| Título: | A New Model for Evolution in a Spatial Continuum |
| Autores: |
Barton, Nick H; Institute of Science and Technology Etheridge, Alison M; University of Oxford Véber, Amandine; Université Paris 11 |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
genealogy, evolution, multiple merger coalescent, spatial continuum, spatial Lambda-coalescent, generalised Fleming-Viot process 60J25, 92D10, 92D15 |
| Descripción: | 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). |
| Idioma: | No aplica |
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