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Letters to Nature
Nature 259, 659 (26 February 1976); doi:10.1038/259659a0

Hypothesis for origin of planktonic patchiness

SIMON A. LEVIN* & LEE A. SEGEL

*Section of Ecology and Systematics and Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York 14853
Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel and Rennselaer Polytechnic Institute, Troy, New York 12181

ALTHOUGH environmental heterogeneity can contribute to the observed patchiness in oceanic planktonic populations, biological interactions between phytoplankton and herbivorous copepods can lead to similar patterns. The phenomenon of spontaneous pattern generation even in a homogeneous environment through the interplay of reaction and movement is a very general property of the class of mathematical ‘reaction–diffusion’ equations used to model such systems, and there are several ways in which such patterns may occur. The result may be either spatiotemporal patterns1 or time-independent spatial patterns. Usually one thinks of diffusion as damping inhomogeneities, and a hypothesis put forward by Steele2 essentially relies on a balance reached between the dehomogenising aspects of local interaction and the homogenising influence of diffusion to produce pattern. On the other hand, it has also been suggested3–6 that in some conditions diffusion can destabilise an otherwise stable interaction (in the manner originally suggested by Turing7) to produce pattern. We have explored5 this further in a nonlinear analysis that describes the final stages of pattern formation, and the resultant calculations provide some insights into the spatial scale of patterns which might arise in this way.

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References

1. Kopell, N., and Howard, L. N., Lectures on Mathematics in the Life Sciences, 7, (edit. by Levin, S. A.), 201–216 (American Mathematical Society, Providence, Rhode Island, 1974).
2. Steele, J. H., Coastal Upwelling Ecosystems Analysis Newsletter, 2 (4), 3–7 (1973); Nature, 248, 83 (1974).
3. Levin, S. A., Am. Nat., 108, 207–228 (1974).
4. Segel, L. A., and Jackson, J. L., J. theor. Biol., 37, 545–559 (1972).
5. Segel, L. A., and Levin, S. A., Top. stat. Mech. Biophys. Proc. AIP Conf., 27, (American Institute of Physics, in the press).
6. Okubo, A., Tech. Rept 86, Chesapeake Bay Inst. (Johns Hopkins University, Baltimore, 1974).
7. Turing, A., Phil. Trans. R. Soc., B237, 37–72 (1952).
8. Holling, C. S., Mem. entom. Soc. Can., 45, 1–60 (1965).
9. Gierer, A., and Meinhardt, H., Lectures on Mathematics in the Life Sciences, 7, (edit. by Levin, S. A.), 163–183 (American Mathematical Society, Providence, Rhode Island, 1974).



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