Abstract
Slower recovery from perturbations near a tipping point and its indirect signatures in fluctuation patterns have been suggested to foreshadow catastrophes in a wide variety of systems1,2. Recent studies of populations in the field and in the laboratory have used time-series data to confirm some of the theoretically predicted early warning indicators, such as an increase in recovery time or in the size and timescale of fluctuations3,4,5,6. However, the predictive power of temporal warning signals is limited by the demand for long-term observations. Large-scale spatial data are more accessible, but the performance of warning signals in spatially extended systems7,8,9,10 needs to be examined empirically3,11,12,13. Here we use spatially extended yeast populations, an experimental system with a fold bifurcation (tipping point)6, to evaluate early warning signals based on spatio-temporal fluctuations and to identify a novel spatial warning indicator. We found that two leading indicators based on fluctuations increased before collapse of connected populations; however, the magnitudes of the increases were smaller than those observed in isolated populations, possibly because local variation is reduced by dispersal. Furthermore, we propose a generic indicator based on deterministic spatial patterns, which we call ‘recovery length’. As the spatial counterpart of recovery time14, recovery length is the distance necessary for connected populations to recover from spatial perturbations. In our experiments, recovery length increased substantially before population collapse, suggesting that the spatial scale of recovery can provide a superior warning signal before tipping points in spatially extended systems.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009)
Scheffer, M. et al. Anticipating critical transitions. Science 338, 344–348 (2012)
Drake, J. M. & Griffen, B. D. Early warning signals of extinction in deteriorating environments. Nature 467, 456–459 (2010)
Carpenter, S. R. et al. Early warnings of regime shifts: a whole-ecosystem experiment. Science 332, 1079–1082 (2011)
Veraart, A. J. et al. Recovery rates reflect distance to a tipping point in a living system. Nature 481, 357–359 (2012)
Dai, L., Vorselen, D., Korolev, K. S. & Gore, J. Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336, 1175–1177 (2012)
Guttal, V. & Jayaprakash, C. Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theor. Ecol. 2, 3–12 (2009)
Dakos, V., Nes, E. H., Donangelo, R., Fort, H. & Scheffer, M. Spatial correlation as leading indicator of catastrophic shifts. Theor. Ecol. 3, 163–174 (2010)
Dakos, V., Kéfi, S., Rietkerk, M., Van Nes, E. H. & Scheffer, M. Slowing down in spatially patterned ecosystems at the brink of collapse. Am. Nat. 177, E153–E166 (2011)
Carpenter, S. R. & Brock, W. A. Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform. Ecosphere 1, art10 (2010)
Lindegren, M. et al. Early detection of ecosystem regime shifts: a multiple method evaluation for management application. PLoS ONE 7, e38410 (2012)
Litzow, M. A., Urban, J. D. & Laurel, B. J. Increased spatial variance accompanies reorganization of two continental shelf ecosystems. Ecol. Appl. 18, 1331–1337 (2008)
Ouyang, Q. & Swinney, H. L. Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352, 610–612 (1991)
van Nes, E. H. & Scheffer, M. Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am. Nat. 169, 738–747 (2007)
May, R. M. Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269, 471–477 (1977)
Scheffer, M., Carpenter, S. & Foley, J. A. Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001)
Staver, A. C., Archibald, S. & Levin, S. A. The global extent and determinants of savanna and forest as alternative biome states. Science 334, 230–232 (2011)
Isbell, F., Tilman, D., Polasky, S., Binder, S. & Hawthorne, P. Low biodiversity state persists two decades after cessation of nutrient enrichment. Ecol. Lett. http://dx.doi.org/10.1111/ele.12066 (2013)
