Parameter constraints of grazing response functions. Implications for phytoplankton bloom initiation


  • Jordi Solé Institut de Ciències del Mar, CSIC
  • Emilio García-Ladona Institut de Ciències del Mar, CSIC
  • Jaume Piera Institut de Ciències del Mar, CSIC
  • Marta Estrada Institut de Ciències del Mar, CSIC



algal blooms, plankton, prey selection, grazing functions, multispecies model, mathematical constraints


Phytoplankton blooms are events of production and accumulation of phytoplankton biomass that influence ecosystem dynamics and may also have effects on socio-economic activities. Among the biological factors that affect bloom dynamics, prey selection by zooplankton may play an important role. Here we consider the initial state of development of an algal bloom and analyse how a reduced grazing pressure can allow an algal species with a lower intrinsic growth rate than a competitor to become dominant. We use a simple model with two microalgal species and one zooplankton grazer to derive general relationships between phytoplankton growth and zooplankton grazing. These relationships are applied to two common grazing response functions in order to deduce the mathematical constraints that the parameters of these functions must obey to allow the dominance of the lower growth rate competitor. To assess the usefulness of the deduced relationships in a more general framework, the results are applied in the context of a multispecies ecosystem model (ERSEM).


Download data is not yet available.


Anderson T.R., Gentleman W.C., Sinha B. 2010. Influence of grazing formulations on the emergent properties of a complex ecosystem model in a global ocean general circulation model. Progr. Oceanogr. 87(1-4): 201-213.

Armstrong R.A. 1994. Grazing limitation and nutrient limitation in marine ecosystems: Steady state solutions of an ecosystem model with multiple food chains. Limnol. Oceanogr. 39(3): 597-608.

Armstrong R.A. 2003. A hybrid spectral representation of phytoplankton growth and zooplancton response: The "control rod" model of plankton interaction. Deep Sea Res. Part II 50: 2895-2916.

Baretta J., Baretta-Bekker J. 1997. Special issue: European regional seas ecosystem model II. J. Sea Res. 38: 169-413.

Baretta J.W., Ebenhöh W., Ruardij P. 1995. The European regional seas ecosystem model: a complex marine ecosystem model. Neth. J. Sea Res. 33: 233-246.

Baretta-Bekker J.G., Baretta J., Rasmussen E. 1995. The microbial food web in the European regional seas ecosystem model. Neth. J. Sea Res. 33: 363-379.

Bell T. 2002. The ecological consequences of unpalatable prey: phytoplankton response to nutrient and predator additions. Oikos 99(1): 59-68.

Buskey E., Hyatt C. 1995. Effects of the Texas (USA) 'brown tide' alga on planktonic grazers. Mar. Ecol. Prog. Ser. 126: 285-292.

Cropp R., Norbury J. 2013. Modelling plankton ecosystems and the Library of Lotka. In: Blackford J., Allen I., et al., Advances in Marine Ecosystem Modelling Research (III). J. Mar. Syst. 125: 3-13.

Ebenhöh W., Baretta-Bekker J., Baretta J. 1997. The primary production module in the marine ecosystem model ERSEM II, with emphasis on the light forcing. J. Sea Res. 38: 173-193.

Flynn K.J. 2002. Toxin production in migrating dinoagellates: a modelling study of PSP producing alexandrium. Harmful Algae, 1: 147-155.

Flynn K.J. 2010. Do external resource ratios matter? Implications for modelling eutrophication events and controlling harmful algal blooms. J. Mar. Syst. 83: 170-180.

Flynn K.J., Iringoien X. 2009. Why aldehyde-induced insidious effects cannot be considered as a diatom defence mechanism against copepods. Mar. Ecol. Prog. Ser. 377: 79-89.

Flynn K.J., Davidson K., Cunningham A. 1996. Prey selection and rejection by a microflagellate; implications for the study and operation of microbial food webs. J. Exp. Mar. Biol. Ecol. 196: 357-372.

Gentleman W.C., Neuheimer A.B. 2008. Functional responses and ecosystem dynamics: how clearance rates explain the influence of satiation, food-limitation and acclimation. J. Plank. Res. 30: 1215-1231.

Gentleman W., Leising A., Frost B., et al. 2003. Functional responses for zooplankton feeding on multiple resources: a critical review of assumed biological dynamics. Deep Sea Res. Part II 50: 2847-2875.

Grover J.P. 1995. Competition, herbivory, and enrichment: nutrient-based models for edible and inedible plants. Am. Nat. 145(5): 746-774.

Guisande C., Frangópulos M., Maneiro I., et al. 2002. Ecological advantages of toxin production by the dinoflagellate Alexandrium minutum under phosphorus limitation. Mar. Ecol. Prog. Ser. 225: 169-176.

Holling C. 1959. Some characteristics of simple types of predation and parasitism. Can. Entom. 91: 385-398.

Holt R., Grover J., Tilman D. 1994. Simple rules for interspecific dominance in systems with exploitative and apparent competition. Am. Nat. 144(5): 741-771.

Irigoien X., Flynn K.J., Harris R.P. 2005. Phytoplankton blooms: a loophole in microzooplankton grazing impact? J. Plankton Res. 27: 313-321.

Jessup C.M., Bohannan B.J.M. 2008. The shape of an ecological trade-off varies with environment. Ecol. Let. 11: 947-959. PMid:18557986

Kierstead H., Slobodkin L. 1953. The size of water masses containing plankton blooms. J. Mar. Res. 12: 141-147.

