Slower recovery in space before collapse of connected populations

Background/Question/Methods

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. 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. 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 needs to be examined empirically. We used spatially extended yeast populations to evaluate early warning signals based on spatio-temporal fluctuations and to identify a novel warning indicator in space. Yeast cells grow cooperatively in sucrose by sharing the hydrolysis products, creating positive feedback between cells that leads to bistability and a tipping point. By increasing the daily dilution factor (equivalent to a mortality rate), we could manipulate yeast populations to collapse at conditions beyond the tipping point. We connected yeast populations spatially through controlled dispersal between nearest neighbors on a one dimensional array. Population densities were recorded daily by measuring optical density.

Results/Conclusions

We found that two leading indicators based on spatio-temporal 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 time, 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. Our work illustrates the important role of spatial coupling, such as the dispersal of populations, in understanding how to apply the current toolbox of warning indicators to natural populations.