Non‐equilibrium spatio‐temporal patterns in models of non‐linear plankton dynamics

SUMMARY 1. Mathematical models of biological population dynamics have not only to account for growth and interactions but also for spatial processes, like random or directed and joint or relative motion of species, as well as the variability of the environment.2. Early attempts began with physico‐chemical diffusion, exponential growth and Lotka‐Volterra type interactions. These approaches have been continuously refined to more realistic descriptions of the development of natural populations.3. The main aim of this paper is to give an extensive introduction to the subject and the bibliography. It then focusses on minimal models of the temporally and spatially continuous dynamics of freshwater and marine plankton as well as other microorganisms, which is best described by non‐linear reaction–diffusion and advection equations.4. The fascinating variety of spatio‐temporal patterns in such systems and the governing mechanisms of their generation and further dynamics are introduced, making use of a model example of the nutrient–plankton–fish food chain. The formation of rotating spiral patterns is presented.