Bayesian phylogenetic inference via Markov chain Monte Carlo methods

We derive a Markov chain to sample from the posterior distribution for a ph ylogenetic tree given sequence information from the corresponding set of or ganisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic m atrix form suggests a simple and effective proposal distribution for select ing candidate trees close to the current tree in the chain. We illustrate t he algorithm with restriction site data on 9 plant species, then extend to DNA sequences from 32 species of fish. The algorithm mixes well in both exa mples from random starting trees, generating reproducible estimates and cre dible sets for the path of evolution.