2015/06/03 by Alison Etheridge, Etheridge, Alison, Nic Freeman +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1506.01158
openalex publication_date 2015/06/03 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of\nthe paths traced out by a system of continuous (one-dimensional) space and time\nbranching and coalescing random walks. This demonstrates a certain universality\nof the net, which we have not seen explored elsewhere. The walks themselves\narise in a natural way as the ancestral lineages relating individuals in a\nsample from a biological population evolving according to the spatial\nLambda-Fleming-Viot process. Our scaling reveals the effect, in dimension one,\nof spatial structure on the spread of a selectively advantageous gene through\nsuch a population.\n