A Bayesian model for gene family evolution

A birth and death process is frequently used for modeling the size of a gene family that may vary along the branches of a phylogenetic tree. Under the birth and death model, maximum likelihood methods have been developed to estimate the birth and death rate and the sizes of ancient gene families (numbers of gene copies at the internodes of the phylogenetic tree). This paper aims to provide a Bayesian approach for estimating parameters in the birth and death model. We develop a Bayesian approach for estimating the birth and death rate and other parameters in the birth and death model. In addition, a Bayesian hypothesis test is developed to identify the gene families that are unlikely under the birth and death process. Simulation results suggest that the Bayesian estimate is more accurate than the maximum likelihood estimate of the birth and death rate. The Bayesian approach was applied to a real dataset of 3517 gene families across genomes of five yeast species. The results indicate that the Bayesian model assuming a constant birth and death rate among branches of the phylogenetic tree cannot adequately explain the observed pattern of the sizes of gene families across species. The yeast dataset was thus analyzed with a Bayesian heterogeneous rate model that allows the birth and death rate to vary among the branches of the tree. The unlikely gene families identified by the Bayesian heterogeneous rate model are different from those given by the maximum likelihood method. Compared to the maximum likelihood method, the Bayesian approach can produce more accurate estimates of the parameters in the birth and death model. In addition, the Bayesian hypothesis test is able to identify unlikely gene families based on Bayesian posterior p-values. As a powerful statistical technique, the Bayesian approach can effectively extract information from gene family data and thereby provide useful information regarding the evolutionary process of gene families across genomes.