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The Λ-lookdown model with selection

Author

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  • Bah, B.
  • Pardoux, E.

Abstract

The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the Λ-coalescent. In particular we formulate the infinite population “Λ-lookdown model with selection”. When the measure Λ gives no mass to 0, we show that the proportion of one of the two types converges, as the population size N tends to infinity, towards the solution to a stochastic differential equation driven by a Poisson point process. We show that one of the two types fixates in finite time if and only if the Λ-coalescent comes down from infinity. We give precise asymptotic results in the case of the Bolthausen–Sznitman coalescent. We also consider the general case of a combination of the Kingman and the Λ-lookdown model.

Suggested Citation

  • Bah, B. & Pardoux, E., 2015. "The Λ-lookdown model with selection," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1089-1126.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:3:p:1089-1126
    DOI: 10.1016/j.spa.2014.10.014
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    Cited by:

    1. Bjarki Eldon, 2023. "Viability Selection at Linked Sites," Mathematics, MDPI, vol. 11(3), pages 1-23, January.

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