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.
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