The deterministic limit of the Moran model: a uniform central limit theorem
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Publication:4596938
zbMATH Open1379.92035arXiv1508.05231MaRDI QIDQ4596938
Author name not available (Why is that?)
Publication date: 11 December 2017
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 . As a consequence, we deduce the convergence of the corresponding stationary distributions.
Full work available at URL: https://arxiv.org/abs/1508.05231
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