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A predator-prey interaction between spatially dispersed populations can be considered as many local interactions connected by dispersal. Even when the local subsystems (cells) quickly become extinct in isolation, an ensemble of interconnected cells can, under certain conditions, persist much longer. These conditions include: (1) sufficiently low exchange rates among cells; or (2) a sufficiently high level of environmental stochasticity (noise), either of which can prevent local populations from becoming synchronized; or (3) a large number of cells within the system. Computer simulations based on a broadly applicable predator-prey model demonstrate the efficacy of the conditions 1-3; neither spatial structure (texture) nor density-dependent dispersal are additionally required to obtain long-term persistence. The critical problem of avoiding synchrony in a spatially contiguous, locally unstable system can apparently be solved by size alone. If the system is large enough, it should tend to fragment into two or more hypercell subsystems with the low exchange rates that permit these subsystems to remain out of phase with each other. Environmental noise that is spatially correlated on scales somewhat smaller than the size of the system may also generate or help maintain the hypercells. These features create a mosaic of fluctuating subpopulations that can yield remarkably constant population densities for the system as a whole.
Philip H. Crowley (Sun,) studied this question.