The Convergence to Equilibrium of Neutral Genetic Models |
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Authors: | P Del Moral L Miclo F Patras S Rubenthaler |
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Institution: | 1. Centre INRIA Bordeaux Sud-Ouest &2. Institut de Mathématiques de Bordeaux , Université Bordeaux I , Talence , France miclo@latp.univ-mrs.fr;4. CNRS UMR 5219 , Institut de Mathématiques de Toulouse, Laboratoire de Statistiques et Probabilités , Toulouse , France;5. CNRS UMR 21, Laboratoire de Mathématiques J. Dieudonné , Université de Nice , Nice , France |
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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 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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Keywords: | Coalescent trees Lyapunov exponent Neutral genetic models Stationary distribution Wright–Fisher model |
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