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Looking forwards and backwards in a bisexual moran model

Published online by Cambridge University Press:  14 July 2016

K. Kämmerle
K. Kämmerle*
Affiliation:
Johannes Gutenberg-Universität Mainz
*
∗ Postal address: Johannes Gutenberg-Universität Mainz, Fachbereich 17 Mathematik, Saarstraße 21, 6500 Mainz, W. Germany.
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Abstract

In this paper a bisexual Moran model is introduced. The population consists of N pairs of individuals. At times t = 1, 2, ·· ·two individuals are born, who ‘choose their parents randomly' and independently of each other. Then one of the pairs is removed and replaced by the two individuals born at that instant.

The extinction probability of the descendants of a single pair and the number of ancestors of a whole generation are studied. A limit result for large population sizes has been derived by diffusion approximation methods.

Keywords

DIFFUSION APPROXIMATIONORNSTEIN–UHLENBECK PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 880 - 885
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Clifford, P. and Sudbury, A. (1985) Looking backwards in time in the Moran model in population genetics. J. Appl. Prob. 22, 437–442.Google Scholar
[2] Ethier, S. N. and Kurtz, T. G. (1986) Markov Processes: Characterization and Convergence. Wiley, New York.Google Scholar
[3] Ewens, W. (1979) Mathematical Population Genetics. Springer-Verlag, Berlin.Google Scholar
[4] Feller, W. (1957) An Introduction to Probability Theory and its Applications, Vol. I. Wiley, New York.Google Scholar
[5] Hoppe, F. M. (1987) The sampling theory of neutral alleles and an urn model in population genetics. J. Math. Biol. 25, 123–160.Google Scholar
[6] Karlin, S. and Taylor, H. M. (1981) A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
[7] Kingman, J. F. C. (1982) On the genealogy of large populations. In Essays in Statistical Science, J. Appl. Prob. 19 A, 27–43.Google Scholar
[8] Kingman, J. F. C. (1982) Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statistics, ed. Koch, G. and Spizzichino, F., North-Holland, Amsterdam, 97–112.Google Scholar
[9] Kingman, J. F. C. (1982) The coalescent. Stoch. Proc. Appl. 13, 235–248.CrossRefGoogle Scholar
[10] Tavare, S. (1984) Line-of-descent and genealogical processes and their applications in population genetics models. Theoret. Popn Biol. 26, 119–164.Google Scholar