Implications of spatial heterogeneity for the paradox of enrichment

Abstract

We analyze a simple model to show that spatial heterogeneity of zooplankton can explain discrepancies between the behavior of classical predator-prey models and the patterns observed in natural planktonic systems. We use a Lotka-Volterra type model of Daphia and algae. Daphnia occupies only a part of total volumes whereas the algae grow in the entire volume and diffuse between the two compartments. This simple spatial structure suffices to explain the observations that (1) natural Daphnia-algae systems tend to be relatively stable up to high nutrient values, 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 practically constant density of edible algae. The model is supported by the results of a laboratory experiment with a cascade of zooplankton-phytoplankton containers, devised originally to test ratio-dependent foraging. We derive minimalizations of our model, which no longer explicitly account for the spatial structure, but still preserve the essential behavior of the full model.