Assessing the functional response Holling type IV for the diatoms–zooplankton interaction

In the marine ecosystem, the prey–predator interaction between diatoms and zooplankton constitutes a key process for carbon transfer from primary producers to higher trophic levels. This relationship is also a fundamental component of the biogeochemical NPZ (Nitrogen–Phytoplankton–Zooplankton) models. The mathematical modeling of this relationship is known as the functional response of the predator’s feeding rate as a function of prey concentration, although the biological processes involved in this relationship and their consequences are uncertain. For instance, observations in nature suggest the existence of some feedback responses of diatoms with their grazers (zooplankton) through the release of toxic compounds that can slow down or inhibit the growth of their predators as a defense mechanism. This phenomenon may occur during the spring bloom of diatoms in highly productive coastal upwelling systems. In this study, we performed an analytical test of the potential effect of this inhibitory factor on NPZ dynamics. We used a 3-differential equation system based on the Holling IV type functional response to describe the dynamics of the NPZ components by examining the behavior of solutions in the infinite over a 3-D space. The analytical approach to NPZ modeling indicated that in the presence of an inhibitory parameter, the system does not reach equilibrium, i.e., diatoms and zooplankton maintain unpredictable dynamics. These findings were consistent with field data observed at a coastal station in central-southern Chile. Our study thus suggests that feedback mechanisms can indeed exist in the diatom–zooplankton relationship in highly productive coastal upwelling systems, and they should be incorporated into biogeochemical NPZ models.