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Stability in Insect Host-Parasite Models

M. P. Hassell and R. M. May
Journal of Animal Ecology
Vol. 42, No. 3 (Oct., 1973), pp. 693-726
DOI: 10.2307/3133
Stable URL: http://www.jstor.org/stable/3133
Page Count: 34
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Stability in Insect Host-Parasite Models
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Abstract

(1) Several models for host-parasite interactions are discussed. Some of these are based on random search where searching efficiency is either assumed to be constant or to depend on host and/or parasite density. In the others, the parasites are assumed to search in a non-random way, tending to aggregate in unit areas where host density is high. The most complex model considered includes three basic parasite responses: the functional response to host density, the response to parasite density and the response to the host distribution. (2) For each of these models, the significant parameters affecting stability are presented and the stability boundaries illustrated where possible. Only mutual interference between searching parasites, aggregation of parasites in unit areas where host density is relatively high and some degree of spatial or temporal asynchrony were found to contribute to stability. (3) The parameters that affect the equilibrium levels of host and parasite populations and those also affecting stability are discussed in the context of biological control. It is concluded that a high basic searching efficiency, a low handling time, some degree of interference and parasite aggregation are all optimum searching characteristics for biological control.

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