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

Apolline Louvet (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Mots clés: spatial Lambda-Fleming-Viot process; range expansion; duality; genealogies; population genetics; limiting process; spatial Lambda-Fleming-Viot process

Domaines: Probabilités [math.PR]

Apolline Louvet. The k-parent spatial Lambda-Fleming-Viot process as a stochastic measure-valued model for an expanding population. 2021. ⟨hal-03154662v1⟩