Institut de Mathématiques de Toulouse

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Séminaire Etudiant

par Baptiste Fedele, jade nardi, Maylis Varvenne - publié le , mis à jour le

  • Jeudi 21 mars 14:00-15:00 - Susely Figueroa - Institut de Mathématiques de Toulouse

    Evolutionary dynamics for phenotypically structured populations in fluctuating environments

    Résumé : I will present the long-term behaviour of a Lotka-Volterra parabolic equation by considering a time-periodic reaction term and a non-local competition. Such an equation describes the dynamics of a phenotypically structured population under the effect of mutations and selection in a fluctuating environment. We prove that the solution of this equation converges in long time to the only periodic solution of the problem that I will then describe asymptotically when the effect of the mutations vanishes. Using a theory based on Hamilton-Jacobi equations with constraint, we prove that the solution concentrates on a single Dirac mass, while the size of the population varies periodically in time. When the effect of mutations is small but non zero, these results can be compared to biological experiments, taking the growth rate in several ways. In particular, I propose to focus at the end, on the impact of climate change on this type of population.