Chaotic Phytoplankton Behaviours
Phytoplankton contribute about 50 percent to the global primary production on Earth [1] and are important for the biogeochemical cycles of carbon, nitrogen, phosphorus, sulfur and other compounds. In the eutrophic zone photosynthesis leads to uptake of carbon by phytoplankton, which is grazed on by zooplankton. Sinking of organic matter due to phytoplankton aggregation and sinking, as well as zooplankton excretion leads to a reduction of carbon and nutrient concentrations at the surface. This process is called the biological pump [2].
Despite the importance of phytoplankton for global biogeochemical cycles and cli mate, their composition and dynamics is still poorly understood. There are only few observations, and many species have not been identified or do not survive in culture. For example, recent research related to the TARA Oceans project showed a far larger diversity of eukaryotic phytoplankton than previously catalogued [3]. Figure 1 shows observations of the relative contribution of different phytoplankton to total biomass at the Santa Monica Bay station.
Fig. 1 Phytoplankton groups observed at Santa Monica Bay (source: Leinweber, A.).
It raises the question whether the dynamics of phytoplankton are chaotic. On the other hand, fluctuations like those in Fig. 1 are not observed on large spatial scales, where external forcings like diffusion override the internal phytoplankton dynamics.
On the modelling side, Lotka-Volterra models of competition and predation have been analysed for nearly 100 years and it was found that chaotic behaviour is possible if at least 4 species are involved [4]. The model of Scheffer [5] is an evolution of the Lotka-Volterra descriptions containing three species and more biology. Here we will use it to analyse interactions between these species, both with and without a physical process (vertical diffusion), to investigate the internal behaviour of the model and whether it is overridden by the physical process.
This article is based on Scheffer’s model [5], which describes the change in concentration of autotrophic phytoplankton(A), herbivorous zooplankton(Z) and carnivorous zooplankton(C) feeding on the herbivorous zooplankton.
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References
[1]Christopher B Field, Michael J Behrenfeld, James T Randerson, and Paul Falkowski. Primary production of the biosphere: integrating terrestrial and oceanic components. science, 281(5374):237–240, 1998.
[2] Jorge L Sarmiento and Nicolas Gruber. Ocean biogeochemical dynamics. Princeton University Press, 2006.
[3] Colomban De Vargas, St´ephane Audic, Nicolas Henry, Johan Decelle, Fr´ed´eric Mah´e, Ramiro Logares, Enrique Lara, C´edric Berney, Noan Le Bescot, Ian Probert, et al. Eukaryotic plankton diversity in the sunlit ocean. Science, 348(6237):1261605, 2015.
[4] JA Vano, JC Wildenberg, MB Anderson, JK Noel, and JC Sprott. Chaos in low dimensional lotka–volterra models of competition. Nonlinearity, 19(10):2391, 2006.
[5] M. Scheffer. Should we expect strange attractors behind plankton dynamics–and if so, should we bother? Journal of Plankton Research, 13:1291–1305, 1991.
[6] Horst Malchow Klaus Jurgens Lutz Becks, Frank M. Hilker and Hartmut Arndt. Ex perimental demonstration of chaos in a microbial food web. Nature Letters, 435:1226– 1229, 2005.