Strong noise limit for population dynamics in incompressible advection

Genetic diversity is at the basis of the evolution process of populations and it is responsible for the populations' degree of fitness to a particular ecosystem. In marine environments many factors play a role in determining the dynamics of a population, including the amount of nutrients, the temperature, and many other stressing factors. An important and yet rather unexplored challenge is to figure out the role of individuals' dispersion, due to flow advection, on population genetics. In this paper we focus on two populations, one of which has a slight selective advantage, advanced by an incompressible two-dimensional flow. In particular, we want to understand how this advective flow can modify the dynamics of the advantageous allele. We generalize, through a theoretical analysis, previous evidence according to which the fixation probability is independent of diffusivity, showing that this is also independent of fluid advection. These findings may have important implications in the understanding of the dynamics of a population of microorganism, such as plankton or bacteria, in marine environments under the influence of (turbulent) currents.