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On the eigenvalue effective size of structured populations
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 1
2015 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 71, no 3, 595-646 p.Article in journal (Refereed) Published
Abstract [en]

A general theory is developed for the eigenvalue effective size () of structured populations in which a gene with two alleles segregates in discrete time. Generalizing results of Ewens (Theor Popul Biol 21:373-378, 1982), we characterize in terms of the largest non-unit eigenvalue of the transition matrix of a Markov chain of allele frequencies. We use Perron-Frobenius Theorem to prove that the same eigenvalue appears in a linear recursion of predicted gene diversities between all pairs of subpopulations. Coalescence theory is employed in order to characterize this recursion, so that explicit novel expressions for can be derived. We then study asymptotically, when either the inverse size and/or the overall migration rate between subpopulations tend to zero. It is demonstrated that several previously known results can be deduced as special cases. In particular when the coalescence effective size exists, it is an asymptotic version of in the limit of large populations.

Place, publisher, year, edition, pages
2015. Vol. 71, no 3, 595-646 p.
Keyword [en]
Eigenvalue effective size, Coalescence theory, Predicted gene diversity, Migration, Perron-Frobenius, Perturbation theory of eigenvalues
National Category
Biological Sciences
Identifiers
URN: urn:nbn:se:su:diva-120907DOI: 10.1007/s00285-014-0832-5ISI: 000359537200005OAI: oai:DiVA.org:su-120907DiVA: diva2:856726
Available from: 2015-09-25 Created: 2015-09-18 Last updated: 2017-12-01Bibliographically approved

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