Séminaire - Reaction-diffusion equations in ecology

Résumé : In this presentation we will be interested in the effect of climate change on species ranges and its consequences on population persistence. To do so we will use reaction-diffusion equations to model the dynamics of a population density with respect to time and space. After explaining the ecological framework and introducing the history of reaction-diffusion equations in ecology, I will describe how from a classical homogeneous reaction-diffusion equation, we can include the effect of climate change and weak Allee effect in the model. Then the main question will be to understand whether the population vanishes or spreads depending on the values of some parameters of the problem and prove that the behaviour of the solution is different from what is known in the case of reaction-diffusion equations with no Allee effect.