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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