Divergence estimation in the presence of incomplete lineage sorting and migration

This paper focuses on the problem of estimating a species tree from multilocus data in the presence of incomplete lineage sorting and migration. We develop a mathematical model similar to IMa2 (Hey 2010) for the relevant evolutionary processes which allows both the the population size parameters and the migration rates between pairs of species tree branches to be integrated out. We then describe a BEAST2 package DENIM which based on this model, and which uses an approximation to sample from the posterior. The approximation is based on the assumption that migrations are rare, and it only samples from certain regions of the posterior which seem likely given this assumption. The method breaks down if there is a lot of migration. Using simulations, Leache et al 2014 showed migration causes problems for species tree inference using the multispecies coalescent when migration is present but ignored. We re-analyze this simulated data to explore DENIMs performance, and demonstrate substantial improvements over *BEAST. We also re-analyze an empirical data set. [isolation-with-migration; incomplete lineage sorting; multispecies coalescent; species tree; phylogenetic analysis; Bayesian; Markov chain Monte Carlo]