Ecological systems can undergo abrupt transitions from one state to an alternative stable state even when the drivers change gradually. Recent studies have developed early warning signals (EWS) of imminent transitions in ecosystem states. EWS are qualitative, i.e. they inform if a system is approaching a transition. However, they cannot provide quantitative estimate of the critical points, i.e. the threshold values of the ecosystem state or of the driver at which a transition will occur. Here, we employed a spatially-explicit stochastic model of vegetation that shows a transition from vegetated to bare state at a critical point and propose a simple method to estimate critical points from spatial data of ecosystems. We then test the applicability of this method to real ecosystems by analysing remotely sensed spatial data from regions of Africa and Australia that exhibit alternative vegetation biomes. Specifically, we used Enhanced Vegetation Index (EVI) as a proxy for vegetation cover and mean annual rainfall as the driver, and estimate critical points at relatively small spatial scales.
Our analyses of the model shows that critical points can be estimated by the values of ecosystem state and the drivers at which the system exhibits maximum spatial variance and spatial autocorrelation. We tested this method to real world data from Africa and Australia. We estimated the critical point of transition and the critical values of the driver (mean annual rainfall) and enhanced vegetation index (EVI) as a proxy of vegetation cover. Our predictions of the critical points match those predicted by other methods using larger datasets. Our study shows that analysis of spatial data can be used to quantify critical points and identify critical regions of ecosystems that are prone to abrupt transitions. The method described here, therefore, can offer a way to estimate critical points at local scales.