HAL - INRIA :: [inria-00239259, version 3] The convergence to equilibrium of neutral genetic models

inria-00239259, version 3

The convergence to equilibrium of neutral genetic models

Pierre Del Moral () ^1, 2, Laurent Miclo () ³, Frédéric Patras ()^a^, 4, Sylvain Rubenthaler ()^a^, 4

Stochastic Analysis and Applications 28, 1 (2009) 123-143

Résumé : 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.

a – Université de Nice Sophia-Antipolis
1 : Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
2 : ALEA (INRIA Bordeaux - Sud-Ouest)
INRIA – Université de Bordeaux – CNRS : UMR5251
3 : Laboratoire d'Analyse, Topologie, Probabilités (LATP)
CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
4 : Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)

inria-00239259, version 3
http://hal.inria.fr/inria-00239259
oai:hal.inria.fr:inria-00239259
Contributeur : Pierre Del Moral <>
Soumis le : Mercredi 13 Février 2008, 10:05:10
Dernière modification le : Mercredi 17 Novembre 2010, 17:38:34

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