Mathematical Modelling of Oxygen - Plankton System under the Climate Change

Oxygen production due to phytoplankton photosynthesis is an important phenomenon keeping in mind the underlying dynamics of marine ecosystems. However, despite its crucial importance, not only for marine but also for terrestrial ecosystems, the coupled oxygen-plankton dynamics have been overlooked. This dissertation aims to provide insight into an oxygen-plankton system using mathematical modelling. We firstly develop a ‘baseline’ oxygen-phytoplankton model which is then further developed through the addition of biologically relevant factors such as plankton respiration and the predator effect of zooplankton. The properties of the model have been studied both in the nonspatial case, which corresponds to a well mixed system with a spatially uniform distribution of species, and in the spatially explicit extension, by taking into account the transport of oxygen and movement of plankton by turbulent diffusion. Since the purpose of this work is to reveal the oxygen dynamics, the effect of global warming is considered taken into consideration and modelled by various oxygen production rates and phytoplankton growth functions in Chapters 5 and 6. It is shown that sustainable oxygen production is only possible in an intermediate range of the production rate. If the oxygen production rate becomes sufficiently low or high, in the course of time, the system’s dynamics shows abrupt changes resulting in plankton extinction and oxygen depletion. We show that the spatial system’s sustainability range is larger that of the corresponding nonspatial system. We show that oxygen production by phytoplankton can stop suddenly if the water temperature exceeds a certain critical threshold. Correspondingly, this dissertation reveals the scenarios of extinction which can potentially lead to an ecological disaster.