The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process
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...
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Format: | Journal article |
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Institute of Mathematical Statistics
2017
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author | Etheridge, A Freeman, N Straulino, D |
author_facet | Etheridge, A Freeman, N Straulino, D |
author_sort | Etheridge, A |
collection | OXFORD |
description | 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. |
first_indexed | 2024-03-06T19:24:03Z |
format | Journal article |
id | oxford-uuid:1b1bbe49-3947-411d-a5b7-a313e41b88fd |
institution | University of Oxford |
last_indexed | 2024-03-06T19:24:03Z |
publishDate | 2017 |
publisher | Institute of Mathematical Statistics |
record_format | dspace |
spelling | oxford-uuid:1b1bbe49-3947-411d-a5b7-a313e41b88fd2022-03-26T10:58:32ZThe Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot processJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1b1bbe49-3947-411d-a5b7-a313e41b88fdSymplectic Elements at OxfordInstitute of Mathematical Statistics2017Etheridge, AFreeman, NStraulino, DWe 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. |
spellingShingle | Etheridge, A Freeman, N Straulino, D The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process |
title | The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process |
title_full | The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process |
title_fullStr | The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process |
title_full_unstemmed | The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process |
title_short | The Brownian net and selection in the Spatial $\Lambda$-Fleming-Viot process |
title_sort | brownian net and selection in the spatial lambda fleming viot process |
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