Advertisement

Journal of Mathematical Biology

, Volume 56, Issue 3, pp 413–434 | Cite as

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

  • Christina T. L. Chen
  • Quo-Shin Chi
  • Stanley A. SawyerEmail author
Article

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.

Keywords

Fixation probability Monotonicity Dominance 

Mathematics Subject Classification (2000)

92B05 92D25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Carr R.N. and Nassar R.F. (1970). Effects of selection and drift on the dynamics of finite populations. Biometrics 26: 41–49 CrossRefGoogle Scholar
  2. 2.
    Crow J. and Kimura M. (1970). An Introduction to Population Genetics Theory. Harper and Row, New York zbMATHGoogle Scholar
  3. 3.
    Ewens W.J. (2004). Mathematical Population Genetics I. Theoretical Introduction. Springer, New York zbMATHGoogle Scholar
  4. 4.
    Ewens W.J. and Thomson C. (1970). Heterozygote selective advantage. Ann. Hum. Genet. 33: 365–376 CrossRefGoogle Scholar
  5. 5.
    Fisher R.A. (1922). On the dominance ratio. Proc. R. Soc. Edinb. 42: 321–341 Google Scholar
  6. 6.
    Fisher R.A. (1930). The distribution of gene ratios for rare mutations. Proc. R. Soc. Edinb. 50: 204–219 Google Scholar
  7. 7.
    Fisher R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford zbMATHGoogle Scholar
  8. 8.
    Hartl D.L. and Clark A.G. (1997). Principles of Population Genetics. Sinauer Associates, Sunderland Google Scholar
  9. 9.
    Kimura M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47: 713–719 Google Scholar
  10. 10.
    Magori K. and Gould F. (2006). Genetically engineered underdominance for manipulation of pest populations: a deterministic model. Genetics 172: 2613–2620 CrossRefGoogle Scholar
  11. 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. 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

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Christina T. L. Chen
    • 1
  • Quo-Shin Chi
    • 2
  • Stanley A. Sawyer
    • 2
    Email author
  1. 1.Department of Genetics, Campus Box 8510Washington University School of MedicineSt. LouisUSA
  2. 2.Department of Mathematics, Campus Box 1146Washington UniversitySt. LouisUSA

Personalised recommendations