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A necessary condition for extinction in those bisexual Galton-Watson branching processes governed by superadditive mating functions

Published online by Cambridge University Press:  14 July 2016

David M. Hull
David M. Hull*
Affiliation:
University of Wisconsin-Milwaukee
*
∗ Postal address: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, U.S.A.
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Abstract

Mating functions considered by Asmussen (1980) and Daley (1968) for the class of bisexual Galton-Watson branching processes (GWBP) are shown to be superadditive. Consideration of a process that allows only sibling mating leads to a necessary condition for almost sure extinction in bisexual GWBP governed by superadditive mating functions. A simple example shows that the condition is not sufficient.

Keywords

BISEXUAL GALTON-WATSON BRANCHING PROCESSSIBLING-MATING-ONLY BRANCHING PROCESSEXTINCTION IN A PROCESSSUPERADDITIVE TWO-PLACE FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 847 - 850
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research partly done at the University of Illinois at Chicago Circle.

References

Asmussen, S. (1980) On some two-sex population models. Ann. Prob. 8, 727–744.Google Scholar
Daley, D. J. (1968a) Extinction conditions for certain bisexual Galton-Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315–322.Google Scholar
Daley, D. J. (1968b) Stochastically monotone Markov chains. Z. Wahrscheinlichkeitsth. 10, 305–317.CrossRefGoogle Scholar