The consequences of stochasticity for self-organized spatial dynamics, persistence and coexistence in spatially extended host-parasitoid communities

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Abstract
We investigate the behaviour of a spatially explicit model of the interaction between two parasitoid species and their common host. One parasitoid species is able to move between host subpopulations at a faster rate than the other parasitoid species which has a higher attack rate. Without space, the model has no equilibrium. With the addition of space, however, Comins & Hassell (1996) have shown that persistence of at least one parasitoid species is generally observed and coexistence of the two parasitoid species can be obtained over a range of parameter values. They observe that this persistence is accompanied by spatial segregation of the competing species within `self-organized' spiral patterns. Here, we investigate the effects of adding various forms of temporal and spatio-temporal stochasticity to the model, and demonstrate that low-to-moderate levels of noise generally inhibit the system from forming clearly defined spirals. Despite this, there are still strong short-range correlations in species densities and this spatial heterogeneity is sufficient to allow persistence and coexistence of competitors. The addition of noise acts to increase the parameter range where the more mobile parasitoid is excluded by the other and decreases the range where the more mobile parasitoid excludes its competitor. Even if the perturbation is strong, for example, with all individuals in a randomly selected 10% of sites being eliminated at each generation, then persistence still occurs and coexistence can be achieved over a suitable range of parameters. Again, the competitive advantage of the more mobile parasitoid is reduced in the presence of this perturbation.