九州大学数理生物学研究室

Spatiotemporal chaos in a two-species plankton model

Merlin C. Köhnke

Institute of Environmental Systems Research
School of Mathematics / Computer Science, Osnabrück University

2019/10/23, 13:30-, at W1-C-909



Abstract

     Phytoplankton and marine cyanobacteria are responsible for nearly half of the global net primary production [1]. Thus, it is crucial to understand plankton population dynamics in order to predict possible impacts of climate change. As a consequence, the modeling of plankton communities has been an active area of research during the last decades [2-4]. A particular striking feature is the often inhomogeneous distribution of plankton [5].
     Here, a two-species (phytoplankton and zooplankton) reaction-diffusion system will be considered. Nonspatial considerations reveal that the zooplankton may go extinct or coexistence (stationary or oscillatory) between zoo- and phytoplankton may emerge depending on the choice of parameters. However, including space, the dynamics are more complex. In particular, spatiotemporal irregular oscillations can rescue the predator from extinction. These oscillations can be characterized as spatiotemporal chaos.
     The results provide a simple mechanism not only for the emergence of inhomogeneous plankton distributions but also for the occurrence of chaos in plankton communities [6]. Possible underlying mechanisms for this phenomenon will be discussed.

References

[1] Worden, A. Z., Wilken, S. (2016). A plankton bloom shifts as the ocean warms. Science, 354(6310), 287-288.
[2] Mimura, M., Murray, J. D. (1978). On a diffusive prey-predator model which exhibits patchiness. Journal of Theoretical Biology, 75(3), 249-262.
[3] Franks, P. J. S., Wroblewski, J. S., Flierl, G. R. (1986). Behavior of a simple plankton model with food-level acclimation by herbivores. Marine Biology, 91(1), 121-129.
[4] Malchow, H., Petrovskii, S., Medvinsky, A. (2001). Pattern formation in models of plankton dynamics. A synthesis. Oceanologica Acta, 24(5), 479-487.
[5] Abbott, M., 1993. Phytoplankton patchiness: ecological implicationsand observation methods. In: Levin, S.A., Powell, T.M., Steele, J.H.(Eds.), Patch Dynamics. Lecture Notes in Biomathematics, vol. 96. Springer-Verlag, Berlin, pp. 37-49.
[6] Benincà, E. et al. (2008). Chaos in a long-term experiment with a plankton community. Nature, 451(7180), 822.

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