Implications of being discrete and spatial for detecting early warning signals of regime shifts

Theory suggests that ecological systems exhibit a pronounced slow down in their dynamics, known as 'critical slowing down' (CSD), before they undergo regime shifts or critical transitions. As a result of CSD, ecosystems exhibit characteristic temporal and spatial changes which can be used as early warning signals of imminent regime shifts. For temporal data, statistical methods to detect these generic indicators of ecosystem resilience are well developed. However, for spatial data, despite a well developed theoretical framework, statistical methods such as data pre-processing and null models to detect EWS are relatively poorly developed. In this manuscript, we investigate the case of a common type of ecological spatial dataset which consists of binary values at each location (e.g. occupied/unoccupied, tree/grass or coralline/bleached). We employ a cellular-automaton based spatially-explicit model which generates data that mimics remotely sensed or field collected high-resolution spatial data with a binary classification of the state variables at each location. We demonstrate that trends in two spatial metrics, spatial variance and spatial skewness, of such binary spatial data lead to false, failed or misleading signals of transitions. We find that, two other indicators, spatial autocorrelation at lag-1 and spectral density ratio, accurately reflect CSD even with binary spatial data. To overcome the problems associated with detection of EWS using spatial variance and skewness, we investigate a data pre-processing method called 'coarse-graining' which is inspired from the physics literature on phase transitions. Coarse-graining reduces the spatial resolution of data by averaging state variables over small scales. Yet, it enables detection of CSD-based spatial indicators of impending critical transitions. In summary, our study provides a theoretical basis, and rigorous evaluation, of coarse-graining as a pre-processing step to analyse spatial datasets with discrete state classifications.