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The transient behaviour of the Moran model in population genetics

Published online by Cambridge University Press:  24 October 2008

Peter Donnelly
Peter Donnelly
Affiliation:
Balliol College, Oxford†
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Abstract

This paper presents an alternative analysis of the behaviour of the Moran model. Using some of the techniques developed in the study of interactive particle systems, a process which is dual to the Moran model is constructed. Exact analysis of this dual process is considerably easier than for the original model. Because of the relationship between the two processes it is then possible to find the distribution of the Moran model.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 349 - 358
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Donnelly, P. J. and Welsh, D. J. A.. Finite particle systems and infection models. Math. Proc. Cambridge Philos. Soc. 94 (1983), 167–182.CrossRefGoogle Scholar
[2]Durrett, R.. An introduction to infinite particle systems. Stochastic Process. Appl. 11 (1981), 109–150.CrossRefGoogle Scholar
[3]Ewens, W. J.. Mathematical Population Genetics. (Springer, 1979).Google Scholar
[4]Griffeath, D.. Additive and Cancellative Interacting Particle Systems. Lecture Notes in Mathematics, vol. 724. (Springer, 1979).CrossRefGoogle Scholar
[5]Harris, T.. Additive set valued Markov processes and percolation methods. Ann. Probab. 6 (1978), 355–378.Google Scholar
[6]Karlin, S. and McGregor, J.. On a genetics model of Moran. Proc. Cambridge Philos. Soc. 58 (1962), 299–311.CrossRefGoogle Scholar
[7]Moran, P. A. P.. Random processes in genetics. Proc. Cambridge Philos. Soc. 54 (1958), 60–71.CrossRefGoogle Scholar
[8]Slater, L. J.. Generalised Hypergeometric Functions (Cambridge University Press, 1966).Google Scholar