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arXiv · 1106.3506

Population genetics in compressible flows

Simone Pigolotti·Roberto Benzi·Mogens H. Jensen·David R. Nelson
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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.

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Simone Pigolotti, Roberto Benzi, Mogens H. Jensen, David R. Nelson. 2011-06-17. Population genetics in compressible flows. https://doi.org/10.1103/physrevlett.108.128102

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