Slowing down in spatially patterned ecosystems at the brink of collapse

Abstract

Predicting the risk of critical transitions, such as the collapse of a population, is important in order to direct management efforts. In any system that is close to a critical transition, recovery upon small perturbations becomes slow, a phenomenon known as critical slowing down. It has been suggested that such slowing down may be detected indirectly through an increase in spatial and temporal correlation and variance. Here, we tested this idea in arid ecosystems, where vegetation may collapse to desert as a result of increasing water limitation. We used three models that describe desertification but differ in the spatial vegetation patterns they produce. In all models, recovery rate upon perturbation decreased before vegetation collapsed. However, in one of the models, slowing down failed to translate into rising variance and correlation. This is caused by the regular self-organized vegetation patterns produced by this model. This finding implies an important limitation of variance and correlation as indicators of critical transitions. However, changes in such self-organized patterns themselves are a reliable indicator of an upcoming transition. Our results illustrate that while critical slowing down may be a universal phenomenon at critical transitions, its detection through indirect indicators may have limitations in particular systems.