Early Warning Signals of Oxygen-Plankton Dynamics: Mathematical Approach

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.

PDF

___

[1] Abbott, M. R., Phytoplankton patchiness: Ecological implications and observation methods, In Patch Dynamics, Springer, 96(1993), 37–49.
[2] Allegretto, W., Mocenni, C., Vicino, A., Periodic solutions in modelling lagoon ecological interactions, Journal of mathematical biology, 51(2005), 367–388.
[3] Edwards, A.M., Brindley, J., Zooplankton mortality and the dynamical behaviour of plankton population models, Bulletin of Mathematical Biology, 61(1999), 303–339.
[4] Fasham, M., The statistical and mathematical analysis of plankton patchiness, Oceanogr. Marine Biology Annual Rev., 16(1978), 43–79.
[5] Guttal, V., Jayaprakash, C., Changing skewness: An early warning signal of regime shifts in ecosystems, Ecology letters, 11(5)(2008), 450-460.
[6] Hull, V., Mocenni, C., Falcucci, M., Marchettini, N., A trophodynamic model for the lagoon of fogliano (italy) with ecological dependent modifying parameters, Ecological modelling, 134(2000), 153–167.
[7] Mackas, D.L., Boyd, C.M., Spectral analysis of zooplankton spatial heterogeneity, Science, 204(1979), 62–64.
[8] Malchow, H., Petrovskii, S.V., Hilker, F.M., Models of spatiotemporal pattern formation in plankton dynamics, Nova Acta Leopoldina NF, 88(2003), 325–340.
[9] Malchow, H., Petrovskii, S.V., Venturino, E., Spatiotemporal patterns in ecology and epidemiology: theory, models, and simulation. Chapman & Hall/CRC Press London, 2008.
[10] Marchettini, N., Mocenni, C., Vicino, A., Integrating slow and fast dynamics in a shallow water coastal lagoon, Annali di chimica, 89(1999), 505–514.
[11] Medvinsky, A.B., et al., Spatiotemporal complexity of plankton and fish dynamics, SIAM Review., 44(2002), 311–370.
[12] Misra, A., Modeling the depletion of dissolved oxygen in a lake due to submerged macrophytes, Nonlinear Anal. Model. Cont., 15(2010), 185–198.
[13] Okubo, A., Diffusion and Ecological Problems: Mathematical Models, Springer-Verlag Berlin, Vol.10, 1980.
[14] Petrovskii, S.V., Malchow, H., Mathematical Models of Marine Ecosystems. Mathematical Models, In: The Encyclopedia of Life Support Systems (EOLSS), EOLSS Publishers, Oxford UK, 2004.
[15] Scheffer, M., Carpenter, S., Foley, J.A., Folke, C., Walker, B., Catastrophic shifts in ecosystems, Nature, 413(6856)(2001), 591.
[16] Scheffer, M., et.al., Early-warning signals for critical transitions, Nature, 461(7260)(2009), 53.
[17] Sekerci, Y., Petrovskii, S., Mathematical modelling of plankton–oxygen dynamics under the climate change, Bulletin of Mathematical Biology, 77(12)(2015), 2325–2353.