The Brownian Net and Selection in the Spatial Lambda-Fleming-Viot Process
Probability
2016-11-17 v2
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 (one-dimensional) space and time branching and coalescing random walks. This demonstrates a certain universality 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, in dimension one, of spatial structure on the spread of a selectively advantageous gene through such a population.
Cite
@article{arxiv.1506.01158,
title = {The Brownian Net and Selection in the Spatial Lambda-Fleming-Viot Process},
author = {Alison Etheridge and Nic Freeman and Daniel Straulino},
journal= {arXiv preprint arXiv:1506.01158},
year = {2016}
}
Comments
37 pages, 5 figures