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Pré-Publication, Document De Travail Année : 2010

Population genetics models with skewed fertilities: a forward and backward analysis

Résumé

Discrete population genetics models with unequal fertilities are considered, with an emphasis on skewed Cannings models, skewed conditional branching process models in the spirit of Karlin and McGregor, and skewed compound Poisson models. Three particular classes of models with skewed fertilities are investigated, the skewed Wright-Fisher model, the skewed Dirichlet model, and the skewed Kimura model. For each class the asymptotic behavior as the total population size $N$ tends to infinity is investigated for power law fertilities and for geometric fertilities. This class of models can exhibit a rich variety of sub-linear or even constant effective population sizes. Therefore, the models are not even necessarily in the domain of attraction of the Kingman coalescent. For a substantial range of the parameters, discrete-time coalescent processes with simultaneous multiple collisions arise in the limit.
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Dates et versions

hal-00525959 , version 1 (13-10-2010)
hal-00525959 , version 2 (12-04-2011)

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  • HAL Id : hal-00525959 , version 1

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Thierry Huillet, Martin Moehle. Population genetics models with skewed fertilities: a forward and backward analysis. 2010. ⟨hal-00525959v1⟩
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