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. 1999 Jun;152(2):807–820. doi: 10.1093/genetics/152.2.807

Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection.

R Bürger 1, A Gimelfarb 1
PMCID: PMC1460636  PMID: 10353920

Abstract

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination.

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Selected References

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  1. 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]
  2. Barton N. H., Turelli M. Evolutionary quantitative genetics: how little do we know? Annu Rev Genet. 1989;23:337–370. doi: 10.1146/annurev.ge.23.120189.002005. [DOI] [PubMed] [Google Scholar]
  3. 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]
  4. Bulmer M. G. The stability of equilibria under selection. Heredity (Edinb) 1971 Oct;27(2):157–162. doi: 10.1038/hdy.1971.81. [DOI] [PubMed] [Google Scholar]
  5. Bürger R., Hofbauer J. Mutation load and mutation-selection-balance in quantitative genetic traits. J Math Biol. 1994;32(3):193–218. doi: 10.1007/BF00163878. [DOI] [PubMed] [Google Scholar]
  6. Bürger R., Lande R. On the distribution of the mean and variance of a quantitative trait under mutation-selection-drift balance. Genetics. 1994 Nov;138(3):901–912. doi: 10.1093/genetics/138.3.901. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Bürger R. On the maintenance of genetic variation: global analysis of Kimura's continuum-of-alleles model. J Math Biol. 1986;24(3):341–351. doi: 10.1007/BF00275642. [DOI] [PubMed] [Google Scholar]
  8. Gavrilets S., Hastings A. Dynamics of genetic variability in two-locus models of stabilizing selection. Genetics. 1994 Oct;138(2):519–532. doi: 10.1093/genetics/138.2.519. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Gavrilets S., Hastings A. Maintenance of genetic variability under strong stabilizing selection: a two-locus model. Genetics. 1993 May;134(1):377–386. doi: 10.1093/genetics/134.1.377. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. 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]
  11. Gimelfarb A. Stable equilibria in multilocus genetic systems: a statistical investigation. Theor Popul Biol. 1998 Oct;54(2):133–145. doi: 10.1006/tpbi.1997.1371. [DOI] [PubMed] [Google Scholar]
  12. 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]
  13. Hill W. G., Rasbash J. Models of long term artificial selection in finite population. Genet Res. 1986 Aug;48(1):41–50. doi: 10.1017/s0016672300024642. [DOI] [PubMed] [Google Scholar]
  14. 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]
  15. 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]
  16. 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]
  17. López M. A., López-Fanjul C. Spontaneous mutation for a quantitative trait in Drosophila melanogaster. II. Distribution of mutant effects on the trait and fitness. Genet Res. 1993 Apr;61(2):117–126. doi: 10.1017/s0016672300031220. [DOI] [PubMed] [Google Scholar]
  18. Mackay T. F., Fry J. D. Polygenic mutation in Drosophila melanogaster: genetic interactions between selection lines and candidate quantitative trait loci. Genetics. 1996 Oct;144(2):671–688. doi: 10.1093/genetics/144.2.671. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Mackay T. F., Lyman R. F., Jackson M. S. Effects of P element insertions on quantitative traits in Drosophila melanogaster. Genetics. 1992 Feb;130(2):315–332. doi: 10.1093/genetics/130.2.315. [DOI] [PMC free article] [PubMed] [Google Scholar]

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