Séance Séminaire

Séminaire de Probabilités et Statistique

Spectral properties of a neutral multi-allelic Moran model (Séminaire SupAgro)

We will present some results on a neutral multi-allelic Moran model, which is a finite continuous-time Markov process. The individuals interact according to two processes: a mutation process where they mutate independently of each other according to an irreducible rate matrix, and a Moran type reproduction process, where two individuals are uniformly chosen, one dies and the other is duplicated. During this talk we will discuss some recent results on the spectrum of the neutral multi-allelic Moran process and we will provide explicit expressions for its eigenvalues as function of the eigenvalues of the rate matrix that drives the mutation process. Our approach does not require that the mutation process be reversible, or even that the mutation matrix be diagonalizable. Additionally, we will discuss some applications of these results to the study of the speed of convergence to stationarity of the Moran process. This presentation is based on a recently submitted work, for which a preprint is available at https://arxiv.org/abs/2010.08809.

WEBINAIRE ouvert à toutes et tous : https://umontpellier-fr.zoom.us/j/85813807839