Wright—Phylogeny of early to middle Paleozoic crinoids
evolution results from multiple probabilistic processes and/or hierarchical integration among characters (Wagner, 2012). Thus, the relative fit of data to these two distributions gives some insight into the dynamics of character change. The analysis herein provides positive evidence supporting lognor- mal over gamma-distributed rates, but only modestly (BF = 4.38). Although the choice of rate distribution had no obvious effect on recovered topologies herein, other workers should nevertheless test alternative distributions and choose the best-fit model for their data (Harrison and Larsson, 2015). The FBD process provides paleontologists with a far more
realistic tree prior model than others previously available. For example, the FBD tree prior has recently been demonstrated to outperform a uniform prior (Matzke and Wright, 2016). Other models, such as the Yule process or simple birth–death process are strongly violated when making phylogenetic inferences from paleontologic data. Moreover, the FBD tree prior has a high level of internal consistency for estimating age dates and a good fit to morphologic and geologic data in empirical, well- characterized data sets (e.g., penguins and canids, see Drummond and Stadler, 2016). Analyses of the crinoid data set herein assumed the simple case of constant rates for macroevolutionary and sampling parameters. However, the FBD process can be extended to a more sophisticated time- varying (i.e., piecewise-constant) model that may be useful for other data sets. Similarly, models could be developed to account for geographic variation in sampling probabilities (Wagner and Marcot, 2013). Such models may be especially beneficial for studies with larger, more comprehensive character matrices spanning similar to longer time intervals than considered herein (Gavryushkina et al., 2014; Zhang et al., 2016). A major innovation of the FBD process as a tree prior is the
ability to account for sampling ancestor–descendant relationships in phylogenetic analysis. Although the notion of discovering ‘true’ ancestors is somewhat contentious (see Smith, 1994; Foote, 1996), modeling studies suggest ancestral morphotaxa are likely present in the fossil record of many paleontologically important groups (Foote, 1996). Gavryushkina et al. (2014) demonstrated that sampled ancestors should be accounted for when estimating phylogenies, even when ancestral morphotaxa are not of specific interest in the analysis, because not including them introduces biases in parameter estimation. Thus, even if sampled ancestors are considered nuisance parameters (Close et al., 2015;Gorscak andO’Connor, 2016), theymay nevertheless be important for accurately estimating more accurate tree topologies and node ages. Parameter estimation under the FBD process does not
require exhaustive sampling of fossil taxa, but it does require a representative random sample of species (e.g., the sampling strategy used herein) (Didier et al., 2012). However, the application of sampled-ancestor tip-dating methods to exhaus- tively sampled species-level (sensu Smith, 1994) or specimen- level data represents an important (but unexplored) frontier in phylogeny-based analyses of macroevolution. For example, coding multiple fossil specimens of species-level morphotaxa from different time horizons and/or geographic localities may provide a means for testing whether speciation events occur primarily through budding or bifurcating cladogenesis (Gavryushkina et al., 2014; Hunt and Slater, 2016). In addition,
809
paleontologists are commonly interested in whether morpho- logic change is punctuated or gradual (Eldredge and Gould, 1972; Hunt, 2008). Testing alternative probabilistic models of character evolution within a similar phylogenetic and sampling framework as described above, where each model makes different assumptions about punctuated versus gradual rates of change (as well as durations of stasis), would provide additional insight into the dynamics of morphologic evolution during speciation events (see Wagner and Marcot, 2010).
The emerging synthesis between paleontology and model-
based phylogenetics contributes to the growing consensus that research programs in systematic paleontology are greatly enhanced when grounded in rigorous analytical approaches (Smith, 1994; Wagner, 2000b; Wagner and Marcot, 2010; Slater and Harmon, 2013; Hunt and Slater, 2016). Many of the analytical tools discussed in this paper were originally developed for non-paleontologic purposes. Thus, it is perhaps not surprising there is plenty of room for future modification and refinement of these techniques to better test paleontologic patterns. Nevertheless, the development and application of these methods has already expanded our ability to quantitatively address macroevolutionary questions. Continued research implementing probabilistic approaches in phylogeny-based paleontology will likely return the favor and provide neonto- logists with evolutionary insights and unique perspectives only accessible to paleontologists.
Acknowledgments
This paper stems from research conducted at The Ohio State University toward the completion of a PhD in Geological Sciences. I thank W.I. Ausich, S.R. Cole, and T.W. Kammer for numerous discussions on crinoid morphology and evolution that helped shape some of the ideas in this manuscript. A. Gavryushkina is thanked for generously providing feedback on mathematical aspects of this paper. G.J. Slater and an anonymous reviewer are thanked for reviewing the manuscript. In particular, I thank G.J. Slater for helpful comments and suggestions regarding sensitivity analyses. S.R. Cole provided helpful assistance illustrating crinoids. K. Hollis, T. Ewin, P. Mayer, and K. Riddigton are thanked for providing access to museum specimens. Lastly, I especially thank S. Edie for kindly providing me with a place to stay while visiting the Field Museum collections. This research was supported by numerous student research grants from the Paleontological Society, Sigma Xi, the Palaeontological Association, the American Federation of Mineralogical and Geological Societies, Friends of Orton Hall, and a Presidential Fellowship from The Ohio State University, as well as a National Science Foundation’s Assembling the Echinoderm Tree of Life grant (DEB 1036416) to W. I. Ausich.
Accessibility of supplemental data
Data available from the Dryad Digital Repository: https://doi. org/10.5061/dryad.6hb7j
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