Strong noise limit for population dynamics in incompressible advection.

Genetic diversity is at the basis of the evolution process of populations and it is responsible for the populations' degree of fitness to a particular ecosystem. In marine environments many factors play a role in determining the dynamics of a population, including the amount of nutrients, the temperature, and many other stressing factors. An important and yet rather unexplored challenge is to figure out the role of individuals' dispersion, due to flow advection, on population genetics. In this paper we focus on two populations, one of which has a slight selective advantage, advanced by an incompressible two-dimensional flow. In particular, we want to understand how this advective flow can modify the dynamics of the advantageous allele. We generalize, through a theoretical analysis, previous evidence according to which the fixation probability is independent of diffusivity, showing that this is also independent of fluid advection. These findings may have important implications in the understanding of the dynamics of a population of microorganism, such as plankton or bacteria, in marine environments under the influence of (turbulent) currents.

Discrete Eulerian model for population genetics and dynamics under flow.

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.

Diffusivity of E. coli-like microswimmers in confined geometries: The role of the tumbling rate.

We analyzed the effect of confinement on the effective diffusion of a run-and-tumble E. coli-like flagellated microswimmer. We used a simulation protocol where the run phases are obtained via a fully resolved swimming problem, i.e., Stokes equations for the fluid coupled with rigid-body dynamics for the microorganism, while tumbles and collisions with the walls are modeled as random reorientation of the microswimmer. For weak confinement, the swimmer is trapped in circular orbits close to the solid walls. In this case, optimal diffusivity is observed when the tumbling frequency is comparable with the angular velocity of the stable orbits. For strong confinement, stable circular orbits disappear and the diffusion coefficient monotonically decreases with the tumbling rate. Our findings are generic and can be potentially applied to other natural or artificial chiral microswimmers that follow circular trajectories close to an interface or in confined geometries.