Wright—Phylogeny of early to middle Paleozoic crinoids


Table 1. Species sampled for phylogenetic analysis. Species


Author


Aethocrinus moorei Alphacrinus mansfieldi Amabilicrinus iranensis


Botryocrinus ramosissimus Carabocrinus radiatus Codiacrinus granulatus Colpodecrinus quadrifidus Corematocrinus plumosus Crotalocrinites verucosus Cupulocrinus humilis


Apektocrinus ubaghsi


Dendrocrinus longidactylus Euspirocrinus spiralis Eustenocrinus springeri Gasterocoma antiqua Glossocrinus naplesensis Heviacrinus melendezi Homalocrinus nanus Hybocrinus conicus


Hybocystites problematicus Ibexocrinus lepton Icthyocrinus laevis Iocrinus subcrassus


Lecanocrinus macropetalus Lecythocrinus eifelianus Manicrinus hybocriniformis Mastigocrinus arboreus Merocrinus typus


Metabolocrinus rossicus Ottawacrinus typus Petalocrinus mirabilis Plicodendrocrinus casei Porocrinus conicus


Guensburg, 2010 Ubaghs, 1969


Webster, Maples, Mawson, and Dastanpour, 2003


Guensburg and Sprinkle, 2009 Angelin, 1878 Billings, 1857 Schultze, 1867


Sprinkle and Kolata, 1982 Goldring, 1923


(Schlotheim, 1820) (Billings, 1857) Hall, 1852


Angelin, 1878 Ulrich, 1925


Goldfuss, 1839 Goldring, 1923


Gil Cid, Alonso, and Pobes, 1996 (Salter, 1873) Billings, 1857 Wetherby, 1880 Lane, 1970


Conrad, 1842


(Meek and Worthen, 1865) Hall, 1852


Müller, 1859


Frest and Strimple, 1978 (Salter, 1873) Walcott, 1884 Jaekel, 1902 Billings, 1887


Weller and Davidson, 1896 Meek, 1871


Proctothylacocrinus longus Protaxocrinus ovalis


Rhenocrinus ramoisissimus Rutkowskicrinus patriciae Sagenocrinites expansus Sphaerocrinus geometricus Streblocrinus brachiatus Thalamocrinus ovatus Thenarocrinus callipygus


Billings, 1857 Kier, 1952


(Angelin, 1878) Jaekel, 1906


McIntosh, 2001 (Phillips, 1839) (Goldfuss, 1831)


Koenig and Meyer, 1965 Miller and Gurley, 1895 Bather, 1890


protocrinids, both Guensburg (2012) and Ausich et al. (2015) recovered tree topologies with Apektocrinus as the sister taxon to the clade comprised of non-camerate crinoids. Thus, the early stratigraphic position, mosaic distribution of plesiomorphic and apomorphic traits, and strong support from previous phylogenetic analyses all indicate Apektocrinus occupies a position near the base of the non-camerate tree (Guensburg and Sprinkle, 2009; Guensburg, 2012; Ausich et al., 2015). Matrix construction required extensive first-hand examination


of well-preserved specimens housed in museum collections and of the published taxonomic literature. When possible, I coded characters from direct observations of type-series specimens for each species. Although emphasis was placed on observing characters from type specimens, non–type specimens were also examined to ensure the character distributions for each species were coded as completely as possible. Specimens were examined from collections within the United States National Museum of Natural History, the Field Museum of Natural History, the Lapworth Museum of Geology, and the Natural History Museum (London).


Phylogenetic analyses


Bayesian phylogenetic analyses were conducted using Markov chain Monte Carlo (MCMC) sampling in the MPI-version of


MrBayes 3.2.5 (Ronquist et al., 2012), which implements MCMC proposals for FBD trees (Zhang et al., 2016). To account for differences among alternative model configurations, multiple phylogenetic analyses were conducted and Bayes factors (BFs) were calculated to statistically compare models. Bayes factors are used in Bayesian model selection to determine which parameter configurations provide the best fit to the data and are equal to twice the difference in marginal log- likelihoods between models (Kass and Raftery, 1995). Follow- ing phylogenetic analyses, I then estimated the marginal log-likelihood of each model using the stepping-stone sampling method (Xie et al., 2010) with 50 steps and powers of β corre- sponding to quantiles of a Beta(0.5, 1.0) distribution. Parsimony-based calculations were performed using PAUP* 4.0a147 (Swofford, 2002). All additional analyses were conducted using custom scripts written in the R statistical computing environment making use of functions from the packages APE (Paradis et al., 2004), and STRAP (Bell and Lloyd, 2015). Details regarding choices of prior distributions, constraints, and MCMC convergence are discussed in the following. Morphologic character evolution was modeled using theMk


modelwith equal transition frequencies among character states and a correction for ascertainment bias in character acquisition (Lewis, 2001). The distribution of rates among characters can assume either a uniform ‘equal rates’ model or explicitly account for rate heterogeneity using a skewed parametric distribution. A preliminary parsimony-based estimation of rate variation in the crinoid character matrix depicts a highly skewed distribution (Fig. 2), strongly suggesting it is unwise to assume a model of equal rates of change among characters. This is particularly striking given that parsimony-based rate distributions tend to underestimate morphologic changes and are therefore slightly biased toward equal rates (Harrison and Larsson, 2015). To further test this hypothesis, I conducted separate analyses assuming equal, lognormal, and gamma distributed rates of character change. Following Harrison and Larsson’s (2015) recommendation, ana- lyseswith gamma or lognormal variation used eight instead of four discrete rate categories (commonly applied to molecular data).


803


Figure 2. Parsimony-based estimate of rate variation among characters. This distribution suggests that many characters evolve slowly, whereas a small number of characters evolve at much higher rates.


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