A simple mathematical model for seasonal planktonic blooms

Abstract

We show how the inclusion of the defense strategy by different species can alter the prediction of simple models. One of the defense strategy by the phytoplankton population against their grazer is the release of toxic chemicals. In turn the zooplankton population reduces there predation rate over toxin producing phytoplankton (TPP) to protect themselves from those toxic chemicals. Thus, when the level of toxicity is high, the grazing pressure is low and when the level of toxicity is low or when the toxin is absent, the grazing pressure is high. Here we have considered a TPP-zooplankton system where the rate of toxin liberation and the predation rate vary with zooplankton abundance. We observe that our proposed model has the potential to show different dynamical behaviour that are similar to that seen in real-world situations. Further, we consider three different functional forms for the distribution of the toxins and compare them using latin hypercube sampling technique and found that the functional forms seem to have no effect in determining the final outcome of the system.