A Λ-Fleming-Viot type model with intrinsically varying population size

2023/11/10 by Julian Kern, Kern, Julian, Bastian Wiederhold +1 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #60G51 #60J25 #60J90 #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2311.06100

openalex publication_date 2023/11/10 · openalex created_date 2023/11/14 · openalex updated_date 2026/08/01

Abstract

We propose an extension of the classical Λ-Fleming-Viot model to intrinsically varying population sizes. During events, instead of replacing a proportion of the population, a random mass dies and a, possibly different, random mass of new individuals is added. The model can also incorporate a drift term, representing infinitesimally small, but frequent events. We investigate elementary properties of the model, analyse its relation to the Λ-Fleming-Viot model and describe a duality relationship. Through the lookdown framework, we provide a forward-in-time analysis of fixation and coming down from infinity. Furthermore, we present a new duality argument allowing one to deduce well-posedness of the measure-valued process without the necessity of proving uniqueness of the associated lookdown martingale problem.

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