Abstract
The role of linkage in influencing heritable variation maintained through a balance between mutation and stabilizing selection is investigated for two different models. In both cases one trait is considered and the interactions within and between loci are assumed to be additive. Contrary to most earlier investigations of this problem no a priori assumptions on the distribution of genotypic values are imposed. For a deterministic two-locus two-allele model with recombination and mutation, related to the symmetric viability model, a complete nonlinear analysis is performed. It is shown that, depending on the recombination rate, multiple stable equilibria may coexist. The equilibrium genetic and genic variances are calculated. For a polygenic trait in a finite population with a possible continuum of allelic effects a simulation study is performed. In both models the equilibrium genetic and genic variances are roughly equal to the house-of-cards prediction or its finite population counterpart as long as the recombination rate is not extremely low. However, negative linkage disequilibrium builds up. If the loci are very closely linked the equilibrium additive genetic variance is slightly lower than the house-of-cards prediction, but the genic variance is much higher. Depending on whether the parameters are in favor of the house-of-cards or the Gaussian approximation, different behavior of the genetic system occurs with respect to linkage.
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Selected References
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- 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]
- Bodmer W. F., Felsenstein J. Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics. 1967 Oct;57(2):237–265. doi: 10.1093/genetics/57.2.237. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Bulmer M. G. The genetic variability of polygenic characters under optimizing selection, mutation and drift. Genet Res. 1972 Feb;19(1):17–25. doi: 10.1017/s0016672300014221. [DOI] [PubMed] [Google Scholar]
- Foley P. Molecular clock rates at loci under stabilizing selection. Proc Natl Acad Sci U S A. 1987 Nov;84(22):7996–8000. doi: 10.1073/pnas.84.22.7996. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hastings A. Monotonic change of the mean phenotype in two-locus models. Genetics. 1987 Nov;117(3):583–585. doi: 10.1093/genetics/117.3.583. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Karlin S., Feldman M. W. Linkage and selection: two locus symmetric viability model. Theor Popul Biol. 1970 May;1(1):39–71. doi: 10.1016/0040-5809(70)90041-9. [DOI] [PubMed] [Google Scholar]
- Keightley P. D., Hill W. G. Quantitative genetic variability maintained by mutation-stabilizing selection balance in finite populations. Genet Res. 1988 Aug;52(1):33–43. doi: 10.1017/s0016672300027282. [DOI] [PubMed] [Google Scholar]
- Lande R. The influence of the mating system on the maintenance of genetic variability in polygenic characters. Genetics. 1977 Jun;86(2 Pt 1):485–498. [PMC free article] [PubMed] [Google Scholar]
- Lande R. The maintenance of genetic variability by mutation in a polygenic character with linked loci. Genet Res. 1975 Dec;26(3):221–235. doi: 10.1017/s0016672300016037. [DOI] [PubMed] [Google Scholar]
- Nagylaki T., Crow J. F. Continuous selective models. Theor Popul Biol. 1974 Apr;5(2):257–283. doi: 10.1016/0040-5809(74)90045-8. [DOI] [PubMed] [Google Scholar]
- Turelli M. Effects of pleiotropy on predictions concerning mutation-selection balance for polygenic traits. Genetics. 1985 Sep;111(1):165–195. doi: 10.1093/genetics/111.1.165. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Turelli M. Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theor Popul Biol. 1984 Apr;25(2):138–193. doi: 10.1016/0040-5809(84)90017-0. [DOI] [PubMed] [Google Scholar]