Volume 27, 2023
|Page(s)||221 - 277|
|Published online||20 January 2023|
Stochastic measure-valued models for populations expanding in a continuum
1 MAP5, Université Paris Cité,
45 rue des Saints-Pères,
2 CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
* Corresponding author: firstname.lastname@example.org
Accepted: 9 December 2022
We model spatially expanding populations by means of two spatial Λ-Fleming Viot processes (or SLFVs) with selection: the k-parent SLFV and the ∞-parent SLFV. In order to do so, we fill empty areas with type 0 “ghost” individuals with a strong selective disadvantage against “real” type 1 individuals, quantified by a parameter k. The reproduction of ghost individuals is interpreted as local extinction events due to stochasticity in reproduction. When k → +∞, the limiting process, corresponding to the ∞-parent SLFV, is reminiscent of stochastic growth models from percolation theory, but is associated to tools making it possible to investigate the genetic diversity in a population sample. In this article, we provide a rigorous construction of the ∞-parent SLFV, and show that it corresponds to the limit of the k-parent SLFV when k → +∞. In order to do so, we introduce an alternative construction of the k-parent SLFV which allows us to couple SLFVs with different selection strengths and is of interest in its own right. We exhibit three different characterizations of the ∞-parent SLFV, which are valid in different settings and link together population genetics models and stochastic growth models.
Mathematics Subject Classification: 60G57 / 60J25 / 92D10 / 60J76 / 92D25
Key words: Spatial Lambda-Fleming-Viot process / range expansion / duality / genealogies / population genetics / limiting process
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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