Gaël Raoul: Dynamics of a spatially structured population facing climate change

We consider an asexual population structured by a phenotypic trait and a spacial variable. The model is a parabolic partial differential equation with a nonlocal (in the phenotypic variable) competition term. We show that propagative fronts exist for that model, and explicit their speed. We can then push the analysis further: describe the dynamics of population in a 2D space with a heterogeneous landscape. We describe then the dynamics of the range of the population.
This approach is interesting for its simplicity (the dynamics of the range is given by an explicit speed of the interface) and because the range of the population can be related to presence-absence maps that are used by field biologists. We illustrate applications of these results:
they can provide an interesting insight to investigate the impact of natural reserves or mountains.