By Yadigar Sekerci and Sergei Petrovskii
12 November 2015
(Bulletin of Mathematical Biology) – We have studied the oxygen–plankton dynamics using a mathematical model that takes into account oxygen production in photosynthesis, plankton respiration, and the effect of zooplankton predation on phytoplankton. The model is described by a system of three coupled ODEs in the nonspatial (well-mixed) case and by three corresponding diffusion–reaction PDEs in the spatially explicit case. The system dynamics have been revealed by some analytical approaches and extensive numerical simulations. We ﬁrst considered a nonspatial system to reveal the structure of the parameter space and showed that the system is sustainable only for intermediate values of the oxygen production rate. For a sufﬁciently low or sufﬁciently high oxygen production rate, plankton goes extinct and oxygen is depleted. For a baseline oxygen–phytoplankton system neglecting the presence of zooplankton, the system is sustainable unless the production rate becomes too low. We then considered the dynamics of the corresponding nonautonomous system where the oxygen production rate slowly changes with time to take into account the increase in the water temperature due to the climate change. We showed that a sufﬁciently large increase or decrease in the production rate results is a bifurcation leading to a sudden depletion of oxygen and plankton extinction. […]
Using a model of coupled oxygen–plankton dynamics, we have identiﬁed another possible consequence of the global warming that can potentially be more dangerous than all others. We have shown that the oxygen production by marine phytoplankton can stop suddenly if the water temperature exceeds a certain critical value. Since the ocean plankton produces altogether more than one half of the total atmospheric oxygen, it would mean oxygen depletion not only in the water but also in the air. Should it happen, it would obviously kill most of life on Earth.