Population growth and persistence in a heterogeneous environment: the role of diffusion and advection

Abstract. The spatio-temporal dynamics of a population present one of the most fascinating as-pects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a pop-ulation on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate basic mathematical techniques and give the critical conditions providing the survival of a population in simple systems and in more complex resource-consumer models which describe the dynamics of phytoplankton in a water column