HAL : hal-00525959, version 2

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Stochastic Models 27, 3 (2011) 521-554

Versions disponibles :

v1 (13-10-2010)

v2 (12-04-2011)

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

Thierry Huillet (  Auteur correspondant ) 1, Martin Moehle 2

(18/08/2011)

Discrete population genetics models with unequal (skewed) fertilities are considered, with an emphasis on skewed versions of Cannings models, conditional branching process models in the spirit of Karlin and McGregor, and compound Poisson models. Three particular classes of models with skewed fertilities are investigated, the Wright-Fisher model, the Dirichlet model, and the 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 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.

1 :	Laboratoire de Physique Théorique et Modélisation (LPTM)
	CNRS : UMR8089 – Université de Cergy Pontoise
2 :	Mathematisches Institut
	Tübingen Universität - Tübingen University

Domaine

:

Mathématiques/Probabilités Sciences du Vivant/Bio-Informatique, Biologie Systémique Informatique/Bio-informatique

Mots Clés : Ancestral process – Cannings model – Compound Poisson model – Dirichlet model – Dirichlet-Kingman coalescent – Duality – Evolutionary processes – Exchangeable coalescent – Karlin and McGregor model – Kimura model – Kingman coalescent – Population dynamics – Simultaneous multiple collisions – Wright-Fisher model

hal-00525959, version 2

http://hal.archives-ouvertes.fr/hal-00525959

oai:hal.archives-ouvertes.fr:hal-00525959

Contributeur : Thierry Huillet <>

Soumis le : Mardi 12 Avril 2011, 11:24:31

Dernière modification le : Mercredi 24 Août 2011, 13:05:32