The Annals of Applied Probability

A new coalescent for seed-bank models

Jochen Blath, Adrián González Casanova, Noemi Kurt, and Maite Wilke-Berenguer

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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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 2 (2016), 857-891.

Dates
Received: November 2014
Revised: February 2015
First available in Project Euclid: 22 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1458651822

Digital Object Identifier
doi:10.1214/15-AAP1106

Mathematical Reviews number (MathSciNet)
MR3476627

Zentralblatt MATH identifier
1339.60137

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 92D10: Genetics {For genetic algebras, see 17D92}

Keywords
Wright–Fisher model seed-bank coalescent coming down from infinity age structure

Citation

Blath, Jochen; González Casanova, Adrián; Kurt, Noemi; Wilke-Berenguer, Maite. A new coalescent for seed-bank models. Ann. Appl. Probab. 26 (2016), no. 2, 857--891. doi:10.1214/15-AAP1106. https://projecteuclid.org/euclid.aoap/1458651822


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