Adding Detritus to a Nutrient-Phytoplankton-Zooplankton Model:A Dynamical-Systems Approach

The dynamics of two plankton population models are investigated to examine sensitivities to model complexity and to parameter values. The models simulate concentrations of nutrients, phytoplankton, zooplankton and detritus in the oceanic mixed layer. In Model 1, zooplankton can graze only upon phytoplankton, whereas in Model 2 they can graze upon phytoplankton and detritus. Both feeding strategies are employed by zooplankton in the ocean, and both are features of models in the literature. Each model here consists of four coupled ordinary differential equations, and can exhibit unforced oscillations (limit cycles) of the four concentrations. By constructing diagrams that show how steady states and oscillations persist as each parameter is varied, a general picture of the dynamics of each model is built up. The addition of the detritus pool to an earlier nutrient–phytoplankton–zooplankton model appears to have little influence on the dynamics when the zooplankton cannot graze upon the detritus (Model 1), but if the zooplankton can graze upon the detritus (Model 2), then the dynamics are affected in a significant way. These results, obtained using the theory of dynamical systems, enhance our knowledge of the factors governing the dynamics of plankton population models.