Predictability of critical transitions

TLDR

Critical transitions in multistable systems, such as species extinctions and climate shifts, are theorized to be preceded by critical slowing down, yet noise can obscure the statistical relevance of early‑warning indicators. This study examines the predictability of critical transitions in conceptual models. Using quadratic integrate‑and‑fire and van der Pol models with external noise, the authors statistically assess prediction success, overall predictability, and the effect of transition magnitude. Indicator performance varies with the specific model and conditions, and predictive accuracy depends on transition magnitude.

Abstract

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition. However, especially in the presence of noise, it is not clear whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions. In this contribution we investigate the predictability of critical transitions in conceptual models. We study the quadratic integrate-and-fire model and the van der Pol model under the influence of external noise. We focus especially on the statistical analysis of the success of predictions and the overall predictability of the system. The performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it. Furthermore, we study the influence of the magnitude of transitions on the predictive performance.