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The distribution of gene frequency in a bisexual diploid population

Published online by Cambridge University Press:  24 October 2008

P. A. P. Moran
P. A. P. Moran
Affiliation:
Australian National UniversityCanberra, A.C.T.
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Extract

In this paper we consider a model of a population in which the individuals are diploid and are of two sexes. The individuals have genotypes aa, Aa and AA and we suppose that mutation is occurring in both directions. By supposing that each step in the process is the result of a single death followed by a birth instead of supposing (as in Wright's models (3)) that all the individuals die together at the same instant, to be replaced by a new generation, the mathematical details are much simplified. In this way it is possible to deal exactly with more complicated situations than that of the population of haploid individuals used by Wright in his study of the effects of mutation in a finite population. Moreover, the present model not only involves zygotes and two sexes but is more realistic for those natural populations in which the generations are overlapping.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 4 , October 1958 , pp. 468 - 474
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

(1)Kolmogoroff, A. N.Math. Ann. 94 (1931), 415.CrossRefGoogle Scholar
(2)Moran, P. A. P.Proc. Camb. Phil. Soc. 54 (1958), 60.CrossRefGoogle Scholar
(3)Wright, S.Statistical genetics in relation to evolution. Actualités Scientifiques et Industrielles (Paris, 1939).Google Scholar
(4)Whittaker, E. T. and Watson, G. N.Modern analysis (Cambridge, 1935).Google Scholar