Inferring critical thresholds of ecosystem transitions from spatial data.

Ecosystems can undergo abrupt transitions between alternative stable states when the driver crosses a critical threshold. Dynamical systems theory shows that when ecosystems approach the point of loss of stability associated with these transitions, they take a long time to recover from perturbations, a phenomenon known as critical slowing down. This generic feature of dynamical systems can offer early warning signals of abrupt transitions. However, these signals are qualitative and cannot quantify the thresholds of drivers at which transition may occur. Here, we propose a method to estimate critical thresholds from spatial data. We show that two spatial metrics, spatial variance and autocorrelation of ecosystem state variable, computed along driver gradients can be used to estimate critical thresholds. First, we investigate cellular-automaton models of ecosystem dynamics that show a transition from a high-density state to a bare state. Our models show that critical thresholds can be estimated as the ecosystem state and the driver values at which spatial variance and spatial autocorrelation of the ecosystem state are maximum. Next, to demonstrate the application of the method, we choose remotely sensed vegetation data (Enhanced Vegetation Index, EVI) from regions in central Africa and northeast Australia that exhibit alternative states in woody cover. We draw transects (8 × 90 km) that span alternative stable states along rainfall gradients. Our analyses of spatial variance and autocorrelation of EVI along transects yield estimates of critical thresholds. These estimates match reasonably well with those obtained by an independent method that uses large-scale (250 × 200 km) spatial data sets. Given the generality of the principles that underlie our method, our method can be applied to a variety of ecosystems that exhibit alternative stable states.