Abstract
Modelling studies of upper ocean phenomena, such as that of the spatial and temporal patchiness in plankton distributions, typically employ coupled biophysical models, with biology in each grid-cell represented by a plankton ecosystem model. It has not generally been considered what impact the choice of grid-cell ecosystem model, from the many developed in the literature, might have upon the results of such a study. We use the methods of synchronisation theory, which is concerned with ensembles of interacting oscillators, to address this question, considering the simplest possible case of a chain of identically represented interacting plankton grid-cells. It is shown that the ability of the system to exhibit stably homogeneous (fully synchronised) dynamics depends crucially upon the choice of biological model and number of grid-cells, with dynamics changing dramatically at a threshold strength of mixing between grid-cells. Consequently, for modelling studies of the ocean the resolution chosen, and therefore number of grid-cells used, could drastically alter the emergent features of the model. It is shown that chaotic ecosystem dynamics, in particular, should be used with care.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Abraham, E., 1998. The generation of plankton patchiness by turbulent stirring. Nature 391, 577–580.
Bainbridge, R., 1956. The size, shape and density of marine phytoplankton concentrations. Biol. Rev. 32, 91–115.
Belykh, I., Belykh, V., Nevidin, K., Hasler, M., 2003. Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos 13(1), 165–178.
Blasius, B., Stone, L., 2000. Nonlinearity and the Moran effect. Nature 406, 846–847.
Caswell, H., Neubert, M.G., 1998. Chaos and closure terms in plankton food chain models. J. Plankton Res. 20(9), 1837–1845.
Edwards, A.M., 2001. Adding detritus to a nutrient–phytoplankton–zooplankton model: A dynamical systems approach. J. Plankton Res. 23(4), 389–413.
Edwards, A.M., Brindley, J., 1996. Oscillatory behaviour in a three-component plankton population model. Dyn. Stab. Syst. 11(4), 347–370.
Edwards, A.M., Brindley, J., 1999. Zooplankton mortality and the dynamical behaviour of plankton population models. Bull. Math. Biol. 61, 303–339.
Elton, C., Nicholson, M., 1942. The ten-year cycle in numbers of the lynx in Canada. J. Anim. Ecol. 11(2), 215–244.
Fujisaka, H., Yamada, T., 1983. Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys. 69, 32–48.
Fussman, G.F., Ellner, S.P., Shertzer, K.W., Hairston, N.G. Jr., 2000. Crossing the Hopf bifurcation in a live predator–prey system. Science 290(5495), 1358–1360.
Grenfall, B.T., Wilson, K., Finkenstädt, B.F., Coulson, T.N., Murray, S., Albon, S.D., Pemberton, J.M., Clutton-Brock, T.H., Crawley, M.J., 1998. Noise and determinism in synchronised sheep dynamics. Nature 394, 673–677.
Gross, T., Ebenhoh, W., Feudel, U., 2006. Long food chains are in general chaotic. OIKOS 109(1), 135–144.
Hastings, A., Powell, T., 1991. Chaos in a three-species food chain. Ecology 72, 896–903.
Hillary, R.M., Bees, M.A., 2004. Plankton lattices and the role of chaos in plankton patchiness. Phys. Rev. E 69(031913).
Lalli, C.M., Parsons, T.R., 1997. Biological Oceanography: An Introduction. Butterworth-Heinemann, The Open University.
Levy, M., Klein, P., 2004. Does the low frequency variability of mesoscale dynamics explain a part of the phytoplankton and zooplankton spectral variability? Proc. R. Soc. Lond. A 460, 1673–1687.
Martin, A.P., 2003. Phytoplankton patchiness: The role of lateral stirring and mixing. Prog. Oceanogr. 57, 125–174.
Martin, A.P., Richards, K.J., 2002. Patchy productivity in the open ocean. Global Biogeochem. Cycles 16(2), 1025–1034.
Okubo, A., 1971. Oceanic diffusion diagrams. Deep-Sea Res. 18, 789–802.
Pikovsky, A., Michael, R., Kurths, J., 2001. Synchronisation: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge, UK.
Popova, E.E., 1995. Non-universal sensitivity of a robust ecosystem model of the ocean upper mixed layer. Ocean Model. 109, 2–5.
Popova, E.E., Lozano, C.J., Srokosz, M.A., Fasham, M.J.R., Haley, P.J., Robinson, A.R., 2002. Coupled 3D physical and biological modelling of the mesoscale variability observed in North-East Atlantic in spring 1997: Biological processes. Deep-Sea Res. I 49, 1741–1768.
Slater, R.D., 1993. Some parametric and structural simulations with a three-dimensional ecosystem model of nitrogen cycling in the North Atlantic euphotic zone. In: Evans, G.T., Fasham, M.J.R. (Eds.), Towards a Model of Ocean Biogeochemical Processes, vol. 10. NATO. Springer-Verlag, Berlin.
Smith, C.L., Richards, K.J., Fasham, M.J.R., 1996. The impact of mesocale eddies on plankton dynamics in the upper ocean. Deep-Sea Res. I 43, 1807–1832.
Srokosz, M.A., Martin, A.P., Fasham, M.J.R., 2003. On the role of biological dynamics in plankton patchiness at the mesoscale: An example from the eastern North Atlantic ocean. J. Mar. Res. 61, 517–537.
Steele, J.H., Henderson, E.W., 1981. A simple plankton model. Am. Nat. 344, 734–741.
Strogatz, S., 1994. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Westview Press, Perseus Books Group.
Totterdell, I.J., 1993. An annotated bibliography of marine biological models. In: Evans, G.T., Fasham, M.J.R. (Eds.), Towards a Model of Ocean Biogeochemical Processes, vol. 10. NATO. Springer-Verlag, Berlin.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guirey, E.J., Bees, M.A., Martin, A.P. et al. Emergent Features Due to Grid-Cell Biology: Synchronisation in Biophysical Models. Bull. Math. Biol. 69, 1401–1422 (2007). https://doi.org/10.1007/s11538-006-9180-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-006-9180-y