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 reconst ructions, and perform other statistical inferences. We employ a Markov chai n Monte Carlo sampler to sample trees and model parameter values from their joint posterior distribution. All statistical inferences are naturally bas ed 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 v alues. On moderately large trees, the computational advantage of our method over bootstrapping a maximum-likelihood analysis can be considerable. In a n example with 31 taxa, the time expended by our software is orders of magn itude less than that a widely used phylogeny package for bootstrapping maxi mum likelihood estimation would require to achieve comparable statistical a ccuracy. While there has been substantial debate over the proper interpreta tion of bootstrap proportions, Bayesian posterior probabilities clearly and directly quantify uncertainty in questions of biological interest, at leas t from a Bayesian perspective. Because our tree proposal algorithms are ind ependent of the choice of likelihood function, they could also be used in c onjunction with likelihood models more complex than those we have currently implemented.