The deterministic limit of the Moran model: a uniform central limit theorem

Abstract

We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or time. We first prove that the latter converges, uniformly in compacts in probability, to the solution of an ordinary differential equation, which is explicitly solved. Next, we study the stability properties of its equilibrium points. Moreover, we show that the fluctuations of the proportion of fit individuals, after a proper normalization, satisfy a uniform central limit theorem in $[0,\infty )$. As a consequence, we deduce the convergence of the corresponding stationary distributions.

Cited by in corpus (7)

• Common ancestor type distribution: a Moran model and its deterministic limit
• A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent
• Lines of descent under selection
• Lines of descent in the deterministic mutation-selection model with pairwise interaction
• Uniform in time propagation of chaos for a Moran model
• On the stationary distribution of the block counting process for population models with mutation and selection
• Solving the selection-recombination equation: Ancestral lines under selection and recombination