Kretzschmar M., Nisbet R., MacCauley E. 1993. A predator-prey model for zooplankton grazing on competing algal populations. Theor. Popul. Biol. 44: 32-66.

Leibold M.A. 1989. Resource edibility and the effects of predators and productivity on the outcome of trophic interactions. Am. Nat. 134: 922-949.

Leibold M.A. 1996. A graphical model of keystone predators in food webs: trophic regulation of abundance, incidence, and diversity patterns in communities. Am. Nat. 147: 784-812.

Leising A., Horner R., Pierson J., et al. 2005. The balance between microzooplankton grazing and phytoplankton growth in a highly productive estuarine fjord. Progr. Oceanogr. 67: 366-383.

Litchman E., Klausmeier C. 2008. Trait-based community ecology of phytoplankton. Annu. Rev. Ecol. Evol. Syst. 39: 615-639.

Maestrini S., Granéli E. 1991. Environmental conditions and ecophysiological mechanisms which led to the 1988 Chrysochromulina polylepis bloom: an hypothesis. Ocean. Acta 14: 397-413.

Margalef R., Estrada M., Blasco D. 1979. Functional morphology of organisms involved in red tides, as adapted do cecaying turbulence. In: Taylor D.L. and Sliger H.H. (eds), Toxic dinoagellate blooms. Elsevier, North Holland, pp. 315-320.

May R.M. 1974. Stability and Complexity in Model Ecosystems. Princeton University Press. 263 pp.

Mitra A., Flynn K. 2005. Predator-prey interactions: is 'ecological stoichiometry' sufficient when good food goes bad? J. Plankton Res. 27: 393-399.

Mitra A., Flynn K. 2006. Promotion of harmful algal blooms by zooplankton predatory activity. Biol. Lett. 2: 194-197. PMid:17148360 PMCid:PMC1618909

Murray J. 1989. Mathematical Biology. Springer, Berlin.

Pätsch J., Radach G. 1997. Long-term simulation of the eutrophication of the North Sea: temporal development of nutrients, chlorophyll and primary production in comparison to observations. J. Sea Res. 38: 275-310.

Pitchford J., Brindley J. 1999. Iron limitation, grazing pressure and oceanic high nutrient-low chlorophyll (HNLC) regions. J. Plankton Res. 21: 525-547.

Radach G., Pätsch J. 1997. Climatological annual cycles of nutrients and chlorophyll in the North Sea. J. Sea Res. 38: 231-248.

Sailley S., Vogt M., Doney S., et al. 2013. Comparing food web structures and dynamics across a suite of global marine ecosystem models. Ecol. Modell. 261-262: 43-57.

Schaffer W.M. 1981. Ecological Abstraction: The Consequences of Reduced Dimensionality in Ecological Models. Ecol. Monogr. 51: 383-401.

Smayda T.J., Reynolds C.S. 2001. Community assembly in marine phytoplankton: application of recent models to harmful dinoagellate blooms. J. Plankton Res. 23(5): 447-461.

Solé J., Estrada M., García-Ladona E. 2006a. Biological controls of Harmful Algal Blooms: A modelling study. J. Mar. Syst. 61: 165-179.

Solé J., García-Ladona E., Estrada M. 2006b. The role of selective predation in Harmful Algal Blooms. J. Mar. Syst. 62: 46-64.

Steele J. 1974. The structure of marine ecosystems. Harvard University Press.

Teramoto E., Kawasaki K., Shigesada N. 1979. Switching effect of predation on competitive prey species. J. Theor. Biol. 79: 303-315.

Tillmann U., Hesse K., Colijn F. 2000. Planktonic primary production in the German Wadden Sea. J. Plankton Res. 22: 1253-1276.

Touzet N., Franco J., Raine R. 2007. Influence of inorganic nutrition on growth and PSP toxin production of Alexandrium minutum (Dinophyceae) from Cork Harbour, Ireland. Toxicon 50: 106-119. PMid:17452045

Truscott J. 1995. Environmental forcing of simple plankton models. J. Plankton Res. 17: 2207-2232.

Truscott J., Brindley J. 1994. Ocean plankton populations as excitable media. Bull. Math. Biol. 56: 981-998.

van Donk E. 1997. Defenses in phytoplankton against grazing induced by nutrient limitation, UV-B stress and infochemicals. Aq. Ecol. 31: 53-58.

Vichi M., Pinardi N., Masina S. 2007. A generalized model of pelagic biogeochemistry for the global ocean ecosystem. Part I: Theory. J. Mar. Syst. 64: 89-109.

Wyatt T., Horwood J. 1973. Model which generates red tides. Nature 244: 238-240.

Yoshida T., Hairston N.H., Ellner S. 2004. Evolutionary trade-off between defence against grazing and competitive ability in a simple unicellular alga, Chlorella vulgaris. Proc. R. Soc. London, 271: 1947-1953. PMid:15347519 PMCid:PMC1691804



How to Cite

Solé J, García-Ladona E, Piera J, Estrada M. Parameter constraints of grazing response functions. Implications for phytoplankton bloom initiation. Sci. mar. [Internet]. 2016Sep.30 [cited 2024Mar.1];80(S1):129-37. Available from:




Most read articles by the same author(s)

1 2 > >>