A population model for $Λ$-coalescents with neutral mutations

Details A population model for $Λ$-coalescents with neutral mutations A population model for $Λ$-coalescents with neutral mutations

2007-02-13

arxiv.org/abs/math/0702367v1

Electronic Communications in Probability 12(2007), 9-20

Mathematics

Probability

15 pages, 4 figures. This version differs in pagination from the published version

Scientific paper

Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $\Lambda$-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by M{\"o}hle (2007).

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