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The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations


Bertoin, Jean (2009). The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. The Annals of Probability, 37(4):1502-1523.

Abstract

We consider a (sub-)critical Galton–Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton–Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition are also given.

Abstract

We consider a (sub-)critical Galton–Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton–Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition are also given.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:15 May 2013 14:49
Last Modified:05 Apr 2016 16:47
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/08-AOP441
Official URL:http://projecteuclid.org/euclid.aop/1248182146
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1180.92063

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