Theory predicts that the approach of catastrophic thresholds in natural systems (e.g., ecosystems, the climate) may result in an increasingly slow recovery from small perturbations, a phenomenon called critical slowing down. We used replicate laboratory populations of the budding yeast Saccharomyces cerevisiae for direct observation of critical slowing down before population collapse. We mapped the bifurcation diagram experimentally and found that the populations became more vulnerable to disturbance closer to the tipping point. Fluctuations of population density increased in size and duration near the tipping point, in agreement with the theory. Our results suggest that indicators of critical slowing down can provide advance warning of catastrophic thresholds and loss of resilience in a variety of dynamical systems.

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 fluctuations3–6. 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 systems7–10 needs to be examined empirically3,11–13. Here we use spatially extended yeast populations, an experimental system displaying a fold bifurcation6, to evaluate early warning signals based on spatio-temporal fluctuations and to identify a novel warning indicator in space. We found that two leading indicators based on fluctuations increased before collapse of connected populations; however, the magnitude of increase was smaller than that observed in isolated populations, possibly because local variation is reduced by dispersal. Furthermore, we propose a generic indicator based on deterministic spatial patterns, “recovery length”. As the spatial counterpart of recovery time14, recovery length is defined as the distance for connected populations to recover from perturbations in space (e.g. a region of poor quality). 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.

Shifting patterns of temporal fluctuations have been found to signal critical transitions in a variety of systems, from ecological communities to human physiology. However, failure of these early warning signals in some systems calls for a better understanding of their limitations. In particular, little is known about the generality of early warning signals in different deteriorating environments. In this study, we characterized how multiple environmental drivers influence the dynamics of laboratory yeast populations, which was previously shown to display alternative stable states [Dai et al., Science, 2012]. We observed that both the coefficient of variation and autocorrelation increased before population collapse in two slowly deteriorating environments, one with a rising death rate and the other one with decreasing nutrient availability. We compared the performance of early warning signals across multiple environments as "indicators for loss of resilience." We find that the varying performance is determined by how a system responds to changes in a specific driver, which can be captured by a relation between stability (recovery rate) and resilience (size of the basin of attraction). Furthermore, we demonstrate that the positive correlation between stability and resilience, as the essential assumption of indicators based on critical slowing down, can break down in this system when multiple environmental drivers are changed simultaneously. Our results suggest that the stability-resilience relation needs to be better understood for the application of early warning signals in different scenarios.early warning signals | population collapse | environmental drivers | stability-resilience relation

Ecosystems can undergo sudden shifts to undesirable states, but recent studies with simple single-species ecosystems have demonstrated that advance warning can be provided by the slowing down of population dynamics near a tipping point. However, it is unclear how this “critical slowing down” will manifest in ecosystems with strong interactions between their components. Here we probe the dynamics of an experimental producer-freeloader ecosystem as it approaches a catastrophic collapse. Surprisingly, the producer population grows in size as the environment deteriorates, highlighting that population size can be a misleading measure of ecosystem stability. By analyzing the oscillatory producer-freeloader dynamics for over 100 generations in multiple environmental conditions, we find that the collective ecosystem dynamics slow down as the tipping point is approached. Analysis of the coupled dynamics of interacting populations may therefore be necessary to provide advance warning of collapse in complex communities.