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

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

10 Nov 2023arXiv:2311.06100links table onlyarchive 2025-07-28

Julian Kern, Bastian Wiederhold

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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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