Dynamics of concentration in a population model structured by age and a phenotypical trait.

vendredi 17 mai 2019, 11h00 - 12h00

We study a mathematical model describing the growth process of a population subject to aging, competition between individuals and rare non-local mutations. Our goal is to describe the asymptotic behavior of the population. In a short time scale, the population density concentrates around the fittest traits i.e it converges to a Dirac mass in the trait variable when a rescaling parameter $\epsilon$ tends to $0$. On a longer time scale, the Dirac mass converges to an evolutionary stable state.
We begin with a model without mutations, much simpler, which allows us to introduce the main ideas and state the full result. Then we discuss the general model and its limits.