Open Access
2017 The Brownian net and selection in the spatial $\Lambda $-Fleming-Viot process
Alison Etheridge, Nic Freeman, Daniel Straulino
Electron. J. Probab. 22: 1-36 (2017). DOI: 10.1214/17-EJP61


We obtain the Brownian net of [24] 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.


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Alison Etheridge. Nic Freeman. Daniel Straulino. "The Brownian net and selection in the spatial $\Lambda $-Fleming-Viot process." Electron. J. Probab. 22 1 - 36, 2017.


Received: 23 November 2016; Accepted: 23 April 2017; Published: 2017
First available in Project Euclid: 28 April 2017

zbMATH: 1364.60104
MathSciNet: MR3646065
Digital Object Identifier: 10.1214/17-EJP61

Primary: 60G99 , 60K35

Keywords: branching , Brownian net , coalescing , spatial $\Lambda $-Fleming-Viot

Vol.22 • 2017
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