Data from: Generic indicators for loss of resilience before a tipping point leading to population collapse

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.理论研究表明，自然系统（如生态系统、气候系统）临近灾变阈值时，其对微小扰动的恢复速率会逐渐放缓，该现象被称为临界慢化（critical slowing down）。本研究采用重复培养的出芽酵母（Saccharomyces cerevisiae）实验室种群，直接观测了种群崩溃前的临界慢化现象。我们通过实验绘制了分岔图（bifurcation diagram），并发现种群越接近临界点（tipping point），对外部扰动的脆弱性越高。在接近临界点时，种群密度的波动幅度与持续时长均出现增加，这与理论预测相符。本研究结果表明，临界慢化指标可为各类动力学系统的灾变阈值与恢复力丧失提供提前预警。