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 Electronic Journal of Probability > Vol. 15(2010) > Paper 7 open journal systems 


A new model for evolution in a spatial continuum

Nick H Barton, Institute of Science and Technology, Austria
Alison M Etheridge, University of Oxford
Amandine Véber, Université Paris 11


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).


Full text: PDF

Pages: 162-216

Published on: February 24, 2010
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Electronic Journal of Probability. ISSN: 1083-6489