Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T05:01:50.284Z Has data issue: false hasContentIssue false

On stochastic population models in genetics

Published online by Cambridge University Press:  14 July 2016

F. P. Kelly*
Affiliation:
University of Cambridge

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.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211229.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, 415438.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. 325345.Google Scholar
Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 118.CrossRefGoogle Scholar
Moran, P. A. P. (1958) Random processes in genetics. Proc. Camb. Phil. Soc. 54, 6072.Google Scholar
Trajstman, A. C. (1974) On a conjecture of G. A. Watterson. Adv. Appl. Prob. 6, 489493.Google Scholar