Two Approaches to Modeling Phytoplankton Biomass Dynamics Based on the Droop Model

Abstract

This work continues the study of the Droop model based on the concept of cell quota. Description of the photosynthetic processes in phytoplankton includes in the model structure. The concept of chlorophyll quota is used. It is the proportion of photosynthetic substances in plant cells. In addition to the chlorophyll quota, the photosynthetic activity of phytoplankton is determined by external conditions, primarily by the level of photosynthetically active radiation (PAR). The model is based on separating the dependence of phytoplankton reproduction on external conditions according to the stages of photosynthesis. The light stage is largely determined by the PAR, and the dark stage is limited by the nutrient resource under the controlling influence of the temperature of the aquatic environment. In order to develop the model, the storage of energy in the light stage of photosynthesis is described in detail. Energy is stored in the form of energy-intensive substances in macroergic molecules (macroergs). The most common cell macroerg is adenosine triphosphate (ATP). The proportion of ATP in phytoplankton varies depending on the light regime and on the energy amount stored in the dark stage. The model includes the Droop kinetics and equations for the dynamics of the chlorophyll quota and the ATP pool. The conditions for the existence and stability of equilibrium solutions are compared for the same values of parameters common to both models. The greatest influence on the dynamic modes of the minimum value of the cell quota has been established. The proportion of biomass associated with the light period of photosynthesis is also significant. For the first model that is the biomass produced during daylight hours. And in terms of the second model, it is the biomass formed due to the energy of ATP stored in the light phase. The influence of the structure of dynamic models on the daily and annual dynamics of phytoplankton was revealed. Scenarios of behavior of models under various lighting conditions, including constant and periodically changing lighting, have been studied.