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Journal of Paleontology 91(4):799–814
morphotaxa, Springer’s (1920) hypothesis can be quantitatively addressed. The posterior probability of a taxon being a sampled ancestor can be estimated as the frequency in which it was recovered to have a zero-length branch in the posterior distribution of trees (Matzke, 2015). Examining the posterior distribution of trees from the best-fit model, the probability of Cupulocrinus humilis (Billings, 1857) being an ancestral morphotaxon is 0.99. Given that a clade is defined to be an ancestor and all of its descendants, Cupulocrinus is removed from the Cladida and placed within the Flexibilia. Additional analyses with more comprehensive sampling of Cupulocrinus and flexible species (including a broader sample of taxon-
specific characters) are needed to further test this hypothesis at finer taxonomic scales. The sister clade to the Flexibilia contains the majority of all
nominal taxa currently placed within the Cladida (sensu Moore and Laudon, 1943). This clade originated prior to the close of the Ordovician and contains most taxa traditionally placed within the orders Dendrocrinida and Cyathocrinida. Note that all species in this clade share a more recent common ancestor with an extant crinoid than with flexible crinoids (Simms and Sevastopulo, 1993). Thus, I propose the name Eucladida to distinguish this important group of crinoids from its sister clade. The recovery of the Glossocrinacea as a clade provides
quantitative support for evolutionary inferences discussed by Webster et al. (2003). These ‘transitional dendrocrinids’ (McIntosh, 2001) are among the first cladids to evolve pinnules and are traditionally placed within the order Poteriocrinida. Most crinoid workers since publication of the Treatise of Invertebrate Paleontology (Moore and Teichert, 1978) have hesitated to recognize the Poteriocrinida because they are widely considered to be polyphyletic (Kammer and Ausich, 1992; McIntosh, 2001). Regardless of their status as a clade or a grade, the crinoids considered poteriocrines in the Treatise are the most dominant and ecologically abundant group of crinoids throughout the middle to late Paleozoic (Ausich et al., 1994). Note that the ancestor of extant articulate crinoids is widely considered to be placed among a paraphyletic group of ‘poteriocrine’ crinoids (Simms and Sevastopulo, 1993; Webster and Jell, 1999; Rouse et al., 2013). The recovery of a clade of poteriocrines herein suggests there may be some phylogenetic structure present among Paleozoic poteriorcrine taxa. However, future analyses sampling younger taxa and a broader sample of Treatise (Moore and Teichert, 1978) poteriocrines are needed to test whether this is the case.
Probabilistic approaches to fossil phylogenies.—Tree-based comparative methods are becoming commonplace in paleon- tology for testing macroevolutionary patterns and processes within a fully phylogenetic context. To date, most of these studies apply an a posteriori timescaling algorithm to an unscaled cladogram (e.g., Brusatte et al., 2008; Hunt and Carrano, 2010; Lloyd et al., 2012; Hopkins and Smith, 2015). Although useful for removing the zero-length branches that arise from polytomies in cladistic hypotheses, many of these a posteriori timescaling methods are problematic because they make ad hoc and unrealistic assumptions regarding node ages and/or ancestor–descendant relationships (Bapst and Hopkins, in press). The cal3 method developed by Bapst (2013) is a
promising a posteriori approach that overcomes many of these problems via a model of branching, extinction, and sampling similar to the FBD process. However, this technique requires a priori estimates of these parameters and can only be applied to unscaled cladograms. The Bayesian tip-dating approach advocated herein simultaneously estimates tree topologies and divergence dates using time-stamped comparative data. Thus, a sample of trees from the posterior distribution of a tip-dated analysis provides a more natural framework for testing macroevolutionary patterns using the fossil record while accounting for uncertainty in tree topology and node ages (Close et al., 2015; Gorscak and O’Connor, 2016). Evaluating the efficacy of competing phylogenetic
methods is a contentious (and sometimes acrimonious) debate, yet inferences using simple probabilistic methods perform well when inferring trees from paleontologic data and can explicitly consider different evolutionary and sampling parameters potentially influencing recovered topologies (Wagner, 1998; Wagner and Marcot, 2010; Wright and Hillis, 2014). Thus, it seems that in the future, more phylogenetic analyses will take advantage of fully probabilistic frameworks such as the one presented herein. However, researchers conducting tree-based comparative analyses on older (or otherwise unscaled) cladograms require an a posteriori time-scaling approach, which might take the form of applying FBD-like divergence dating methods to a fixed cladistic topology (Bapst and Hopkins, in press). Regardless of whether Bayesian tip-dating or a model- based a posteriori method like cal3 becomes the dominant approach to timescaling trees in the future, it is apparent that both of these approaches recover more accurate estimates and are strongly recommended over ad hoc methods when conduct- ing downstream macroevolutionary analyses. Evolutionary patterns among early to middle Paleozoic
crinoids strongly favor models incorporating rate heterogeneity among characters and among lineages. This not only supports previous investigations demonstrating differential disparity patterns among crinoid clades (Foote, 1994; Deline and Ausich, 2011), but may also be a more general feature of morphologic evolution. Probabilistic models of morphologic evolution commonly assume either uniform or gamma distributed rates among characters. Models of rate variation predict some characters evolve at higher rates than others (and therefore anticipate a degree of homoplasy in the data). Variable rate distributions are potentially more realistic than an equal rates model because morphologic characters commonly experience different selective pressures and/or developmental constraints. Moreover, accounting for rate variation has a practical value because it may help resolve branches at different levels in a phylogenetic tree (Wright and Hillis, 2014). Until recently, only uniform and gamma distributions were
available to model rate variation among characters in common software packages for Bayesian inference (Huelsenbeck et al., 2015). However, Wagner (2012) found that fossil data sets commonly favor lognormal rather than gamma distributed rates, particularly for echinoderm and mollusk character matrices. It is interesting to note that gamma and lognormal rate distributions arise from different underlying processes of character evolution. Gamma rate distributions assume rates are Poisson processes, whereas lognormal rate distributions suggest morphologic
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