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Genetics. Dec 1973; 75(4): 733–756.
PMCID: PMC1213045

Gene Flow and Selection in a Cline


A model of the effect of gene flow and natural selection in a continuously distributed, infinite population is developed. Different patterns of spatial variation in selective pressures are considered, including a step change in the environment, a "pocket" in the environment and a periodically varying environment. Also, the problem of the effect of a geographic barrier to dispersal is analyzed. The results are: (1) there is a characteristic length scale of variation of gene frequencies, (see PDF). The population cannot respond to changes in environmental conditions which occur over a distance less than the characteristic length. The result does not depend either on the pattern of variation in selective pressures or on the exact shape of the dispersal function. (2) The reduction in the fitness of the heterozygote causes a cline in gene frequencies to become steeper. (3) A geographic barrier to dispersal causes a drastic change in the gene frequencies at the barrier only when almost all of the individuals trying to cross the barrier are stopped.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Hamilton WD. The genetical evolution of social behaviour. I. J Theor Biol. 1964 Jul;7(1):1–16. [PubMed]
  • Hanson WD. Effects of partial isolation (distance), migration, and different fitness requirements among environmental pockets upon steady state gene frequencies. Biometrics. 1966 Sep;22(3):453–468. [PubMed]
  • Kimura M, Weiss GH. The Stepping Stone Model of Population Structure and the Decrease of Genetic Correlation with Distance. Genetics. 1964 Apr;49(4):561–576. [PMC free article] [PubMed]

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