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Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change
Abstract
Ocean dynamics is known to have a strong effect on the global climate change and on the composition of the atmosphere. In particular, it is estimated that about 70 % of the atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. However, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. In this paper, we address this issue theoretically by considering a model of a coupled plankton–oxygen dynamics where the rate of oxygen production slowly changes with time to account for the ocean warming. We show that a sustainable oxygen production is only possible in an intermediate range of the production rate. If, in the course of time, the oxygen production rate becomes too low or too high, the system’s dynamics changes abruptly, resulting in the oxygen depletion and plankton extinction. Our results indicate that the depletion of atmospheric oxygen on global scale (which, if happens, obviously can kill most of life on Earth) is another possible catastrophic consequence of the global warming, a global ecological disaster that has been overlooked.
Keywords
Phytoplankton Global warming Oxygen depletion Extinction Pattern formationNotes
Acknowledgments
The authors are thankful to Nikolay Brilliantov (Leicester) for stimulating discussions at the early stage of this study.
Appendix
∙∙ Extinction state 𝐸1=(0,0,0)E1=(0,0,0)
References
-
Abbott MR (1993) Phytoplankton patchiness: ecological implications and observation methods. In: Levin SA, Powell TM, Steele JH (eds) Patch dynamics. Lecture notes in biomathematics, vol 96. Springer, Berlin, pp 37–49Google Scholar
-
Addy K, Green L (1997) Dissolved oxygen and temperature. Fact Sheet No. 96–3, Natural Resources Facts, University of Rhodes IslandGoogle Scholar
-
Allegretto W, Mocenni C, Vicino A (2005) Periodic solutions in modelling lagoon ecological interactions. J Math Biol 51:367–388CrossRefMathSciNetzbMATHGoogle Scholar
-
Andersson A, Haecky P, Hagstrom A (1994) Effect of temperature and light on the growth of micro- nano- and pico-plankton: impact on algal succession. Mar Biol 120:511–520CrossRefGoogle Scholar
-
Behrenfeld MJ, Falkowski PG (1997) A consumers guide to phytoplankton primary productivity models. Limnol Oceanogr 42:1479–1491CrossRefGoogle Scholar
-
Berestycki H, Desvillettes L, Diekmann O (2014) Can climate change lead to gap formation? Ecol Complex 20:264–270CrossRefGoogle Scholar
-
Bonnefon O, Coville J, Garnier J, Hamel F, Roques L (2014) The spatio-temporal dynamics of neutral genetic diversity. Ecol Complex 20:282–292CrossRefGoogle Scholar
-
Breitburg DL, Loher T, Pacey CA, Gerstein A (1997) Varying effects of low dissolved oxygen on trophic interactions in an estuarine food web. Ecol Monogr 67:489–507CrossRefGoogle Scholar
-
Chapelle A, Ménesguen A, Deslous-Paoli J-M et al (2000) Modelling nitrogen, primary production and oxygen in a Mediterranean lagoon: impact of oysters farming and inputs from the watershed. Ecol Model 127:161–181CrossRefGoogle Scholar
-
Charlson RJ, Lovelock JE, Andreae MO, Warren SG (1987) Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate. Nature 326:655–661CrossRefGoogle Scholar
-
Childress JJ (1975) The respiratory rates of midwater crustaceans as a function of depth of occurrence and relation to the oxygen minimum layer of Southern California. Compar Biochem Physiol Part A Physiol 50:787–799CrossRefGoogle Scholar
