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. 2002 May;161(1):419–433. doi: 10.1093/genetics/161.1.419

Pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance.

Xu-Sheng Zhang 1, Jinliang Wang 1, William G Hill 1
PMCID: PMC1462112  PMID: 12019255

Abstract

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (V(s)) and the genetic variance maintained in segregating populations (V(G)) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, V(G) increases to an asymptote as the population size increases. Both V(G) and V(s) are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher V(G) but also a high V(s) (V(s) in phenotypic standard deviation units, which is always larger than the ratio V(P)/V(m)), implying weak apparent stabilizing selection. If the mutational variance V(m) is approximately 10(-3)V(e) (V(e), environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

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Selected References

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  1. Barton N. H., Keightley P. D. Understanding quantitative genetic variation. Nat Rev Genet. 2002 Jan;3(1):11–21. doi: 10.1038/nrg700. [DOI] [PubMed] [Google Scholar]
  2. 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]
  3. Caballero A., Keightley P. D. A pleiotropic nonadditive model of variation in quantitative traits. Genetics. 1994 Nov;138(3):883–900. doi: 10.1093/genetics/138.3.883. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Chavarrías D., López-Fanjul C., García-Dorado A. The rate of mutation and the homozygous and heterozygous mutational effects for competitive viability: a long-term experiment with Drosophila melanogaster. Genetics. 2001 Jun;158(2):681–693. doi: 10.1093/genetics/158.2.681. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Davies E. K., Peters A. D., Keightley P. D. High frequency of cryptic deleterious mutations in Caenorhabditis elegans. Science. 1999 Sep 10;285(5434):1748–1751. doi: 10.1126/science.285.5434.1748. [DOI] [PubMed] [Google Scholar]
  6. Elena S. F., Lenski R. E. Test of synergistic interactions among deleterious mutations in bacteria. Nature. 1997 Nov 27;390(6658):395–398. doi: 10.1038/37108. [DOI] [PubMed] [Google Scholar]
  7. Gavrilets S., de Jong G. Pleiotropic models of polygenic variation, stabilizing selection, and epistasis. Genetics. 1993 Jun;134(2):609–625. doi: 10.1093/genetics/134.2.609. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. 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]
  9. Gimelfarb A. How much genetic variation can be maintained by genotype-environment interactions? Genetics. 1990 Feb;124(2):443–447. doi: 10.1093/genetics/124.2.443. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hill W. G. Predictions of response to artificial selection from new mutations. Genet Res. 1982 Dec;40(3):255–278. doi: 10.1017/s0016672300019145. [DOI] [PubMed] [Google Scholar]
  11. Houle D., Morikawa B., Lynch M. Comparing mutational variabilities. Genetics. 1996 Jul;143(3):1467–1483. doi: 10.1093/genetics/143.3.1467. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. KIMURA M. On the probability of fixation of mutant genes in a population. Genetics. 1962 Jun;47:713–719. doi: 10.1093/genetics/47.6.713. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Keightley P. D., Caballero A. Genomic mutation rates for lifetime reproductive output and lifespan in Caenorhabditis elegans. Proc Natl Acad Sci U S A. 1997 Apr 15;94(8):3823–3827. doi: 10.1073/pnas.94.8.3823. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Keightley P. D., Davies E. K., Peters A. D., Shaw R. G. Properties of ethylmethane sulfonate-induced mutations affecting life-history traits in Caenorhabditis elegans and inferences about bivariate distributions of mutation effects. Genetics. 2000 Sep;156(1):143–154. doi: 10.1093/genetics/156.1.143. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Keightley P. D. The distribution of mutation effects on viability in Drosophila melanogaster. Genetics. 1994 Dec;138(4):1315–1322. doi: 10.1093/genetics/138.4.1315. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Kimura M. A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc Natl Acad Sci U S A. 1965 Sep;54(3):731–736. doi: 10.1073/pnas.54.3.731. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Kingsolver J. G., Hoekstra H. E., Hoekstra J. M., Berrigan D., Vignieri S. N., Hill C. E., Hoang A., Gibert P., Beerli P. The strength of phenotypic selection in natural populations. Am Nat. 2001 Mar;157(3):245–261. doi: 10.1086/319193. [DOI] [PubMed] [Google Scholar]
  18. Kondrashov A. S. Measuring spontaneous deleterious mutation process. Genetica. 1998;102-103(1-6):183–197. [PubMed] [Google Scholar]
  19. 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]
  20. 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]
  21. Nielsen R. Statistical tests of selective neutrality in the age of genomics. Heredity (Edinb) 2001 Jun;86(Pt 6):641–647. doi: 10.1046/j.1365-2540.2001.00895.x. [DOI] [PubMed] [Google Scholar]
  22. Roff D. A., Mousseau T. A. Quantitative genetics and fitness: lessons from Drosophila. Heredity (Edinb) 1987 Feb;58(Pt 1):103–118. doi: 10.1038/hdy.1987.15. [DOI] [PubMed] [Google Scholar]
  23. Shaw R. G., Byers D. L., Darmo E. Spontaneous mutational effects on reproductive traits of arabidopsis thaliana. Genetics. 2000 May;155(1):369–378. doi: 10.1093/genetics/155.1.369. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Slatkin M. Frequency- and density-dependent selection on a quantitative character. Genetics. 1979 Nov;93(3):755–771. doi: 10.1093/genetics/93.3.755. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Tanaka Y. The Genetic Variance Maintained by Pleiotropic Mutation. Theor Popul Biol. 1996 Apr;49(2):211–231. doi: 10.1006/tpbi.1996.0012. [DOI] [PubMed] [Google Scholar]
  26. 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]
  27. 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]
  28. Vassilieva L. L., Lynch M. The rate of spontaneous mutation for life-history traits in Caenorhabditis elegans. Genetics. 1999 Jan;151(1):119–129. doi: 10.1093/genetics/151.1.119. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Wloch D. M., Szafraniec K., Borts R. H., Korona R. Direct estimate of the mutation rate and the distribution of fitness effects in the yeast Saccharomyces cerevisiae. Genetics. 2001 Oct;159(2):441–452. doi: 10.1093/genetics/159.2.441. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Yu N., Zhao Z., Fu Y. X., Sambuughin N., Ramsay M., Jenkins T., Leskinen E., Patthy L., Jorde L. B., Kuromori T. Global patterns of human DNA sequence variation in a 10-kb region on chromosome 1. Mol Biol Evol. 2001 Feb;18(2):214–222. doi: 10.1093/oxfordjournals.molbev.a003795. [DOI] [PubMed] [Google Scholar]
  31. 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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