# Information about publication

# Interacting Regime Shifts in Ecosystems: Implication for Early Warnings

## William Brock and Stephen Carpenter. 2009.

### Abstract:

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. 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 squared eigenvalue approaches 1 from below. This source, called squealing, is well-studied. The second source of variance, called flickering, is brief excursions between attractors. Flickering has rarely been analyzed in the literature.Analysis presented here accounts for both sources of variance. Complex systems exhibit many kinds of thresholds. The case of a single threshold may not fully account for the changes in variance that may occur in systems subject to multiple thresholds. Interacting thresholds may muffle or magnify variance near critical thresholds. Whether muffling or magnification occurs, and the size of the effect, depends 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. Simulation studies using a lake food web model 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.

*Keywords: Alternative stable states, critical transition, early warning, lakes, regime shift, trophic cascade, variance*