COMBINING COMPATIBILITY AND MK MODELS TO TEST FOR CORRELATED CHARACTER CHANGE, AND ITS IMPLICATIONS FOR DIVERGENCE TIME ESTIMATION AND DISPARITY

Correlated change among anatomical characters remains a major challenge to reconstructing phylogenetic relationships and divergence times within clades. This is a concern because developmental biological theory predicts that many (if not most) characters belong to modules that make joint change among linked characters common even if some independent change is permissible. If we have prior reason to posit a module (or some other set of linked characters), then we can use modified Mk models (Mk-corr) to jointly estimate divergence times and separates rates of independent and joint change given some cladistic topology and character data. Truly independent change is simply a special case of this where rates of joint change are zero. The problem then becomes how to identify such sets of characters. Most of the methods for identifying modules rely on morphometric studies of large populations, which is not only laborious, but also not an option for many taxa in the fossil record. We might posit linked sets based on prior biological knowledge, but we often lack such insights even for many extant clades. Fortunately, correlated change and independent change models make distinct predictions about compatibility patterns among characters. For example, linked changed followed by independent change for two binary characters can generate 00→11→01 sequences on phylogeny (where 00 represents taxa possessing primitive states for both taxa), whereas independent change typically generates 00→10→11 or 00→10+01. Thus, excess “stratigraphic incompatibility” suggests linked change. Here, I use stratigraphic compatibility to identify possible linked sets among 26 characters coded for 15 Ordovician-Devonian pleurocystitid echinoderms originally published by Sumrall & Sprinkle (1995 J. Paleo. 68:742) and updated in two subsequent papers. Using reversible jump Markov-Chain Monte Carlo analyses to consider different “modules” under Mk-corr suggest at least two modules (of 5 and 4 characters, respectively). By attributing much early change to “modular” change, tip-dating using Mk-corr posits much younger divergence times among pleurocystitids than does tip-dating assuming independent change, and also suggests that the major burst of disparity early in clade history reflects at least in part correlated change.