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Bioinformatics Advance Access first published online on November 14, 2007
This version published online on November 22, 2007
Bioinformatics, 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 a,*, Hervé Philippe a and Nicolas Lartillot b

aCanadian Institute for Advanced Research, Département de Biochimie, Université de Montréal, C.P. 6821, Succ. Centre-ville, Montréal, Québec CANADA, H3C 3J7,bLaboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, URM 5506, CNRS-Université de Montpellier 2, Montpellier FRANCE

*To whom correspondence should be addressed. Nicolas Rodrigue, E-mail: nicolas.rodrigue{at}umontreal.ca


  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 effcient than the conventional pruning-based sampler, with decorrelation times between draws from the posterior reduced by a factor of twenty or more.

Contact: nicolas.rodrigue{at}umontreal.ca

Associate Editor: Prof. Keith Crandall

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

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