(PDF) S.R. Cole. 2019. Hierarchical controls on extinction selectivity across the diplobathrid crinoid phylogeny

Identifying correlates of extinction risk is important for understanding the underlying mechanisms driving differential rates of extinction and variability in the temporal durations of taxa. Increasingly, it is recognized that the effects of multiple, potentially interacting variables and phylogenetic relationships should be incorporated when studying extinction selectivity to account for covariation of traits and shared evolutionary history. Here, I explore a variety of biological and ecological controls on genus longevity in the global fossil record of diplobathrid crinoids by analyzing the combined effects of species richness, habitat preference, body size, filtration fan density, and food size selectivity. I employ a suite of taxic and phylogenetic approaches to (1) quantitatively compare and rank the relative effects of multiple factors on taxonomic longevity and (2) determine how phylogenetic comparative approaches alter interpretations of extinction selectivity. I find controls on diplobathrid genus duration are hierarchically structured, where species richness is the primary predictor of duration, habitat is the secondary predictor, and combinations of ecological and biological traits are tertiary controls. Ecology plays an important but complex role in the generation of crin-oid macroevolutionary patterns. Notably, tolerance of environmental heterogeneity promotes increased genus duration across diplobathrid crinoids, and the effects of traits related to feeding ecology vary depending on habitat lithology. Finally, I find accounting for phylogeny does not consistently decrease the significance of correlations between traits and genus duration, as is commonly expected. Instead, the strength of relationships between traits and duration may increase, decrease, or remain statistically similar, and both the magnitude and direction of these shifts are generally unpredictable. However, traits with strong correlations and/or moderately large effect sizes (Cohen's f 2 > 0.15) under taxic approaches tend to remain qualitatively unchanged under phylogenetic approaches.

Paleobiology, 2019, pp. 1–20 DOI: 10.1017/pab.2019.37 Phylogenetic Paleoecology Special Issue Hierarchical controls on extinction selectivity across the diplobathrid crinoid phylogeny Selina R. Cole Abstract.—Identifying correlates of extinction risk is important for understanding the underlying mechanisms driving differential rates of extinction and variability in the temporal durations of taxa. Increasingly, it is recognized that the effects of multiple, potentially interacting variables and phylogenetic relationships should be incorporated when studying extinction selectivity to account for covariation of traits and shared evolutionary history. Here, I explore a variety of biological and ecological controls on genus longevity in the global fossil record of diplobathrid crinoids by analyzing the combined effects of species richness, habitat preference, body size, ﬁltration fan density, and food size selectivity. I employ a suite of taxic and phylogenetic approaches to (1) quantitatively compare and rank the relative effects of multiple factors on taxonomic longevity and (2) determine how phylogenetic comparative approaches alter interpretations of extinction selectivity. I ﬁnd controls on diplobathrid genus duration are hierarchically structured, where species richness is the primary predictor of duration, habitat is the secondary predictor, and combinations of ecological and biological traits are tertiary controls. Ecology plays an important but complex role in the generation of crinoid macroevolutionary patterns. Notably, tolerance of environmental heterogeneity promotes increased genus duration across diplobathrid crinoids, and the effects of traits related to feeding ecology vary depending on habitat lithology. Finally, I ﬁnd accounting for phylogeny does not consistently decrease the signiﬁcance of correlations between traits and genus duration, as is commonly expected. Instead, the strength of relationships between traits and duration may increase, decrease, or remain statistically similar, and both the magnitude and direction of these shifts are generally unpredictable. However, traits with strong correlations and/or moderately large effect sizes (Cohen’s f 2 > 0.15) under taxic approaches tend to remain qualitatively unchanged under phylogenetic approaches. Selina R. Cole. Division of Paleontology, American Museum of Natural History, Central Park West at 79th Street, New York, New York 10024, U.S.A.; and Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Post Ofﬁce Box 37012, MRC 121, Washington, D.C. 20013-7012, U.S.A. E-mail: scole@amnh.org. Accepted: 28 September 2019 Data available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.533j6c3 Introduction Fundamental to the ﬁelds of paleontology, evolutionary biology, and conservation biology is the phenomenon of extinction. Differential rates of extinction result in heterogeneity in the longevity of taxa across clades and through time (McKinney 1997; Jablonski 2008a). The fossil record is an indispensable source of information on how past species responded to extinction pressures, with implications for understanding the extinction risk faced by species today (Harnik et al. 2012). It provides a detailed framework for exploring whether certain environmental, biological, and/or ecological traits can be identiﬁed as universal predictors of extinction risk, or whether the role of certain traits varies across clades and © 2019 The Paleontological Society. All rights reserved. through time. A number of factors have been linked to extinction selectivity in the fossil record across many clades, such as geographic range size (e.g., Payne and Finnegan 2007; Powell 2007; Jablonski 2008a; Foote et al. 2008; Harnik et al. 2014) and niche breadth (Kammer et al. 1997, 1998; Liow 2007; Heim and Peters 2011; Nurnberg and Aberhan 2013; Smits 2015), as well as factors that are more taxon speciﬁc, such as larval dispersal in mollusks (Hansen 1978; Gilli and Martinell 1994; Jablonski and Hunt 2006). Other factors have variable effects in different taxonomic groups, such as body size (Jablonski 1996; Harnik 2011; Tomiya 2013) and morphologic variation/complexity (Villier and Korn 2004; Liow 2004, 2006; Hopkins 2011; Kolbe et al. 2011). Many of 0094-8373/19 Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 2 SELINA R. COLE these traits have also been implicated in increased extinction risk of modern species (Purvis et al. 2000; Thomas et al. 2004). When investigating extinction selectivity, there are two notable sources of potential error. First, many biological traits may covary and/or be governed by the same underlying mechanisms. Failing to account for potential relationships among variables may result in spurious interpretations of the complex, interacting processes driving extinction selectivity (Wootton 1994; Jablonski 2005). A number of studies have attempted to tease apart the effects of interacting factors using multivariate linear regression (e.g., Liow 2007; Crampton et al. 2010; Harnik 2011; Hopkins 2011; Harnik et al. 2014), but the relative contribution of multiple variables on taxonomic duration has rarely been quantiﬁed. Second, phylogenetic effects can play a role in extinction selectivity and/or confound the apparent signal of other variables (Green et al. 2011; Smith and Roy 2006; Purvis 2008; Fritz and Purvis 2010; Soul and Friedman 2017; Congreve et al. 2018). Taxic approaches cannot fully account for shared evolutionary history among closely related taxa, and most incorrectly treat taxa as phylogenetically independent units. As a result, the value of incorporating explicit phylogenetic hypotheses into studies of extinction selectivity using comparative methods has been recognized in recent years (e.g., Friedman 2009; Hopkins 2011; Harnik et al. 2014; Puttick et al. 2017; Field et al. 2018). Here, I use the fossil record of diplobathrid crinoids to (1) assess the effects of multiple factors on extinction selectivity, both with and without phylogenetic nonindependence taken into account, and (2) determine the relative contribution of biological and ecological traits to diplobathrid genus duration. Diplobathrids are a model group for this study, because they have an extensive stratigraphic range (Late Ordovician [Floian] to Upper Mississippian [Serpukhovian]), a well-sampled fossil record (Cole 2017), and a well-resolved phylogeny that is nearly comprehensive at the genus level, including 100 genera (Cole 2018). In addition, many aspects of crinoid ecology can be extracted from skeletal features that readily preserve in fossil specimens, facilitating investigation of the role ecology played during their evolutionary history (Cole et al. 2019). Traits investigated were body size, species richness, niche breadth, density of the ﬁltration fan, and food size selectivity. To identify signiﬁcant correlations between these traits and the duration of diplobathrid genera in the fossil record, I employed multiple linear regression, which accounts for covariation between variables without phylogenetic context, and phylogenetic generalized least squares, which takes phylogenetic relationships of the study taxa into account. I calculated phylogenetic signal to explore the degree to which characters are phylogenetically structured, and calculated Cohen’s f 2, a measure of effect size, to determine the relative contribution of variables to diplobathrid duration and to compare the inﬂuence of variables on duration among groups. Using these approaches, the following key questions were addressed concerning extinction selectivity and genus duration in diplobathrid crinoids: (1) What are the signiﬁcant predictors of extinction? (2) What are the relative contributions of those predictors? (3) Do ecological traits, such as habitat preference and ecomorphologic variation, play a signiﬁcant role in genus longevity? (4) How does incorporating phylogenetic structure affect interpretations of extinction selectivity? Trait Selection and Crinoid Ecology The ﬁrst three traits investigated in this study—body size, species richness, and habitat preference/niche breadth—were chosen because they have been identiﬁed as notable correlates of extinction from previous studies. As a result, one goal of this study was to determine whether the correlations of these traits with extinction would hold true for diplobathrid crinoids. For example, signiﬁcant correlations between body size and extinction risk have been documented for many vertebrate groups (Gaston and Blackburn 1997; Friedman 2009; Tomiya 2013; Lyons et al. 2016), but body size is not consistently correlated with extinction risk in invertebrates (e.g., Lockwood 2005; Harnik 2011). Likewise, it has been recognized that species richness corresponds to the persistence of higher taxa (Jablonski 1991; McKinney 1997), Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY but few studies have tested this correlation explicitly. Niche breadth has also been investigated for multiple vertebrate and invertebrate groups; taxa with greater niche breadth (i.e., generalist taxa) generally have been found to have increased taxonomic longevity (Baumiller 1993; Liow 2007; Nurnburg and Aberhan 2013; but see Colles et al. [2009] for a more detailed review). In this study, niche breadth is measured as a function of habitat preference, which is thought to represent a major environmental control on the distribution of different crinoid groups (Kammer et al. 1997, 1998). The other two traits investigated—ﬁltration fan density and food size selectivity—were included because they reﬂect ecologically signiﬁcant traits by which crinoids partition niches (Ausich 1980; Cole et al. 2019), and thus might be expected to have macroevolutionary signiﬁcance over the history of Diplobathrida. Crinoids are epifaunally tiered passive suspension feeders that ﬁnely partition niche space on the basis of feeding ecology (Breimer 1969; Meyer 1973; Ausich 1980; Ausich and Bottjer 1982; Baumiller 1997; Messing et al. 2017). Notably, there are many skeletal features in the arms of crinoids (e.g., arms, pinnules, brachials, ambulacral grooves) that dictate the maximum size of food particles captured, the efﬁciency of the ﬁltration fan, and the environmental conditions that are optimal for feeding (Ausich 1980; Kammer 1985; Kammer and Ausich 1987, 2006; Holterhoff 1997; Brower 2007; Baumiller 2008). The relationships between these ecomorphologic characters and niche partitioning in crinoids has been extensively documented in both fossil and living crinoids (Meyer 1973; Macurda and Meyer 1974; Ausich 1980; Kitazawa et al. 2007; Baumiller 2008; see Cole et al. [2019] for a more detailed review). The ecological traits included in this study reﬂect two of the most important aspects of feeding ecology (Ausich 1980; Cole et al. 2019). Filtration fan density (the total number of feeding appendages in a given area) affects feeding by altering the ﬂow of water through the ﬁltration fan, and food size selectivity (controlled by the size of the terminal feeding appendages) dictates the maximum size of the food particle that can be captured. 3 Data and Methods Measuring Stratigraphic Duration.—Genus duration was measured as the total duration of a genus in millions of years (Myr) given its constituent species. Stage-level bins were used for Ordovician, Devonian, and Mississippian occurrences, whereas series-level bins were used for Silurian occurrences to maintain time bins of roughly equal duration (mean 7.7 Myr, median 7.7 Myr). Although division into ﬁner time bins would be desirable, temporal resolution is variable for the taxa used in this study because of their global distribution and broad stratigraphic ranges. Thus, stage- and series-level time bins were used for estimating genus duration so that taxa were treated at a similar scale of resolution. Genus duration in millions of years was tabulated using the 2013 Bibliography of Paleozoic Crinoids (Webster and Webster 2014), which was updated to include newly described taxa and to match current divisions of the International Chronostratigraphic Chart. Genera were assumed to originate at the beginning of the time bin in which they ﬁrst occurred and to terminate at the end of the time bin in which they last occurred. Genera with species occurring in only one stage were assigned a duration equal to that of the stage. Phylogenetic Framework.—Paleobiological studies often treat taxa as independent units, despite the fact that species have shared evolutionary history. The nonindependence of species’ evolution is important to take into account, because species that diverged more recently from a common ancestor will share more evolutionary history than species that diverged less recently. This may result in greater similarity between features of closely related taxa, such as morphology, ecology, and/or geographic distribution (Felsenstein 1985; Harvey and Pagel 1991; Wiens 2004; Jablonski and Hunt 2006; Losos 2008; Hopkins 2011; Harnik et al. 2014). Here, trees recovered from a recent phylogeny of diplobathrid crinoids (Cole 2018) were employed as a framework to take into account the effect of shared evolutionary history on genus duration (Fig. 1). The previous analysis of diplobathrid phylogeny assessed relationships among 101 Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 4 SELINA R. COLE FIGURE 1. Phylogenetic relationships, durations, lithologies, and species numbers for diplobathrid crinoid genera. Tree topology is based on the strict consensus of 15 most-parsimonious trees recovered from a parsimony analysis of all wellpreserved diplobathrid genera. Symbols at the terminal tips represent the lithologic environment in which genera occur, and the numbers following tips represent number of species within each genus. Stage-level stratigraphic ranges are plotted for each genus to the right of the tree; each square represents one stage; stages not scaled to duration. Sp., number of species per genus; Ord., Ordovician; Sil., Silurian; Dev., Devonian; Miss., Mississippian. Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY diplobathrid genera (all but 4 of the currently valid genera) using 135 discrete morphologic characters. Fifteen most-parsimonious trees were recovered, which were largely congruent with trees resulting from Bayesian analysis (see Cole [2018] for further details). In the present study, outgroup taxa were pruned from the tree along with Cleiocrinus because of its uncertain assignment to Diplobathrida (Cole 2018). As a result, all tree-based analyses of extinction selectivity used a phylogenetic framework containing 100 diplobathrid genera. For evolutionary hypotheses to be incorporated into comparative studies, the tree must ﬁrst be scaled to provide branch lengths for the tree in units of time (Bapst 2014). Each of the 15 most-parsimonious trees recovered by Cole (2018) were time-scaled 100 times using the “basic” approach in the R package paleotree (Bapst 2012) with the binned version of the timePaleoPhy function (bin_timePaleoPhy), in which the placement of internal nodes represents the earliest appearance of a taxon contained within the clade (Norell 1992; Smith 1994). In this approach, node ages are randomly drawn from uniform distributions corresponding to ﬁrst appearance interval times. Time-scaling trees using the ﬁrst appearance method results in zero-length internal branches that cannot be used in comparative studies (Hunt and Carrano 2010), so to circumvent this issue, a small, arbitrary amount of time (0.01 Myr) was added to each zero-length branch. This standard approach allows the tree to be used for comparative phylogenetic analyses without signiﬁcantly altering the tree’s structure or the subsequent results (Hopkins 2011; Bapst 2013; Harnik et al. 2014). All subsequent tree-based analyses were conducted over the recovered distribution of 1500 time-scaled trees. Morphologic and Ecological Data.—To address whether ecological variables were predictors of genus duration, measurement data were collected for multiple continuous skeletal traits that are directly tied to ecological functions. Morphologic data were collected for 295 specimens across 185 species and 100 genera (Supplementary Material). Measurements were taken directly from specimens for all taxa available for study at the Smithsonian National Museum of Natural History, the 5 London Natural History Museum, the Lapworth Museum, and the Chicago Field Museum. For taxa that did not have specimens at accessible museums, measurements were collected from published literature. Measurement averages for each genus were calculated from all specimens measured for that genus. Measurements collected were calyx width (measured where the arms become free), pinnule density (the number of pinnules per 5 mm of arm length), pinnule width, arm length (from the edge of the calyx where the arms become free to the distal terminus), brachial width, and the number of terminal feeding appendages (i.e., the total number of pinnules). Arm length and calyx width were used to calculate the area of the ﬁltration fan: A = p(L + r)2 − pr2 (1) where A is the area of the ﬁltration fan, L is the arm length, and r is the radius of the calyx (Cole et al. [2019], modiﬁed from Ausich [1980]). Although stem length plays an important role in crinoid niche partitioning along with feeding structures (Ausich 1980; Ausich and Bottjer 1982; Cole et al. 2019), preservation of complete stems is rare. Only 7% of genera investigated in this study preserved at least one specimen with a complete stem, so stem length was not considered here. Because species niches are complex and multidimensional, they cannot be adequately represented by a single trait (Ausich 1980; Pianka et al. 2017; Cole et al. 2019). For example, continuously varying traits relating to crinoid feeding structures like arm number, pinnule and brachial dimensions, as well as the arrangement of arms and pinnules, can combine in countless ways to create ﬁltration fans that vary in their density, feeding efﬁciency, and ability to capture food particles of different sizes. For this reason, it is the combined effect of multiple ecological traits rather than the individual traits themselves that should be evaluated when characterizing ecological niches. This is typically done through ordination of ecological and/or ecomorphologic traits followed by identifying the trait(s) that correspond to the major axes of variation Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 6 SELINA R. COLE (e.g., Pianka et al. 2017; Cole et al. 2019). Here, a principal component analysis (PCA) was conducted in PAST (Hammer et al. 2001) on the morphologic data collected for diplobathrids. Traits included in the analysis were the number of terminal arm tips, the area of the ﬁltration fan, brachial width, pinnule width, and pinnule density. Because many of the traits have high variance (up to three orders of magnitude), variables were log transformed before multivariate analysis. The ﬁrst three components resulting from the PCA accounted for more than 95% of the variance in morphologic data (64.4%, 24.0%, and 6.6%, respectively) and were interpreted as body size, ﬁltration fan density, and maximum food particle size, respectively, based on their corresponding loadings (Supplementary Table 1). When analyzing morphologic data using PCA, the ﬁrst principal component (PC 1) typically represents size (Humphries et al. 1981; Revell 2009). Here, all morphologic variables had high positive loadings for PC 1, which is consistent with a strong positive relationship between these variables and overall body size. PC 2 represents the density of the ﬁltration fan, particularly with regard to the number of terminal arm tips and pinnule density. PC 3 was interpreted as corresponding to maximum food size (hereafter “food size”), which relates to brachial width and, to a lesser extent, pinnule width. In all subsequent analyses, scores for the ﬁrst three principal components were used to investigate the relationship between taxonomic duration and ecomorphologic traits. For brevity, variables are hereafter referred to using trait names rather than PC axes interpreted as corresponding to those traits. Environmental and Species Data.—Lithology is an important factor in crinoid ecology, because it relates to many aspects of the environment, including water turbulence, turbidity, temperature, depth, and proximity to the shore. As a result, lithology can be used as a coarse proxy for habitat preference, and previous work has indicated signiﬁcant differences in the distribution of crinoid clades across habitats with different types of sediments (Kammer 1985; Holterhoff 1997; Kammer and Ausich 1987, 2006). I collected lithologic data from the rock matrix associated with specimens examined and/or from lithologic descriptions of the associated formations in published literature. Lithology was categorized as carbonate, siliciclastic, or mixed, and each genus was assigned to lithology based on the rock type(s) in which its constituent species were found. Genera with occurrences that were exclusively in carbonate or siliciclastic rocks were assigned “carbonate” or “siliciclastic” lithologies, respectively. “Mixed” lithology was assigned to (1) genera whose constituent species occurred in mixed siliciclastic–carbonate rocks (i.e., specimens were preserved in rock composed of a mixture of siliciclastic and carbonate material, indicating the individual lived in a mixed siliciclastic–carbonate environment during life) and (2) genera that had constituent species that occurred in both pure siliciclastic and pure carbonate rocks. The ﬁnal variable investigated as a potential correlate of duration was species richness, as measured by the number of species per genus. I tabulated the number of species in each genus using the 2013 Bibliography of Paleozoic Crinoids (Webster and Webster 2014), supplemented with more recently described taxa not included in the bibliography. Species described from noncalyx material (e.g., only stem or arm fragments) were excluded, as were species that are not currently valid (Supplementary Material). Analyses.