Holling, C. S. Resilience and stability of ecological systems. Annu. Rev. Ecol. Syst. 4, 1–23 (1973)
Scheffer, M. Critical Transitions in Nature and Society (Princeton Univ. Press, 2009)
Kleinen, T., Held, H. & Petschel-Held, G. The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation. Ocean Dyn. 53, 53–63 (2003)
Brock, W. A. & Carpenter, S. R. Interacting regime shifts in ecosystems: implication for early warnings. Ecol. Monogr. 80, 353–367 (2010)
Boettiger, C. & Hastings, A. Early warning signals and the prosecutor’s fallacy. Proc. R. Soc. Lond. B 279,. 4734–4739 (2012)
Rietkerk, M., Dekker, S. C., De Ruiter, P. C. & Van de Koppel, J. Self-organized patchiness and catastrophic shifts in ecosystems. Science 305, 1926–1929 (2004)
Kéfi, S. et al. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449, 213–217 (2007)
Gore, J., Youk, H. & Van Oudenaarden, A. Snowdrift game dynamics and facultative cheating in yeast. Nature 459, 253–256 (2009)
Fernández, A. & Fort, H. Catastrophic phase transitions and early warnings in a spatial ecological model. J. Stat. Mech. P09014 (2009)
Sole, R. V., Manrubia, S. C., Luque, B., Delgado, J. & Bascompte, J. Phase transitions and complex systems. Complexity 1, 13–26 (1996)
Ries, L., Fletcher, R. J., Battin, J. & Sisk, T. D. Ecological responses to habitat edges: mechanisms, models, and variability explained. Annu. Rev. Ecol. Evol. Syst. 35, 491–522 (2004)
Harper, K. A. et al. Edge influence on forest structure and composition in fragmented landscapes. Conserv. Biol. 19, 768–782 (2005)
DeCarlo, L. T. & Tryon, W. W. Estimating and testing autocorrelation with small samples: a comparison of the c-statistic to a modified estimator. Behav. Res. Ther. 31, 781–788 (1993)
Legendre, P. & Fortin, M. J. Spatial pattern and ecological analysis. Vegetatio 80, 107–138 (1989)
Moran, P. A. P. Notes on continuous stochastic phenomena. Biometrika 37, 17–23 (1950)
Acknowledgements
We would like to thank D. Vorselen, T. Krieger, D. Seekell, M. Pace and members of the Gore laboratory (A. Sanchez, M. Datta, E. Yurtsev, T. Artemova, K. Axelrod and A. Chen) for comments on the manuscript. T. Krieger performed initial simulations for the connected populations. Y. Zhang and O. Ornek collected preliminary data for the experiment to measure recovery length. This work was supported by a Whitaker Health Sciences Fund Fellowship (to L.D.), a Pappalardo Fellowship (to K.S.K.), an NIH R00 Pathways to Independence Award (NIH R00 GM085279-02), an NIH New Innovator Award (NIH DP2), an NSF CAREER Award, a Sloan Research Fellowship, the Pew Scholars Program and the Allen Investigator Program.
Author information
Authors and Affiliations
Contributions
L.D., K.S.K. and J.G. designed the study. L.D. performed the experiments and analysis. K.S.K. and J.G. assisted with the analysis. L.D., K.S.K. and J.G. wrote the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
This file contains Supplementary Figures 1-11, Supplementary Tables 1-2, Supplementary Notes 1-4 and Supplementary References. (PDF 1034 kb)
Rights and permissions
About this article
Cite this article
Dai, L., Korolev, K. & Gore, J. Slower recovery in space before collapse of connected populations. Nature 496, 355–358 (2013). https://doi.org/10.1038/nature12071
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nature12071
This article is cited by
-
Dynamical indicators in time series of healthcare expenditures predict mortality risk of older adults following spousal bereavement
BMC Geriatrics (2022)
-
Identifying critical transitions in complex diseases
Journal of Biosciences (2022)
-
Eigenvalues of the covariance matrix as early warning signals for critical transitions in ecological systems
Scientific Reports (2019)
-
Flickering in Information Spreading Precedes Critical Transitions in Financial Markets
Scientific Reports (2019)
-
When increasing population density can promote the evolution of metabolic cooperation
The ISME Journal (2018)
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.