title: 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 investigate 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. We find localization on convergence zones, and very rapid extinction compared to well-mixed populations. For a linear velocity sink, one finds a bimodal distribution of fixation times. The long-lived states in this case are demixed configurations with a single interface, whose location depends on the fitness advantage.
authors.affiliation: The Niels Bohr Institut, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
authors.forename: Simone
authors.initials: S
authors.lastname: Pigolotti
authors.forename: Roberto
authors.initials: R
authors.lastname: Benzi
authors.forename: Mogens H
authors.initials: MH
authors.lastname: Jensen
authors.forename: David R
authors.initials: DR
authors.lastname: Nelson
mesh_terms: D000818:Animals; D003163:Competitive Behavior; D003198:Computer Simulation; D004641:Emigration and Immigration; D005828:Genetics, Population / Q000379:methods*; D008957:Models, Genetic; D013269:Stochastic Processes