On mathematical modelling of complex ecosystems: Application to marine planktonic patchiness

Abstract

Mathematical modeling of complex ecosystems is very difficult due to the very large number of components in the real ecosystem. Conceptual subdivision into interacting sub-systems is necessarily subjective and is made in view of explaining a particular aspect of the reality. In this paper, the North Sea planktonic ecosystem is reduced to a rather simple mathematical model with the purpose of showing the possibility of a spontaneous spatial emergence of plankton patches by diffusive instability. Due to the dependence of diffusion coefficients on the differential diameters of phytoplankton and herbivorous zooplankton patches, respectively, the spatially homogeneous steady state is unstable for spatial perturbations with wavelengths belonging to a certain range of values. As a consequence, these perturbations amplify leading to spatial heterogeneity. © 1977 Biologische Anstalt Helgoland.