The convergence to equilibrium of neutral genetic models

Pierre Del Moral 1, 2 Laurent Miclo 3 Frédéric Patras 1 Sylvain Rubenthaler 1
2 ASPI - Applications of interacting particle systems to statistics
UR1 - Université de Rennes 1, Inria Rennes – Bretagne Atlantique , CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both for finite and infinite types (or alleles) models. We then analyze the decays to the equilibrium of finite populations in terms of the convergence to stationarity of their first common ancestor. We estimate the Lyapunov exponent of the distribution flows with respect to the total variation norm. We give bounds on these exponents only depending on the stability with respect to mutation of a single individual; they are inversely proportional to the population size parameter.
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Pierre Del Moral, Laurent Miclo, Frédéric Patras, Sylvain Rubenthaler. The convergence to equilibrium of neutral genetic models. Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2009, 28 (1), pp.123-143. ⟨10.1080/07362990903415833⟩. ⟨inria-00239259v4⟩

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