Early Warning Signals of Oxygen-Plankton Dynamics: Mathematical Approach

Abstract

Any significant decrease in net oxygen production by phytoplankton is likely to result in the loss ofatmospheric oxygen and the global extinction of living beings owing to more than half of the atmospheric oxygenprovided by marine phytoplankton. The rate of oxygen production is known to depend on water temperature andhence can therefore be affected by global warming. In this work, it is assumed that oxygen production varies withtime under the effect of increasing temperature. This ecological problem is addressed theoretically by a couple ofplankton-oxygen dynamics. A nonlinear mathematical model is considered to investigate the effect of temperatureon oxygen-plankton dynamics. The model is analysed analytical and numerical ways, based on the behavior andcomplexity of the system’s steady state. From the analysis of the model, it has been observed that as temperaturelevel goes above the critical threshold of oxygen production rate the equilibrium density of plankton populationdecrease due to a decrease in oxygen concentration. It has also been shown that the system can exhibit sustainabledynamics that can still lead to an environmental disaster, i.e. oxygen depletion and plankton extinction. In this case,extinction takes place after a considerable length of time.