Conditions for patchiness in plankton models

Plankton patchiness in homogeneous physical environments is studied in this paper assuming that all involved populations disperse diffusively. A recent but powerful sufficient condition for the emergence of spatial patterns in models with any number of species is systematically applied to all food chain and food web plankton models and the result is rather sharp: all models explicitly containing phytoplankton, zooplankton and planktivorous fish suggest zooplankton patchiness, while models not containing phytoplankton or fish populations do not. The results are in agreement with many previous but particular theoretical studies on plankton patchiness and Turing instability, and a testable prediction of the models satisfying the sufficient predictions is that zooplankton should be more patchy than phytoplankton, a property that is often seen in natural settings. An application to a complex model with five compartments (nutrient, phytoplankton, zooplankton, planktivorous fish, carnivorous fish) highlights the predictive power of the method.