Skip to main content

Advertisement

SpringerLink
Log in

Effects of dominance on the probability of fixation of a mutant allele

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

We consider whether the fixation probability of an allele in a two-allele diploid system is always a monotonic function of the selective advantage of the allele. We show that while this conjecture is correct for intermediate dominance, it is not correct in general for either overdominant or underdominant alleles, and that for some parameter ranges the fixation probability can initially decrease and then increase as a function of the amount of selection. We have partial results that characterize the ranges of parameters for which this happens.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Carr R.N. and Nassar R.F. (1970). Effects of selection and drift on the dynamics of finite populations. Biometrics 26: 41–49

    Article  Google Scholar 

  2. Crow J. and Kimura M. (1970). An Introduction to Population Genetics Theory. Harper and Row, New York

    MATH  Google Scholar 

  3. Ewens W.J. (2004). Mathematical Population Genetics I. Theoretical Introduction. Springer, New York

    MATH  Google Scholar 

  4. Ewens W.J. and Thomson C. (1970). Heterozygote selective advantage. Ann. Hum. Genet. 33: 365–376

    Article  Google Scholar 

  5. Fisher R.A. (1922). On the dominance ratio. Proc. R. Soc. Edinb. 42: 321–341

    Google Scholar 

  6. Fisher R.A. (1930). The distribution of gene ratios for rare mutations. Proc. R. Soc. Edinb. 50: 204–219

    Google Scholar 

  7. Fisher R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford

    MATH  Google Scholar 

  8. Hartl D.L. and Clark A.G. (1997). Principles of Population Genetics. Sinauer Associates, Sunderland

    Google Scholar 

  9. Kimura M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47: 713–719

    Google Scholar 

  10. Magori K. and Gould F. (2006). Genetically engineered underdominance for manipulation of pest populations: a deterministic model. Genetics 172: 2613–2620

    Article  Google Scholar 

  11. Malécot G. (1952). Les processus stochastiques et la méthode des fonctions génératrices ou caractéristiques. Publ. Inst. Stat. Univ. Paris 1, Fasc 3: 1–116

    Google Scholar 

  12. Nei M. and Roychoudhury A.K. (1973). Probabiility of fixation and mean fixation time of an overdominant mutation. Genetics 74: 371–380

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Genetics, Campus Box 8510, Washington University School of Medicine, 4444 Forest Park Parkway, St. Louis, MO, 63108, USA

    Christina T. L. Chen

  2. Department of Mathematics, Campus Box 1146, Washington University, St. Louis, MO, 63130, USA

    Quo-Shin Chi & Stanley A. Sawyer

Authors
  1. Christina T. L. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Quo-Shin Chi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stanley A. Sawyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stanley A. Sawyer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, C.T.L., Chi, QS. & Sawyer, S.A. Effects of dominance on the probability of fixation of a mutant allele. J. Math. Biol. 56, 413–434 (2008). https://doi.org/10.1007/s00285-007-0121-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-007-0121-7

Keywords

Mathematics Subject Classification (2000)

Search

Navigation