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. 1993 Jun;134(2):609–625. doi: 10.1093/genetics/134.2.609

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

S Gavrilets 1, G de-Jong 1
PMCID: PMC1205502  PMID: 8325491

Abstract

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection'' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.

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Selected References

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  1. Barton N. H. Pleiotropic models of quantitative variation. Genetics. 1990 Mar;124(3):773–782. doi: 10.1093/genetics/124.3.773. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Barton N. H. The maintenance of polygenic variation through a balance between mutation and stabilizing selection. Genet Res. 1986 Jun;47(3):209–216. doi: 10.1017/s0016672300023156. [DOI] [PubMed] [Google Scholar]
  3. Barton N. H., Turelli M. Adaptive landscapes, genetic distance and the evolution of quantitative characters. Genet Res. 1987 Apr;49(2):157–173. doi: 10.1017/s0016672300026951. [DOI] [PubMed] [Google Scholar]
  4. Barton N. H., Turelli M. Natural and sexual selection on many loci. Genetics. 1991 Jan;127(1):229–255. doi: 10.1093/genetics/127.1.229. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Cavener D. R., Clegg M. T. Evidence for biochemical and physiological differences between enzyme genotypes in Drosophila melanogaster. Proc Natl Acad Sci U S A. 1981 Jul;78(7):4444–4447. doi: 10.1073/pnas.78.7.4444. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Ewens W. J., Thomson G. Properties of equilibria in multi-locus genetic systems. Genetics. 1977 Dec;87(4):807–819. doi: 10.1093/genetics/87.4.807. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Gillespie J. H., Turelli M. Genotype-environment interactions and the maintenance of polygenic variation. Genetics. 1989 Jan;121(1):129–138. doi: 10.1093/genetics/121.1.129. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Gimelfarb A. Additive variation maintained under stabilizing selection: a two-locus model of pleiotropy for two quantitative characters. Genetics. 1986 Mar;112(3):717–725. doi: 10.1093/genetics/112.3.717. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Gimelfarb A. Genotypic variation for a quantitative character maintained under stabilizing selection without mutations: epistasis. Genetics. 1989 Sep;123(1):217–227. doi: 10.1093/genetics/123.1.217. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hastings A. Second-order approximations for selection coefficients at polygenic loci. J Math Biol. 1990;28(4):475–483. doi: 10.1007/BF00178330. [DOI] [PubMed] [Google Scholar]
  11. Kondrashov A. S., Turelli M. Deleterious mutations, apparent stabilizing selection and the maintenance of quantitative variation. Genetics. 1992 Oct;132(2):603–618. doi: 10.1093/genetics/132.2.603. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Nagylaki T. The maintenance of genetic variability in two-locus models of stabilizing selection. Genetics. 1989 May;122(1):235–248. doi: 10.1093/genetics/122.1.235. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Slatkin M. On treating the chromosome as the unit of selection. Genetics. 1972 Sep;72(1):157–168. doi: 10.1093/genetics/72.1.157. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Zhivotovsky L. A., Gavrilets S. Quantitative variability and multilocus polymorphism under epistatic selection. Theor Popul Biol. 1992 Dec;42(3):254–283. doi: 10.1016/0040-5809(92)90015-l. [DOI] [PubMed] [Google Scholar]

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