Evolutionary Model for the Statistical Divergence of Paralogous and Orthologous Gene Pairs Generated by Whole Genome Duplication and Speciation

We outline a principled approach to the analysis of duplicate gene similarity distributions, based on a model integrating sequence divergence and the process of fractionation of duplicate genes resulting from whole genome duplication (WGD). This model allows us to predict duplicate gene similarity distributions for a series of two or three WGD, for whole genome triplication followed by a WGD, and for triplication, followed by speciation, followed by WGD. We calculate the probabilities of all possible fates of a gene pair as its two members proliferate or are lost, predicting the number of surviving pairs from each event. We discuss how to calculate maximum likelihood estimators for the parameters of these models, illustrating with an analysis of the distribution of paralog similarities in the poplar genome.