MIGRATION ALONE CAN PRODUCE PERSISTENCE OF HOST-PARASITOID MODELS

Examines different initial conditions of otherwise identical coupled systems. This mechanism can maintain bounded oscillations of even a small number of deterministic Nicholson-Bailey models of host-parasitoid interactions coupled by migration. Single-patch models of this sort are notoriously unstable, exhibiting trajectories with population explosions and crashes of increasing amplitude. Persistence and complicated dynamics are possible when the number of patches is large enough. The author here examines the parameter values for which stable oscillations exist in a globally coupled system, indicating that low migration rates are indeed necessary for persistence by this mechanism but that increasing the number of patches may not increase probabilities of persistence. This mechanism of persistence operates even in the presence of some stochasticity in the model parameters. -from Author