table A1): (1) a stricter one requiring a minimum of 20 rather than ten occurrences and a deviation from expected frequency of occurrence of a given lithology at a probability of 0.01 rather than 0.05; (2) a weaker one with a minimum of five occurrences and a probability of 0.1; (3) an alternative null hypothesis that all genera are expected to have equal numbers of carbonate and clastic occurrences (Foote 2006; Miller and Foote 2009).
Locations of collections were assigned in the main analysis by using estimated paleocoordinates (C. Scotese personal communication to the Paleobiology Database 2001). As stated above, this should make little difference when geographic range and areal extent of lithology are measured with equal-area cells, because most cells will fall within a single plate. As expected, there is little quantitative difference in the results if locations are assigned to modern coordinates (Table A1).
Adjusting Sampled Area of Tropical and Extratropical Latitudes
Assuming that the regression line of Figure 7 approximates the areal extent of tropical sampling in the absence of bias, data were subsampled so that the proportion of equal-area cells in each stage would fall on this line. Ptrop is the desired proportion of sampled cells falling in the tropics, Ntrop is the observed number of cells in the tropics, and Ntot is the total number of cells. If the observed proportion Ntrop/Ntot is greater than Ptrop, then the tropics must be downsampled, and the number of tropical cells retained is given by
In practice this is truncated to an integer. For example, there are 131 cells sampled in the Tremadocian, 100 (76%) of which are tropical. The expected proportion according to the regression line is 65%. Substituting into the foregoing equation, we find that keeping 57 tropical cells and all 31 extratropical cells yields the desired proportion of 65% tropical coverage. Thus 57 tropical cells, and all the collections contained therein, are randomly chosen and retained, while the remaining 43 tropical cells and all their collections are omitted. If extratropical latitudes are oversampled, they are similarly downsampled so the expected proportion of tropical coverage is attained. This procedure is repeated for every stage. The analysis of the resulting data set yields results compatible with the analysis of the raw data (Table A1).
A Model of Decoupled Lithologic Extent and Geographic Range
The purpose of describing this model is not to claim that it is realistic, but rather to show that it is possible to simulate data with genera that have strong lithologic preferences, and with substantial temporal variation in lithologic extent, but in which the methods used herein do not force a correlation between lithologic extent and geographic range.
For each of N stages, M genera originate and subsequently show exponential survivorship with extinction rate q. Half of the genera are randomly assigned a carbonate preference and half a clastic preference, with the probability, Ppref, of occurring in the preferred lithology set to a uniform random number between 0.7 and 0.9. The landscape is divided into Ncell equal-area cells. In each stage, the proportion of collections that are carbonates, Pcarb, is a uniform random number between 0.3 and 0.7. (This range of values is similar to the empirical range.) The proportion of clastic collections, Pclast, is equal to 1−Pcarb. In each stage, Ncoll collections are randomly assigned a lithology, with probabilities equal to Pcarb and Pclast for the corresponding stage, and each collection is randomly assigned to one of the cells. Finally, for each genus that is extant in the stage, the number of cells it occupies and the number of collections in which it occurs are drawn at random from Poisson distributions with parameter λ1 and λ2 (equal to the mean number of cells per genus and the mean number of collections per genus), with the conditions that the specific collections drawn for the genus must be contained within the cells that have been drawn, and that the probability of drawing a collection with a genus's preferred lithology is equal to its particular value of Ppref. Note that the geographic range of a genus is drawn independently of the areal extent of its preferred lithology. The simulated data are then processed exactly as the empirical data. (Results are essentially the same if genera are classified by their initially assigned affinities rather than affinities determined from the frequency of occurrence in the respective lithologies.) For the simulations presented here, Ncell = 1000, Ncoll = 1000, N = 20, M = 50, q = 0.1, λ1 = 10, and λ2 = 20, but other values yield compatible results.
Figure A1 shows the lithology-range associations for 1000 simulations. About 10% of the associations are significantly positive at p < 0.05, more than the 5% we would expect by chance. However, the carbonate and clastic associations are negatively correlated, a feature not seen in empirical data, so that none of the simulations yield significantly positive associations for both lithologies. It therefore seems unlikely that the methods used here are forced to detect range-lithology associations where none exist.
Imposing Uniform Representation of Carbonates and Clastics
There are several ways to reduce temporal variation in the representation of lithologies. One reasonable approach would be to focus on large changes between successive stages. For example, if there is a large jump in the proportion of clastic collections from one stage to the next, one could sample fewer clastic collections from the second stage. How many fewer, however? One possibility is to down-sample until the proportions in successive stages do not differ significantly in the statistical sense. In analyses not presented here, I have used this approach and found it to have rather minor effects on the results. Instead, I will present results of a more draconian sampling scheme. In the observed data, there are Ncarb carbonate collections and Nclast clastic collections in each stage; let Nmin be the minimum of these two. Then, for each stage, Nmin collections of the more common lithology are sampled at random, and all of the collections of the less common lithology are retained, so that the two lithologies are equally represented. The analysis then proceeds as for the original empirical data. This subsampling procedure was repeated 1000 times. The results (Fig. A2) show that the lithology-range relationship is diminished but not eliminated.
Geographic Range of Eurytopes versus Genera with Clear Affinities
The genera that have no clear affinity overlap with the carbonate and clastic groups in terms of their distribution of lithologic occurrences (Fig. 1), and in many cases it is not possible to assign them an affinity simply because they have relatively few occurrences. In fact, the median number of occurrences of these genera collectively is 18, compared with 28 for the genera having clear affinities. Thus, all else being equal, we would expect them to have smaller sampled geographic ranges. Therefore, I operationally designated as eurytopes the subset of no-affinity genera that have deviations between expected and observed frequency of carbonate (or clastic) occurrence of less than or equal to 0.1, i.e., the inner part of the distribution of Figure 1C. These have nearly the same median total number of occurrences per genus (26) as do the genera with distinct affinities (28). I also made a second, stricter designation corresponding to those genera with deviations of less than or equal to 0.05; these genera have a median of 28 occurrences. For every stage, I tabulated the mean geographic range of genera with distinct affinities (carbonate and clastic combined) and the mean range of eurytopes. The results are shown in Figure A3. The two designations of eurytopes show either slightly smaller or slightly larger geographic ranges on average compared with the genera having distinct affinities.
Supplemental materials deposited at Dryad: doi: 10.5061/dryad.76082
- Accepted 9 January 2014.