Slower recovery in space before collapse of connected populations

• Published in: Nature (London) Vol. 496; no. 7445; pp. 355 - 358
• Main Authors: Dai, Lei, Korolev, Kirill S., Gore, Jeff
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 18.04.2013; Nature Publishing Group
• Subjects: Animal, plant and microbial ecology; Biological and medical sciences; Dilution; Dispersal; Ecosystem; Ecosystems; Experiments; Feedback; Fundamental and applied biological sciences. Psychology; General aspects. Techniques; Humanities and Social Sciences; Hydrolysis; letter; Methods and techniques (sampling, tagging, trapping, modelling...); Models, Biological; Mortality; multidisciplinary; Population density; Saccharomyces cerevisiae - cytology; Saccharomyces cerevisiae - metabolism; Science; Spatio-Temporal Analysis; Standard deviation; Studies; Sucrose - metabolism; System theory; Time series; Tropical forests; Yeasts; Ascomycota; Fungi; Ecological connectivity; Spatial distribution; Population; Perturbation; Experimental study; Recovery; Saccharomyces cerevisiae; Dispersion
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature12071

Early warning signals of systems collapse include increased recovery time after perturbations, and here spatially extended, connected yeast populations are used to identify a new warning indicator: recovery length after spatial disturbances. Measuring distance to a tipping point The behaviour of complex systems near tipping points, where a small change can lead to a large shift in the state of the system, is notoriously difficult to predict. Recent studies have identified temporal factors such as recovery time and changes in size and timescale of fluctuations that precede some tipping points. Lei Dai et al . grew populations of the budding yeast that were spatially connected through controlled dispersal between nearest neighbours, and looked for spatiotemporal patterns that anticipated population collapse after perturbation — the introduction of sucrose solution more highly diluted than its surroundings. As the distance from the diluted patch increased, yeast population density increased towards a steady state. The distance required for recovery by connected populations was much greater when populations were close to collapse. This work introduces the concept of 'recovery length' as a spatial counterpart to recovery time, and as boundaries between regions of different quality are ubiquitous in nature, many systems in the oceans and on land might be expected to be subject to such spatial instability. 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 systems 1 , 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 fluctuations 3 , 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 systems 7 , 8 , 9 , 10 needs to be examined empirically 3 , 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 time 14 , 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.