Appears in collection : 2022 - T1 - WS3 - Mathematical models in ecology and evolution

Joint work with Amandine Véber.

Population expansions in dimension 2 or higher are characterized by the emergence of sectors at the front edge, in which all individuals have the same genetic type. This phenomenon is a consequence of stochasticity in reproduction at the front, where population densities are lower and genetic drift more pronounced. Yet little is known of the proper-ties of these sectors, partly due to a lack of population genetics processes adapted to an expansion setting. In this talk, I will present a family of stochastic population genetics processes allowing to study expanding populations, based on the spatial Lambda-Fleming Viot process. Their key feature is the use of "ghost individuals" to model empty areas, adapting a concept from interacting particle systems theory and first introduced in population genetics in Hallatschek & Nelson (2008) and Durrett & Fan (2016). These ghost individuals can reproduce as well, modeling local extinctions due to stochasticity in reproduction, but with a strong selective disadvantage against "real individuals". Then, I will focus on the limiting process obtained by letting the selective advantage of real individuals become infinitely strong, that is, assuming local extinctions are no longer possible. This limiting process is reminiscent of the Eden growth model, but continuous in space, and associated to tools allowing to study genetic diversity. I will explain to what extent its growth properties are similar to the ones of the Eden model.