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A Mendelian Markov process with multinomial transition probabilities

Published online by Cambridge University Press:  14 July 2016

R. G. Khazanie  and
H. E. McKean
R. G. Khazanie
Affiliation:
University of Vermont
H. E. McKean
Affiliation:
Purdue University
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Extract

The utility of the moments of the binomial distribution in finding the n-stage transition probabilities was indicated by Khazanie and McKean (1966). In this paper, maintaining the same breeding structure as in the two-allele case, it is proposed to extend the technique to cover the multiallelic case in general, with specific emphasis on the triallelic case. The existing literature on the multiple allelic case is at best scanty (see for example Kimura (1955)). Section 6 will briefly touch on a further extension to multiple loci which segregate independently.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 353 - 364
Copyright
Copyright © Applied Probability Trust 

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References

[1] Khazanie, R. G. (1965) On a Mendelian Markov Process with Multinomial Transition Probabilities. Ph. D. thesis, Purdue University Libraries.Google Scholar
[2] Khazanie, R. G. and Mckean, H. E. (1965) A Mendelian Markov process with multinomial transition probabilities. II. Multiple alleles and multiple loci. Mimeo series No. 36, Dept. of Statistics, Purdue University.Google Scholar
[3] Khazanie, R. G. and Mckean, H. E. (1966) A Mendelian Markov process with binomial transition probabilities. Biometrika 53, 37–48.CrossRefGoogle ScholarPubMed
[4] Kimura, M. (1955) Random genetic drift in multi-allelic locus. Evolution 9, 419–435,CrossRefGoogle Scholar