Large population limits for a mutation-selection Moran model

par Josué Corujo

vendredi 7 avr. 2023, 11:00 → 12:00 Europe/Paris

Salle K. Johnson (Institut de Mathématiques de Toulouse)

During this talk we will cover some recent results on a mutation-selection multi-allelic Moran model. This model is a continuous-time Markov chain describing the evolution of the allelic types of individuals in a constant-size population, which interacts according to two different mechanisms. First, a mutation process, where individuals change their types independently among them, and second, a Moran type reproduction process, when one individual dies and another reproduces. This reproduction process makes the evolution of the individuals no longer independent and complexes the mathematical study of this model. Our results include a uniform in time bound for the convergence of the proportion of individuals of each type, when the size of the population is large, and also a study of the fluctuations of this convergence. Additionally, we will also comment on the interpretation of this Moran model as a particle process whose empirical probability measure approximates a quasi-stationary distribution, in the same spirit as the Fleming–Viot particle systems.

This talk is based on the paper https://doi.org/10.1016/j.spa.2022.09.006, a work in collaboration with Bertrand Cloez.