Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Examples of the simplex projection method.
Figure 2: Examples of the S-map method for the four time series from Fig. 1.

References

  1. 1

    Scheffer, M., Carpenter, S., Foley, J. A., Folkes, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Steele, J. H. & Henderson, E. W. Modeling long-term fluctuations in fish stocks. Science 224, 985–987 (1984)

    ADS  CAS  Article  Google Scholar 

  3. 3

    May, R. M. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Ludwig, D., Jones, D. & Holling, C. S. Qualitative analysis of insect outbreak systems: the spruce budworm and the forest. J. Anim. Ecol. 47, 315–332 (1978)

    Article  Google Scholar 

  5. 5

    Sugihara, G. & May, R. M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time-series. Nature 344, 734–741 (1990)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Sugihara, G. et al. Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts. Proc. Natl Acad. Sci. USA 96, 14210–14215 (1999)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Dixon, P. A., Milicich, M. J. & Sugihara, G. Episodic fluctuations in larval supply. Science 283, 1528–1530 (1999)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Dixon, P. A., Milicich, M. J. & Sugihara, G. in Nonlinear Dynamics and Statistics (ed. Mees, A. I.) 339–364 (Birkhauser, Boston, 2001)

    Google Scholar 

  9. 9

    Wunsch, C. The interpretation of short climate records, with comments on the North Atlantic and Southern Oscillations. Bull. Am. Meteorol. Soc. 80, 245–256 (1999)

    ADS  Article  Google Scholar 

  10. 10

    Rudnick, D. L. & Davis, R. E. Red noise and regime shifts. Deep-Sea Res. I 50, 691–699 (2003)

    Article  Google Scholar 

  11. 11

    Mantua, N. The Pacific Decadal Oscillation (PDO). http://jisao.washington.edu/pdo/PDO.latest (2004).

  12. 12

    Hurrell, J. North Pacific (NP) Index information. http://www.cgd.ucar.edu/~jhurrell/np.html (2003).

  13. 13

    National Center for Atmospheric Research. Southern Oscillation Index. http://www.cgd.ucar.edu/cas/catalog/climind/soi.html (2004).

  14. 14

    SIO Shore Station. http://www.mlrg.ucsd.edu/shoresta/index.html (2001).

  15. 15

    Hsieh, C. H. et al. A comparison of long-term trends and variability in populations of larvae of exploited and unexploited fishes in the Southern California region: a community approach. Prog. Oceanogr. (submitted)

  16. 16

    Rebstock, G. A. Climatic regime shifts and decadal-scale variability in calanoid copepod populations off southern California. Glob. Change Biol. 8, 71–89 (2002)

    ADS  Article  Google Scholar 

  17. 17

    Washington Department of Fish and Wildlife and Oregon Department of Fish and Wildlife. Status Report: Columbia River fish runs and fisheries 19382000 Table 3 (2004).

  18. 18

    Hare, S. R. & Mantua, N. J. Empirical evidence for North Pacific regime shifts in 1977 and 1989. Prog. Oceanogr. 47, 103–145 (2000)

    ADS  Article  Google Scholar 

  19. 19

    deYoung, B. et al. Detecting regime shifts in the ocean: data considerations. Prog. Oceanogr. 60, 143–164 (2004)

    ADS  Article  Google Scholar 

  20. 20

    Mantua, N. Methods for detecting regime shifts in large marine ecosystems: a review with approaches applied to North Pacific data. Prog. Oceanogr. 60, 165–182 (2004)

    ADS  Article  Google Scholar 

  21. 21

    McGowan, J. A., Bograd, S. J., Lynn, R. J. & Miller, A. J. The biological response to the 1977 regime shift in the California Current. Deep-Sea Res. II 50, 2567–2582 (2003)

    ADS  Article  Google Scholar 

  22. 22

    Sutherland, J. Multiple stable points in natural communities. Am. Nat. 108, 859–873 (1974)

    Article  Google Scholar 

  23. 23

    May, R. M. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645–647 (1974)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Sugihara, G., Grenfell, B. & May, R. Distinguishing error from chaos in ecological time-series. Phil. Trans. R. Soc. Lond. B 330, 235–251 (1990)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Sugihara, G. Nonlinear forecasting for the classification of natural time-series. Phil. Trans. R. Soc. Lond. A 348, 477–495 (1994)

    ADS  Article  Google Scholar 

  26. 26

    Sugihara, G., Allan, W., Sobel, D. & Allan, K. D. Nonlinear control of heart rate variability in human infants. Proc. Natl Acad. Sci. USA 93, 2608–2613 (1996)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Hasselmann, K. Stochastic climate models. 1. Theory. Tellus 28, 473–485 (1976)

    ADS  Article  Google Scholar 

  28. 28

    Patil, D. A. S., Hunt, B. R. & Carton, J. A. Identifying low-dimensional nonlinear behavior in atmospheric data. Mon. Weath. Rev. 129, 2116–2125 (2001)

    ADS  Article  Google Scholar 

  29. 29

    Moser, H. G. et al. Distributional atlas of fish larvae and eggs in the Southern California Bight region: 1951–1998. California Cooperative Oceanic Fisheries Investigations Atlas 34, 1–166 (2001)

    Google Scholar 

  30. 30

    Hastings, H. M. & Sugihara, G. Fractals: A User's Guide for the Natural Sciences (Oxford Univ., New York, 1993)

    Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to George Sugihara.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Methods

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)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing