Social and ecological systems are inherently complex, with numerous moving parts, interconnections, and nonlinear feedbacks. Such complex systems are often robust to perturbations, but under systematic forcing may exhibit dramatic changes in behavior. Recent studies have shown that such tipping points may be preceded by characteristic statistical fluctuations such as divergence of the sample variance and increasing autocorrelation coefficient. Although there has been much interest in developing “early warning systems” using such statistics, this goal has been hampered by the sensitivity of these time series methods to model tuning as well as common data problems that do not align with theoretical models, such as data discretization, observation error, observation aggregation, and spatial or temporal heterogeneities. We asked whether more complicated models incorporating such observation processes exhibit the same properties as the underlying dynamical system. That is, we asked “Are tipping points detectable?” Here, we report new theory and resulting analytical methods that overcome these obstacles.
Results/Conclusions
The proposed new methods were validated using stochastic simulations of models for host-parasite interactions. We find that the behavior of some quantities previously reported to exhibit general properties during the approach to a tipping point may be idiosyncratic, while other statistics emerge as novel early warning indicators. These results suggest that we are only just beginning to understand the dynamics of “near critical” complex systems. The overarching implication of these findings is that suitably chosen methods for anticipating tipping points in nonlinear systems may perform well, even in the face of severe data deficiencies. These methods are expected to be widely generalizable to complex systems in ecology and environmental science.