Fixation Probabilities in Weakly Compressible Fluid Flows

Abstract

Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at which passively traveling photosynthetic organisms are restricted to live. In this report, we seek to quantitatively study genetics under flow. To this end, we couple an off-lattice agent-based simulation of two populations in 1D to a weakly compressible velocity field--first a sine wave and then a shell model of turbulence. We find for both cases that even in a regime where the overall population structure is approximately unaltered, the flow can significantly diminish the effect of a selective advantage on fixation probabilities. We understand this effect in terms of the enhanced survival of organisms born at sources in the flow and the influence of Fisher genetic waves.

arXiv comment8 pages, 6 figures; SI: 9 pages, 3 figures

References in corpus (8)

• Gene surfing
• Fisher waves in the strong noise limit
• Population genetics in compressible flows
• Population dynamics at high Reynolds number
• Growth, competition and cooperation in spatial population genetics
• Fisher equation with turbulence in one dimension
• Fast flowing populations are not well mixed
• Motion, fixation probability and the choice of an evolutionary process

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• Flow spatial structure determines pattern instabilities in nonlocal models of population dynamics
• Discrete Eulerian model for population genetics and dynamics under flow
• Turbulent mixing controls fixation of growing antagonistic populations