Ecosystem Regime Shifts: Early Warning Indicators and Non-Linear Dynamics

Regime shifts are rapid, sometimes irreversible, changes to non-linear feedback mechanisms that occur when ecosystems transition between alternate stable states. Ecosystem regime shifts sometimes have severe consequences for human well being including eutrophication in lakes, desertification, and fisheries collapses. Statistical anomalies such as increased autocorrelation and variance may warn of impending shifts, indicating that adaptive management is necessary. To this effect, I proposed heteroskedasticity as a new, powerful early warning indicator for ecosystem regime shifts. Heteroskedasticity is a type of clustered variance that can occur in time series or in spatial data. I hypothesized that statistically significant heteroskedasticity would be present in ecosystems approaching regime shifts, but would not be present in ecosystems without regime shifts. I further hypothesized that tests for heteroskedasticity in time and space would minimize the occurrence of false positive warnings. I expected the null hypothesis of no significant heteroskedasticity to ease interpretation of early warning indicators and relax the need for pristine reference systems to compare to perturbed systems. I tested these hypotheses using simulated data from stochastic ecosystem models and data collected during a whole-lake regime shift experiment. The simulated data comprised regime shifts with a variety of mechanisms, but in all cases heteroskedasticity was a powerful and easily interpreted early warning indicator. In the whole-ecosystem experiment, heteroskedasticity tests warned of an impending tipping point well in advance of other indicators like autocorrelation and variance. This shows that tests for heteroskedasticity can be effective at spatial and temporal scales relevant to ecosystem management. The heteroskedasticity indicator contributed by my dissertation satisfies practical requirements for an early warning indicator including that it is powerful, minimizes false positives, and does not require a pristine reference system. Overall, my dissertation contributes both a valuable tool for ecosystem management and for developing fundamental understanding of food webs as complex nonlinear systems.