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April 2016 A new coalescent for seed-bank models
Jochen Blath, Adrián González Casanova, Noemi Kurt, Maite Wilke-Berenguer
Ann. Appl. Probab. 26(2): 857-891 (April 2016). DOI: 10.1214/15-AAP1106

Abstract

We identify a new natural coalescent structure, which we call the seed-bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where “dormant forms” of individuals (such as seeds or spores) may jump a significant number of generations before joining the “active” population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright–Fisher model with geometric seed-bank age structure if the average time of seed dormancy scales with the order of the total population size $N$. This extends earlier results of Kaj, Krone and Lascoux [J. Appl. Probab. 38 (2011) 285–300] who show that the genealogy of a Wright–Fisher model in the presence of a “weak” seed-bank effect is given by a suitably time-changed Kingman coalescent. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. In particular, the seed-bank coalescent “does not come down from infinity,” and the time to the most recent common ancestor of a sample of size $n$ grows like $\log\log n$. This is in line with the empirical observation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.

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Jochen Blath. Adrián González Casanova. Noemi Kurt. Maite Wilke-Berenguer. "A new coalescent for seed-bank models." Ann. Appl. Probab. 26 (2) 857 - 891, April 2016. https://doi.org/10.1214/15-AAP1106

Information

Received: 1 November 2014; Revised: 1 February 2015; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1339.60137
MathSciNet: MR3476627
Digital Object Identifier: 10.1214/15-AAP1106

Subjects:
Primary: 60K35
Secondary: 92D10

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 2016
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