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2010 A New Model for Evolution in a Spatial Continuum
Nick Barton, Alison Etheridge, Amandine Véber
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Electron. J. Probab. 15: 162-216 (2010). DOI: 10.1214/EJP.v15-741


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).


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Nick Barton. Alison Etheridge. Amandine Véber. "A New Model for Evolution in a Spatial Continuum." Electron. J. Probab. 15 162 - 216, 2010.


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

zbMATH: 1203.60107
MathSciNet: MR2594876
Digital Object Identifier: 10.1214/EJP.v15-741

Primary: 60J25
Secondary: 92D10 , 92D15

Keywords: Evolution , genealogy , Generalised Fleming-Viot process , multiple merger coalescent , spatial continuum , spatial Lambda-coalescent


Vol.15 • 2010
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