Geodesic
Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection
A. B. Ryabov1 ; B. Blasius1
1 Institute for Chemistry and Biology of Marine Environment (ICBM), Oldenburg University, 26111 Oldenburg, Germany
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 42-86.

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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.
DOI : 10.1051/mmnp:2008064

A. B. Ryabov 1 ; B. Blasius 1

1 Institute for Chemistry and Biology of Marine Environment (ICBM), Oldenburg University, 26111 Oldenburg, Germany 
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A. B. Ryabov; B. Blasius. Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 42-86. doi : 10.1051/mmnp:2008064. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008064/

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