We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of
the paths traced out by a system of continuous space and time branching and
coalescing random walks. This demonstrates a certain robustness of the net,
which we have not seen explored elsewhere. The walks themselves arise in a
natural way as the ancestral lineages relating individuals in a sample from a
biological population evolving according to the spatial Lambda-Fleming-Viot
process. Our scaling reveals the effect of spatial structure on the spread of a
selectively advantageous gene through such a population.
%0 Generic
%1 etheridge2015brownian
%A Etheridge, Alison
%A Freeman, Nic
%A Straulino, Daniel
%D 2015
%K Brownian_net SLFV branching_coalescing_random_walk isolation_by_distance one_dimension spatial_coalescent
%T The Brownian Net and Selection in the Spatial Lambda-Fleming-Viot
Process
%U http://arxiv.org/abs/1506.01158
%X We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of
the paths traced out by a system of continuous space and time branching and
coalescing random walks. This demonstrates a certain robustness of the net,
which we have not seen explored elsewhere. The walks themselves arise in a
natural way as the ancestral lineages relating individuals in a sample from a
biological population evolving according to the spatial Lambda-Fleming-Viot
process. Our scaling reveals the effect of spatial structure on the spread of a
selectively advantageous gene through such a population.
@misc{etheridge2015brownian,
abstract = {We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of
the paths traced out by a system of continuous space and time branching and
coalescing random walks. This demonstrates a certain robustness of the net,
which we have not seen explored elsewhere. The walks themselves arise in a
natural way as the ancestral lineages relating individuals in a sample from a
biological population evolving according to the spatial Lambda-Fleming-Viot
process. Our scaling reveals the effect of spatial structure on the spread of a
selectively advantageous gene through such a population.},
added-at = {2016-03-25T19:21:59.000+0100},
author = {Etheridge, Alison and Freeman, Nic and Straulino, Daniel},
biburl = {https://www.bibsonomy.org/bibtex/25192f75d7c82cf97683ce634a2c6d779/peter.ralph},
interhash = {d68e45a07d72cfb5be5af2fc2e471ffa},
intrahash = {5192f75d7c82cf97683ce634a2c6d779},
keywords = {Brownian_net SLFV branching_coalescing_random_walk isolation_by_distance one_dimension spatial_coalescent},
note = {cite arxiv:1506.01158Comment: 43 pages, 5 figures},
timestamp = {2016-03-25T19:21:59.000+0100},
title = {The {Brownian} Net and Selection in the Spatial {Lambda}-{Fleming}-{Viot}
Process},
url = {http://arxiv.org/abs/1506.01158},
year = 2015
}