The role of higher predation in plankton population models

Abstract

Zooplankton mortality in plankton population models is often represented by the so-called closure term. Recently, much attention has been paid to the choice of functional form used for the closure term, primarily due to the influential paper by Steele and Henderson (J. Plankton Res., 14, 157-172, 1992). Here we reveal an inconsistency in the normalization of Steele and Henderson's models and show that unforced short-term oscillations (limit cycles) can occur when a quadratic closure term is used. Furthermore, we contradict the hypothesis regarding the relationship between nutrient steady-state values and the choice of closure term: using the seven-component plankton model of Fasham (The Global Carbon Cycle, Heimann, M. (ed.), pp. 457-504, 1993) with four alternative closure terms, we find the nutrient value to depend more upon the choice of parameter values than on the choice of closure term. However, our results agree with and strengthen the general conclusion of Steele and Henderson's work: that the choice of closure term can strongly influence the dynamics of models.