Mathematics

The genetic competition for biological species living in marine environments can be severely influenced by fluid advection. Very often, in oceans and in lakes, cell generation times are precisely in the inertial range of eddy turnover times and therefore the influence of turbulence must be properly taken into account. We employ both an off-lattice agent-based simulation as well as an on-site density-based model to describe two competing populations in one and in two spatial dimensions under the influence of advecting (turbulent) velocity fields. The novel on-site density-based model allows to accurately and efficiently describe the dynamics of the population and the genetics of large number of individuals, making this the ideal tool to study populations in two dimensions. We find that the presence of compressible turbulent velocity fields can have a very strong effect on genetic competitions. In particular, even in regimes where the overall population structure is approximately unaltered, the flow can significantly diminish the effect of a selective advantage on fixation probabilities. We explain this effect in terms of the enhanced survival of organisms born at the sources in the flow and the influence of Fisher genetic waves. 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 of the influence of Fisher genetic waves.

 

Ref. "Fixation probabilities in weakly compressible fluid flows”, Abigail Plummer, Roberto Benzi, David R. Nelson, and Federico Toschi, PNAS January 8, 2019 116 (2) 373-378; https://doi.org/10.1073/pnas.1812829116