A Dirichlet process model for detecting positive selection in protein-coding DNA sequences

Most methods for detecting Darwinian natural selection at the molecular level rely on estimating the rates or numbers of non-synonymous and synonymous changes in an alignment of protein-coding DNA sequences. In some of these methods, the nonsynonymous rate of substitution is allowed to vary across the sequence, permitting the identification of single amino acid positions that are under positive natural selection. However, it is unclear which probability distribution should be used to describe how the nonsynonymous rate of substitution varies across the sequence. One widely used solution is to model variation in the nonsynonymous rate across the sequence as a mixture of several discrete or continuous probability distributions. Unfortunately, there is little population genetics theory to inform us of the appropriate probability distribution for among-site variation in the nonsynonymous rate of substitution. Here, we describe an approach to modeling variation in the nonsynonymous rate of substitution by using a Dirichlet process mixture model. The Dirichlet process allows there to be a countably infinite number of nonsynonymous rate classes and is very flexible in accommodating different potential distributions for the nonsynonymous rate of substitution. We implemented the model in a fully Bayesian approach, with all parameters of the model considered as random variables.