Electronic Journal of Probability

The Brownian net and selection in the spatial $\Lambda $-Fleming-Viot process

Alison Etheridge, Nic Freeman, and Daniel Straulino

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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.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 39, 36 pp.

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

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Zentralblatt MATH identifier

Primary: 60G99: None of the above, but in this section 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Brownian net spatial $\Lambda $-Fleming-Viot branching coalescing

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Etheridge, Alison; Freeman, Nic; Straulino, Daniel. The Brownian net and selection in the spatial $\Lambda $-Fleming-Viot process. Electron. J. Probab. 22 (2017), paper no. 39, 36 pp. doi:10.1214/17-EJP61. https://projecteuclid.org/euclid.ejp/1493345026

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