Sufficient noise and turbulence can induce phytoplankton patchiness

Hiroshi Serizawa, Takashi Amemiya, Kiminori Itoh

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DOI: 10.4236/ns.2010.24040                

Abstract

Phytoplankton patchiness ubiquitously obser- ved in marine ecosystems is a simple phy- sical phenomenon. Only two factors are required for its formation: one is persistent variations of inhomogeneous distributions in the phytopl- ankton population and the other is turbulent stirring by eddies. It is not necessary to assume continuous oscillations such as limit cycles for realization of the first factor. Instead, a certain amount of noise is enough. Random fluctua-tions by environmental noise and turbulent ad-vection by eddies seem to be common in open oceans. Based on these hypotheses, we pro-pose seemingly the simplest method to simulate patchiness formation that can create realistic images. Sufficient noise and turbulence can induce patchiness formation even though the system lies on the stable equilibrium conditions. We tentatively adopt the two-component model with nutrients and phytoplankton, however, the choice of the mathematical model is not essen-tial. The simulation method proposed in this study can be applied to whatever model with stable equilibrium states including one-com-ponent ones.

Keywords

Eddy; Fluctuation; Noise; Patchiness; Reaction-Advection-Diffusion Model; Turbulence

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Martin, A.P. (2003) Phytoplankton patchiness: The role of lateral stirring and mixing. Progress in Oceanography, 57(2), 125-174.
[2]	Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Malchow, H. and Li, B.-L. (2002) Spatiotemporal com-plexity of plankton and fish dynamics. SIAM Review, 44(3), 311-370.
[3]	Abraham, E.R. (1998) The generation of plankton patchi-ness by turbulent stirring. Nature, 391(6667), 577-580.
[4]	Neufeld, Z., Haynes, P.H., Garçon, V. and Sudre, J. (2002) Ocean fertilization experiments may initiate a large scale phytoplankton bloom. Geophysical Research Letters, 29(11), 1-4.
[5]	Tzella, A. and Haynes, P.H. (2007) Small-scale spatial structure in plankton distributions. Biogeosciences, 4(2), 173-179.
[6]	Serizawa, H., Amemiya, T. and Itoh, K. (2008) Patchi-ness in a minimal nutrient-phytoplankton model. Journal of Biosciences, 33(3), 391-403.
[7]	Dyke, P.P.G. and Robertson, T. (1985) The simulation of offshore turbulent dispersion using seeded eddies. Ap-plied Mathematical Modelling, 9(6), 429-433.
[8]	Serizawa, H., Amemiya, T. and Itoh, K. (2009) Noise- triggered regime shifts in a simple aquatic model. Eco-logical Complexity, 6(3), 375-382.
[9]	Vainstein, M.H., Rubí, J.M. and Vilar, J.M.G. (2007) Stochastic population dynamics in turbulent fields. The European Physical Journal-Special Topics, 146(1), 177- 187.
[10]	Spagnolo, B., Valenti, D. and Fiasconaro, A. (2004) Noise in ecosystems: A short review. Mathematical Biosciences and Engineering, 1(1), 185-211.
[11]	Provata, A., Sokolov, I.M. and Spagnolo, B. (2008) Edi-torial: Ecological complex systems. The European Physical Journal B, 65(3), 307-314.
[12]	Guttal, V. and Jayaprakash, C. (2007) Impact of noise on bistable ecological systems. Ecological Modelling, 201 (3-4), 420-428.
[13]	Spagnolo, B., Fiasconaro, A. and Valenti, D. (2003) Noise induced phenomena in Lotka-Volterra systems. Fluctuation and Noise Letters, 3(2), 177-185.
[14]	Serizawa, H., Amemiya, T. and Itoh, K. (2009) Patchi-ness and bistability in the comprehensive cyanobacterial model (CCM). Ecological Modelling, 220(6), 764-773.
[15]	Okubo, A. (1971) Oceanic diffusion diagram. Deep Sea Research and Oceanographic Abstracts, 18(8), 789-802.
[16]	Becks, L., Hilker, F.M., Malchow, H., Jürgens, K. and Arndt, H. (2005) Experimental demonstration of chaos in a microbial food web. Nature, 435(30), 1226-1229.