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).