Advisor: Vladimir Minin

Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organisms carrying the trait. We have developed a new Markov chain Monte Carlo (MCMC) algorithm, based on a continuous-time Markov chain (CTMC) technique called uniformization, that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared, far more favorable than the cubic relationship inherit in state-of-the-art methods that rely on exponentiating CTMC rate matrices. We apply our new stochastic mapping technique to two data sets enabling two distinct hypothesis tests through the use of Bayes factors. The first hypothesis test concerns the reproductive parity mode of the most recent common ancestor of squamates. The second hypothesis test concerns the number of times bioluminescent bacterial photophores developed in cephalopods. In both cases there were concerns that the standard CTMC model of trait evolution for a binary morphological trait was insufficient due to rate matrix heterogeneity across the phylogeny. To address these concerns we developed a Markov modulated Markov process model of trait evolution and integrated this hidden rates model with our matrix exponentiation-free stochastic mapping technique.