Big ecological changes often involve regime shifts in which a critical threshold is crossed. Thresholds are often difficult to measure, and transgressions of thresholds come as surprises. If a critical threshold is approached gradually, however, there are early warnings of the impending regime shift. For example, in a one-dimensional ecosystem dynamics, autocorrelation approaches 1 from below, variance and skewness increase, and variance spectra shift to lower frequencies. Here we focus on variance, an indicator easily computed from monitoring data.
There are two distinct sources of increased variance near a critical threshold. One is the amplification of small shocks that occurs as the square of the modulus of the leading eigenvalue (or leading pair of eigenvalues in the complex case) approaches 1 from below. This source, called “squealing,” is well-studied. The second source of variance, called “flickering,” involves brief excursions between attractors.
Interacting regime shifts may muffle or magnify variance near critical thresholds. Whether muffling or magnification occurs, and the size of the effect, depend on the product of the feedback between the state variables times the correlation of these variables' responses to environmental shocks. If this product is positive, magnification of the variance will occur. If the product is negative, muffling or magnification can occur depending on the relative magnitudes of these and other effects. Therefore, monitoring programs should measure variates that have opposite responses to the critical transition. If the correlations to environmental shocks have the same sign, the variance of at least one variate will be magnified as the critical transition is approached.
Simulation studies suggest that muffling may sometimes interfere with detection of early warning signals of regime shifts. However, more important effects of muffling and magnification may come from their effect on flickering, when random shocks trigger a state change in a system with low resilience. Muffling decreases the likelihood that a random shock will trigger a regime shift. Magnification has the opposite effect. Magnification is most likely when feedbacks are positive and state variables have positively correlated responses to environmental shocks. These results help delimit the conditions when regime shifts are more likely to cascade through complex systems.