English

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

Probability 2023-11-13 v1

Abstract

We propose an extension of the classical Λ\Lambda-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\Lambda-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.

Keywords

Cite

@article{arxiv.2311.06100,
  title  = {A $\Lambda$-Fleming-Viot type model with intrinsically varying population size},
  author = {Julian Kern and Bastian Wiederhold},
  journal= {arXiv preprint arXiv:2311.06100},
  year   = {2023}
}
R2 v1 2026-06-28T13:17:24.204Z