WIAS Preprint No. 3053, (2023)

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


Authors

  • Kern, Julian
    ORCID: 0000-0002-8231-0736
  • Wiederhold, Bastian

2020 Mathematics Subject Classification

  • 60J25 60G51 60J90

Keywords

  • Fleming-Viot, Λ-Fleming-Viot, Wright-Fisher, measure-valued Markov process, martingale probem, lookdown construction, coalescent, Markov Mapping Theorem, varying population size, Lévy process

Abstract

We propose an extension of the classical ?-Fleming-Viot model to intrinsically varying pop- ulation 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 el- ementary 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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