THE APPLICATION OF MARKOV CHAIN MONTE CARLO APPROACHES TO MACROEVOLUTIONARY PALEOBIOLOGY

Systematists have made considerable progress in assessing different possible models of evolution over a range of plausible phylogenetic scenarios. Much of this has focused on Markov Chain Monte Carlo (MCMC) approaches, where models tested in assessed given the relative likelihoods of numerous trees. However, these models focus on issues that obviously affect data among extant taxa. Thus, several issues of concern to paleontologists have not gotten as much attention, but could be addressed using MCMC approaches. For example, one could use MCMC approaches to assess the relative per-character information of two fundamentally different homology schemes for a clade. Similarly, one could assess stratigraphic fit by summing the likelihoods of different trees positing different amounts of stratigraphic gaps. The example on which I will focus concerns speciation models suggested by the fossil record: anagenetic change (e.g., “Darwinian” speciation), pulsed change with changes distributed continuously through time (e.g., punctuated change), and pulsed change concentrated in particular intervals (e.g., turnover pulses). Fundamentally, this is simply a particular set of cases for estimates of divergence times: continuous anagenetic change requires the most time (and thus the deepest divergences) for some likely amount of change, whereas turnover pulses can allow for much shallower divergence times given the same likely amounts of change by concentrated changes in speciation events and concentrating speciation events in pulses. Using Akaike’s weights to accommodate the differing numbers of parameters (with anagenetic change requiring the fewest and pulsed turnover requiring the most), I apply MCMC to two groups of Ordovician gastropods, the Lophospiridae and the Bucaniidae, using morphological and stratigraphic data. In both cases, we can reject continuous anagenetic change fairly emphatically with one case (the Lophospiridae) allowing us to reject continuous speciation also. Future directions include adding mixture modeling to assess the relative contributions of these models to each clade’s evolution.