Phylogenetic Inference for Binary Data on Dendograms Using Markov Chain Monte Carlo

Using a stochastic model for the evolution of discrete characters among a group of organisms, we derive a Markov chain that simulates a Bayesian posterior distribution on the space of dendograms. A transformation of the tree into a canonical cophenetic matrix form, with distinct entries along its superdiagonal, suggests a simple proposal distribution for selecting candidate trees "close" to the current tree in the chain. We apply the consequent Metropolis algorithm to published restriction site data on nine species of plants. The Markov chain mixes well from random starting trees, generating reproducible estimates and confidence sets for the path of evolution.