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On the extended Moran model and its relation to coalescents with multiple collisions

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  • Huillet, Thierry
  • Möhle, Martin

Abstract

We study the asymptotics of the extended Moran model as the total population size N tends to infinity. Two convergence results are provided, the first result leading to discrete-time limiting coalescent processes and the second result leading to continuous-time limiting coalescent processes. The limiting coalescent processes allow for multiple mergers of ancestral lineages (Λ-coalescent). It is furthermore verified that any continuous time Λ-coalescent (with Λ any probability distribution) can arise in the limit. Typical examples of extended Moran models are discussed, with an emphasis on models being in the domain of attraction of beta coalescents or Λ-coalescents with Λ being log infinitely divisible.

Suggested Citation

  • Huillet, Thierry & Möhle, Martin, 2013. "On the extended Moran model and its relation to coalescents with multiple collisions," Theoretical Population Biology, Elsevier, vol. 87(C), pages 5-14.
    • Handle: RePEc:eee:thpobi:v:87:y:2013:i:c:p:5-14
    DOI: 10.1016/j.tpb.2011.09.004
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    1. Bertoin, J. & van Harn, K. & Steutel, F. W., 1999. "Renewal theory and level passage by subordinators," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 65-69, October.
    2. Schweinsberg, Jason, 2003. "Coalescent processes obtained from supercritical Galton-Watson processes," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 107-139, July.
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    Cited by:

    1. Kukla, Jonas & Möhle, Martin, 2018. "On the block counting process and the fixation line of the Bolthausen–Sznitman coalescent," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 939-962.

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