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Systematic Biology 2004 53(6):904-913; doi:10.1080/10635150490522629
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© 2004 Society of Systematic Biologists

Frequentist Properties of Bayesian Posterior Probabilities of Phylogenetic Trees Under Simple and Complex Substitution Models

John P. Huelsenbeck1 and Bruce Rannala2

1 Section of Ecology, Behavior and Evolution, Division of Biological Sciences, University of California San Diego La Jolla, California 92093–0116, USA E-mail: johnh{at}biomail.ucsd.edu
2 Genome Center & Section of Evolution and Ecology, University of California Davis, One Shields Avenue Davis California 95616, USA

Edited by Thomas Buckley: Associate Editor


   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.

Keywords: Bayesian estimation; Markov chain Monte Carlo; posterior probability; prior probability

Received July 22, 2003; Revised November 18, 2003; Accepted July 18, 2004
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