Interactions of traveling waves in the context of population genetics


Evolution is driven by forces that constantly reshape the genetic distribution observed in a population. Selection occurs on the genotypes of individuals within a single population present in a given environment; while dispersal of individuals in this environment takes place. In the case of several loci for a sexual population, recombination between loci introduces a new layer of complexity.

Here we investigate a two-locus two-allele model which accounts for selection, dispersal through diffusion in space (homogeneous and heterogeneous spaces will be explored) and recombination with an arbitrary rate, in order to determine the interaction between loci under selective pressures. A system of $3$ coupled PDEs is established and studied.

Classical behaviors of solutions in the case of a single Fisher–KPP PDE (one locus) pertain to the family of traveling waves or stationary solutions (clines). In the case of two loci, interactions between the waves can occur. This phenomenon is studied using generalized traveling waves. Different kind of interactions are shown, and predictions of the outcome are given.

23 Jul 2018