The Brownian Net and Selection in the Spatial Lambda-Fleming-Viot Process

TL;DR

This paper demonstrates that the Brownian net, a universal scaling limit of branching and coalescing random walks, models ancestral lineages in spatial Lambda-Fleming-Viot populations, revealing effects of spatial structure on gene spread.

Contribution

It establishes the Brownian net as the scaling limit of ancestral lineages in the spatial Lambda-Fleming-Viot process, highlighting universality and spatial effects on gene propagation.

Findings

Brownian net arises as the scaling limit of branching-coalescing random walks.

Spatial structure influences the spread of advantageous genes in one dimension.

The Brownian net provides a universal framework for ancestral lineages in spatial populations.

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.