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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 2 open journal systems 


A population model for Λ-coalescents with neutral mutations

Andreas Nordvall Lagerås, Department of Mathematics, Stockholm University


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 Λ-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).


Full text: PDF

Pages: 9-20

Published on: February 4, 2007
Bibliography
  1. Bertoin, J. and Le Gall, J.-F. (2003). Stochastic flows associated to coalescent processes. Probability Theory and Related Fields 126, 261–288. MR1990057
  2. Dong, R., Gnedin, A. and Pitman, J. (2006). Exchangeable partitions derived from Markovian coalescents. Preprint arXiv:math.PR/0603745 v1
  3. Gnedin, A. and Pitman, J. (2005). Regenerative composition structures. Annals of Probability 33(2), 445–479. MR2122798
  4. Kingman, J.F.C. (1982). The coalescent. Stochastic Processes and their Applications 13, 235–248. MR0671034
  5. Kingman, J.F.C. (1993). Poisson Processes. Oxford University Press, New York. MR1207584
  6. Möhle, M. (2006). On sampling distributions for coalescent processes with simultaneous multiple collisions. Bernoulli 12(1), 35–53. MR2202319
  7. Möhle, M. (2007). On a class of non-regenerative sampling distributions. Forthcoming in Combinatorics, Probability and Computing. doi:10.1017/S0963548306008212
  8. Möhle, M. and Sagitov, S. (2001). A classification of coalescent processes for haploid exchangeable population models. Annals of Probability 29(4), 1547–1562. MR1880231
  9. Pitman, J. (1999). Coalescents with multiple collisions. Annals of Probability 27(4), 1870–1902. MR1742892
  10. Sagitov, S. (1999). The general coalescent with asynchronous mergers of ancestral lines. Journal of Applied Probability 36(4), 1116–1125. MR1742154
  11. Schweinsberg, J. (2000). Coalescents with simultaneous multiple collisions. Electronic Journal of Probability 5, paper 12. MR1781024
















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Electronic Communications in Probability. ISSN: 1083-589X