Population genetics in compressible flows

TL;DR

This paper investigates how compressible flows influence competition dynamics between two species, revealing faster fixation times and reduced carrying capacity due to advection effects in various flow scenarios.

Contribution

It introduces a model combining population genetics with compressible flow fields, analyzing the impact on fixation times and species extinction in different flow configurations.

Findings

Advection significantly reduces fixation times.

Compressible flows lower the global carrying capacity.

Localization leads to faster species extinction.

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.