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Extinction times for certain predator–prey processes

Published online by Cambridge University Press:  14 July 2016

C. J. Ridler-Rowe
C. J. Ridler-Rowe*
Affiliation:
Imperial College of Science and Technology
*
∗ Postal address: Department of Mathematics, Imperial College of Science and Technology, Huxley Building, Queen's Gate, London SW7 2BZ, UK.
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Abstract

Finiteness of mean extinction times for certain predator-prey models has been established by Hitchcock (1986) with the aid of a criterion of Reuter (1957). Using this criterion and a ‘minimisation' lemma this note shows that the mean extinction times tend to zero as the combined initial population of predators and prey becomes large.

Keywords

MARKOV POPULATION PROCESSUSE OF CRITERIA FOR MEAN ABSORPTION TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 612 - 616
Copyright
Copyright © Applied Probability Trust 1988 

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References

Hitchcock, S. E. (1986) Extinction probabilities in predator-prey models. J. Appl. Prob. 23, 1–13.Google Scholar
Reuter, G. E. H. (1957) Denumerable Markov processes and the associated contraction semigroups on 1. Acta. Math. 97, 1–46.Google Scholar
Reuter, G. E. H. (1961) Competition processes. Proc. 4th Berkeley Symp. Math. Statist. Prob. 2, 421–430.Google Scholar
Ridler-Rowe, C. J. (1967) On a stochastic model of an epidemic. J. Appl. Prob. 4, 19–33.Google Scholar