# PDE Models to Study the Spatial and Evolutionary Dynamics of a Population in a Heterogeneous Environment

Gael Raoul^{*}

The understanding of many biologic phenomena indeed require to consider both Darwinian evolution and spatial dynamics. We focus here on the case of a population living in a linear environmental gradient. The population is structured by a phenotypic trait (that is a physical characteristic of an individual, e.g. its weight or size) and a spatial variable. The models are then parabolic equations with non local competition terms. We perform an analysis of the propagative fronts for such models.

Mathematics Subject Classification: 35C07 35Q92

Keywords: Darwinian evolution; spatial dynamics; parabolic equation model;

Minisymposion: Modelling and Optimization in Mathematical Biology