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Journal Article

Slowing Down in Spatially Patterned Ecosystems at the Brink of Collapse

Vasilis Dakos, Sonia Kéfi, Max Rietkerk, Egbert H. van Nes and Marten Scheffer
The American Naturalist
Vol. 177, No. 6 (June 2011), pp. E153-E166
DOI: 10.1086/659945
Stable URL:
Page Count: 14
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AbstractPredicting the risk of critical transitions, such as the collapse of a population, is important in order to direct management efforts. In any system that is close to a critical transition, recovery upon small perturbations becomes slow, a phenomenon known as critical slowing down. It has been suggested that such slowing down may be detected indirectly through an increase in spatial and temporal correlation and variance. Here, we tested this idea in arid ecosystems, where vegetation may collapse to desert as a result of increasing water limitation. We used three models that describe desertification but differ in the spatial vegetation patterns they produce. In all models, recovery rate upon perturbation decreased before vegetation collapsed. However, in one of the models, slowing down failed to translate into rising variance and correlation. This is caused by the regular self-organized vegetation patterns produced by this model. This finding implies an important limitation of variance and correlation as indicators of critical transitions. However, changes in such self-organized patterns themselves are a reliable indicator of an upcoming transition. Our results illustrate that while critical slowing down may be a universal phenomenon at critical transitions, its detection through indirect indicators may have limitations in particular systems.

Notes and References

This item contains 45 references.

