Minimal models of top-down control of phytoplankton

1. A set of models describing the dynamics of top-down control of phytoplan kton by Daphnia in lakes is reviewed. The basis of these models is a simple and well-known model that has been used, among other things, to demonstrat e the paradox of enrichment. 2. We discuss minimal extensions that allow this model to mimic the effects of spatial heterogeneity, planktivory, seasonality and inedible algae. 3. These models generate hypotheses about mechanisms that may cause pattern s observed in the field such as: Spatial heterogeneity stabilizes plankton dynamics, and causes enrichment t o result in a gradual increase of both zooplankton and algal biomass. Daphnia populations can collapse at a threshold level of predation pressure from fish, rather than gradually become less abundant. Absence of Daphnia in summer may typically be caused by the combination of food shortage followed by suppression by fish. The spring clear-water phase and various other aspects of the typical seaso nal dynamics of Daphnia and algal biomass can simply be explained from the seasonal rise and fall of rates of biological processes and the reproductio n cycle of fish. Depending on the conditions, cyanobacterial dominance can be stimulated but also suppressed by Daphnia. 4. We discuss the way in which such very simple models may contribute to th e building of theories about plankton dynamics in the field, and the caveat s of interpreting wrongly the message from models.