Bayesian Analysis of Partitioned Data

Variation in the evolutionary process across the sites of nucleotide sequence alignments is well established, and is an increasingly pervasive feature of datasets composed of gene regions sampled from multiple loci and/or different genomes. Inference of phylogeny from these data demands that we adequately model the underlying process heterogeneity; failure to do so can lead to biased estimates of phylogeny and other parameters. Traditionally, process heterogeneity has been accommodated by first assigning sites to data subsets based on relevant prior information (reflecting codon positions in protein-coding DNA, stem and loop regions of ribosomal DNA, etc.), and then estimating the phylogeny and other model parameters under the resulting mixed model. Here, we consider an alternative approach for accommodating process heterogeneity that is similar in spirit to this conventional mixed-model approach. However, rather than treating the partitioning scheme as a fixed assumption of the analysis, we treat the process partition as a random variable using a Dirichlet process prior model, where the phylogeny is estimated by integrating over all possible process partitions for the specified data subsets. We apply this method to simulated and empirical datasets, and compare our results to those estimated previously using conventional mixed-model selection criteria based on Bayes factors. We find that estimation under the Dirichlet process prior model discovers novel process partitions that may more effectively balance error variance and estimation bias, while rendering phylogenetic inference more robust to process heterogeneity by virtue of integrating estimates over all possible partition schemes. (Keywords: Bayesian phylogenetic inference; Dirichlet process prior; Markov chain Monte Carlo; maximum likelihood; partitioned analyses; process heterogeneity.)