Uniformization for sampling realizations of Markov processes: applications to Bayesian implementations of codon substitution models.
BACKGROUND
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.
Rodrigue
Nicolas
N
Canadian Institute for Advanced Research, Département de Biochimie, Université de Montréal, C.P. 6821, Succ. Centre-ville, Montréal, Québec Canada. nicolas.rodrigue@umontreal.ca
Philippe
Hervé
H
Lartillot
Nicolas
N
D000465:Algorithms; D001499:Bayes Theorem; D002874:Chromosome Mapping / Q000379:methods*; D003062:Codon / Q000235:genetics*; D003198:Computer Simulation; D019143:Evolution, Molecular; D008390:Markov Chains; D008957:Models, Genetic; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods; D010802:Phylogeny; D018401:Sample Size; D016415:Sequence Alignment / Q000379:methods*; D017422:Sequence Analysis, DNA / Q000379:methods*
D003062:Codon