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Stochastic models for interference between searching insect parasites

Published online by Cambridge University Press:  17 February 2009

Phil Diamond
Phil Diamond
Affiliation:
Mathematics Department, University of Queensland, St. Lucia, Queensland 4067, Australia.
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Abstract

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Competition between a finite number of searching insect parasites is modelled by differential equations and birth-death processes. In the one species case of intraspecific competition, the deterministic equilibrium is globally stable and, for large populations, approximates the mean of the stationary distribution of the process. For two species, both inter- and intraspecific competition occurs and the deterministic equilibrium is globally stable. When the birth-death process is reversible, it is shown that the mean of the stationary distribution is approximated by the equilibrium. Confluent hypergeometric functions of two variables are important to the theory.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 3 , January 1989 , pp. 268 - 277
Copyright
Copyright © Australian Mathematical Society 1989

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