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The probability of fixation of a favoured allele in a subdivided population

Published online by Cambridge University Press:  14 April 2009

N. H. Barton
N. H. Barton
Affiliation:
Division of Biological Sciences, University of Edinburgh, King's Buildings, Edinburgh EG9 3JT, U.K.
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In a stably subdivided population with symmetric migration, the chance that a favoured allele will be fixed is independent of population structure. However, random extinction introduces an extra component of sampling drift, and reduces the probability of fixation. In this paper, the fixation probability is calculated using the diffusion approximation; comparison with exact solution of the discrete model shows this to be accurate. The key parameters are the rates of selection, migration and extinction, scaled relative to population size (S = 4Ns, M = 4Nm, Λ = 4Nλ); results apply to a haploid model, or to diploids with additive selection. If new colonies derive from many demes, the fixation probability cannot be reduced by more than half. However, if colonies are initially homogeneous, fixation probability can be much reduced. In the limit of low migration and extinction rates (M, Λ ≪ 1), it is 2s/{1 + (Λ/MS)(1 −exp(−S))}, whilst in the opposite limit (S ≪ 1), it is 4sM/{Λ(Λ + M)}. In the limit of weak selection (M, Λ ≫ 1), it is 4sM/{Λ(Λ + M)}. These factors are not the same as the reduction in effective population size (Ne/N), showing that the effects of population structure on selected alleles cannot be understood from the behaviour of neutral markers.

Information

Type
Research Article
Information
Genetics Research , Volume 62 , Issue 2 , October 1993 , pp. 149 - 157
Copyright
Copyright © Cambridge University Press 1993

References

Barton, N. H. (1993). Linkage and the limits to natural selection. Genetics (submitted).Google Scholar
Crow, J. F. & Kimura, M. (1970). Introduction to Population Genetics Theory. New York: Harper and Row.Google Scholar
Ewens, W. F. (1979). Mathematical Population Genetics. Berlin: Springer-Verlag.Google Scholar
Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford: Oxford University Press.Google Scholar
Keightley, P. D. (1991). Genetic variance and fixation probabilities at quantitative trait loci in mutation-selection balance. Genetical Research 58, 139–144.Google Scholar
Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713–719.Google Scholar
Lande, R. (1979). Effective deme sizes during long-term evolution estimated from rates of chromosomal rearrangement. Evolution 33, 234–251.CrossRefGoogle ScholarPubMed
Lande, R. (1985). The fixation of chromosomal rearrangements in a subdivided population with local extinction and recolonization. Heredity 54, 323–332.CrossRefGoogle Scholar
Madalena, F. E. & Hill, W. G. (1972). Population structure in artificial selection programmes: simulation studies. Genetical Research 20, 75–99.Google Scholar
Maruyama, T. (1970). Fixation probability of genes in a subdivided population. Genetical Research 15, 221–225.Google Scholar
Maruyama, T. & Kimura, M. (1980). Genetic variability and effective population size when local extinction and recolonization of subpopulations are frequent. Proceedings of the National Academy of Sciencess, USA 77, 6710–6714.Google Scholar
Maruyama, T. (1971). An invariant property of a geographically structured population. Genetical Research 18, 81–84.Google Scholar
Michalakis, Y. and Olivieri, I. (1993). The influence of local extinctions on the probability of fixation of chromosomal rearrangements. Journal of Evolutionary Biology 6, 153–170.Google Scholar
Rouhani, S. and Barton, N. H. (1993). Group selection and the ‘shifting balance’. Genetical Research 61: 127–135.CrossRefGoogle Scholar
Slatkin, M. (1977). Gene flow and genetic drift in a species subject to frequent local extinctions. Theoretical Population Biology 12, 253–262.CrossRefGoogle Scholar
Slatkin, M. (1981). Fixation probabilities and fixation times in a subdivided population. Evolution 35, 477–488.CrossRefGoogle Scholar
Tachida, H. & lizuka, M. (1991). Fixation probability in spatially changing environments. Genetical Research 58, 243–251.Google Scholar
Whitlock, M. C. & McCauley, D. E. (1990). Some population genetic consequences of colony formation and extinction: genetic correlations within founding groups. Evolution 44, 1717–1724.Google Scholar
Wolfram, S. (1991). Mathematica. New York: Addison Wesley.Google Scholar