Speaker: Likai Jiao, Humboldt–Universit¨at zu Berlin
Title: Continuum seed-bank model
Language: Chinese
Time & Venue: 2024.04.26 15:00-16:00 N620
Abstract: In this talk, we introduce the continuum seed-bank model which is a natural generalization of Blath et al. (2016) and Greven, den Hollander, et al. (2022) to accommodate more general dormancy time distributions, such as a type of Pareto distribution. To this end, we first formulate an infinite-dimensional SDE and show that it has a unique strong solution, referred to as the continuum seed-bank diffusion. This diffusion process serves as a Markovian lift of a non-Markovian Volterra process. We construct a discretetime Wright-Fisher type model with finitely many seed-banks, and demonstrate that the continuum seed-bank diffusion, under the weak-⋆ topology, is the scaling limit of the allele frequency process in a suitable sequence of such models. Furthermore, we establish a duality relation between the continuum seed-bank diffusion and a continuous-time and -state Markov jump process. The latter is the block counting process of a partition-valued Markov jump process, referred to as the continuum seed-bank coalescent. We discuss some basic properties of the coalescent process such as scaling limit interpretation, exchangeability, limiting distribution of the ancestral line, and comparisons of E[TMRCA]. We prove that E[TMRCA] is finite if and only if the expected dormancy time is finite. As a byproduct, we also derive the limiting distribution of the continuum seed-bank diffusion. Additionally, we show that the continuum seed-bank coalescent does not come down from infinity, and provide asymptotic bounds of E[TMRCA] in certain special cases.
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