Non-linear dynamics of marine ecosystem models

Abstract

Despite a rapid trend towards more realistic Nutrient-Phytoplankton-Zooplankton (NPZ) models, in which zooplankton are presented with multiple nutritional resources, investigations into the fundamental dynamics of these newer models have been limited. The objective of this dissertation was to explore the dynamical behavior of such NPZ models parameterized for the coastal Gulf of Alaska. With alternative stationary forcing regimes and zooplankton grazing functions, the dynamics of one-dimensional NPZ models were investigated for a range of specific predation rates (h) and predation exponents (q), which together define the form of the predation (model closure) function. Oscillations in state variables are shown to be an intrinsic property of the NPZ models, not dependent on variable seasonal forcing for their existence. Increasing mixed layer diffusivity or reducing mixed layer depth increased model excitability; it is hypothesized that this is due to the resultant increase in flux of utilizable nutrient. Model behavior was also strongly influenced by the form of both the grazing and predation functions. For all of the grazing functions implemented, 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 steady equilibrium solutions that simultaneously comprised non-zero concentrations for all model components could not be found. The inclusion of sinking detritus in the model had important implications for the composition and excitability of model solutions, generally increasing the region of q-h space for which oscillatory solutions were found. Therefore, in order to correctly simulate the depth-explicit concentrations of model components, or to have an accurate understanding of the potential excitability of the system, inclusion of this component is valuable. This dissertation highlights the importance of understanding the potential impact that choice of functional response may have on the intrinsic oscillatory nature of a model prior to interpreting results from coupled bio-physical simulations. As we come to rely more on ecosystem models as a tool to interpret marine ecosystem functionality it will be important to improve our understanding of the non-linear behavior inherent in these models.