  The spatio-temporal dynamics of a population present one of the most
fascinating aspects 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 population 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.
