Rannala B: Frequentist properties of Bayesian posterior probabilities of phylogenetic trees under simple and complex substitution models. Syst Biol 2004

Abstract. — What does the posterior probability of a phylogenetic tree mean? This simulation study shows that Bayesian posterior probabilities have the meaning that is typically ascribed to them; the posterior probability of a tree is the probability that the tree is correct, assuming that the model is correct. At the same time, the Bayesian method can be sensitive to model misspecification, and the sensitivity of the Bayesian method appears to be greater than the sensitivity of the nonparametric bootstrap method (using maximum likelihood to estimate trees). Although the estimates of phylogeny obtained by use of the method of maximum likelihood or the Bayesian method are likely to be similar, the assessment of the uncertainty of inferred trees via either bootstrapping (for maximum likelihood estimates) or posterior probabilities (for Bayesian estimates) is not likely to be the same. We suggest that the Bayesian method be implemented with the most complex models of those currently available, as this should reduce the chance that the method will concentrate too much probability on too few trees. [Bayesian estimation; Markov chain Monte Carlo; posterior probability; prior probability.] Quantifying the uncertainty of a phylogenetic estimate is at least as important a goal as obtaining the phyloge-netic estimate itself. Measures of phylogenetic reliability not only point out what parts of a tree can be trusted when interpreting the evolution of a group, but can guid