Regulation of Predator-Prey Systems through Spatial Interactions: A Possible Solution to the Paradox of Enrichment

Many natural predator-prey systems oscillate but persist with densities staying well away from zero. Non-spatial predator-prey models predict that in environments where prey on itself can do well, a predator-prey system can oscillate with troughs in which the populations become vanishingly small. This phenomenon has become known as the paradox of enrichment. In this paper the role of space in bounding overall population oscillations is analysed in the simplest version of spatial predator-prey models: a two-patch model for a Lotka-Volterra system and a Rosenzweig-MacArthur system with logistic prey growth and Holling type II functional response of predator to prey density within each patch. It was found that the spatial interactions can bound the fluctuations of the predator-prey system and regulate predator and prey populations, even in the absence of density dependent processes. The spatial dynamics take the form of locally asynchronous fluctuations. Enrichment of the environment in a two-patch model does not necessarily have the paradoxical consequence that the populations reach densities where extinction is likely to occur.