Electronic Journal of Probability

Coalescent processes in subdivided populations subject to recurrent mass extinctions

Jesse Taylor and Amandine Véber

Full-text: Open access

Abstract

We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population that experiences sporadic mass extinction events. By exploiting a separation of time scales that occurs within a class of structured population models generalizing Wright's island model, we show that as the number of demes tends to infinity, the limiting form of the genealogy can be described in terms of the alternation of instantaneous scattering phases that depend mainly on local demographic processes, and extended collecting phases that are dominated by global processes. When extinction and recolonization events are local, the genealogy is described by Kingman's coalescent, and the scattering phase influences only the overall rate of the process. In contrast, if the demes left vacant by a mass extinction event are recolonized by individuals emerging from a small number of demes, then the limiting genealogy is a coalescent process with simultaneous multiple mergers (a $\Xi$-coalescent). In this case, the details of the within-deme population dynamics influence not only the overall rate of the coalescent process, but also the statistics of the complex mergers that can occur within sample genealogies. These results suggest that the combined effects of geography and disturbance could play an important role in producing the unusual patterns of genetic variation documented in some marine organisms with high fecundity.

Article information

Source
Electron. J. Probab. Volume 14 (2009), paper no. 9, 242-288.

Dates
Accepted: 29 January 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819470

Digital Object Identifier
doi:10.1214/EJP.v14-595

Mathematical Reviews number (MathSciNet)
MR2471665

Zentralblatt MATH identifier
1190.60066

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J75: Jump processes

Keywords
genealogy Xi-coalescent extinction/recolonization disturbance metapopulation population genetics separation of time scales

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Taylor, Jesse; Véber, Amandine. Coalescent processes in subdivided populations subject to recurrent mass extinctions. Electron. J. Probab. 14 (2009), paper no. 9, 242--288. doi:10.1214/EJP.v14-595. https://projecteuclid.org/euclid.ejp/1464819470.


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