  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.
