A limit theorem for trees of alleles in branching processes with rare neutral mutations

Abstract : We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small. We shall establish that for an appropriate regime, the process of the sizes of the allelic sub-families converges in distribution to a certain continuous state branching process (i.e. a Jirina process) in discrete time. Itô's excursion theory and the Léevy-Itô decomposition of subordinators provide fundamental insights for the results.
Type de document :
Pré-publication, Document de travail
2009
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https://hal.archives-ouvertes.fr/hal-00373262
Contributeur : Jean Bertoin <>
Soumis le : jeudi 25 juin 2009 - 10:59:07
Dernière modification le : lundi 29 mai 2017 - 14:25:01
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 13:24:10

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AsymptAllel.pdf
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  • HAL Id : hal-00373262, version 2
  • ARXIV : 0904.0581

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INSMI | UPMC | PSL | USPC | PMA

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Jean Bertoin. A limit theorem for trees of alleles in branching processes with rare neutral mutations. 2009. <hal-00373262v2>

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