A New Model for Evolution in a Spatial Continuum (original) (raw)
2010 A New Model for Evolution in a Spatial Continuum
Nick Barton,Alison Etheridge,Amandine Véber
Author Affiliations +
Nick Barton,1 Alison Etheridge,2 Amandine Véber3
1Institute of Science and Technology
2University of Oxford
3Université Paris 11
Electron. J. Probab. 15: 162-216 (2010). DOI: 10.1214/EJP.v15-741
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).
Citation
Nick Barton. Alison Etheridge. Amandine Véber. "A New Model for Evolution in a Spatial Continuum." Electron. J. Probab. 15 162 - 216, 2010. https://doi.org/10.1214/EJP.v15-741
Information
Accepted: 3 February 2010; Published: 2010
First available in Project Euclid: 1 June 2016
Digital Object Identifier: 10.1214/EJP.v15-741
Subjects:
Primary: 60J25
Secondary: 92D10, 92D15
Keywords: Evolution, genealogy, Generalised Fleming-Viot process, multiple merger coalescent, spatial continuum, spatial Lambda-coalescent
Vol.15 • 2010
