Are pelagic systems inherently unstable? a model study

Abstract

Recent model work on patchiness of biological factors in the open sea (Steele, 1974a; Dubois, 1975) neglect the recycling of nutrients, which is necessary for continuous primary production. Steele shows that an inherently unstable primary producer—herbivore system together with diffusive processes can cause patchiness in these populations. The purpose of the present study is to investigate the stability properties of phytoplankton-zooplankton models, when recycling is taken into account, and how these properties are influenced by the use of Michaelis-Menten expressions for grazing and nutrient uptake. Also the effects of two different so called threshold functions in the grazing are investigated (i.e. functions, which give low or zero zooplankton filtration rate at low food concentrations). An analytical investigation of a two-component model shows that the incorporation of recycling pathways radically changes the stability properties of the model. Simulations of a four-component model with nutrient recycling confirm this conclusion and furthermore given the following results: 1. (1) If one or two of the three recycling pathways in the model are omitted, the model remains stable, but exhibits a greater tendency to damped oscillations if perturbed. 2. (2) When Michaelis-Menten functions are used for both the nutrient dependence of phytoplankton production and the dependence of zooplankton grazing on food concentration or only for the latter, asymptotically stable as well as nonconvergent oscillating cases can be obtained depending on the parameter values. With a Michaelis-Menten function only in the primary production, exclusively asymptotically stable cases were obtained, but some of these exhibited so weakly damped oscillations, that they in practice Could be considered non-convergent. 3. (3) Only one of the two tested threshold responses in zooplankton grazing have a marked stabilizing effect on the model It is pointed out, that during the highly productive seasons the recycling of matter is a vital feature of the pelagic phytoplankton-zooplankton system, and that only in special cases can an omission of the recycling processes in a functional model of this system be justified.