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Local fluctuations of genetic processes defined on two time scales, with applications to effective size estimation
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22020 (English)In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 131, p. 79-99Article in journal (Refereed) Published
Abstract [en]

In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive process, around a quasi equilibrium fix point, whereas the fix point itself varies more slowly according to a diffusion process, along a lower-dimensional subspace. Under mild regularity conditions, the fluctuations have a magnitude inversely proportional to the square root of the population size N, and hence can be used to estimate a broad class of genetically effective population sizes N-e, with genetic data from one time point only. In this way we are able to unify a number of existing notions of effective size, as well as proposing new ones, for instance one that quantifies the extent to which genotype frequencies fluctuate around Hardy-Weinberg equilibrium. (C) 2019 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2020. Vol. 131, p. 79-99
Keywords [en]
Autoregressive process, Effective population size, Markov process, Structured population, Quasi equilibrium
National Category
Mathematics Biological Sciences
Identifiers
URN: urn:nbn:se:su:diva-179571DOI: 10.1016/j.tpb.2019.11.006ISI: 000510527700008PubMedID: 31778709OAI: oai:DiVA.org:su-179571DiVA, id: diva2:1416792
Available from: 2020-03-25 Created: 2020-03-25 Last updated: 2020-03-25Bibliographically approved

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