Multidimensional Λ-Wright-Fisher processes with general frequency-dependent selection

2019/03/15 by Adrián González Casanova, Casanova, Adrian Gonzalez, Charline Smadi +1
Mathematics · Medicine · Social Sciences · #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1903.06406

openalex publication_date 2019/03/15 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample potential parents in the previous generation before choosing the 'strongest' one, by allowing individuals to use any rule to choose their real parent. Via a large population limit, we obtain a generalisation of Λ-Fleming Viot processes allowing for non transitive interactions between types. We provide fixation properties, and give conditions for these processes to be realised as solutions of stochastic differential equations.

Related

• Duality and Fixation in Ξ-Wright-Fisher processes with frequency-dependent selection
• Λ-Wright--Fisher processes with general selection and opposing environmental effects: fixation and coexistence
• The Lambda-Fleming-Viot process and a connection with Wright-Fisher diffusion
• The spatial Λ-Fleming-Viot process in a random environment
• On the boundary classification of Λ-Wright-Fisher processes with frequency-dependent selection