Environmental Variability, Migration, and Persistence in Host-Parasitoid Systems

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Abstract
Many populations of insects are thought to be limited by the action of natural enemies, but controversy has surrounded the basic dynamic framework of such systems. Two different views, equilibrium and "spreading of risk," have arisen, and they differ radically in their emphasis on the roles of environmental variability, spatial subdivision, and migration. A class of hybrid host-parasitoid models is presented, which incorporates elements of both theories, and its persistence behavior is compared with predictions of these theories. Local-stability analysis is used to explore the behavior of the model in an equilibrium setting, in the absence of environmental variability. Spatial subdivision and migration have no effect (or a detrimental one) on the stability of a collection of host-parasitoid subpopulations; they therefore have no effect on persistence in an equilibrium setting. Persistence is also shown to be unlikely in the absence of density-dependent coupling between the host and parasitoid, despite environmental variability and migration. When these features are combined, however, even an unstable host-parasitoid system can be highly persistent. I also show that (1) migration can strongly buffer host and parasitoid densities, but if migration rates themselves are high or too strongly density-dependent, persistence may not occur; (2) environmental variability, model stability, and migration rate have qualitative effects on host density and variability; and (3) the temporal patterns of parasitism are also affected by migration and environmental variability.