Test of early warning signals at ecological thresholds
To identify early warning signals of critical transitions, we evaluated the variability of the diversity and function measures along the land use gradients. An increase in variability has been considered an early warning signal for regime shifts between alternative states (Schefferet al. 2009). To test for this, we used a moving window approach along the land use gradients. All plots were sorted from lowest to highest LUI, or its components, and then, the variance of each diversity and function measure was calculated across each subset of 15 plots along the gradient (i.e. if plots are ranked from 1 to 150, the first subset included plots 1-15, next subset plots 2-16, until the last subset included plots 136-150). Each subset accounts for 10% of the plots and covers a range of 0.2 ± 0.01 LUI, 26 ± 1.3 livestock unit · grazing days · ha-1 · y-1, 0.25 ± 0.01 cuts · y-1 and 6.4 ± 0.6 kg N · ha-1 · y-1. To test if the variance in a given subset was significantly different from expectation, the expected variance for any subset was estimated by assembling 2000 subsets of 15 random plots and estimating the variance for each random subset. We then calculated the 95% confidence interval across these random subsets as the values at percentiles 2.5 and 97.5. Although early warning signals were originally developed for temporal data, spatial gradients are frequently used as proxies, when appropriate temporal series are not available (Blois et al. 2013; Kéfi et al.2014; Eby et al. 2017). Nevertheless, to prevent potential confounding factors causing high variability related to local environmental conditions (Huston 1999), we tested for increasing variability through time for those variables with temporal data available. Specifically, we calculated for each plot, the variance through time of the functions or diversities. We then related the temporal variance in diversity or functioning to the average LUI of the plot. Results using temporal variation were similar to those using spatial variation (higher variance at LUI values close to the threshold, Figure S5).