Forecasting Critical Transitions and Bifurcation Diagrams of Natural Populations

Recent studies demonstrate that several early warning signals based on the analysis of measured time series can successfully provide an alarm when an ecological system approaches a tipping point. However, predicting key aspects of the system's future stability and dynamics still remains a challenge.
We introduce a unique approach to forecast critical transitions as well as key characteristics of the pre- and post-transition dynamics of natural populations based on observations of the system response to (small or large) perturbations only in the pre-transition regime. We evaluate the method experimentally, using as a model ecological system a population of budding yeast with cooperative growth which exhibits a catastrophic transition as the environment deteriorates. Our results highlight that by monitoring the system's response to (small or large) perturbations in the pre-transition regime, it is possible to gain crucial information about the future system’s safety and stability, such as the quantitative distance to upcoming transition, the type of upcoming transition (i.e., catastrophic/non-catastrophic) and future equilibriums of the system. We envision this approach to be used in stability analysis of natural populations, where maximum safety is desired.