Environmental Change Effect on Oxygen-Plankton System: Mathematical Approach
Oxygen loss in a water body is a significant environmental issue, also accountable for the extinction of marine fauna. Therefore, oxygen production by marine phytoplankton photosynthesis is thought to hold the key to the underlying structure of oxygen dynamics in the marine ecosystem. However, the oxygen concentration is not only determined by primary production. This oxygen concentration also depends on its consumption such as biochemical reaction in the water body, consumption by marine animals, water-air reaeration, etc. Plankton respiration is one of the these factors that play an important role in water body oxygen concentration. Therefore, in this work, this issue is addressed theoretically by considering the oxygen-phytoplankton-zooplankton model to make an insight into system dynamics under the effect of changing environmental condition on phytoplankton growth rate. The difference between this work and the literature is the specific paremeter value of $B$, suggesting that the changing environment has an effect on the growth rate of phytoplankton. A nonlinear mathematical model is considered to investigate the effect of temperature on oxygen-plankton dynamics with Holling Type II function as respiration of plankton species. The model is studied in both theoretical and numerical forms, based on the existence and behavior of the system's steady state. Moreover, it is noticed from the simulation, oxygen depletion can arise if the temperature exceeds a certain critical level. Interestingly, in a certain parameter range, our model shows the formation of spatial patterns that are qualitatively the same to those observed in field observations
Keywords:
Differential equation, oxygen consumption, respiration growth rate,
___
- Addy, K., Green, L., Natural Resources Facts, Fact Sheet No.96-3, Dissolved Oxygen and Temperature, University of Rhodes Island, 1997.
- Andersson, A., Haecky, P., Hagstrom, A., \textit{Effect of temperature and light on the growth of micro-nano-and pico-plankton: impact on algal succession}, Marine Biology, \textbf{120}(1994), 511--520.
- Broecker, W.S., Peng, T.H., Tracers in The Sea, Lamont-Doherty Geological Observatory, Palisades, New York, 1982.
- Childress, J.J., \textit{The respiratory rates of midwater crustaceans as a function of depth of occurrence and relation to the oxygen minimum layer of southern california}, Comparative Biochemistry and Physiology Part A: Physiology, \textbf{50}(1975), 787--799.
- Costanza, R., d'Arge, et al., \textit{The value of the world's ecosystem services and natural capital}, \textbf{29}(1998), 13--15.
- Denman, K., Hofmann, E., Marchant, H., Marine biotic responses and feedbacks to environmental change and feedbacks to climate, in Climate Change 1995, The Science of Climate Change, edited by Houghton, J.T., et al., Cambridge University Press, 1996, 483--516.
- Enquist, B.J., et al., \textit{Scaling metabolism from organisms to ecosystems}, Nature, \textbf{423}(2003), 639--642.
- Eppley, R.W., \textit{Temperature and phytoplankton growth in the sea}, Fish. Bull, \textbf{70}(1972), 1063--1085.
- Harris, G., Phytoplankton Ecology-Structure, Function and Fluctuation, Springer, 1986.
- Hull, V., Mocenni, C., Falcucci, M., Marchettini, N., \textit{A trophodynamic model for the lagoon of fogliano (italy) with ecological dependent modifying parameters}, Ecological Modelling, \textbf{134}(2000), 153--167.
- Hoppe, H.G., Gocke, K., Koppe, R., Begler, C., \textit{Bacterial growth and primary production along a north-south transect of the atlantic ocean}, Nature, \textbf{416}(2002), 168--171.
- Jenkins, W.J., \textit{Oxygen utilization rates in North Atlantic subtropical gyre and primary production in oligotrophic systems}, Nature, \textbf{300(5889)}(1982), 246.
- Jin, Z., Charlock, T.P., Smith, W.L., Rutledge, K., \textit{A parametrization of ocean surface albedo}, Geophysical Research Letters, \textbf{31}(2004).
- Li, W., Smith, J., Platt, T., \textit{Temperature response of photosynthetic capacity and carboxylase activity in arctic marine phytoplankton}, Marine Ecology Progress Series, \textbf{17}(1984), 237--243.
- Moss, B.R., Ecology of Fresh Waters: Man and Medium, Past to Future, John Wiley \& Sons, 2009.
- Okubo, A., Okubo, A., Diffusion and Ecological Problems: Mathematical Models. Springer-Verlag Berlin, Vol.10, 1980.
- Simpson, J.T., Volunteer Lake Monitoring: A Methods Manual, EPA 440/4-91-002, 1991, 16--21, 70--72.
- Steele, J.H., \textit{Environmental control of photosynthesis in the sea}, Limnology and Oceanography, \textbf{7}(1962), 137--150.
- Sekerci, Y., Petrovskii, S., \textit{Mathematical modelling of plankton--oxygen dynamics under the climate change}, Bulletin of Mathematical Biology, \textbf{77(12)}(2015), 2325--2353.
- Petrovskii, S., Sekerci, Y., Venturino, E., \textit{Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change}, Journal of Theoretical Biology, \textbf{424}(2017), 91-109.
- ISSN: 2148-1830
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2013
- Yayıncı: MATEMATİKÇİLER DERNEĞİ