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: email@example.com
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.