A mechanistic model of the adaptation of phytoplankton photosynthesis

Abstract

The mechanistic model of the phytoplankton photosynthesis-light intensity relationship by Eilers and Peeters (1988.Ecol. Modelling 42, 199–215) is investigated mathematically. The model is based on the physiological idealization of transition probabilities between states of the photosynthetic factories,PSF. The model was found to have under constant light condition a globally stable unique positive equilibrium, while under periodically varying light (e.g. daily periodicity) there exists a unique globally asymptotically stable periodic solution. Based on this, the adaptation to a change of light intensity is defined as a process by which the state ofPSF converges to an equilibrium. Assuming that phytoplankton regulates its photosynthetic production rate with a certain strategy which maximizes production, two such possible strategies were examined. Both the instantaneous and the integral maximal photosynthetic production were shown to have the same result. With realistic qualitative assumptions of the shape of the dependence of the four model parameters on the light intensity to which phytoplankton is adapted, the numerical values of parameters under both constant and periodically varying conditions are determined by applying Pontryagin's maximum principle.