IMPLICATIONS OF SPATIAL HETEROGENEITY FOR THE PARADOX OF ENRICHMENT

We analyze a simple model to show that spatial heterogeneity of zoopla nkton can explain discrepancies between the behavior of classical pred ator-prey models and the patterns observed in natural planktonic syste ms. We use a Lotka-Volterra type model of Daphnia and algae. Daphnia o ccupies only part of a total volume whereas the algae grow in the enti re volume and diffuse between the two compartments. This simple spatia l structure suffices to explain the observations that (1) natural Daph nia-algae systems tend to be relatively stable up to high nutrient val ues, and that (2) in the presence of Daphnia edible algae do increase with enrichment. Additionally, the model trivially explains confusing observations of oscillating Daphnia densities in the presence of a pra ctically constant density of edible algae. The model is supported by t he results of a laboratory experiment with a cascade of zooplankton-ph ytoplankton containers, devised originally to test ratio-dependent for aging. We derive minimalizations of our model, which no longer explici tly account for the spatial structure, but still preserve the essentia l behavior of the full model.