The convergence to equilibrium of neutral genetic models
DEL MORAL, Pierre
Laboratoire Jean Alexandre Dieudonné [JAD]
Applications of interacting particle systems to statistics [ASPI]
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Laboratoire Jean Alexandre Dieudonné [JAD]
Applications of interacting particle systems to statistics [ASPI]
DEL MORAL, Pierre
Laboratoire Jean Alexandre Dieudonné [JAD]
Applications of interacting particle systems to statistics [ASPI]
< Reduce
Laboratoire Jean Alexandre Dieudonné [JAD]
Applications of interacting particle systems to statistics [ASPI]
Language
en
Article de revue
This item was published in
Stochastic Analysis and Applications. 2009, vol. 28, n° 1, p. 123-143
Taylor & Francis: STM, Behavioural Science and Public Health Titles
English 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 ...Read more >
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.Read less <
English Keywords
Lyapunov exponent
coalescent trees
Wright-Fisher model
neutral genetic models
stationary distribution
Origin
Hal imported