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Searching for Convergence in Phylogenetic Markov Chain Monte Carlo

Beiko, Robert G., Keith, Jonathan M., Harlow, Timothy J., & Ragan, Mark A (2006) Searching for Convergence in Phylogenetic Markov Chain Monte Carlo. Systematic Biology, 55(4), pp. 553-565.

Abstract

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, δ and ε, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a "metachain" to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely.

Impact and interest:

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36 citations in Web of Science®

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ID Code: 8012
Item Type: Journal Article
Additional Information: For more information, please refer to the publisher's website (link above) or contact the author: j.keith@qut.edu.au
Additional URLs:
Keywords: Bayesian phylogenetic inference, heating parameter, Markov chain Monte Carlo, replicated chains
ISSN: 1063-5157
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2006 Taylor & Francis
Deposited On: 07 Jun 2007
Last Modified: 29 Feb 2012 23:29

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