Literature Cited
  • ['Aguiar, M. R., and O. E. Sala. 1999. Patch structure, dynamics and implications for the functioning of arid ecosystems. Trends in Ecology & Evolution 14:273–277.']
  • ['Bailey, R. M. 2010. Spatial and temporal signatures of fragility and threshold proximity in modelled semi-arid vegetation. Proceedings of the Royal Society B: Biological Sciences 278:1064–1071, doi:10.1098/rspb.2010.1750.']
  • ['Biggs, R., S. R. Carpenter, and W. A. Brock. 2009. Turning back from the brink: detecting an impending regime shift in time to avert it. Proceedings of the National Academy of Sciences of the USA 106:826–831.']
  • ['Carpenter, S. R. 2003. Regime shifts in lake ecosystems: pattern and variation. Excellence in Ecology Series. Vol. 15. International Ecology Institute, Oldendorf/Luhe.']
  • ['Carpenter, S. R., and W. A. Brock. 2006. Rising variance: a leading indicator of ecological transition. Ecology Letters 9:311–318.']
  • ['Chow, S. N., J. MalletParet, and E. S. VanVleck. 1996. Dynamics of lattice differential equations. International Journal of Bifurcation and Chaos 6:1605–1621.']
  • ['Dakos, V., E. van Nes, R. Donangelo, H. Fort, and M. Scheffer. 2010. Spatial correlation as leading indicator of catastrophic shifts. Theoretical Ecology 3:163–174.']
  • ['Donangelo, R., H. Fort, V. Dakos, M., Scheffer, and E. H. van Nes. 2010. Early warnings for catastrophic shifts in ecosystems: comparison between spatial and temporal indicators. International Journal of Bifurcation and Chaos 20:315–321.']
  • ['Eppinga, M. B., P. C. de Ruiter, M. J. Wassen, and M. Rietkerk. 2009. Nutrients and hydrology indicate the driving mechanisms of peatland surface patterning. American Naturalist 173:803–818.']
  • ['Guttal, V., and C. Jayaprakash. 2007. Impact of noise on bistable ecological systems. Ecological Modelling 201:420–428.']
  • ['———. 2008. Changing skewness: an early warning signal of regime shifts in ecosystems. Ecology Letters 11:450–460.']
  • ['———. 2009. Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theoretical Ecology 2:3–12.']
  • ['Hastings, A., and D. B. Wysham. 2010. Regime shifts in ecological systems can occur with no warning. Ecology Letters 13:464–472.']
  • ['Held, H., and T. Kleinen. 2004. Detection of climate system bifurcations by degenerate fingerprinting. Geophysical Research Letters 31:L23207.']
  • ['HilleRisLambers, R., M. Rietkerk, F. van den Bosch, H. T. Prins, and H. De Kroon. 2001. Vegetation pattern formation in semi-arid grazing systems. Ecology 82:50–61.']
  • ['Holling, C. S. 1973. Resilience and stability of ecological systems. Annual Review of Ecology and Systematics 4:1–23.']
  • ['Ives, A. R., B. Dennis, K. L. Cottingham, and S. R. Carpenter. 2003. Estimating community stability and ecological interactions from time-series data. Ecological Monographs 73:301–330.']
  • ['Janssen, R. H. H., M. B. J. Meinders, E. H. van Nes, and M. Scheffer. 2008. Microscale vegetation-soil feedback boosts hysteresis in a regional vegetation-climate system. Global Change Biology 14:1104–1112.']
  • ['Judd, S. L., and M. Silber. 2000. Simple and superlattice Turing patterns in reaction-diffusion systems: bifurcation, bistability, and parameter collapse. Physica D 136:45–65.']
  • ['Kéfi, S., M. Rietkerk, M. van Baalen, and M. Loreau. 2007a. Local facilitation, bistability and transitions in arid ecosystems. Theoretical Population Biology 71:367–379.']
  • ['Kéfi, S., M. Rietkerk, C. L. Alados, Y. Pueyo, V. P. Papanastasis, A. ElAich, and P. C. de Ruiter. 2007b. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449:213–217.']
  • ['Kéfi, S., M. Rietkerk, M. Roy, A. Franc, P. C. de Ruiter, and M. Pascual. 2011. Robust scaling in ecosystems and the meltdown of patch size distributions before extinction. Ecology Letters 14:29–35.']
  • ['Keitt, T. H., M. A. Lewis, and R. D. Holt. 2001. Allee effects, invasion pinning, and species’ borders. American Naturalist 157:203–216.']
  • ['Knowlton, N. 1992. Thresholds and multiple stable states in coral reef community dynamics. American Zoologist 32:674–682.']
  • ['Legendre, P., and M. J. Fortin. 1989. Spatial pattern and ecological analysis. Plant Ecology 80:107–138.']
  • ['Millennium Assessment. 2005. Ecosystems and human well-being: our human planet: summary for decision makers. Island, Washington, DC.']
  • ['Neumaier, A., and T. Schneider. 2001. Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software 27:27–57.']
  • ['Pascual, M., and F. Guichard. 2005. Criticality and disturbance in spatial ecological systems. Trends in Ecology & Evolution 20:88–95.']
  • ['Reynolds, J. F., D. M. S. Smith, E. F. Lambin, B. L. Turner, M. Mortimore, S. P. J. Batterbury, T. E. Downing, et al. 2007. Global desertification: building a science for dryland development. Science 316:847–851.']
  • ['Rietkerk, M., and J. van de Koppel. 2008. Regular pattern formation in real ecosystems. Trends in Ecology & Evolution 23:169–175.']
  • ['Rietkerk, M., M. C. Boerlijst, F. van Langevelde, R. HilleRisLambers, J. van de Koppel, L. Kumar, H. H. T. Prins, and A. M. de Roos. 2002. Self-organization of vegetation in arid ecosystems. American Naturalist 160:524–530.']
  • ['Rietkerk, M., S. C. Dekker, P. C. de Ruiter, and J. van de Koppel. 2004. Self-organized patchiness and catastrophic shifts in ecosystems. Science 305:1926–1929.']
  • ['Scheffer, M. 1998. Ecology of shallow lakes. Chapman & Hall, London.']
  • ['Scheffer, M., S. Carpenter, J. A. Foley, C. Folke, and B. Walker. 2001. Catastrophic shifts in ecosystems. Nature 413:591–596.']
  • ['Scheffer, M., J. Bascompte, W. A. Brock, V. Brovkin, S. R. Carpenter, V. Dakos, H. Held, E. H. van Nes, M. Rietkerk, and G. Sugihara. 2009. Early-warning signals for critical transitions. Nature 461:53–59.']
  • ['Shnerb, N. M., P. Sarah, H. Lavee, and S. Solomon. 2003. Reactive glass and vegetation patterns. Physical Review Letters 90:038101.']
  • ['Strogatz, S. H. 1994. Nonlinear dynamics and chaos with applications to physics, biology, chemistry and engineering. Perseus, Cambridge.']
  • ['Turing, A. M. 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B: Biological Sciences 237:37–72.']
  • ['van Baalen, M. 2000. Pair approximation for different spatial geometries. Pages 359–387 in U. Diekmann, R. Law, and J. A. J. T. Metz, eds. The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, Cambridge.']
  • ['van de Koppel, J., M. Rietkerk, N. Dankers, and P. M. Herman. 2005. Scale-dependent feedback and regular spatial patterns in young mussel beds. American Naturalist 165:E66–E77.']
  • ['van Nes, E. H., and M. Scheffer. 2003. Alternative attractors may boost uncertainty and sensitivity in ecological models. Ecological Modeling 159:117–124.']
  • ['———. 2005. Implications of spatial heterogeneity for regime shifts in ecosystems. Ecology 86:1797–1807.']
  • ['———. 2007. Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. American Naturalist 169:738–747.']
  • ['von Hardenberg, J., E. Meron, M. Shachak, and Y. Zarmi. 2001. Diversity of vegetation patterns and desertification. Physical Review Letters 8719:198101.']
  • ['Wissel, C. 1984. A universal law of the characteristic return time near thresholds. Oecologia (Berlin) 65:101–107.']
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