-
Childress JJ (1976) Effects of pressure, temperature and oxygen on the oxygen consumption rate of the midwater copepod Gaussia princeps. Mar Biol 39:19–24CrossRefGoogle Scholar
-
Cosner C (2014) Challenges in modeling biological invasions and population distributions in a changing climate. Ecol Complex 20:258–263CrossRefGoogle Scholar
-
Culos GJ, Tyson RC (2014) Response of poikilotherms to thermal aspects of climate change. Ecol Complex 20:293–306CrossRefGoogle Scholar
-
Cushing DH (1975) Marine ecology and fisheries. Cambridge University Press, CambridgeGoogle Scholar
-
Davenport J, Trueman ER (1985) Oxygen uptake and buoyancy in zooplanktonic organisms from the tropical Eastern Atlantic. Compar Biochem Physiol Part A Physiol 81:857–863CrossRefGoogle Scholar
-
Decker MB, Breitburg DL, Purcell JE (2004) Effects of low dissolved oxygen on zooplankton predation by the ctenophore Mnemiopsis leidyi. Mar Ecol Progr Ser 280:163–172CrossRefGoogle Scholar
-
Denman K, Hofmann E, Marchant H (1996) Marine biotic responses and feedbacks to environmental change and feedbacks to climate. In: Houghton JT et al (eds) Climate change 1995. The science of climate change. Cambridge University Press, Cambridge, pp 483–516Google Scholar
-
Devol AH (1981) Vertical distribution of zooplankton respiration in relation to the intense oxygen minimum zones in two British Columbia fjords. J Plankt Res 3:593–602CrossRefGoogle Scholar
-
Enquist BJ, Economo EP, Huxman TE et al (2003) Scaling metabolism from organisms to ecosystems. Nature 423:639–642CrossRefGoogle Scholar
-
Eppley RW (1972) Temperature and phytoplankton growth in the sea. Fish Bull 70:1063–1085Google Scholar
-
Fasham M (1978) The statistical and mathematical analysis of plankton patchiness. Oceanogr Mar Biol Ann Rev 16:43–79Google Scholar
-
Fasham MJR, Ducklow HW, McKelvie SM (1990) A nitrogen-based model of plankton dynamics in the oceanic mixed layer. J Marine Res 48:591–639CrossRefGoogle Scholar
-
Ferrarini A, Rossi G, Mondoni A, Orsenigo S (2014) Prediction of climate warming impacts on plant species could be more complex than expected. Evidence from a case study in the Himalaya. Ecol Complex 20:307–314CrossRefGoogle Scholar
-
Franke U, Hutter K, Johnk K (1999) A physical-biological coupled model for algal dynamics in lakes. Bull Math Biol 61:239–272CrossRefGoogle Scholar
-
Franssen SU, Gu J, Bergmann N et al (2011) Transcriptomic resilience to global warming in the seagrass Zostera marina, a marine foundation species. Proc Natl Acad Sci USA 108:19276–19281CrossRefGoogle Scholar
-
Gliwicz MZ (1986) Predation and the evolution of vertical migration in zooplankton. Nature 320:746–748CrossRefGoogle Scholar
-
Greene CH, Widder EA, Youngbluth MJ, Tamse A, Johnson GE (1992) The migration behavior, fine structure, and bioluminescent activity of krill sound-scattering layers. Limnol Oceanogr 37:650–658CrossRefGoogle Scholar
-
Hamme RC, Keeling RF (2008) Ocean ventilation as a driver of interannual variability in atmospheric potential oxygen. Tellus B 60:706–717CrossRefGoogle Scholar
-
Hancke K, Glud RN (2004) Temperature effects on respiration and photosynthesis in three diatom-dominated benthic communities. Aquat Microb Ecol 37:265–281CrossRefGoogle Scholar
-
Harris GP (1986) Phytoplankton ecology: structure, function and fluctuation. Springer, BerlinCrossRefGoogle Scholar
-
