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Marine species reproduce and compete while being advected by turbulent flows.It is largely unknown, both theoretically and experimentally, how populationdynamics and genetics are changed by the presence of fluid flows. Discreteagent-based simulations in continuous space allow for accurate treatment ofadvection and number fluctuations, but can be computationally expensive foreven modest organism densities. In this report, we propose an algorithm toovercome some of these challenges. We first provide a thorough validation ofthe algorithm in one and two dimensions without flow. Next, we focus on thecase of weakly compressible flows in two dimensions. This models organisms suchas phytoplankton living at a specific depth in the three-dimensional,incompressible ocean experiencing upwelling and/or downwelling events. We showthat organisms born at sources in a two-dimensional time-independent flowexperience an increase in fixation probability.

Discrete Eulerian model for population genetics and dynamics under flow