Alexander B. Medvinsky, Russian Academy of Sciences, Pushchino, Moscow Region, Russia
Dmitry A. Tikhonov, Russian Academy of Sciences, Pushchino, Moscow Region, Russia
Jörg Enderlein, University of Regensburg Regensburg, Germany
Horst Malchow, University of Osnabrück, Osnabrück, Germany

Abstract: The fascinating variety of spatio-temporal patterns in aquatic ecosystems and the understanding of the governing mechanisms of its generation and further dynamics requires ongoing experimental and theoretical studies. After introducing a certain hybrid mathematical model, this paper makes an attempt to demonstrate that the predation of a mobile planktivorous fish school on zooplankton can initiate both plankton pattern formation and fish school walks. Nonlinear interactions in the model of a fish-zooplankton-algae trophic chain prevent a simple intuitive understanding of the system dynamics. It is shown that the fish school predation and motion can give rise to plankton spiral waves. In the course of the spiral wave formation, the amplitudes of the spatially averaged plankton density oscillations are decreasing dramatically. Fish school walks are shown to resemble a fractional Brownian motions with a Hurst exponent depending on the fish predation rate.

Keywords: marine plankton, predator-prey interactions, reaction-diffusion equations, fish school motion, cellular automaton, wave propagation