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The Galton-Watson predator-prey process

Published online by Cambridge University Press:  14 July 2016

John Coffey  and
Wolfgang J. Bühler
John Coffey*
Affiliation:
Purdue University Calumet
Wolfgang J. Bühler*
Affiliation:
Johannes Gutenberg-Universität Mainz
*
∗Postal address: Department of Mathematical Sciences, Purdue University Calumet, Hammond, IN 46323, USA.
∗∗Postal address: Fachbereich Mathematik, Johannes Gutenberg-Universität Mainz, Saarstr. 21, D-W6500 Mainz, Germany.
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Abstract

A probabilistic predator-prey model is constructed using linked discrete-time branching-type processes. A necessary and sufficient condition for positive probability of survival of both populations is given.

Keywords

DISCRETE-TIME PROBABILISTIC PREDATOR-PREY PROCESSBRANCHING PREDATOR-PREY PROCESSCONDITIONS FOR POSITIVE PROBABILITY OF SURVIVAL FOR BOTH POPULATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 9 - 16
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Partially supported by a Scholarly Research Release award (Spring, 1989) from the College of Liberal Arts and Sciences, Purdue University Calumet.

References

[1] Erickson, K. B. (1973) Self annihilating branching processes. Ann. Prob. 1, 926–946.CrossRefGoogle Scholar
[2] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[3] Karlin, S. and Kaplan, N. (1973) Criteria for extinction of certain population growth processes with interacting types. Adv. Appl. Prob. 5, 183–199.Google Scholar
[4] Neveu, J. (1975) Discrete-Parameter Martingales. North-Holland, Amsterdam.Google Scholar
[5] Schuh, H.-J. (1976) A condition for the extinction of a branching process with an absorbing lower barrier. J. Math. Biol. 3, 271–281.Google Scholar