Field patterns and experimental results suggest that the effect of zooplankton grazing on the abundance of large colonial cyanobacteria may differ strongly from case to case. In this article we present an extensive analysis of a model that describes the competition between cyanobacteria of the Oscillatoria group and green algae exploited by Daphnia. In particular, we study the response of the model to changes in the nutrient concentration and predation by zooplanktivorous fish. The analysis is repeated for an array of different assumptions on the nutritional value of cyanobacteria and selectivity of zooplankton grazing. When fish predation pressure is so high that Daphnia density is negligible, there is competitive exclusion between the two primary producers, and over a range of nutrient levels, there are two alternative attractors: one with only cyanobacteria and one with only green algae. When fish predation pressure is lower, zooplankton becomes important, and if grazing by these animals is sufficiently selective, this may cause a third attractor on which Daphnia, cyanobacteria, and algae coexist. This "mixed" attractor may be stationary, oscillatory, or chaotic. Depending on the nutrient level, the nutritional value of cyanobacteria, and the selectivity of zooplankton, cyanobacterial dominance may be either induced or eliminated in response to reduced fish predation. This is well in line with the confusing array of field studies and experimental results.
