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).
%0 Journal Article
%1 barton2010continuum
%A Barton, Nick
%A Etheridge, Alison
%A Véber, Amandine
%D 2010
%J Electronic Journal of Probability
%K Fleming_Viot SLFV coalescent_theory lambda_coalescent spatial_coalescent spatial_structure
%P 162-216
%T A new model for evolution in a spatial continuum
%U http://ejp.ejpecp.org/article/view/741
%V 15
%X 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).
@article{barton2010continuum,
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).
},
added-at = {2010-06-15T19:58:51.000+0200},
author = {Barton, Nick and Etheridge, Alison and Véber, Amandine},
biburl = {https://www.bibsonomy.org/bibtex/2bf70818b97eb2fb4c08cce364b960829/peter.ralph},
interhash = {1c4098e765f127ced6afe3f6836c69a5},
intrahash = {bf70818b97eb2fb4c08cce364b960829},
journal = {Electronic Journal of Probability},
keywords = {Fleming_Viot SLFV coalescent_theory lambda_coalescent spatial_coalescent spatial_structure},
pages = {162-216},
paper = {7},
timestamp = {2016-03-25T19:19:33.000+0100},
title = {A new model for evolution in a spatial continuum},
url = {http://ejp.ejpecp.org/article/view/741},
volume = 15,
year = 2010
}