Previous studies based on simple non-spatial model have suggested that autoparasitism, in which females develop as primary endoparasitoids of hosts while males develop at the expense of primary parasitoids, stabilizes host-parasitoid steady state. To date, however, how the stabilizing role of autoparasitism would be affected by more complex spatial factors has not been adequately investigated. To address the issue, here we analyzed a spatially extended two-patch host-parasitoid model and compared it with the corresponding non-spatial model. Results showed that in the non-spatial model and the case of autoparasitoid, the host-parasitoid steady states can be unstable if the host׳s intrinsic rate of growth and/or carrying capacity is sufficiently large. However, in the spatially extended two-patch model with parasitoid migration, the unstable host-parasitoid steady states in each local patch may become stable, provided there is certain spatial unevenness in host growth and/or carrying capacity. Therefore, the migration of parasitoid together with spatial unevenness in host growth and/or carrying capacity stabilizes the host-parasitoid interactions. The stabilizing effects are stronger with the host density-dependent migration of parasitoid than with the random migration of parasitoid. In the case of primary parasitoid, the model demonstrated similar stabilizing effects associated with the migration of parasitoid. However, the parameter conditions for stability are much more stringent than in the case of autoparasitoid. We concluded that the stabilizing effects of parasitoid migration and autoparasitism can add to each other, leading to more stable host-parasitoid interactions.
Keywords: Autoparasitism; Biocontrol; Functional response; Parasitoid migration; Two-patch model.
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