Celia García-Pareja: Diffusion limit for Markovian models of evolution in structured populations with migration

Abstract: The evolution of microbial subpopulations that migrate within spatial structures has gained interest in recent years. Questions of relevance include, for instance, the ability of a migrant mutant to take over the population (fixate). Estimating fixation probabilities is, however, usually hindered by the lack of analytical formulas and by computational complexity of simulation-based strategies when considering large populations. In this work, we study several population genetics models where the population is divided into D subpopulations (called demes) consisting of two types of individuals, mutants and wild-types, that evolve through discrete Markovian updates. We prove that under certain assumptions all the considered models converge to the same dffusion approximation, which we call universal. This diffusion approximation is amenable to simulation strategies that underly methods of statistical inference while significantly reducing computational costs. In all models, each Markovian update follows two phases: First, a local growth phase in each subpopulation, where the growth of each type of individual depends on its fitness, and then a sampling phase that implements migration between subpopulations. Our proof relies on existing diffusion approximation results for degenerate diffusions but requires further technicalities due to fact that sample sizes in each deme are not necessarily fixed but change randomly with each update. This is joint work with Alia Abbara and Anne-Florence Bitbol at EPF Lausanne.