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Fixation in Conditional Branching Process Models in Population Genetics

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Thomas Prince  and
Neville Weber
Thomas Prince*
Affiliation:
University of Sydney
Neville Weber*
Affiliation:
University of Sydney
*
∗Postal address: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia.
∗Postal address: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia.
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Abstract

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An alternative version of the necessary and sufficient condition for almost sure fixation in the conditional branching process model is derived. This formulation provides an insight into why the examples considered in Buckley and Seneta (1983) all have the same condition for fixation.

Keywords

Fixationbranching processWright-Fisher modelbisexual model

MSC classification

Secondary: 92D25: Population dynamics (general) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 1103 - 1110
Copyright
Copyright © Applied Probability Trust 2007 

References

Buckley, M. J. and Seneta, E. (1983). The genetic balance between varying population size and selective neutrality. J. Math. Biol. 17, 217–222.CrossRefGoogle Scholar
Daley, D. J. (1968). Extinction conditions for certain Galton–Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315–322.CrossRefGoogle Scholar
Donnelly, P. (1986). A genealogical approach to variable-population-size models in population genetics. J. Appl. Prob. 23, 283–296.Google Scholar
Karlin, S. and McGregor, J. (1964). Direct product branching processes and related Markov chains. Proc. Nat. Acad. Sci. USA 51, 598–602.Google Scholar
Möhle, M. (1997). Fixation in bisexual models with variable population sizes. J. Appl. Prob. 34, 436–448.Google Scholar
Moran, P. A. P. (1958). Random processes in genetics. Proc. Camb. Philos. Soc. 54, 60–71.Google Scholar
Moran, P. A. P. and Watterson, G. A. (1959). The genetic effects of family structure in natural populations. Austral. J. Biol. Sci. 12, 1–15.Google Scholar