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Models of clines

Published online by Cambridge University Press:  01 July 2016

D. Y. Downham
D. Y. Downham*
Affiliation:
Department of Computational and Statistical Science, University of Liverpool
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Extract

The imago of the peppered moth exists in two sharply distinguished forms, speckled and black. Clarke and Sheppard (1966) have shown that the frequency of the black moth decreases from 99% in Liverpool to 10% in North Wales. If these frequencies are in equilibrium, albeit dynamic equilibrium, then such a gradient is called a cline. Haldane (1948) briefly describes several clines, and then defines a model that may represent the life-cycle of certain species. The assumptions defining his model are as follows.

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 7 - 10
Copyright
Copyright © Applied Probability Trust 1974 

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References

Bishop, J. A. (1972) An experimental study of the cline of industrial melanism in Biston Betularia (Lepidoptera) between urban Liverpool and rural North Wales. Jour. Anim. Ec. 41, 209–243.CrossRefGoogle Scholar
Clarke, C. A. and Sheppard, P. M. (1966) A local survey of the distribution of industrial melanic forms in the moth Biston Betularia and estimates of the selective value of these in an industrial environment. Proc. Roy. Soc. B 165, 424–439.Google Scholar
Griffiths, P. (1972) Ph. D. Thesis. University of Liverpool.Google Scholar
Haldane, J. B. S. (1948) The theory of a cline. Jour. Gen. 48, 277–284.CrossRefGoogle ScholarPubMed
Rall, L. B. (1969) Computation Solution of Nonlinear Operator Equations. Wiley, New York.Google Scholar