The prospect of rapid dynamic changes in the environment is a pressing concern that has profound management and public policy implications1,2. Worries over sudden climate change and irreversible changes in ecosystems are rooted in the potential that nonlinear systems have for complex and ‘pathological’ behaviours1,2. Nonlinear behaviours have been shown in model systems3 and in some natural systems1,4,5,6,7,8, but their occurrence in large-scale marine environments remains controversial9,10. Here we show that time series observations of key physical variables11,12,13,14 for the North Pacific Ocean that seem to show these behaviours are not deterministically nonlinear, and are best described as linear stochastic. In contrast, we find that time series for biological variables5,15,16,17 having similar properties exhibit a low-dimensional nonlinear signature. To our knowledge, this is the first direct test for nonlinearity in large-scale physical and biological data for the marine environment. These results address a continuing debate over the origin of rapid shifts in certain key marine observations as coming from essentially stochastic processes or from dominant nonlinear mechanisms1,9,10,18,19,20. Our measurements suggest that large-scale marine ecosystems are dynamically nonlinear, and as such have the capacity for dramatic change in response to stochastic fluctuations in basin-scale physical states.
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We thank the Scripps Institution of Oceanography Pelagic Invertebrates Collection, the California Cooperative Oceanic Fisheries Investigation, the Oregon and Washington Departments of Fish and Wildlife, and G. Rebstock, for the availability and use of their data. R. Davis, D. Field, N. Mantua, G. Rebstock, C. Reiss, D. Rudnick, L.-F. Bersier and J. Bascompte provided discussion and comments on this work. Our study was funded by a NOAA initiative to improve the analysis of ecological data and its use in fisheries management (C.H.), the National Marine Fisheries Service and the Edna Bailey Sussman Fund (C.H.), NSF/LTER CCE ‘Nonlinear Transitions in the California Current Coastal Pelagic Ecosystem’ (C.H., G.S.), California Sea Grant (S.G.), the University of California Marine Council through the Network for Environmental Observations of the Coastal Ocean (A.L.), the Sugihara Family Trust (G.S.), and the Deutsche Bank Complexity Fund (G.S.). All co-authors contributed equally to this effort.
Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.
The supplementary methods contain a detailed technical exposition of the simplex-projection technique and the S-map modelling technique. In addition to the text, Supplementary Figures S1 and S2 illustrate the simplex-projection and S-map techniques are embedded in the document. (DOC 477 kb)
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Hsieh, C., Glaser, S., Lucas, A. et al. Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean. Nature 435, 336–340 (2005). https://doi.org/10.1038/nature03553
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