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Quasi equilibrium, variance effective size and fixation index for populations with substructure
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Zoology.
2014 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 69, no 5, 1057-1128 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we develop a method for computing the variance effective size , the fixation index and the coefficient of gene differentiation of a structured population under equilibrium conditions. The subpopulation sizes are constant in time, with migration and reproduction schemes that can be chosen with great flexibility. Our quasi equilibrium approach is conditional on non-fixation of alleles. This is of relevance when migration rates are of a larger order of magnitude than the mutation rates, so that new mutations can be ignored before equilibrium balance between genetic drift and migration is obtained. The vector valued time series of subpopulation allele frequencies is divided into two parts; one corresponding to genetic drift of the whole population and one corresponding to differences in allele frequencies among subpopulations. We give conditions under which the first two moments of the latter, after a simple standardization, are well approximated by quantities that can be explicitly calculated. This enables us to compute approximations of the quasi equilibrium values of , and . Our findings are illustrated for several reproduction and migration scenarios, including the island model, stepping stone models and a model where one subpopulation acts as a demographic reservoir. We also make detailed comparisons with a backward approach based on coalescence probabilities.

Place, publisher, year, edition, pages
2014. Vol. 69, no 5, 1057-1128 p.
Keyword [en]
Autoregressive time series, Island model, Quasi equilibrium, Stepping stone models, Spatial allele frequency fluctuations, Structured populations, Temporal allele frequency fluctuations
National Category
Biological Sciences Mathematics
URN: urn:nbn:se:su:diva-109946DOI: 10.1007/s00285-013-0728-9ISI: 000343820700001OAI: diva2:767783


Available from: 2014-12-02 Created: 2014-12-02 Last updated: 2014-12-02Bibliographically approved

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Hössjer, OlaRyman, Nils
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