Journal of Genetics

, Volume 74, Issue 1–2, pp 19–24 | Cite as

A compact proof of Fisher’s Fundamental Theorem for multiple loci

  • Narayan Behera


A systematic method is formulated to carry out theoretical analysis in a multilocus multiallele genetic system. As a special application, the Fundamental Theorem of Natural Selection is proved (in the continuous time model) for a multilocus multiallele system if all pairwise linkage disequilibria are zero.


Evolution natural selection allele frequency variance in fitness integral variational principle 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Behera N. 1995 Variational principles in evolution.Bull. Math. Biol. (in press)Google Scholar
  2. Crow J. F. and Kimura M. 1970An introduction to population genetic theory (New York: Harper and Row) pp. 117–118Google Scholar
  3. Crow J. F. 1990 Fisher’s contribution to genetics and evolution.Theoret. Pop. Biol. 38: 263–275CrossRefGoogle Scholar
  4. Edwards A. W. F. 1994 The Fundamental Theorem of Natural Selection.Biol. Rev. Cambridge Philos. Soc. 69: 443–474.PubMedCrossRefGoogle Scholar
  5. Ewens W. J. 1989 An interpretation and proof of the Fundamental Theorem of Natural Selection.Theoret. Pop. Biol. 36: 167–180CrossRefGoogle Scholar
  6. Fisher R. A. 1930The genetical theory of natural selection (Oxford: Clarendon Press)Google Scholar
  7. Kimura M. 1958 On the change of population fitness by natural selection.Heredity 12: 145–167CrossRefGoogle Scholar
  8. Nagylaki T. 1976 The evolution of one- and two-locus systems.Genetics 83: 583–600PubMedGoogle Scholar
  9. Nagylaki T. 1991 Error bounds for the fundamental and secondary theorems of natural selection.Proc. Natl. Acad. Sci. USA 88: 2402–2406PubMedCrossRefGoogle Scholar
  10. Price G. R. 1972 Fisher’s ‘Fundamental Theorem’ made clear.Ann. Hum. Genet. 36: 129–140PubMedCrossRefGoogle Scholar
  11. Svirezhev Y. M. 1972 Optimum principles in genetics. InStudies on theoretical genetics (ed.) V. A. Ratner (Novosibirsk: USSR Academy of Sciences) pp. 85–102Google Scholar
  12. Wright S. 1988 Surfaces of selective value revisited.Am. Nat. 131: 115–123CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 1995

Authors and Affiliations

  • Narayan Behera
    • 1
  1. 1.Developmental Biology and Genetics LaboratoryIndian Institute of ScienceBangaloreIndia

Personalised recommendations