Ecosystems can undergo abrupt transitions from one state to an alternative stable state when the driver crosses a threshold or a critical point. Dynamical systems theory suggests that systems take long to recover from perturbations near such transitions. This leads to characteristic changes in the dynamics of the system, which can be used as early warning signals of imminent transitions. However, these signals are qualitative and cannot quantify the critical points. Here, we propose a method to

more »

... estimate critical points quantitatively from spatial data. We employ a spatial model of vegetation that shows a transition from vegetated to bare state. We show that the critical point can be estimated as the ecosystem state and the driver values at which spatial variance and autocorrelation are maximum. We demonstrate the validity of this method by analysing spatial data from regions of Africa and Australia that exhibit alternative vegetation biomes.