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Weak convergence of non-neutral genealogies to Kingman's coalescent
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Brown, Suzie, Jenkins, Paul, Johansen, Adam M. and Koskela, Jere (2023) Weak convergence of non-neutral genealogies to Kingman's coalescent. Stochastic Processes and their Applications, 162 . pp. 76-105. doi:10.1016/j.spa.2023.04.016 ISSN 0304-4149.
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Official URL: https://doi.org/10.1016/j.spa.2023.04.016
Abstract
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both applications. Under neutrality, when fitnesses of particles are independent from those of their parents, rescaled genealogies are known to converge to Kingman’s coalescent. Recent work has established convergence under non-neutrality, but only for finite-dimensional distributions. We prove weak convergence of non-neutral genealogies on the space of càdlàg paths under standard assumptions, enabling analysis of the whole genealogical tree.
| Item Type: | Journal Article | ||||||||||||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QH Natural history > QH426 Genetics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Population genetics -- Mathematical models, Statistical physics | ||||||||||||||||||||||||||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||||||||||||||||||||||||
| Publisher: | Elsevier Science BV | ||||||||||||||||||||||||||||||
| ISSN: | 0304-4149 | ||||||||||||||||||||||||||||||
| Official Date: | August 2023 | ||||||||||||||||||||||||||||||
| Dates: |
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| Volume: | 162 | ||||||||||||||||||||||||||||||
| Page Range: | pp. 76-105 | ||||||||||||||||||||||||||||||
| DOI: | 10.1016/j.spa.2023.04.016 | ||||||||||||||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||||||||||||||
| Description: | This work was supported by the Engineering and Physical Sciences Research Council, the Medical Research Council, the Alan Turing Institute, and the Alan Turing Institute-Lloyd’s Register Foundation Programme on Data-centric Engineering, under grant numbers EP/L016710/1, EP/N510129/1, EP/R034710/1, EP/R044732/1, EP/T004134/1 and EP/V049208/1. |
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| Date of first compliant deposit: | 21 April 2023 | ||||||||||||||||||||||||||||||
| Date of first compliant Open Access: | 26 May 2023 | ||||||||||||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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