@article{EJP741,
author = {Nick Barton and Alison Etheridge and Amandine Véber},
title = {A New Model for Evolution in a Spatial Continuum},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {genealogy, evolution, multiple merger coalescent, spatial continuum, spatial Lambda-coalescent, generalised Fleming-Viot process},
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).},
pages = {no. 7, 162-216},
issn = {1083-6489},
doi = {10.1214/EJP.v15-741},
url = {http://ejp.ejpecp.org/article/view/741}}