# Math-Bio seminar: "Bayesian inference of evolutionary divergence with genomic data under diverse demographic models"

In the study of diverging populations and species, a common goal is to disentangle the conflicting signals of prolonged genetic drift (elevating divergence) and gene exchange (removing it). In this talk, I present a new Bayesian method for estimating demographic history using population genomic samples. Several key innovations are introduced that allow the study of diverse models within an Isolation with Migration framework. The new method implements a 2-step analysis, with an initial Markov chain Monte Carlo (MCMC) phase that samples simple coalescent trees, followed by the calculation of the joint posterior density for the parameters of a demographic model. In step 1, the MCMC sampling phase, the method uses a reduced state space, consisting of coalescent trees without migration paths, and a simple importance sampling distribution without the demography of interest. Once obtained, a single sample of trees can be used in step 2 to calculate the joint posterior density for model parameters under multiple diverse demographic models, without having to repeat MCMC runs. Migration paths are not included in the state space of the MCMC phase, but rather are handled by analytic integration using a Markov chain as a representation of genealogy in step 2 of the analysis. Because of the separation of coalescent events from migration events and the demography of interest, the method is scalable to a large number of loci with excellent MCMC mixing properties. With an implementation of the new method in the computer program MIST, I demonstrate the methodâ€™s accuracy, scalability and other advantages using simulated data and DNA sequences of two common chimpanzee subspecies: Pan troglodytes (P. t.) troglodytes and P. t. verus.