Hastings A (2001) Transient dynamics and persistence of ecological systems. Ecol Lett 4:215–220CrossRefGoogle Scholar
-
Hastings A (2004) Transients: the key to long-term ecological understanding? Trends Ecol Evolut 19:39–45CrossRefGoogle Scholar
-
Hein B, Viergutz C, Wyrwa J, Kirchesch V, Schöl A (2014) Modelling the impact of climate change on phytoplankton dynamics and the oxygen budget of the Elbe river and estuary (Germany). In: Kopmann R (ed) Lehfeldt R. Hamburg, ICHE, pp 1035–1042Google Scholar
-
Hoppe H-G, Gocke K, Koppe R, Begler C (2002) Bacterial growth and primary production along a North-South transect of the Atlantic Ocean. Nature 416:168–171CrossRefGoogle Scholar
-
Huisman J, Weissing FJ (1995) Competition for nutrients and light in a mixed water column: a theoretical analysis. Am Nat 146:536–564CrossRefGoogle Scholar
-
Huisman J, van Oostveen P, Weissing FJ (1999) Species dynamics in phytoplankton blooms: incomplete mixing and competition for light. Am Nat 154:46–68CrossRefGoogle Scholar
-
Huisman J, Sharples J, Stroom JM, Visser PM, Kardinaal WEA, Verspa JM, Sommeijer B (2004) Changes in turbulent mixing shift competition for light between phytoplankton species. Ecology 85:2960–2970CrossRefGoogle Scholar
-
Hull V, Mocenni C, Falcucci M, Marchettini N (2000) A trophodynamic model for the Lagoon of Fogliano (Italy) with ecological dependent modifying parameters. Ecol Model 134:153–167CrossRefGoogle Scholar
-
Hull V, Parrella L, Falcucci M (2008) Modelling dissolved oxygen dynamics in coastal lagoons. Ecol Model 211:468–480CrossRefGoogle Scholar
-
Intergovernmental Panel on Climate Change (2014) Climate change 2014: synthesis report. In: Team Core Writing, Pachauri RK, Meyer LA (eds) Contribution of working groups I, II and III to the fifth assessment report of the intergovernmental panel on climate change. IPCC, GenevaGoogle Scholar
-
Jones RI (1977) The importance of temperature conditioning to the respiration of natural phytoplankton communities. Brit Phycol J 12:277–285CrossRefGoogle Scholar
-
Keeling RF, Kortzinger A, Gruber N (2010) Ocean deoxygenation in a warming world. Mar Sci 2:199–229CrossRefGoogle Scholar
-
Kremer J, Nixon SW (1978) A coastal marine ecosystem: simulation and analysis. Springer, BerlinCrossRefGoogle Scholar
-
Kyriazopoulos P, Nathan J, Meron E (2014) Species coexistence by front pinning. Ecol Complex 20:271–281CrossRefGoogle Scholar
-
Li W, Smith J, Platt T (1984) Temperature response of photosynthetic capacity and carboxylase activity in arctic marine phytoplankton. Mar Ecol Progr Ser 17:237–243CrossRefGoogle Scholar
-
Long A, Tyson RC (2014) Integrating Homo sapiens into ecological models: imperatives of climate change. Ecol Complex 20:325–334CrossRefGoogle Scholar
-
Mackas DL, Boyd CM (1979) Spectral analysis of zooplankton spatial heterogeneity. Science 204:62–64CrossRefGoogle Scholar
-
Malchow H, Petrovskii SV, Hilker FM (2003) Models of spatiotemporal pattern formation in plankton dynamics. Nova Acta Leopoldina NF 88:325–340Google Scholar
-
Malchow H, Petrovskii SV, Venturino E (2008) Spatiotemporal patterns in ecology and epidemiology: theory, models, and simulation. CRC Press, Boca RatonGoogle Scholar
-
Matear R, Hirst A, McNeil B (2000) Changes in dissolved oxygen in the SouthernOcean with climate change. Geochem Geophys Geosyst 1(11):2000GC000086Google Scholar
-
