Uniform in time propagation of chaos for a Moran model

This article studies the limit of the empirical distribution induced by a mutation-selection multi-allelic Moran model. Our results include a uniform in time bound for the propagation of chaos in Lp of order N, and the proof of the asymptotic normality with zero mean and explicit variance, when the number of individuals tend towards infinity, for the approximation error between the empirical distribution and its limit. Additionally, we explore 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.