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.
At a glance
- Early-warning signals for critical transitions. Nature 461, 53–59 (2009) et al.
- Anticipating critical transitions. Science 338, 344–348 (2012) et al.
- Early warning signals of extinction in deteriorating environments. Nature 467, 456–459 (2010) &
- Early warnings of regime shifts: a whole-ecosystem experiment. Science 332, 1079–1082 (2011) et al.
- Recovery rates reflect distance to a tipping point in a living system. Nature 481, 357–359 (2012) et al.
- Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336, 1175–1177 (2012) , , &
- Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theor. Ecol. 2, 3–12 (2009) &
- Spatial correlation as leading indicator of catastrophic shifts. Theor. Ecol. 3, 163–174 (2010) , , , &
- Slowing down in spatially patterned ecosystems at the brink of collapse. Am. Nat. 177, E153–E166 (2011) , , , &
- Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform. Ecosphere 1, art10 (2010) &
- Early detection of ecosystem regime shifts: a multiple method evaluation for management application. PLoS ONE 7, e38410 (2012) et al.
- Increased spatial variance accompanies reorganization of two continental shelf ecosystems. Ecol. Appl. 18, 1331–1337 (2008) , &
- Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352, 610–612 (1991) &
- Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am. Nat. 169, 738–747 (2007) &
- Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269, 471–477 (1977)
- Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001) , &
- The global extent and determinants of savanna and forest as alternative biome states. Science 334, 230–232 (2011) , &
- Low biodiversity state persists two decades after cessation of nutrient enrichment. Ecol. Lett. http://dx.doi.org/10.1111/ele.12066 (2013) , , , &
- Resilience and stability of ecological systems. Annu. Rev. Ecol. Syst. 4, 1–23 (1973)
- 2009) Critical Transitions in Nature and Society (Princeton Univ. Press,
- The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation. Ocean Dyn. 53, 53–63 (2003) , &
- Interacting regime shifts in ecosystems: implication for early warnings. Ecol. Monogr. 80, 353–367 (2010) &
- Early warning signals and the prosecutor’s fallacy. Proc. R. Soc. Lond. B 279,. 4734–4739 (2012) &
- Self-organized patchiness and catastrophic shifts in ecosystems. Science 305, 1926–1929 (2004) , , &
- Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449, 213–217 (2007) et al.
- Snowdrift game dynamics and facultative cheating in yeast. Nature 459, 253–256 (2009) , &
- Catastrophic phase transitions and early warnings in a spatial ecological model. J. Stat. Mech. P09014 (2009) &
- Phase transitions and complex systems. Complexity 1, 13–26 (1996) , , , &
- Ecological responses to habitat edges: mechanisms, models, and variability explained. Annu. Rev. Ecol. Evol. Syst. 35, 491–522 (2004) , , &
- Edge influence on forest structure and composition in fragmented landscapes. Conserv. Biol. 19, 768–782 (2005) et al.
- Estimating and testing autocorrelation with small samples: a comparison of the c-statistic to a modified estimator. Behav. Res. Ther. 31, 781–788 (1993) &
- Spatial pattern and ecological analysis. Vegetatio 80, 107–138 (1989) &
- Notes on continuous stochastic phenomena. Biometrika 37, 17–23 (1950)
- Supplementary Information (1 MB)
This file contains Supplementary Figures 1-11, Supplementary Tables 1-2, Supplementary Notes 1-4 and Supplementary References.