A $\Lambda$-Fleming-Viot type model with intrinsically varying population size
Abstract
We propose an extension of the classical -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 -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.
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}
}