Abstract
We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which ``hides'' additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability.
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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]
- Bürger R. Linkage and the maintenance of heritable variation by mutation-selection balance. Genetics. 1989 Jan;121(1):175–184. doi: 10.1093/genetics/121.1.175. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 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]
- Hastings A. Four simultaneously stable polymorphic equilibria in two-locus two-allele models. Genetics. 1985 Jan;109(1):255–261. doi: 10.1093/genetics/109.1.255. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hastings A. Maintenance of polygenic variation through mutation-selection balance: bifurcation analysis of a biallelic model. J Math Biol. 1990;28(3):329–340. doi: 10.1007/BF00178781. [DOI] [PubMed] [Google Scholar]
- Hastings A. Multilocus population genetics with weak epistasis. I. Equilibrium properties of two-locus two-allele models. Genetics. 1985 Apr;109(4):799–812. doi: 10.1093/genetics/109.4.799. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hastings A. Unexpected behavior in two locus genetic systems: an analysis of marginal underdominance at a stable equilibrium. Genetics. 1982 Sep;102(1):129–138. doi: 10.1093/genetics/102.1.129. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hoppensteadt F. C. A slow selection analysis of two locus, two allele traits. Theor Popul Biol. 1976 Feb;9(1):68–81. doi: 10.1016/0040-5809(76)90036-8. [DOI] [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]
- Karlin S., McGregor J. Application of method of small parameters to multi-niche population genetic models. Theor Popul Biol. 1972 Jun;3(2):186–209. doi: 10.1016/0040-5809(72)90026-3. [DOI] [PubMed] [Google Scholar]
- LEWONTIN R. C. THE INTERACTION OF SELECTION AND LINKAGE. II. OPTIMUM MODELS. Genetics. 1964 Oct;50:757–782. doi: 10.1093/genetics/50.4.757. [DOI] [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. The evolution of one- and two-locus systems. Genetics. 1976 Jul;83(3 PT2):583–600. [PMC free article] [PubMed] [Google Scholar]
- 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]
- 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]