Predator-prey interactions in a nonequilibrium context: the metapopulationapproach to modeling "hide-and-seek" dynamics in a spatially explicit tri-trophic system

Predators and prey are usually heterogeneously distributed in space so that the ability of the predators to respond to the distribution of their prey may have a profound influence on the stability and persistence of a predato r-prey system. A special type of dynamics is "hide-and-seek" characterized by a high turnover rate of local populations of prey and predators, because once th predators have found a patch of prey they quickly overexploit it. whereupon the starving predators either should move to better places or die . Continued persistence of prey and predators thus hinges on a long-term ba lance between local extinctions and founding of new subpopulations. The col onization rate depends on the rate of emigration from occupied patches and the likelihood of successfully arriving at a suitable new patch, while exti nction rate depends on the local population dynamics. Since extinctions and colonizations are both discrete probabilistic events, these phenomena are most adequately modeled by means of a stochastic model. In order to demonst rate the qualitative differences between a deterministic and stochastic app roach to population dynamics, a spatially explicit tritrophic predator-prey model is developed in a deterministic and a stochastic version. The model is parameterized using data for the two-spotted spider mite Tetranychus urt icae) and the phytoseiid mite predator Phytoseiulus persimilis inhabiting g reenhouse cucumbers. Simulations show that the deterministic and stochastic approaches yield dif ferent results. The deterministic version predicts that the populations wil l exhibit violent fluctuations, implying that the system is fundamentally u nstable. In contrast. the stochastic version predicts that the two species will be able to coexist in spite of frequent local extinctions of both spec ies, provided the system consists of a sufficiently large number of local p opulations. This finding is in agreement with experimental results. It is t herefore concluded that demographic stochasticity in combination with dispe rsal is capable of producing and maintaining sufficient asynchrony between local populations to ensure long-term regional (metapopulation) persistence .