Modélisation probabiliste et éco-évolution d'une population diploïde

Abstract : We study the random modeling and the genetic evolution of diploid populations, in an eco-evolutionary context. The population is always modeled by a multi-type birth-and-death process with interaction and whose birth rates are designed to model Mendelian reproduction. In particular, the population size is not assumed to be constant, and can be small. In a first part, we provide a probabilistic study of the mutational meltdown, a phenomenon in which the size of a small population decreases more and more rapidly due to more and more frequent fixations of deleterious mutations. We give a formula for the fixation probability of a slightly deleterious allele, as a function of the initial genetic composition of the population and we prove the existence of a mutational meltdown under a rare mutations hypothesis. Besides, we give numerical results and detailed biological interpretations of the observed behaviors. In particular, we study the impact of the mutational meltdown on the mean population size dynamics and we quantify this phenomenon in terms of demographic parameters. In a second part, under an approximation of large population size and frequent birth and death events, we first study the convergence toward a slow-fast stochastic dynamics and the quasi-stationary behavior of a diploid population characterized by its genetic composition at one bi-allelic locus. In particular, we study the possibility of a long time coexistence of the two alleles in the population conditioned on non extinction. Next, we generalize this slow-fast dynamics for a population presenting an arbitrary finite number of alleles. The population is finally modeled by a measure-valued stochastic process that converges when the number of alleles goes to infinity, toward a generalized Fleming-Viot superprocess with randomly evolving population size and diploid additive selection.
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https://pastel.archives-ouvertes.fr/pastel-00918257
Contributor : Camille Coron <>
Submitted on : Friday, December 13, 2013 - 10:55:10 AM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
Long-term archiving on : Friday, March 14, 2014 - 2:55:22 AM

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Camille Coron. Modélisation probabiliste et éco-évolution d'une population diploïde. Probabilités [math.PR]. Ecole Polytechnique X, 2013. Français. ⟨pastel-00918257⟩

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