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The dispersion of a neutral allele considered as a branching process

Published online by Cambridge University Press:  14 July 2016

Kenny S. Crump  and
John H. Gillespie
Kenny S. Crump*
Affiliation:
National Institute of Environmental Health Sciences, National Institutes of Health
John H. Gillespie
Affiliation:
National Institute of Environmental Health Sciences, National Institutes of Health
*
*On leave from Louisiana Tech University.
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Abstract

The spatial dispersion of a neutral allele is described using the theory of multitype branching processes in which the types represent colonies between which individuals can migrate. Each mutant individual averages less than one offspring, so the mutant population faces certain extinction. Expressions are given for the first two moments of the total number of individuals to visit specified colonies in one, two and three dimensions. Data from Drosophila populations are used to show the improbability of the same neutral allele occurring at widely separated localities.

Keywords

NEUTRAL ALLELEBRANCHING PROCESSMIGRATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 208 - 218
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Dobzhansky, T. and Wright, S. (1947) Genetics of natural populations. XV. Rate of diffusion of a mutant gene through a population of Drosophila pseudo obscura . Genetics 32, 303–324.CrossRefGoogle Scholar
[2] Ewens, W. J. (1969) Population Genetics. Methuen, London.CrossRefGoogle Scholar
[3] Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.Google Scholar
[4] Lebedev, N. N. (1965) Special Functions and Their Applications. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
[5] Kimura, M. and Crow, J. F. (1964) The number of alleles that can be maintained in a finite population. Genetics 49, 725–738.Google Scholar
[6] Maradudin, A. A., Montroll, E. W., Weiss, G. H., Herman, R. and Milnes, H. W. (1960) Green's functions for monatomic simple cubic lattices. Mem. Acad. R. Belg. 14, fasc. 7.Google Scholar
[7] Maruyama, T. (1969) Genetic correlation in the stepping stone model with nonsymmetric migration rates. J. Appl. Prob. 6, 463–477.Google Scholar
[8] McCrea, W. H. and Whipple, F. J. W. (1940) Random paths in two and three dimensions. Proc. R. Soc. Edinburgh 60, 281–298.CrossRefGoogle Scholar
[9] Mode, C. J. (1971) Multitype Branching Processes. American Elsevier, New York.Google Scholar
[10] Pearson, C. E. (1974) Handbook of Applied Mathematics. Van Nostrand Reinhold, New York.Google Scholar
[11] Weiss, G. H. and Kimura, M. (1965) A mathematical analysis of the stepping stone model of genetic correlation. J. Appl. Prob. 2, 129–149.Google Scholar