Recursions for a class of sampling distributions of allele configurations are derived for the situation where the genealogy of the underlying population is modelled by a coalescent process with simultaneous multiple collisions of ancestral lineages. These recursions describe a new family of partition structures in terms of the composition probability function, parametrized by the infinitesimal rates of the coalescent process. For the Kingman coalescent process with only binary mergers of ancestral lines, the recursion reduces to that known for the classical Ewens sampling distribution. We solve the recursion for the star-shaped coalescent. The asymptotic behaviour of the number Kn of alleles (types) for large sample size n is studied, in particular for the star-shaped coalescent and the Bolthausen-Sznitman coalescent.
Publié le : 2006-02-14
Classification:
Bolthausen-Sznitman coalescent,
composition probability function,
Ewens sampling formula,
mutation rate,
neutral infinite alleles model,
partition structure,
sampling distribution,
simultaneous multiple collisions,
star-shaped tree
@article{1141136647,
author = {M\"ohle, M.},
title = {On sampling distributions for coalescent processes with simultaneous multiple collisions},
journal = {Bernoulli},
volume = {12},
number = {2},
year = {2006},
pages = { 35-53},
language = {en},
url = {http://dml.mathdoc.fr/item/1141136647}
}
Möhle, M. On sampling distributions for coalescent processes with simultaneous multiple collisions. Bernoulli, Tome 12 (2006) no. 2, pp. 35-53. http://gdmltest.u-ga.fr/item/1141136647/