—All analyses were performed in RStudio v. 1.1.463. To assess the effect of habitat on taxonomic longevity, I ﬁrst determined whether genus durations within subsets of lithologic data (carbonate, mixed, siliciclastic) differed signiﬁcantly by performing a Tukey’s honest signiﬁcant difference (HSD) test on lithology ANOVA data. This approach simultaneously applies pairwise comparisons to the means of all treatments to ﬁnd means with signiﬁcant differences. On the basis of the Tukey’s HSD test results (see “Results” for further information), all subsequent analyses were performed using lithologic subsets (carbonate, mixed, and siliciclastic) and the full data set including all three lithologies. Separate analyses were conducted both with and without the potential effects of phylogeny taken into account. For taxonomic analyses that did not consider phylogenetic nonindependence, I ﬁrst calculated Spearman’s rank Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY correlation coefﬁcients to determine whether species number, body size, ﬁltration fan density, and/or maximum food size were signiﬁcantly correlated with genus duration. Second, multiple linear regression (MLR) was employed to determine the additive effects of multiple variables on genus duration. Finally, Akaike’s information criterion (AIC) was applied to all MLR models (i.e., models representing all possible combinations of potential explanatory variables), and small sample size–corrected AIC scores (AICc) were used to identify the combination of variables that best explained the data. For phylogeny-based analyses, I ﬁrst employed phylogenetic generalized least squares (PGLS) so that the effect of phylogeny could be incorporated while estimating correlation between duration and the other variables of interest (Felsenstein 1985; Grafen 1989; Symonds and Blomberg 2014). Analyses were run using functions from the R packages nlme and ape (Paradis et al. 2004; Pinhero et al. 2018) with a Brownian motion model of evolution implemented. This is a “random walk” model that predicts traits will change randomly through time, and thus trait covariance between taxa is expected to decrease through time as changes accumulate along branch lengths (Harmon 2018). PGLS was conducted for both the full model that contained all variables considered and for models containing all possible combinations of variables. AICc scores were then calculated using geiger to identify the combination of variables that constituted the “optimal” model (Harmon et al. 2008). Analyses were run over all 1500 timescaled trees, and the results were used to calculate mean β coefﬁcients, mean p-values, and the percentage of trees for which recovered p-values were less than α = 0.05. Because results of PGLS using full and optimal models were qualitatively similar (Supplementary Tables 3, 4), only results of the full models containing all variables are discussed. To determine whether there is evidence for phylogenetic structuring of traits, I calculated Pagel’s λ for all variables using the phylosig function from the R package phytools to determine the degree of phylogenetic signal in each trait under a Brownian motion model of evolution (Pagel 1999; Cooper et al. 2010; Revell 7 2012). Pagel’s λ was calculated for each of the 1500 time-scaled trees, and mean λ and associated p-values were computed for the distribution of trees. Blomberg’s K, a commonly used alternative measure of phylogenetic signal (Blomberg et al. 2003), was not used, because it is sensitive to incomplete branch-length information (Molina-Venegas and Rodríguez 2017), which was the case in the data set used here. Pagel’s λ, on the other hand, has been shown to be robust to suboptimal branch-length information and thus was considered preferable for this study (MolinaVenegas and Rodríguez 2017). Finally, I calculated Cohen’s f 2, a measure of effect size, for all variables with and without phylogeny considered to determine the degree to which each variable contributed to genus duration (Cohen 1988). Although Cohen’s f 2 has not been commonly used for paleontological data, the metric can be used to determine the magnitude and relative effect of variables in multiple regression models by assessing the strength of the relationship between a predictor variable and one or more dependent variables. In addition, effect size can be compared directly among models, which makes this metric valuable for studies including multiple predictor variables or comparing subsets of data (Selya et al. 2012). Cohen’s f 2is calculated using R 2 values recovered from multiple regression analyses, so it can be applied to both standard MLR and PGLS (Selya et al. 2012: eq. 2): f2 = R2AB − R2A 1 − R2AB (2) where B is the variable of interest and A is the combination of all other variables excluding B. R2AB then is the proportion of variance accounted for by all variables together, whereas R2A is the proportion of variance accounted for when B is excluded (Selya et al. 2012). For example, in this study, Cohen’s f 2 for species number is calculated using: f 2 species = R2sp+size+ffd+food − R2size+ffd+food 1 − R2sp+size+ffd+food (3) where subscripts denote the variables included Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 8 SELINA R. COLE in each regression model used to calculate R 2 values (sp = species number, size = body size, ffd = ﬁltration fan density, food = maximum food size). In MLR, R 2 values can be recovered from the summary of results from the lm() function in base R and used to calculate Cohen’s f 2. For PGLS, however, R 2 values are not automatically supplied but can be calculated from recovered log-likelihood scores using the approach outlined by Nagelkerke (1991: eq. 1b; Anderson 2008: Appendix A.7): 2 R2 = 1 − exp − (l full − lnull ) N (4) Where lnull is the log likelihood of the null model containing only the intercept term, lfull is the log likelihood of the full model containing all variables, and N is the sample size; this is known as the Cox and Snell R 2 (Cox and Snell 1989; Nagelkerke 1991). Here, I calculated Cohen’s f 2 values for the four variables of interest for both MLR and PGLS models. For all PGLS models, Cohen’s f 2 values were calculated for each of the 1500 time-scaled trees, and mean f 2 values were then calculated for each variable. Using Cohen’s f 2, a trait is considered to have signiﬁcant effect size if f 2 ≥ 0.02 (Cohen 1988). In addition, the magnitude of effect size is considered small if 0.02 ≥ f 2 ≥ 0.15, moderate if 0.15 ≥ f 2 ≥ 0.35, and large if f 2 ≥ 0.35 (Cohen 1988). Results Lithologic Environment Analyses.—Of the 99 taxa (out of 100) for which lithologic data were available, 55 occurred only in carbonate environments, 15 occurred in mixed carbonate/siliciclastic environments, and 29 occurred only in siliciclastic environments. ANOVA indicated that the taxa occurring in different lithologic environments are not all from the same distribution ( p = 0.004; Fig. 2A). The Tukey’s HSD test indicates signiﬁcant differences in the mean durations of taxa occurring in mixed versus carbonate lithologies and mixed versus siliciclastic lithologies but not between siliciclastic and carbonate lithologies (Table 1, Fig. 2B). Genera from mixed lithologies have signiﬁcantly longer durations than those found in carbonate or siliciclastic lithologies (Fig. 2). Predictors of Duration.—Spearman’s rank correlation indicates a signiﬁcant positive correlation between duration and number of species per genus for the full data set and for all lithologic subsets (Table 2, Fig. 3). In FIGURE 2. Relationship between lithologic environment and stratigraphic duration of genera. A, Box plot of major lithologic types with respect to duration. Error bars represent 95% conﬁdence intervals, horizontal black lines represent means. B, Pairwise comparisons from Tukey’s HSD (honest signiﬁcant difference) using ANOVA of lithologic data. Brackets represent 95% family-wise conﬁdence intervals; conﬁdence intervals not containing 0 indicate difference between groups is statistically signiﬁcant. Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY TABLE 1. Tukey’s multiple comparison of means at the 95% family-wise conﬁdence level. Comparisons are given for each combination of lithologic subsets. Bolded p-values represent statistically signiﬁcant differences between taxonomic durations for lithologies. Lithologies are listed in the order compared, so negative differences indicate taxa occurring in the ﬁrst lithology tend to have shorter durations relative to those in the second lithology, and positive differences indicate taxa occurring in the ﬁrst lithology have longer durations relative to those in the second lithology. Lithologies compared Mixed vs. carbonate Siliciclastic vs. carbonate Siliciclastic vs. mixed Differences p-value 13.414 −0.999 −14.413 5.57 × 10−3 9.514 6.49 × 10−3 addition, duration is signiﬁcantly correlated with body size for the full data set, but not for any of the lithologic subsets. Likewise, ﬁltration fan density and food size do not correlate signiﬁcantly with duration for the full data set or any of the lithologic subsets. MLR recovers a signiﬁcant positive correlation between duration and the number of species within a genus for the full data set as well as for all lithologic subsets (Table 3, Fig. 4). For genera occurring in carbonate environments, food size is also signiﬁcantly correlated with duration. None of the other variables (body size, food size, or ﬁltration fan density) correlate signiﬁcantly with duration at α = 0.05, regardless of lithologic environment. For the full, carbonate, and mixed data sets, optimal models (e.g., the combination of variables with the best ﬁt to the observed data) identiﬁed by AICc scores contain the same variables identiﬁed as signiﬁcant predictors in multiple regression analyses (Supplementary Table 2). Species number was the only variable in the optimal model for all lithologies combined and the mixed subset, and the best-ﬁt model for the carbonate subset includes both species 9 number and food size. For the siliciclastic subset, the optimal model includes both species number and ﬁltration fan density. However, in each of the lithologic subsets, ΔAIC is very small for several other models, suggesting support for the optimal models is not robust. When phylogeny was incorporated into regression analyses using PGLS, variables that were signiﬁcantly correlated with genus duration changed for lithologic subsets but not for total combined lithology (Table 4, Fig. 5). Results of PGLS for all lithologies combined are identical to multiple regression, for which only species number is signiﬁcantly correlated with duration (mean p = 6.31 × 10−4, p < 0.05 = 100%) (Figs. 4, 5). When correlations of traits for carbonate data were evaluated using PGLS, all signiﬁcant correlations disappeared. By contrast, accounting for phylogeny within mixed and siliciclastic subsets resulted in recovery of additional signiﬁcant correlates of duration. Whereas only species number was a signiﬁcant predictor for mixed and siliciclastic lithologies under MLR, PGLS of mixed lithologies recovered species number (mean p = 4.08 × 10−8, p < 0.05 = 100%), body size (mean p = 0.004, p < 0.05 = 100%), and food size (mean p = 0.038, p < 0.05 = 80.6%) as signiﬁcant predictors. For PGLS of siliciclastic lithologies, both species number (mean p = 4.03 × 10−6, p < 0.05 = 100%) and body size (mean p = 4.87 × 10−2, p < 0.05 = 60.7%) were recovered as signiﬁcant predictors of duration (Figs. 4, 5). For PGLS, optimal models identiﬁed by AICc scores contain different variables than those identiﬁed as signiﬁcant correlates of duration (Supplementary Table 3). The optimal model for all lithologies combined includes species number, body size, and ﬁltration fan density; for the carbonate subset it includes only species number; for the mixed subset it includes TABLE 2. Spearman’s rank correlations between duration and species number, body size, crown shape, and ﬁltration fan density. Bold values are statistically signiﬁcant; asterisks (*) indicate p-value range. *p < 0.05; **p < 0.01; ***p < 0.001. Spearman’s rho Duration vs. species number Duration vs. body size Duration vs. ﬁltration fan density Duration vs. food size All lithologies Carbonate Mixed Siliciclastic 0.657*** 0.290*** 0.061 −0.049 0.612*** 0.147 0.202 −0.116 0.87*** 0.438 0.153 −0.046 0.63*** 0.306 −0.069 0.007 Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 10 SELINA R. COLE FIGURE 3. Scatter plots of all variables as a function of duration with least squares regression lines plotted for each lithologic subset. Data are subsetted by lithologic environment. See Table 2 for signiﬁcance of correlations. species number, body size, and food size; and for the siliciclastic subset it includes species number and body size. As with results from MLR, however, there were multiple, alternative models for each lithologic subset with only marginally larger AICc scores, suggesting equivocal support for optimal models. Effect Size.—Cohen’s f 2 values calculated from MLR recovered a large effect size for species number across the three lithologic subsets as well as for all lithologies combined (Table 5). For all total combined lithologies, no other variables were recovered with signiﬁcant effect sizes (Table 5). For the carbonate subset, small effect sizes were recovered for ﬁltration fan density ( f 2 = 0.04) and food size ( f 2 = 0.08). Within the mixed subset, moderate effect sizes were recovered for body size ( f 2 = 0.33) and food size ( f 2 = 0.17), and small effect size was recovered for ﬁltration fan density ( f 2 = 0.10). The only other signiﬁcant effect size within the siliciclastic subset was for ﬁltration fan density ( f 2 = 0.10) (Table 5). TABLE 3. Results of multiple linear regression for the additive effects of species number, body size, food size, and ﬁltration fan on duration. Coefﬁcients ±1 SE are given for the full data set, including all lithologies and for lithologic subsets. Bold values are statistically signiﬁcant; asterisks (*) indicate p-value range. *p < 0.05; **p < 0.01; ***p < 0.001. Coefﬁcient ± 1 SE Trait All lithologies Carbonate Mixed Siliciclastic Species number Body size Filtration fan density Food size 1.77 ± 0.17*** 2.34 ± 2.17 −0.15 ± 3.46 3.82 ± 6.57 3.07 ± 0.68*** −1.74 ± 3.67 10.82 ± 7.35 35.67 ± 15.51* 1.62 ± 0.17*** 14.64 ± 8.11 10.97 ± 11.26 26.61 ± 20.3 3.44 ± 0.84*** 0.26 ± 2.64 −4.86 ± 3.13 −1.79 ± 6.01 Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY 11 FIGURE 4. Scatter plots of species number versus genus duration for all lithologies combined and for lithologic subsets. Solid lines represent regression lines from multiple linear regression (upper row) and phylogenetic generalized least squares (lower row). Shaded areas represent 95% conﬁdence intervals. All regression lines are signiﬁcant with the exception of that for PGLS of carbonate data. When phylogeny was accounted for by calculating Cohen’s f 2 from PGLS results, the signiﬁcance and magnitude of effect size for traits changed in several ways (Table 5, Fig. 5). For total combined lithologies, species number remained the only variable with large effect size, but the magnitude of effect increased from 1.17 to 7.88. In addition, effect sizes of the other three traits increased from nonsigniﬁcant values to small effect size. Similarly, when phylogeny was incorporated in the mixed lithology subset, species number retained a large effect size, and body size, ﬁltration fan density, and food size increased to large effect sizes (Table 5). For the siliciclastic subset under the PGLS model, effect size for species number remained large, ﬁltration fan density decreased to a nonsigniﬁcant level, and body size and food size increased from nonsigniﬁcant to medium and small TABLE 4. Results of phylogenetic generalized