We consider a (sub-)critical GaltonWatson process with neutral muta-
tions (infinite alleles model), and decompose the entire population into clus-
ters 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 GaltonWatson processes and a version
of the ballot theorem. Some limit theorems related to the distribution of the
allelic partition are also given.
Beschreibung
MR: Publications results for "MR Number=(2546753)"
%0 Journal Article
%1 MR2546753
%A Bertoin, Jean
%D 2009
%J Ann. Probab.
%K branching_processes ewens_sampling_formula neutral_variation partitions
%N 4
%P 1502--1523
%R 10.1214/08-AOP441
%T The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations
%U http://dx.doi.org/10.1214/08-AOP441
%V 37
%X We consider a (sub-)critical GaltonWatson process with neutral muta-
tions (infinite alleles model), and decompose the entire population into clus-
ters 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 GaltonWatson processes and a version
of the ballot theorem. Some limit theorems related to the distribution of the
allelic partition are also given.
@article{MR2546753,
abstract = { We consider a (sub-)critical GaltonWatson process with neutral muta-
tions (infinite alleles model), and decompose the entire population into clus-
ters 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 GaltonWatson processes and a version
of the ballot theorem. Some limit theorems related to the distribution of the
allelic partition are also given.
},
added-at = {2009-11-19T18:49:39.000+0100},
author = {Bertoin, Jean},
biburl = {https://www.bibsonomy.org/bibtex/25c1a3a7879fe385019cc39dfb0466882/peter.ralph},
coden = {APBYAE},
description = {MR: Publications results for "MR Number=(2546753)"},
doi = {10.1214/08-AOP441},
fjournal = {The Annals of Probability},
interhash = {177b89240823bedfa449c7e977ecbec1},
intrahash = {5c1a3a7879fe385019cc39dfb0466882},
issn = {0091-1798},
journal = {Ann. Probab.},
keywords = {branching_processes ewens_sampling_formula neutral_variation partitions},
mrclass = {60J80},
mrnumber = {MR2546753},
number = 4,
pages = {1502--1523},
timestamp = {2009-11-19T18:49:39.000+0100},
title = {The structure of the allelic partition of the total population for {G}alton-{W}atson processes with neutral mutations},
url = {http://dx.doi.org/10.1214/08-AOP441},
volume = 37,
year = 2009
}