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

Understand

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.