least squares for the additive effects of species number, body size, food size, and ﬁltration fan on duration. Mean β coefﬁcients and p-values calculated across a distribution of 1500 time-scaled trees are given, along with the percentage of trees for which p < 0.05 was recovered. Bold values are statistically signiﬁcant. Lithology All lithologies Carbonate Mixed Siliciclastic Trait Mean β coefﬁecient Mean p-value % p < 0.05 Species number Body size Filtration fan density Food size Species number Body size Filtration fan density Food size Species number Body size Filtration fan density Food size Species number Body size Filtration fan density Food size 2.015 −4.706 2.096 5.622 0.934 −1.969 5.270 20.601 1.417 21.246 11.658 34.665 3.667 −3.276 0.252 4.053 6.31 × 10 0.130 0.355 0.488 0.230 0.497 0.512 0.387 4.08 × 10−8 4.40 × 10−3 0.077 0.038 4.03 × 10−6 4.87 × 10−2 0.758 0.347 100% 55.7% 16.1% 10.9% 42.0% 4.5% 7.1% 21.1% 100% 100% 9.6% 80.6% 100% 60.7% 0% 3.3% −4 Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 12 SELINA R. COLE FIGURE 5. Results of phylogenetic generalized least squares and corresponding Cohen’s f 2 values for each variable. Panels are divided by lithology: A, All lithologies combined; B, carbonate; C, mixed; and D, siliciclastic. For each panel, upper box plots give the distribution of β coefﬁcients for each of the four variables calculated over a distribution of 1500 time-scaled trees, and mean p-values are given along with the percentage of trees for which p < 0.05 were recovered. Lower box plots in each panel give the distribution of log(Cohen’s f 2), a measure of effect size. Horizontal lines represent the thresholds for small ( f 2 > 0.02, dotted line), moderate ( f 2 > 0.15, dashed line), and large ( f 2 > 0.35, solid line) effect sizes as deﬁned by Cohen (1988). effect sizes, respectively. When phylogeny was accounted for in the carbonate subset, the effect of species number on duration decreased from a large to a small effect size, and body size increased from a nonsigniﬁcant level to a small effect size; effect sizes for both ﬁltration fan density and food size remained small (Table 5, Fig. 5). Phylogenetic Signal.—Values of Pagel’s λ calculated for species number, body size, ﬁltration fan density, food size, lithology, and stratigraphic duration of genera indicated signiﬁcant TABLE 5. Effect size of traits on duration as given by Cohen’s f 2. Effect size was calculated for multiple regression and phylogenetic generalized least squares models using all considered variables. Asterisks (*) indicate magnitude of effect size based on values given by Cohen (1988). Effect size: *small ( f 2 > 0.02); **medium ( f 2 > 0.15); ***large ( f 2 > 0.35). Note that for several traits, f 2 values are only marginally signiﬁcant ( f 2 ≈ 0.02). Regression model Lithology f2 Species number f2 Body size f2 Filtration fan density f2 Food size 1.17*** 0.41*** 9.19*** 0.70*** 0.01 4.49 × 10−3 0.33** 3.88 × 10−4 1.86 × 10−5 0.04* 0.10* 0.10* 3.56 × 10−3 0.08* 0.17** 3.68 × 10−3 0.07* 0.02* 1.37*** 0.21** 0.02* 0.02* 0.42*** 6.53 × 10−3 0.02* 0.06* 0.61*** 0.06* Multiple regression All lithologies Carbonate Mixed Siliciclastic Phylogenetic generalized least squares All lithologies Carbonate Mixed Siliciclastic 7.88*** 0.10* 22.56*** 1.61*** Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY 13 TABLE 6. Phylogenetic signal of traits across the distribution of diplobathrid crinoid trees. Mean Pagel’s λ and p-values calculated across all time-scaled trees are given, along with the proportion of trees for which p-values < 0.05 were recovered. Trait Mean Pagel’s λ Proportion of p-values < 0.05 Mean p-value 0.305 0.628 0.382 0.345 0.526 0.203 100% 100% 100% 100% 100% 100% 1.88 × 10−4 7.54 × 10−29 7.37 × 10−16 7.36 × 10−12 1.99 × 10−21 9.75 × 10−4 Species number Body size Filtration fan density Food size Lithology Duration phylogenetic signal for all traits (Table 6). The highest mean λ values were recovered for body size (mean λ = 0.628) and lithology (mean λ = 0.526), and the lowest mean values were recovered for duration (mean λ = 0.203) and species number (mean λ = 0.305). Although values of λ varied (widely, in some cases) for traits, all mean p-values were statistically signiﬁcant, and 100% of p-values calculated from all 1500 time-scaled trees were < 0.05 (Table 6, Fig. 6). Discussion Phylogeny and Extinction Risk.—Several recent studies on extinction selectivity in the fossil record have not found considerable differences between taxic and phylogenetic approaches (e.g., Crampton et al. 2010; Hopkins 2011; Harnik et al. 2014). By contrast, in the four sets of comparisons investigated here (all lithologies combined and the three lithologic environment subsets), I identiﬁed notable differences between some, but not all, results when phylogeny was incorporated. Although the results of taxic and phylogenetic approaches were broadly similar, accounting for phylogenetic structure altered interpretations considerably in some cases. Notably, incorporating phylogeny did not consistently weaken correlations between traits and duration, as is commonly (but incorrectly) expected (Rohlf 2007). Instead, both the strength and the direction of certain relationships changed under comparative methods for all lithologic subsets. Changes in the signiﬁcance of correlations under MLR versus PGLS models appear unpredictable a priori, with traits increasing, decreasing, or remaining the same. By contrast, many changes in Cohen’s f 2 values (or lack thereof) appear to be tied to the magnitude of the effect size and are thus somewhat predictable. All traits with medium or large effect sizes under taxonomic approaches retained at least small effect sizes when phylogeny was accounted for, whereas traits with small effect sizes under MLR lost all signiﬁcant effect under PGLS. In some cases, however, new traits with signiﬁcant effect sizes emerged under PGLS with no apparent connection to their effect sizes under MLR. Differences between results of taxic and phylogenetic approaches in this study suggest non-phylogenetic methods recover similar results only when correlation is strong and/or effect size is very large. For example, I ﬁnd that traits with moderate to large ( f 2 > 0.15) effect sizes are likely to retain signiﬁcant effect size when phylogeny is accounted for. However, phylogenetic approaches may recover additional traits with signiﬁcant effect sizes with no obvious criteria predicting the traits for which this may occur. Likewise, changes in the signiﬁcance of correlation between traits and duration do not appear predictable. Overall, these results show interpretations of extinction selectivity can be altered in unpredictable ways when phylogeny is taken into account and highlight the importance of a comparative approach when investigating correlates of extinction risk. All of the traits considered, including genus duration and lithologic environment, were found to have signiﬁcant phylogenetic signals (Table 6). Because this indicates phylogenetic structuring of traits across at least part of the diplobathrid tree, analyses incorporating phylogeny should provide results that more realistically reﬂect the evolutionary processes responsible for generating observed patterns. As a result, the majority of the following discussion will focus on the results of phylogenetic rather than taxic approaches. Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 14 SELINA R. COLE FIGURE 6. Phylogenetic signal of traits across the diplobathrid phylogeny. Distributions represent values of Pagel’s λ calculated for each trait over 1500 time-scaled trees. Species Richness and Extinction Risk.