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On stochastic population models in genetics

Published online by Cambridge University Press:  14 July 2016

F. P. Kelly
F. P. Kelly*
Affiliation:
University of Cambridge
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Abstract

Trajstman (1974) has shown that two different population models used to study the number of mutant forms maintained in a population have a certain marginal stationary distribution in common. In this note a general stochastic population model is proposed which subsumes these two models and shows that their transition rates are also related.

Keywords

GENETIC POPULATION MODELSEQUILIBRIUM DISTRIBUTIONREVERSIBILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 127 - 131
Copyright
Copyright © Applied Probability Trust 1976 

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References

Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
Karlin, S. and Mcgregor, J. (1967) The number of mutant forms maintained in a population. Proc. 5th Berkeley Symp. Math. Statist. Prob. 4, 415–438.Google Scholar
Kendall, D. G. (1975) Some problems in mathematical genealogy. Perspectives in Probability and Statistics: Papers in Honour of M. S. Bartlett, ed. Gani, J. Applied Probability Trust: distributed by Academic Press, London. 325–345.Google Scholar
Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 1–18.CrossRefGoogle Scholar
Moran, P. A. P. (1958) Random processes in genetics. Proc. Camb. Phil. Soc. 54, 60–72.Google Scholar
Trajstman, A. C. (1974) On a conjecture of G. A. Watterson. Adv. Appl. Prob. 6, 489–493.Google Scholar