A model for resolving the plankton paradox:: coexistence in open flows

1. Recent developments in the field of chaotic advection in hydrodynamical/environmental flows encourage us to revisit the population dynamics of competing species in open aquatic systems. 2. We assume that these species are in competition for a common limiting resource in. open flows with chaotic advection dynamics. As an illustrative example, we consider a time periodic two-dimensional flow of viscous fluid (water) around a cylindrical obstacle. 3. Individuals accumulate along a fractal set in the wake of the cylinder, which acts as a catalyst for the biological reproduction process. While in homogeneous, well mixed environments only one species could survive this competition, coexistence of competitors is typical in our hydrodynamical system. 4. It is shown that a steady state sets in after sufficiently long times. In this state, the relative density of competitors is determined rather by the fractal nature of the spatial distribution of the advected species, and by their initial conditions, than by their competitive abilities. We argue that two factors, the strong chaotic mixing along a fractal set and the boundary layer around the obstacle, are responsible for the coexistence.