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. I hypothesized that tests for heteroskedasticity in time and space would be sensitive early warning indicators that also minimized the occurrence of false positive warnings. I further hypothesized that statistically significant heteroskedasticity would be present in ecosystems approaching regime shifts, but would not be present in ecosystems without regime shifts. The null hypothesis of no significant heteroskedasticity eases interpretation of early warning indicators and relaxes the need for pristine reference systems with which to compare to perturbed systems. I tested these hypotheses using data from a whole-lake regime shift experiment and simulated data from stochastic ecosystem models. In all cases, tests for heteroskedasticity were powerful and easily interpreted early warning indicators. My dissertation demonstrates early warning indicators can be effective at spatial and temporal scales relevant to ecosystem management. The conditional 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 fundamental understanding of food webs as complex nonlinear systems.