On the Dynamics of Host-Parasite-Hyperparasite Interactions

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Abstract
A mathematical model is proposed which purports to describe the interaction of a herbivorous host parasitized by a primary parasite which while developing is itself subject to parasitism by the secondary parasite. The important parameters for this interaction are identified and their effect on the feasibility and stability of the system documented. Certain combinations of parameters permit both a host-primary and a host-primary-secondary system to have a locally stable equilibrium. Where this occurs the introduction of a secondary always resulted in the 3 spp. equilibrium being attained. Two effects are noted that are relevant for biological control. Where the host-primary system is stable a secondary will always weaken effective control of the host. Where the host-primary system displays oscillations introduction of a secondary may result in a stable 3 spp. equilibrium. The range of parameter space allowing a stable 3 spp. equilibrium is small compared with that of the 2 spp. system. A 3 spp. system is most easily produced where secondary efficiency exceeds that of the primary.