—Of the variables assessed here, the strongest control on genus longevity of diplobathrid crinoids appears to be the number of species within a genus. The strong correlation between species number and duration is recovered consistently for taxonomic investigations of all lithologic subsets, and when the effect of phylogeny is considered using PGLS, species number remains signiﬁcantly correlated with duration for all lithologic environments except carbonates (Fig. 4). Species number is also the only trait for which a signiﬁcant effect size is recovered regardless of lithologic environment investigated or the regression model used. Additionally, species number is the only common component among all optimal models identiﬁed by AIC. As noted, a number of alternative models have only marginally larger AICc values than the optimal models, but in most cases these alternative models contain species number (Supplementary Tables 2, 3). Finally, Cohen’s f 2 values reveal species richness has the greatest effect size regardless of subsetting by lithologic environment, indicating it has a greater relative contribution to genus duration than do the other traits (Table 5). Several non–mutually exclusive reasons may explain why species number corresponds so strongly to the duration of diplobathrid genera. First, higher species richness means random extinction is less likely to wipe out all species within a clade, and there are many examples supporting species richness as a trait that buffers against extinction, at least during intervals of background extinction (Jablonski 1986; Payne and Finnegan 2007; Smits 2015; Foote et al. 2016). Second, species number frequently correlates strongly with geographic range size (Jablonski and Roy 2003; Foote et al. 2016), and an inverse relationship between geographic range size and extinction risk has been documented for many fossil groups (Hansen 1980; Jablonski and Hunt 2006; Payne and Finnegan 2007; Powell 2007; Foote et al. 2008; Harnik et al. 2014; Smits 2015; see McKinney [1997] for a review). Although geographic range size was not addressed in this study and range data are not currently available, based on the expected relationship between species number and geographic range, it is very possible that diplobathrid genera with greater numbers of constituent species had more extensive geographic ranges that would have buffered genera from extinction, allowing them to persist in the fossil record. In addition, geographic ranges of genera and other higher taxa can also interact synergistically with species richness to increase resilience to extinction via increased ecological diversity (Foote et al. 2016), but as with species richness alone, this buffering is more pronounced during background extinctions than mass extinctions (Jablonski 1986; Payne and Finnegan 2007). Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY Another potential explanation for the signiﬁcant correlation between genus duration and species number may relate to species selection, speciﬁcally “strict-sense species selection” (sensu Jablonski 2008b), wherein differences in speciation and/or extinction rates arise from emergent, heritable properties at the species level (Vrba 1984; Okasha 2006; Jablonski 2008b; Rabosky and McCune 2010; Stadler 2011). As a result, heritable species-level traits that have a signiﬁcant effect on net diversiﬁcation, such as geographic range size (Jablonski 1987; Hunt et al. 2005; Jablonski and Hunt 2006), may play an important role in survivorship. Strong phylogenetic signal recovered for species richness of diplobathrid genera indicates species number is conserved across at least part of the phylogeny and, by extension, suggests speciation and extinction rates are heritable among diplobathrid crinoids. Although further investigation would be necessary to conﬁrm the role, if any, of species selection in the longevity of diplobathrid genera, such results would complement a previous study that found support for species selection in monobathrid crinoids, the sister group to diplobathrids (Simpson 2010). Habitat Breadth and Extinction Risk.—I interpret habitat, as deﬁned by lithologic environment, to be the secondary control on duration of diplobathrid genera, following species number. Tukey’s HSD test results indicate signiﬁcant differences in duration corresponding to lithologic environment (Fig. 2, Table 1). Further, species number correlates signiﬁcantly with duration for most lithologic subsets, whereas the signiﬁcance of other ecological traits is highly variable among lithologic subsets. This provides additional support for the hierarchical ranking of species richness as the primary control and lithology as the secondary control on diplobathrid genus duration. Taxa inhabiting environments with mixed lithologies were found to have signiﬁcantly longer durations than those living in exclusively siliciclastic or exclusively carbonate environments (Fig. 2, Table 1). Many of the physical environmental conditions of carbonate versus siliciclastic depositional settings result in strikingly different habitats with dramatic differences in current strength and type, 15 water depth, suspended sediment, and substrate conditions. As a result, genera with constituent species occurring in both carbonate and siliciclastic environments and/or in environments with alternating carbonate and siliciclastic sedimentation must be capable of coping with more extreme habitat variation (Kammer 1985; Kammer and Ausich 1987; Holterhoff 1997; Kammer et al. 1998). Thus, I attribute the longer durations of crinoid genera from mixed lithologic environments to greater tolerance of environmental heterogeneity. An inverse relationship between extinction risk and environmental tolerance/niche breadth has been documented in many other groups (Liow 2007; Heim and Peters 2011; Nurnberg and Aberhan 2013; see Colles et al. [2009] for a review), including crinoids (Kammer et al. 1997, 1998), in keeping with Simpson’s rule of “survival of the unspecialized” (1944). Investigations of species longevity of Mississippian crinoids found that clades with higher mean eurytopy scores (a proxy for niche breadth calculated from the mean number of facies per species) were composed of longer-lived species (Kammer et al. 1997, 1998). Although the type of environmental data used in this study of diplobathrids (lithology type) is different from that used by Kammer et al. (1997, 1998; the eurytopy index), the same overall pattern is recovered: greater environmental tolerance results in increased taxonomic longevity. The results presented here indicate this pattern holds true within crinoid clades, as well between crinoid clades. Ecology and Extinction Risk.—Body size, ﬁltration fan density, and food size are considered tertiary controls on diplobathrid genus duration. The degree of correlation and effect size of these traits differ between lithologic environments, indicating that controls on longevity vary within habitats. Body size was a signiﬁcant predictor of crinoid genus duration only for mixed and siliciclastic environments when phylogeny was taken into account. The correlation between body size and duration was positive for mixed environments but negative for siliciclastic environments (Table 4). Many previous investigations have found extinction risk increases with larger body size, especially in vertebrates, as a result of covariation between body size and other traits that Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 16 SELINA R. COLE increase extinction risk, such as low reproductive rate, longer generation time, and smaller population size (Gaston and Blackburn 1997; Purvis et al. 2000; Cardillo et al. 2005; Tomiya 2013). By contrast, in marine invertebrates, larger body size may improve survivorship through mechanisms like increased larval production, or it may not correlate with extinction risk, because attributes that are more important for survivorship may not covary with body size (Williams 1975; Jablonski 1996; McKinney 1997). As a result, there is extensive heterogeneity in the correlations between taxonomic survivorship and body size in marine invertebrates (Jablonski 1996; Lockwood 2005; Crampton et al. 2010; Harnik 2011), which suggests body size plays a complex macroevolutionary role in invertebrate groups that may be taxon speciﬁc. Within crinoids, minimal treatment has been given to understanding potential