Abstract
A simple nutrient-phytoplankton model is used to explore the dynamics of phytoplankton blooms. The model exhibits excitable behaviour in the sense that a large scale outbreak can only be triggered when a critical nutrient threshold is exceeded. The model takes into account several features often neglected but whose combined effect proves very important: (i) rapid nutrient recycling associated with the microbial loop and patch formation; (ii) self-shading; and (iii) a bottom-up approach, whereby nutrient levels are responsible for both the triggering and the demise of the bloom. Although the literature is replete with studies of ‘top-down’ models in which zooplankton grazing control the triggering and demise of the bloom, bottom-up models are nevertheless appropriate in many circumstances. We provide a full mathematical investigation of the effects of these three different features in an excitable system framework.
Similar content being viewed by others
References
Anderson, N. J. (1995). Naturally eutrophic lakes: reality, myth or myopia? Trends Ecol. Evol. 10, 137–138.
Azam, F., B. C. Cho, D. C. Smith and M. Simon (1990). Bacterial cycling of matter in the pelagic zone of aquatic ecosystems, in Large Lakes—Ecological Structure and Function, M. M. Tilzer and C. Serruya (Eds), Berlin: Springer, pp. 477–488.
Azam, F., T. Fenchel, J. G. Gray, L. A. Meyer-Reil and F. Thingstad (1983). The ecological role of water-column microbes in the sea. Mar. Ecol. Prog. Ser. 10, 257–263.
Beltrami, E. (1989). A mathematical model of brown tides. Estuaries 12, 13–17.
Beltrami, E. and T. O. Carroll (1994). Modeling the role of viral disease in recurrent phytoplankton blooms. J. Math. Biol. 32, 857–863.
Clother, D. R. and J. Brindley (1999). Excitabilty of an age-structured plankton ecosystem. J. Math. Biol. 39, 377–420.
DeAngelis, D. L. (1992). Dynamics of Nutrient Cycling and Food Webs, London: Chapman and Hall.
Dugdale, R. C. (1967). Nutrient limitation in the sea: dynamics, identification, and significance. Limnol. Oceanogr. 12, 685–695.
Durrett, R. and S. A. Levin (1994). The importance of being discrete (and spatial). Theor. Popul. Biol. 46, 363–394.
Edwards, A. M. and J. Brindley (1996). Oscillatory behaviour in a three-component plankton population model. Dyn. Stab. Syst. 11, 347–370.
Edwards, A. M. and J. Brindley (1999). Zooplankton mortality and the dynamical behaviour of plankton population models. Bull. Math. Biol. 61, 303–339.
Goldman, J. C. (1984). Oceanic nutrient cycles, in Flows of Energy and Materials in Marine Ecosystems: Theory and Practice, M. J. R. Fasham (Ed.), New York: Plenum Press, pp. 137–1170.
Goldman, C. R. and A. J. Horne (1983). Limnology, McGraw-Hill International Book Company.
Griffiths, B. M. (1939). Early references to water blooms in British Lakes. Proc. Limn. Soc. London 151, 12–19.
Huisman, J. P. and F. J. Weissing (1994). Light-limited growth and competition for light in well-mixed aquatic environments: an elementary model. Ecology 75, 507–520.
Huppert, A., B. Blasius and L. Stone (2002). A model of phytoplankton blooms. Am. Nat. 159, 156–171.
Kirk, J. T. O. (1994). Light and Photosynthesis in Aquatic Ecosystem, 2nd edn, Cambridge: Cambridge University Press.
Martin, A. P. (2003). Phytoplankton patchiness: the role of lateral stirring and mixing. Prog. Ocean. 57, 125–174.
May, R. M. (1977). Thresholds and breakpoints in ecosystem with multiplicity of stable states. Nature 269, 471–477.
Mitchell, J. G., O. Akira and J. A. Fuhrman (1985). Microzones surrounding phytoplankton form the basis for stratified marine microbial ecosystem. Nature 316, 58–59.
Pearsall, W. H. (1932). Phytoplankton in the English Lakes. II. The composition of the phytoplankton in relation to dissolved substance. J. Ecol. 20, 241–261.
Pitchford, J. W. (1997). Dynamics of multi-species plankton populations. PhD thesis, University of Leeds.
Pitchford, J. W. and J. Brindley (1999). Iron limitation, grazing pressure and oceanic high nutrient-low chlorophyll (HNLC) regions. J. Plank. Res. 21, 525–547.
Scheffer, M., S. Carpenter, J. A. Foley, C. Folke and B. Walker (2001). Catastrophic shifts in ecosystems. Nature 431, 591–596.
Slobodkin, L. B. (1999). Akira Okubo and the theory of blooms. Oceanography 12, 9–14.
Stone, L. and T. Berman (1993). Positive feedback in aquatic ecosystems: The case of microbial loop. Bull. Math. Biol. 55, 919–936.
Stone, L. and R. S. J. Weisburd (1992). Positive feedback in aquatic ecosystems. Trends Ecol. Evol. 7, 263–267.
Sukenik, A. et al. (2002). Isreal Oceanographic and Liimnological Annual Research Report.
Truscott, J. E. and J. Brindley (1994a). Ocean plankton populations as excitable media. Bull. Math. Biol. 56, 981–998.
Truscott, J. E. and J. Brindley (1994b). Equilibria, stability and excitability in a general-class of plankton population-models. Philos. Trans. R. Soc. Lond. A 347, 703–718.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huppert, A., Olinky, R. & Stone, L. Bottom-up excitable models of phytoplankton blooms. Bull. Math. Biol. 66, 865–878 (2004). https://doi.org/10.1016/j.bulm.2004.01.003
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1016/j.bulm.2004.01.003