# Discrete Eulerian model for population genetics and dynamics under flow

## TL;DR

This paper introduces a novel algorithm for simulating population genetics in fluid flows, validated in 1D and 2D, revealing increased fixation probabilities in certain flow conditions, with implications for marine species dynamics.

## Contribution

The paper presents a new algorithm that efficiently models population genetics under fluid flow, validated in multiple dimensions, and applied to marine species in weakly compressible flows.

## Key findings

- Organisms at sources in flow have higher fixation probabilities.
- Algorithm accurately models advection and fluctuations in population dynamics.
- Flow conditions significantly influence genetic fixation outcomes.

## Abstract

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.