Electronic Journal of Probability

The seed bank coalescent with simultaneous switching

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

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We introduce a new Wright-Fisher type model for seed banks incorporating “simultaneous switching”, which is motivated by recent work on microbial dormancy ([21], [28]). We show that the simultaneous switching mechanism leads to a new jump-diffusion limit for the scaled frequency processes, extending the classical Wright-Fisher and seed bank diffusion limits. We further establish a new dual coalescent structure with multiple activation and deactivation events of lineages. While this seems reminiscent of multiple merger events in general exchangeable coalescents, it actually leads to an entirely new class of coalescent processes with unique qualitative and quantitative behaviour. To illustrate this, we provide a novel kind of condition for coming down from infinity for these coalescents, applying a recent approach of Griffiths [12].

Article information

Electron. J. Probab., Volume 25 (2020), paper no. 27, 21 pp.

Received: 14 February 2019
Accepted: 8 December 2019
First available in Project Euclid: 21 February 2020

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

seed banks dormancy coalescent simultaneous switching coming down from infinity

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Blath, Jochen; González Casanova, Adrián; Kurt, Noemi; Wilke-Berenguer, Maite. The seed bank coalescent with simultaneous switching. Electron. J. Probab. 25 (2020), paper no. 27, 21 pp. doi:10.1214/19-EJP401. https://projecteuclid.org/euclid.ejp/1582254383

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