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On the offspring number distribution in a genetic population

Published online by Cambridge University Press:  14 July 2016

M. W. Feldman*
Affiliation:
Monash University and Stanford University

Extract

We consider a dioecious diploid population of N individuals, N1 males and N2 = NN1 females. The alleles will be represented by a and A, and the population reproduces according to the Wright scheme, that is, by random mating with non-overlapping generations.

Type
Research Papers
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Crow, J. F. and Kimura, M. (1956) Some genetic problems in natural populations. Proceedings of the Third Berkeley Symposium in Mathematical Statistics and Probability, V, 122. University of California Press.Google Scholar
Feller, William (1951) Diffusion processes in genetics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 227246, University of California Press.Google Scholar
Karlin, Samuel and Mcgregor, James (1964) Direct product branching processes and related Markov chains, Proc. Nat. Acad. Sci., 51, 598602.CrossRefGoogle ScholarPubMed
Karlin, Samuel (1966) Stochastic Processes, Academic Press, New York.Google Scholar
Kimura, M. (1957) Some problems of stochastic processes in genetics. Ann. Math. Statist. 28, 882901.CrossRefGoogle Scholar
Kimura, Motoo and Crow, James F. (1963) The measurement of effective population number. Evolution 17, No. 3, 279288.CrossRefGoogle Scholar
Moran, P. A. P. (1958a) Random processes in genetics. Proc. Cambridge Philos. Soc. 54, 6071.CrossRefGoogle Scholar
Moran, P. A. P. (1958b) A general theory of the distribution of gene frequencies II. Nonoverlapping generations. Proc. Roy. Soc., B, 149, 113116.Google Scholar
Moran, P. A. P. and Watterson, G. A. (1959) The genetic effects of family structure in natural populations, Austral. J. Biol. Sci. 12, 115.CrossRefGoogle Scholar
Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar
Watterson, G. A. (1960) Ph. D. Thesis (unpublished), Australian National University.Google Scholar
Watterson, G. A. (1962) Some theoretical aspects of diffusion theory in population genetics. Ann. Math. Statist. 33, 939957.CrossRefGoogle Scholar
Watterson, G. A. (1964) The application of diffusion theory to two population models of Moran. J. Appl. Prob. 1, 233246.CrossRefGoogle Scholar
Wright, S. (1931) Evolution in Mendelian populations. Genetics 16, 97159.CrossRefGoogle ScholarPubMed