Anticipating or merely characterizing change: How well do early warning signals work in more complex and chaotic regimes?

Early warning signals (EWS) are used widely across fields such as ecology and virology to anticipate transitions like lake biodiversity changes and virus dissemination, and have recently shown promise as signals for mental health transitions. The statistical signals indicating an upcoming transition are often mathematically derived from dynamical system models, such as increases in variance as a marker of critical slowing down. As of yet, EWS have largely been applied to simple transitions such as the saddle-node bifurcation, yet it is widely conjectured that more complex transitions occur within systems as non-linear and high-dimensional as those found within psychopathology. To narrow this gap, we compare the performance of generic EWS in characterizing and anticipating more complex, higher-dimensional transitions between different dynamical regimes. In a numerical study of a four-dimensional Generalised Lotka-Volterra model under varying observational noise intensities, we focus on a noisy, periodic, and chaotic regime, which are traversed by two types of transitions: the birth of a limit cycle in a Hopf bifurcation and the creation of a chaotic attractor via a period-doubling cascade. Our simulation study approximates Ecological Momentary Assessment data collection, where data may be analysed in real-time without access to the full timeseries to detect a transition. In addition, to address the challenges arising in the move from theory to real-world psychological data, such as high dimensionality, non-linearity, noise, and non-stationarity, we include a relatively unexplored method in the EWS literature, namely Recurrence Quantification Analysis (RQA). RQA is a popular model-free nonlinear timeseries method which identifies recurrent patterns in line structures of the timeseries’ distance matrix. Our study emphasizes the limitations of EWS with respect to more complex transitions: Do these measures anticipate upcoming changes or merely characterize the regime change that has already occurred?