Asymptotic analysis of an integro-differential model from quantitative genetics

by Sepideh Mirrahimi

Tuesday Jun 10, 2025, 11:15 AM → 12:15 PM Europe/Paris

Salle J. Cavailles (IMT)

We provide an asymptotic analysis of a nonlinear integro-differential equation which describes the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is modeled via a nonlinear integral term, known as the 'infinitesimal model'. Considering a   small  variance regime, we prove that the phenotypic distribution remains close to a Gaussian profile with a fixed small variance and we characterize the dynamics of the mean phenotypic trait via an ordinary differential equation. While similar properties were already proved for a closely related model using a Hopf-Cole transformation and perturbative analysis techniques, we provide an alternative proof which simplifies considerably the analysis. Our method relies on a direct study of the dynamics of the moments of the phenotypic distribution and a Lipschitz property of the Wasserstein distance. This is a joint work with J. Guerand and M. Hillairet.