Fixation Probabilities in Compressible Turbulence

Competition between two biological species can change dramatically in a turbulent environment, where survival of the fittest, number fluctuations, and fluid advection can all play an important role. Turbulent effects are particularly interesting when the cell generation time is within the inertial range of eddy turnover times, as is often the case for photosynthetic bacteria in oceans and lakes. We couple an off-lattice agent-based simulation of two populations in one dimension with a velocity field generated by a shell model, and find that compressible turbulence can wash out the effect of selective advantage on fixation probabilities. By examining fixation events in simple sinusoidal flows, frozen snapshots of our turbulent velocity field, and well-mixed systems with a time-dependent carrying capacity, we find we can explain a large portion of our results by only considering long wavelength, slowly-varying features of turbulence. We uncover a suppression of fixation probabilities connected to the behavior of Fisher genetic waves.