Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-09T10:15:15.967Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 9 - 16
Copyright
Copyright © Applied Probability Trust 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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