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Bioinformatics Advance Access originally published online on November 14, 2007
Bioinformatics 2008 24(1):56-62; doi:10.1093/bioinformatics/btm532
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© The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Uniformization for sampling realizations of Markov processes: applications to Bayesian implementations of codon substitution models

Nicolas Rodrigue 1,*, Hervé Philippe 1 and Nicolas Lartillot 2

1Canadian Institute for Advanced Research, Département de Biochimie, Université de Montréal, C.P. 6821, Succ. Centre-ville, Montréal, Québec Canada, H3C 3J7 and 2Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, URM 5506, CNRS-Université de Montpellier 2, Montpellier, France

*To whom correspondence should be addressed.


  Abstract

Motivation: Mapping character state changes over phylogenetic trees is central to the study of evolution. However, current probabilistic methods for generating such mappings are ill-suited to certain types of evolutionary models, in particular, the widely used models of codon substitution.

Results: We describe a general method, based on a uniformization technique, which can be utilized to generate realizations of a Markovian substitution process conditional on an alignment of character states and a given tree topology. The method is applicable under a wide range of evolutionary models, and to illustrate its usefulness in practice, we embed it within a data augmentation-based Markov chain Monte Carlo sampler, for approximating posterior distributions under previously proposed codon substitution models. The sampler is found to be more efficient than the conventional pruning-based sampler with the decorrelation times between draws from the posterior reduced by a factor of 20 or more.

Contact: nicolas.rodrigue{at}umontreal.ca

Associate Editor: Keith Crandall

Received on May 29, 2007; revised on September 9, 2007; accepted on October 16, 2007

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