Chaos in plankton models: Foraging strategy and seasonal forcing

The dynamics of plankton ecosystems have long been of interest to ecologists and mathematicians, with some of the earliest examples of chaotic dynamics being provided by ecological models. Mortality terms were initially identified as determinants of chaos in simple ecosystem models, but relatively little attention has been given to the role of grazing terms. The behaviour of omnivores has arisen as a particularly interesting case. Recent experiments have revealed that plankton omnivores may change their feeding behaviour in response to changes in temperature, and is therefore of interest to plankton modellers contributing models of biogeochemical cycling in the ocean to climate models. In this paper we consider the role of an omnivorous zooplankton's foraging strategy, seasonal variations and the choice of functional forms on the dynamics of a simple two prey–one predator plankton model, within a Conservative-Normal framework. We find that assumptions about the way the predator forages for food, the specific form for grazing and mortality terms, and seasonal changes in the environment all qualitatively affect the predictions that the model will produce. In particular, discriminate foraging and seasonal variations engender chaotic dynamics while Holling Type III grazing and quadratic mortality terms suppress chaotic dynamics.