Intrinsic dynamics and stability properties of size-structured pelagic ecosystem models

Abstract

Although pelagic ecosystem models, coupled with ocean circulation models, are being widely used to quantify fluxes of nutrients and carbon in the ocean at regional and basin scales, relatively little work has been done on understanding their intrinsic dynamics independently of physical forcing. In this study, the dynamics of three common formulations for the NPZD class of models (nutrient, phytoplankton, zooplankton and detritus) using two different types of predation functional response are analysed and compared. Our goal is to characterize the stability properties of this class of models with respect to variations in light and total nutrient concentrations. Despite important structural differences, the different model formulations all show asymptotic stable equilibria at low total nutrient concentrations and high to moderate light intensities, and limit cycle oscillations at low light intensities and high total nitrogen concentrations. Limit cycles are formed through a Hopf bifurcation as a phase lag develops between predator (Z i ) and prey (P i or Z i-1 ) due to a relatively sharp increase in the growth rate of the prey in relation to that of the predator. The use of variable preferences in the functional response provides a density-dependent mechanism that allows the system to self-regulate, increasing system stability considerably, but does not eliminate the instabilities completely. Instabilities occur at light and nutrient levels that correspond to those observed on the bottom of the euphotic zone near the nutricline, where the deep chlorophyll maximum is usually located. This suggests that the deep chlorophyll maximum might be dynamically unstable. This dynamic disequilibrium in species composition and the characteristically long transient times would allow species persistence in the presence of seasonal and mesoscale variations and provide a mechanism for species coexistence in the relatively homogeneous open ocean environment, thereby providing a potential solution for the 'paradox of plankton'. In the multi-species models, the higher diversity of species (wider range of values for the biological parameters) allows biological activity (photosynthesis, grazing and predation) to occur under a wider range of light and nutrient conditions, resulting in higher primary and secondary production and lower nutrient concentrations at light intensities equivalent to those in the upper part of the euphotic zone, than in the single-species model.