Population genetics in compressible flows

Abstract

We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field and fitness advantage, number fluctuations lead to a coarsening dynamics typical of the stochastic Fisher equation. We then study three examples of compressible advecting fields: a shell model of turbulence, a sinusoidal velocity field and a linear velocity sink. In all cases, advection leads to a striking drop in the fixation time, as well as a large reduction in the global carrying capacity. Despite localization on convergence zones, one species goes extinct much more rapidly than in well-mixed populations. For a weak harmonic potential, one finds a bimodal distribution of fixation times. The long-lived states in this case are demixed configurations with a single boundary, whose location depends on the fitness advantage.