Electronic Journal of Probability

A New Model for Evolution in a Spatial Continuum

Nick Barton, Alison Etheridge, and Amandine Véber

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Abstract

We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans (1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of sidelength L as L tends to infinity. Under appropriate conditions (and on a suitable timescale) we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).

Article information

Source
Electron. J. Probab. Volume 15 (2010), paper no. 7, 162-216.

Dates
Accepted: 3 February 2010
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819792

Digital Object Identifier
doi:10.1214/EJP.v15-741

Mathematical Reviews number (MathSciNet)
MR2594876

Zentralblatt MATH identifier
1203.60107

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 92D10: Genetics {For genetic algebras, see 17D92} 92D15: Problems related to evolution

Keywords
genealogy evolution multiple merger coalescent spatial continuum spatial Lambda-coalescent generalised Fleming-Viot process

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

Citation

Barton, Nick; Etheridge, Alison; Véber, Amandine. A New Model for Evolution in a Spatial Continuum. Electron. J. Probab. 15 (2010), paper no. 7, 162--216. doi:10.1214/EJP.v15-741. https://projecteuclid.org/euclid.ejp/1464819792.


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