Martin AP (2003) Phytoplankton patchiness: the role of lateral stirring and mixing. Progr Oceanogr 57:125–174CrossRefGoogle Scholar
-
Medvinsky AB, Petrovskii SV, Tikhonova IA, Malchow H, Li B-L (2002) Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev 44:311–370CrossRefMathSciNetzbMATHGoogle Scholar
-
Misra A (2010) Modeling the depletion of dissolved oxygen in a lake due to submerged macrophytes. Nonlin Anal Model Cont 15:185–198zbMATHGoogle Scholar
-
Monin AS, Yaglom AM (1971) Statistical fluid mechanics: mechanics of turbulence, vol 1. MIT Press, CambridgeGoogle Scholar
-
Moss BR (2009) Ecology of fresh waters: man and medium, past to future. Wiley, LondonGoogle Scholar
-
Najjar RG, Walker HA, Anderson PJ et al (2000) The potential impacts of climate change on the mid-Atlantic coastal region. Clim Res 14:219–233CrossRefGoogle Scholar
-
Najjar RG, Pyke CR, Adams MB et al (2010) Potential climate-change impacts on the Chesapeake Bay. Estuar Coastal Shelf Sci 86:1–20CrossRefGoogle Scholar
-
Nguyen KDT, Morley SA, La CH et al (2011) Upper temperature limits of tropical marine ectotherms: global warming implications. PLoS ONE 6(12):e29340CrossRefGoogle Scholar
-
Okubo A (1980) Diffusion and ecological problems: mathematical models. Springer, BerlinzbMATHGoogle Scholar
-
Petrovskii SV, Malchow H (2001) Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. Theor Popul Biol 59:157–174CrossRefzbMATHGoogle Scholar
-
Petrovskii SV, Malchow H (2004) Mathematical models of marine ecosystems. In: The encyclopedia of life support systems (EOLSS). EOLSS Publishers, OxfordGoogle Scholar
-
Petrovskii SV, Li B-L, Malchow H (2004) Transition to spatiotemporal chaos can resolve the paradox of enrichment. Ecol Complex 1:37–47CrossRefGoogle Scholar
-
Petrovskii SV, Morozov AY, Venturino E (2002) Allee effect makes possible patchy invasion in a predator-prey system. Ecol Lett 5:345–352CrossRefGoogle Scholar
-
Petrovskii SV, Kawasaki K, Takasu F, Shigesada N (2001) Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species. Japan J Ind Appl Maths 18:459–481CrossRefMathSciNetzbMATHGoogle Scholar
-
Pinel-Alloul B (1995) Spatial heterogeneity as a multiscale characteristic of zooplankton community. Hydrobiologia 300(301):17–42CrossRefGoogle Scholar
-
Prosser CL (1961) Oxygen: respiration and metabolism. In: Prosser CL, Brown FA (eds) Comparative animal physiology. WB Saunders, Philadelphia, pp 165–211Google Scholar
-
Raven JA, Geider RJ (1988) Temperature and algal growth. New Phytol 110:441–461CrossRefGoogle Scholar
-
Robinson C (2000) Plankton gross production and respiration in the shallow water hydrothermal systems of Milos, Aegean Sea. J Plankt Res 22:887–906CrossRefGoogle Scholar
-
Shaffer G, Leth O, Ulloa O et al (2000) Warming and circulation change in the Eastern South Pacific Ocean. Geophys Res Lett 27:1247–1250CrossRefGoogle Scholar
-
Sekerci Y, Petrovskii S (2015) Mathematical modelling of spatiotemporal dynamics of oxygen in a plankton system. Math Model Nat Phenom 7:96–114CrossRefMathSciNetGoogle Scholar
-
Steele JH (1978) Spatial pattern in plankton communities. Plenum, LondonCrossRefGoogle Scholar
-
Steel JA (1980) Phytoplankton models. In: LeCren ED, Lowe-McConnell RH (eds) Functioning of freshwater ecosystems, vol 2. Cambridge University Press, Cambridge, pp 220–227Google Scholar
-
Williamson P, Gribbin J (1991) How plankton change the climate. N Sci 129:48–52Google Scholar
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