Electronic Communications in Probability

A population model for $\Lambda$-coalescents with neutral mutations

Andreas Lagerås

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Abstract

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 Möhle (2007).

Article information

Source
Electron. Commun. Probab., Volume 12 (2007), paper no. 2, 9-20.

Dates
Accepted: 4 February 2007
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465224945

Digital Object Identifier
doi:10.1214/ECP.v12-1245

Mathematical Reviews number (MathSciNet)
MR2284043

Zentralblatt MATH identifier
1130.60057

Subjects
Primary: 60G09: Exchangeability
Secondary: 60G57: Random measures 92D25: Population dynamics (general)

Keywords
population model coalescent mutations exchangeability sampling formula

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Lagerås, Andreas. A population model for $\Lambda$-coalescents with neutral mutations. Electron. Commun. Probab. 12 (2007), paper no. 2, 9--20. doi:10.1214/ECP.v12-1245. https://projecteuclid.org/euclid.ecp/1465224945


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References

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