Sequence diversity under the multispecies coalescent with Yule process and constant population size

The study of sequence diversity under phylogenetic models is now classic. Theoretical studies of diversity under the Kingman coalescent appeared shortly after the introduction of the coalescent. In this paper we revisit this topic under the multispecies coalescent, an extension of the single population model to multiple populations. We derive exact formulas for the sequence dissimilarity of two sequences drawn at random under a basic multispecies setup. The multispecies model uses three parameters—the species tree birth rate under the pure birth process (Yule), the species effective population size and the mutation rate. We also discuss the effects of relaxing some of the model assumptions.

► We describe the stochastic multi-species coalescent model for sequence evolution.
► We define average sequence dissimilarity, a key statistic under the model.
► We derive a direct formula for within and between average sequence dissimilarity.
► We examine the effect of model enhancements on average sequence dissimilarity.
► We show two practical uses of the formulas.