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The k-parent spatial Lambda-Fleming-Viot process as a stochastic measure-valued model for an expanding population

Abstract : We model spatially expanding populations by means of a spatial Λ-Fleming Viot process (SLFV) with selection : the k-parent SLFV. We fill empty areas with type 0 "ghost" individuals, which have a strong selective disadvantage against "real" type 1 individuals. This model is a special case of the SLFV with selection introduced in [19, 22] : natural selection acts during all reproduction events, and the fraction of individuals replaced during a reproduction event is constant equal to 1. Letting the selective advantage k of type 1 individuals over type 0 individuals grow to +∞, and without rescaling time nor space, we obtain a new model for expanding populations, the ∞-parent SLFV. This model is reminiscent of the Eden growth model [13], but with an associated dual process of potential ancestors, making it possible to investigate the genetic diversity in a population sample. In order to obtain the limit k → +∞ of the k-parent SLFV, we introduce an alternative construction of the k-parent SLFV adapted from [38], which allows us to couple SLFVs with different selection strengths.
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https://hal-univ-paris.archives-ouvertes.fr/hal-03154662
Contributor : Apolline Louvet <>
Submitted on : Wednesday, March 3, 2021 - 3:20:37 PM
Last modification on : Wednesday, June 2, 2021 - 4:26:04 PM

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  • HAL Id : hal-03154662, version 1
  • ARXIV : 2103.02902

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Apolline Louvet. The k-parent spatial Lambda-Fleming-Viot process as a stochastic measure-valued model for an expanding population. 2021. ⟨hal-03154662⟩

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