Robustness of early warning signals for catastrophic and non-catastrophic transitions

Abstract

Early warning signals (EWS) are statistical indicators that a rapid regime shift may be forthcoming. Their development has given ecologists hope of predicting rapid regime shifts before they occur. Accurate predictions, however, rely on the signals being appropriate to the system in question. Most of the EWS commonly applied in ecology have been studied in the context of one specific type of regime shift (the type brought on by a saddle-node bifurcation, at which one stable equilibrium point collides with an unstable equilibrium and disappears) under one particular perturbation scheme (temporally uncorrelated noise that perturbs the net population growth rate in a density independent way). Whether and when these EWS can be applied to other ecological situations remains relatively unknown, and certainly underappreciated. We study a range of models with different types of dynamical transitions (including rapid regime shifts) and several perturbation schemes (density-dependent uncorrelated or temporally-correlated noise) and test the ability of EWS to warn of an approaching transition. We also test the sensitivity of our results to the amount of available pre-transition data and various decisions that must be made in the analysis (i.e. the rolling window size and smoothing bandwidth used to compute the EWS). We find that EWS generally work well to signal an impending saddle-node bifurcation, regardless of the autocorrelation or intensity of the noise. However, EWS do not reliably appear as expected for other types of transition. EWS were often very sensitive to the length of the pre-transition time series analyzed, and usually less sensitive to other decisions. We conclude that the EWS perform well for saddle-node bifurcation in a range of noise environments, but different methods should be used to predict other types of regime shifts. As a consequence, knowledge of the mechanism behind a possible regime shift is needed before EWS can be used to predict it.