Probabilistic early warning signals

Ecological communities and other complex systems can undergo abrupt and long-lasting reorganization, a regime shift, when deterministic or stochastic factors bring them to the vicinity of a tipping point between alternative states. Such changes can be large and often arise unexpectedly. However, theoretical and experimental analyses have shown that changes in correlation structure, variance, and other standard indicators of biomass, abundance, or other descriptive variables are often observed prior to a state shift, providing early warnings of an anticipated transition. Natural systems manifest unknown mixtures of ecological and environmental processes, hampered by noise and limited observations. As data quality often cannot be improved, it is important to choose the best modeling tools available for the analysis. We investigate three autoregressive models and analyze their theoretical differences and practical performance. We formulate a novel probabilistic method for early warning signal detection and demonstrate performance improvements compared to nonprobabilistic alternatives based on simulation and publicly available experimental time series. The probabilistic formulation provides a novel approach to early warning signal detection and analysis, with enhanced robustness and treatment of uncertainties. In real experimental time series, the new probabilistic method produces results that are consistent with previously reported findings. Robustness to uncertainties is instrumental in the common scenario where mechanistic understanding of the complex system dynamics is not available. The probabilistic approach provides a new family of robust methods for early warning signal detection that can be naturally extended to incorporate variable modeling assumptions and prior knowledge.