Etheridge, A., Freeman, N.P. and Straulino, D. (2017) The Brownian Net and Selection in the Spatial Lambda-Fleming-Viot Process. Electronic Journal of Probability, 22. 39.
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Brownian net; spatial Λ-Fleming-Viot; branching; coalescing |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 May 2017 15:13 |
Last Modified: | 29 May 2020 09:16 |
Published Version: | https://doi.org/10.1214/17-EJP61 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/17-EJP61 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:105931 |