Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Stochastic measure-valued models for populations expanding in a continuum (2103.02902v3)

Published 4 Mar 2021 in math.PR

Abstract: We model spatially expanding populations by means of two spatial $\Lambda$-Fleming Viot processes (or SLFVs) with selection: the k-parent SLFV and the $\infty$-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 $\rightarrow$ +$\infty$, the limiting process, corresponding to the $\infty$-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 $\infty$-parent SLFV, and show that it corresponds to the limit of the k-parent SLFV when k $\rightarrow$ +$\infty$. 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 $\infty$-parent SLFV, which are valid in different settings and link together population genetics models and stochastic growth models.

Summary

We haven't generated a summary for this paper yet.