Markov chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees

We further develop the Bayesian framework for analyzing aligned nucleotide sequence data to reconstruct phylogenies, assess uncertainty in the reconstructions, and perform other statistical inferences. We employ a Markov chain Monte Carlo sampler to sample trees and model parameter values from their joint posterior distribution. All statistical inferences are naturally based on this sample. The sample provides a most-probable tree with posterior probabilities for each clade, information that is qualitatively similar to that for the maximum-likelihood tree with bootstrap proportions and permits further inferences on tree topology, branch lengths, and model parameter values. On moderately large trees, the computational advantage of our method over bootstrapping a maximum-likelihood analysis can be considerable. In an example with 31 taxa, the time expended by our software is orders of magnitude less than that a widely used phylogeny package for bootstrapping maximum likelihood estimation would require to achieve comparable statistical accuracy. While there has been substantial debate over the proper interpretation of bootstrap proportions, Bayesian posterior probabilities clearly and directly quantify uncertainty in questions of biological interest, at least from a Bayesian perspective. Because our tree proposal algorithms are independent of the choice of likelihood function, they could also be used in conjunction with likelihood models more complex than those we have currently implemented.