Non-linear dynamics of a pelagic ecosystem model with multiple predator and prey types

Using numerical techniques, we explored the dynamics of a one-dimensional, six-component nutrient–phytoplankton–zooplankton (NPZ) model in which zooplankton grazed on a mixed prey field. Five alternative functional forms were implemented to describe zooplankton grazing, and the form for predation on mesozooplankton was prescribed by a product of a specific predation rate (h) and the mesozooplankton concentration raised to a power (q), which we varied between one and two. With all five grazing functions, Hopf bifurcations, where the form of the solution transitioned between steady equilibrium and periodic limit cycles, persisted across the q–h parameter space. Regardless of the values of h and q, with some forms of the grazing function, we were unable to find steady equilibrium solutions that simultaneously comprised non-zero concentrations for all six model components. Extensions of Michaelis–Menten-based single resource grazing formulations to multiple resources resulted in periodic solutions for a large portion of the q–h space. Conversely, extensions of the sigmoidal grazing formulation to multiple resources resulted in steady solutions for a large portion of q–h parameter space. Our results demonstrate the consequences of the functional form of biological processes on the form of the model solutions. Both the steady or oscillatory nature of state variable concentrations and the likelihood of their elimination are important considerations for ecosystem-modelling studies, particularly when attempting to model an ecosystem in which multiple phytoplankton and zooplankton components are thought to persist simultaneously for at least a portion of the seasonal cycle.