This paper examines the phenomenon of algal blooms in phytoplankton po
pulations in the context of a simple spatially homogeneous model. The
effects of a changing environment are represented by time dependence i
n the model's parameters. It is argued that the interaction of grazing
pressure and nutrient limitation gives rise to excitability in the dy
namics of the model. This property allows the use of asymptotic analys
is to derive a connection between the nature of the environmental forc
ing and the production of a bloom. Numerical experiments demonstrate t
he accuracy of this analysis and also show hew, and under what conditi
ons, its effectiveness starts to break down. Some of the biological im
plications of these results are discussed.