Skip to main content

Advertisement

Log in

A Delay-Diffusion Model of Marine Plankton Ecosystem Exhibiting Cyclic Nature of Blooms

  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

The cyclic nature of blooms is a very interesting characteristic of marine plankton ecosystem. Release of toxins by some phytoplanktons has an important role on planktonic interactions and hence on regulating the blooms. A mathematical model describing the phytoplankton-zooplankton interaction with these characteristics is studied. The time needed for liberation of toxins by phytoplanktons is considered. To account for the spatial heterogeneity of an aquatic environment, diffusivity of different plankton populations is also incorporated into the system. Stability and bifurcation behaviour of different steady states are analysed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Duinker, J. and Wefer, G.: Das CO2-Problem und die Rolle des Ozeans, Naturwissenschahten 81 (1994), 237–242.

    CAS  Google Scholar 

  2. Provasoli, L.: Recent progress: An overview, in Taylor and Seliger (eds.), Toxic Dinoflagellate Blooms, Elsevier/North-Holland, 1978, p. 1.

  3. Nishijima, T. and Hata, Y.: The dynamics of vitamin B12 and its relation to the outbreak of Chattonella red tides in Harima Nada, the Seto inland sea, in T. Okaichi (ed.), Red Tides: Biology, Environmental Science and Toxicology, Elsevier, Amsterdam, 1989, p. 257.

    Google Scholar 

  4. Truscott, J.E. and Brindley, J.: Ocean Plankton Populations as Excitable Media, Bull. Math. Biol. 56 (1994), 981–998.

    Google Scholar 

  5. Almeida Machado, P.: Dinoflagellate blooms on the Brazilian South Atlantic coast, in Taylor and Seligers (eds.), Toxic Dinoflagellate Blooms, Elsevier, 1978, p. 29.

  6. Work, T.M. et al.: Domonic acid in toxication of brown pelicans and cormorants in Santa Cruz, California, in T.J. Smayda and Y. Shimuza (eds.), Toxic Phytoplankton Blooms in the Sea, Vol. 3, Elsevier, 1993, pp. 643–649.

  7. Steidinger, K.A. et al.: Pfiesteria Piscicida a New Toxic Dinoflagellate Genus and Species of the Order Dinamoebales, J. Phycol. 32 (1996), 157–164.

    Article  Google Scholar 

  8. Nielsen, T.G. et al.: Effects of a Chrysochromulina polylepis Subsurface Bloom on the Plankton Community, Mar. Ecol. Prog. Ser. 62 (1990), 21–35.

    Google Scholar 

  9. Aure, J. and Rey, F.: Oceanographic Conditions in the Sandsfjord System, Western Norway, After a Bloom of the Prymnesiophyte Prymnesium parvum Carter in August 1990, Sarsia 76 (1992), 247–254.

    Google Scholar 

  10. Hallegraeff, G.M.: A Review of Harmful Algae Blooms and the Apparent Global Increase, Phycologia 32 (1993), 79–99.

    Google Scholar 

  11. Keating, K.I.: Algal metabolite influence on bloom sequence in eutrophic freshwater ponds. E.P.A. Ecological Monograph Series (EPA. 600/3-76-081. Washington, DC), 1976, p. l48.

  12. Kirk, K. and Gilbert, J.: Variations in Herbivore Response to Chemical Defences: Zooplankton Foraging on Toxic Cyanobacteria, Ecology 73 (1992), 2208.

    Google Scholar 

  13. Fay, P.: The Blue-Greens, Arnold, London, 1983.

    Google Scholar 

  14. Buskey, E.J. and Stockwell, D.A.: Effects of a persistent ‘brown tide’ on zooplankton population in the Laguna Madre of Southern Texas, in T.J. Smayda and Y. Shimuzu (eds.), Toxic Phytoplankton Blooms in the Sea. Elsevier, Amsterdam, 1993, pp. 659–666.

    Google Scholar 

  15. Estep, K.W. et al.: Predation by Copepods upon Natural Populations of Phaeocystis pouchetii as a Function of the Physiological State of the Prey, Mar. Ecol. Prog. Ser. 67 (1990), 235–249.

    Google Scholar 

  16. Hansen, F.C.: Tropic Interaction Between Zooplankton and Phaeocystis cf. Globosa., Helgol Meeresunters 49, 283–293.

  17. Huntley, M.E. et al.: Chemically Mediated Rejection of Dinoflagellate Prey by the Copepods Calanus pacificus and Paracalanus parvus: Mechanism, Occurance and Significance, Mar. Ecol. Prog. Ser. 28 (1986), 105–120.

    Google Scholar 

  18. Buskey, E.J. and Hyatt, C.J.: Effects of the Texas (USA) Brown Tide Alga on Planktonic Grazers, Mar. Ecol. Prog. Ser. 126 (1995), 285–292.

    Google Scholar 

  19. Nejstgaard, J.C. and Solberg, P.T.: Repression of Copepod Feeding and Fecundity by the Toxic Haptophyte Prymnesium patelliferum, Sarsia 81 (1996), 339–344.

    Google Scholar 

  20. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer, Dordrecht, 1992.

    Google Scholar 

  21. Cushing, J.M.: Integrodifferential Equations and Delay Models in Population Dynamics, Lect. Notes in Biomath., Vol. 20, Springer-Verlag, Berlin, 1977.

    Google Scholar 

  22. Kuang, Y.: Delay-Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.

    Google Scholar 

  23. MacDonald, N.: Biological Delay Systems: Linear Stability Theory, Cambridge University Press, New York, 1989.

    Google Scholar 

  24. Chattopadhyay, J. et al.: A Delay Differential Equation Model on Harmful Algal Blooms in the Presence of Toxic Substances, IMA. J. Math. Appl. Med. Biol. 19 (2002), 137–161.

    CAS  PubMed  Google Scholar 

  25. Steele, J.H.: Stability of plankton ecosystem, in M.B. Usher and M.H. Williams (eds.), Ecological Stability, Chapman and Hall, London, 1974.

    Google Scholar 

  26. Sjoberge, S.: Are Pelagic Systems Inherently Unstable? A Model Study, Ecol. Model. 3 (1977), 17–37.

    Article  Google Scholar 

  27. Okubo, A.: Diffusion and Ecological Problems: Modern Perspective, Interdisciplinary Applied Mathematics., Vol. 14, Springer, Berlin, 2001.

    Google Scholar 

  28. Murray, J.D.: Mathematical Biology, Springer, Berlin, 2002.

    Google Scholar 

  29. Edwards, A.M. and Brindley, J.: Zooplankton Mortality and the Dynamical Behaviour of Plankton Population Model, Bull. Math. Biol. 61 (1999), 303.

    Article  Google Scholar 

  30. Beltrami, E. and Carroll, T.O.: Modelling the Role of Viral Diseases in Recurrent Phytoplankton Blooms, J. Math. Biol. 32 (1994), 857–863.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. Mukhopadhyay.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mukhopadhyay, B., Bhattacharyya, R. A Delay-Diffusion Model of Marine Plankton Ecosystem Exhibiting Cyclic Nature of Blooms. J Biol Phys 31, 3–22 (2005). https://doi.org/10.1007/s10867-005-2306-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-005-2306-x

Key words

Navigation