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

2007/11/24 by Jean Bertoin, Bertoin, Jean · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #60 J 10 #60 J 80 #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Probability (math.PR) #math.PR #msc:10 #msc:60 #msc:80 #q-bio.PE

paper · pdf · doi:10.48550/arxiv.0711.3852

This version corrects a significant mistake in the first one

openalex publication_date 2007/11/24 · arxiv created 2009/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Allele trees for the mother-dependent neutral mutations model and their scaling limits in the rare mutations regime

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