Natural populations can experience catastrophic collapse in response to small changes in environmental conditions, and recovery after such a collapse can be exceedingly difficult. Tipping points marking population collapse and other catastrophic thresholds in ecological systems may correspond to a fold bifurcation in the dynamics of the system. Theory predicts that the approach of bifurcations will result in an increasingly slow recovery from small perturbations, a phenomenon called critical slowing down. Measurement of theoretically predicted early warning signals before an unambiguous fold bifurcation is needed to confirm the feasibility of using critical slowing down to anticipate catastrophic transitions. We used replicate laboratory populations of the budding yeast Saccharomyces cerevisiae to demonstrate the direct observation of critical slowing down before population collapse. Yeast grow cooperatively in the sugar sucrose, displaying the Allee effect and a fold bifurcation in population dynamics. Yeast cultures were maintained in a well-mixed condition and population densities were recorded before daily serial dilution by measuring optical density. Statistical indicators, such as variance, autocorrelation, skewness, etc., were calculated at each environmental condition over an ensemble of replicate populations.
Results/Conclusions
We mapped the bifurcation diagram experimentally and found that fluctuations of population density increased in size and timescale near the fold bifurcation, in agreement with theory. We further assessed the utility of early warning signals by observing them in two different slowly deteriorating environments, one with a rising mortality rate and the other one with a decreasing nutrient supply. In both conditions, the warning signals preceded the population collapse, but the detection time of the signals depended on the specific environment and the rate of deterioration. Our results demonstrate that critical slowing down can provide early warning signals before a fold bifurcation, specifically before the collapse of a population subject to the Allee effect in a deteriorating environment. The results also suggest the potential value of complementing the use of parametric population models with early warning signals to assess population stability.