Dependence of fish school movement and plankton spatial distributions on the phytoplankton growth rate

In this paper we investigate the spontaneous emergence and the dynamics of patchiness in spatially distributed communities of plankton, which plays a key role in the matter rotation on earth. Patchiness is often supposed to be due to hydrodynamical factors (diffusion and advection). In contrast to this approach, we consider the formation of plankton patches as a result of interactions in the trophic chain nutrient - phytoplankton - zooplankton-fish. We present a mathematical model of such interactions, which combines a continuous description of the plankton spatio-temporal dynamics and a discrete description of the fish school movement. We show that the fish school can give rise to plankton patches. In turn, fish school walks are shown to depend on phytoplankton growth rate. We show also that the Hurst exponent characterizing the fish school movement in the diffusion approximation depends on phytoplankton growth rate.</p