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The spatio-temporal dynamics of a population present one of the mostfascinating aspects and challenges for ecological modelling. In this article wereview some simple mathematical models, based on one dimensionalreaction-diffusion-advection equations, for the growth of a population on aheterogeneous habitat. Considering a number of models of increasing complexitywe investigate the often contrary roles of advection and diffusion for thepersistence of the population. When it is possible we demonstrate basicmathematical techniques and give the critical conditions providing the survivalof a population, in simple systems and in more complex resource-consumer modelswhich describe the dynamics of phytoplankton in a water column.

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