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