ecological advantages of different body sizes (Holterhoff 1997). In certain crinoid faunas, body size has been found to covary with sedimentary environment, although a driving mechanism for this pattern has not been identiﬁed (Watkins and Hurst 1977). Because the results presented here recover body size as a signiﬁcant correlate of genus duration across some lithologic environments, it is possible that a similar underlying process may be controlling both patterns. The relationships between genus duration and the two traits investigated that relate to feeding ecology—ﬁltration fan density and maximum food size—are also notable. A previous study of survivorship across multiple crinoid groups identiﬁed ﬁltration fan density as an important predictor of longevity, particularly when comparing pinnulate and apinnulate crinoids (Baumiller 1993). By contrast, I found ﬁltration fan density was not a signiﬁcant predictor of diplobathrid genus longevity, although it did have a signiﬁcant effect size for taxa occurring in all but siliciclastic environments (Fig. 5, Tables 4, 5). Similarly, I found maximum food size had signiﬁcant effect size for all lithologic subsets but was only a signiﬁcant predictor of survivorship for taxa in mixed lithologic environments, where taxa that could capture larger food particles had longer durations. This may indicate these longer-lived taxa were generalists with regard to food size selectivity, that is, they were able to capture both large and small food particles because of wide ambulacra and associated feeding structures (however, note that this correspondence between increasing ambulacral width and decreasing selectivity for food size may be applicable to pinnulate diplobathrids but does not hold true for all crinoids, particularly those with more open and/or apinnulate ﬁltration fans that are unable to capture smaller food particles) (Kammer 1985; Kammer and Ausich 1987). Food size selectivity is not recovered as a signiﬁcant correlate of duration for any of the other lithologic environments. The minimal correlation between ecology and taxonomic duration is somewhat unexpected for two reasons. First, ﬁltration fan density and food particle size are important components of niche differentiation in crinoids and determine whether a crinoid is a specialist or generalist in its feeding ecology (Ausich 1980; Holterhoff 1997; Cole et al. 2019). For example, specialist crinoids are those with denser ﬁltrations fans and the ability to capture only small food particles (as controlled by ambulacral width), because they require more speciﬁc environmental conditions for optimal feeding and can only capture a narrow range of food particles. As a result, it would be expected that specialist diplobathrids with denser ﬁltration fans and more restricted food size selectivity would be more prone to extinction, regardless of lithologic environment. Second, there are many documented examples of strong covariation between structure of the ﬁltration fan and environmental settings (Kammer and Ausich 1987; Holterhoff 1997; Kammer et al. 1997, 1998; Brower 2007), because ﬁltration fans of different densities require different environmental conditions for optimal feeding to occur (Ausich 1980; Baumiller 1992; Kammer and Ausich 2006). If covariation between ﬁltration fan structure and habitat were conserved across diplobathrids, we would expect ﬁltration fan density to be a signiﬁcant predictor of duration, especially for total combined lithologies. However, no such pattern is recovered. Instead, habitat and feeding ecology appear to be decoupled in diplobathrids, at least insofar as their effects on genus Downloaded from https://www.cambridge.org/core. IP address: 104.162.153.198, on 15 Nov 2019 at 02:36:57, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2019.37 HIERARCHICAL CONTROLS ON EXTINCTION SELECTIVITY duration are concerned. These results indicate substantial heterogeneity in the effect of feeding ecology on taxonomic longevity. Further, when coupled with conclusions from previous investigations (Baumiller 1993; Kammer et al. 1997, 1998), it appears that the inﬂuence of ecology on taxonomic survivorship may vary across phylogenetic scales, where fan structure is important across crinoid clades, but plays a minimal role within the diplobathrid clade. Conclusions Investigation of macroevolutionary patterns in the fossil record should ideally account for both the inﬂuence of phylogeny and the effect of potentially interacting variables to avoid overly simpliﬁed and/or potentially distorted conclusions. Here, I applied a broad range of analytical techniques to the fossil record of diplobathrid crinoids to determine (1) the relative contributions of multiple variables to extinction selectivity and (2) how phylogeny effects interpretations of extinction selectivity. From these approaches, I identiﬁed a series of hierarchically nested variables that operate in concert to control crinoid extinction selectivity. Notably, I found species richness was the primary variable controlling diplobathrid genus duration, which likely correlates with larger geographic range size. I identiﬁed habitat, deﬁned by lithologic environment (carbonate, mixed, or siliciclastic), as the secondary predictor of diplobathrid genus duration. Genera inhabiting mixed lithologic settings were found to have signiﬁcantly longer durations than those occurring in exclusively siliciclastic or carbonate environments, which I attribute to higher environmental tolerance and greater niche breadth of taxa occurring in mixed environments. Finally, I identiﬁed two ecological variables (ﬁltration fan density and food size) along with body size as weaker, tertiary controls on diplobathrid extinction selectivity. The effect of these variables on extinction selectivity differed widely among lithologic subsets, suggesting pressures of selective extinction vary between habitats. These results contrast with a previous study that identiﬁed ﬁltration fan density as an important predictor of survivorship across Crinoidea as a whole (Baumiller 17 1993). Here, fan density had a signiﬁcant effect on genus duration only for diplobathrid crinoids occurring in mixed lithologic environments. This heterogeneity in the effect of ecological traits on crinoid extinction selectivity demonstrates these traits play a complex role in the generation of crinoid macroevolutionary patterns, with results depending on both phylogenetic scale and lithologic environment considered. Incorporation of phylogeny into the study of diplobathrid longevity was found to have unpredictable effects on the association between traits and genus duration. In most cases, predictor variables that had strong associations with duration and moderately large effect sizes (Cohen’s f 2 > 0.15) under taxic approaches, such as species richness, were still recovered under phylogenybased analyses. However, accounting for phylogeny unexpectedly revealed new correlations and/or signiﬁcant effect sizes for some variables, whereas other variables lost their associations with duration entirely. These results suggest strong associations recovered under taxic approaches will still be recovered under phylogenetic approaches, but many nuances might be overlooked. Importantly, moderate to weak correlations might not be detected, and other variables might be erroneously identiﬁed as signiﬁcant predictors of extinction selectivity. Thus, caution should be used when interpreting results from studies that do not explicitly incorporate phylogenetic hypotheses. Acknowledgments This research was supported through student research grants from the Paleontological Society and Ohio State University’s Friends of Orton Hall fund. Additional support was provided through a Presidential Fellowship (The Ohio State University), a Springer Postdoctoral Fellowship (Smithsonian Institution, National Museum of Natural History) and a Kathryn W. Davis Postdoctoral Fellowship (American Museum of Natural History). 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