Field patterns and experimental results suggest that the effect of zooplank
ton grazing on the abundance of large colonial cyanobacteria may differ str
ongly from case to case. In this article we present an extensive analysis o
f a model that describes the competition between cyanobacteria of the Oscil
latoria group and green algae exploited by Daphnia. In particular, we study
the response of the model to changes in the nutrient concentration and pre
dation by zooplanktivorous fish. The analysis is repeated for an array of d
ifferent assumptions on the nutritional value of cyanobacteria and selectiv
ity of zooplankton grazing. When fish predation pressure is so high that Da
phnia density is negligible, there is competitive exclusion between the two
primary producers, and over a range of nutrient levels, there are two alte
rnative attractors: one with only cyanobacteria and one with only green alg
ae. When fish predation pressure is lower, zooplankton becomes important, a
nd if grazing by these animals is sufficiently selective, this may cause a
third attractor on which Daphnia, cyanobacteria, and algae coexist. This "m
ixed" attractor may be stationary, oscillatory, or chaotic. Depending on th
e nutrient level, the nutritional value of cyanobacteria, and the selectivi
ty of zooplankton, cyanobacterial dominance may be either induced or elimin
ated in response to reduced fish predation. This is well in line with the c
onfusing array of field studies and experimental results.