DEL MORAL, Pierre; MICLO, Laurent; PATRAS, Frédéric; RUBENTHALER, Sylvain

doi:10.1080/07362990903415833

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DEL MORAL, Pierre
Laboratoire Jean Alexandre Dieudonné [JAD]
Applications of interacting particle systems to statistics [ASPI]

MICLO, Laurent
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

PATRAS, Frédéric
Laboratoire Jean Alexandre Dieudonné [JAD]

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Stochastic Analysis and Applications. 2009, vol. 28, n° 1, p. 123-143

Taylor & Francis: STM, Behavioural Science and Public Health Titles

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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.< Réduire

Mots clés en anglais

Lyapunov exponent

coalescent trees

Wright-Fisher model

neutral genetic models

stationary distribution

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The convergence to equilibrium of neutral genetic models

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