Populations structured by phenotype: models for natural selection and adaptive dynamics
vendredi 18 octobre 2019, 11h00 - 12h00
We aim to describe the asymptotic behaviour of a population structured by phenotype, subject to competition between individuals. In a short time scale, we observe a selection phenomenon, i.e., the population density concentrates around the fittest phenotype. On a longer time scale, we observe the adaptive dynamics, i.e., the fittest phenotype evolves (and eventually converges).
We begin with a toy example to introduce the well known « Hamilton-Jacobi » approach. Then, we consider a population which is also structured by age, and explain how to adapt the method. Finally, we discuss the much more intricate model where we add the effect of (non-local) mutations. This last model features a highly non-linear and non-local Hamilton-Jacobi equation. Our main result is that we identify both the singular part and the corrector in the limiting population. (Joint work with B.Perthame and C.Taing)