$\Lambda$-Seed-Bank-Wright-Fisher process conditioned on fixation
Abstract
We investigate the -Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this process on the eventual fixation of a specified genetic type. The resulting process is again a -Wright-Fisher process with a seed bank, but now features coordinated mutations driven by a random switching environment. Our analysis relies on two key techniques: the lookdown construction and sampling duality. These tools provide a pathwise construction of the conditioned process while preserving a means to recover the conditioned population genealogy. The resulting genealogy corresponds to a structured -coalescent with coordinated mutations determined by the switching environment.
Cite
@article{arxiv.2511.20483,
title = {$\Lambda$-Seed-Bank-Wright-Fisher process conditioned on fixation},
author = {María Clara Fittipaldi and Adrián González Casanova and Julio Ernesto Nava Trejo},
journal= {arXiv preprint arXiv:2511.20483},
year = {2025}
}