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© 2005 Society of Systematic Biologists
Polytomies and Bayesian Phylogenetic Inference
1 Department of Ecology and Evolutionary Biology, University of Connecticut 75 N. Eagleville Road, Unit 3043, Storrs, Connecticut 06269–3043, USA E-mail: paul.lewis{at}uconn.edu (P.O.L.)
2 School of Computational Science and Information Technology (CSIT), 150-F Dirac Science Library, Florida State University Tallahassee, Florida 32306–4120, USA
Edited by Thomas Buckley: Associate Editor
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Abstract |
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Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short branch lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.
Keywords: Bayesian; phylogenetics; polytomy; reversible-jump MCMC; star tree; unresolved
Received September 18, 2003; Revised October 28, 2003; Accepted December 13, 2004
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