Extended Data Fig. 5: Influence of the sliding window analysis on the thresholds driven by land use intensification (LUI).

We show the two LUI-thresholds and associated changes in the parameters, that is (a) the Root Mean Square Error (RMSE), (b) the coefficient of determination (r²), (c) the Y-intercept [α] and the slope [β] of the Skewness-Kurtosis relationship (SKR) along the LUI gradient. We used a sliding window analysis to evaluate changes in parameters along the LUI gradient (see Method). For each parameter, we tested the influence of the size of the window considered. Briefly, we ordered all grassland communities across all years according to their LUI value. We selected the first 300 grassland communities with the lowest LUI. We fitted Median-Based Linear Models (light grey) and computed the RMSE, the r², the Y-intercept estimator α and the slope estimator β of the relationship. We removed the community with the lowest value of LUI among the 300 observations, and added a community scoring the next higher value to repeat the same calculations. We repeated this loop as many times as communities remained to explore how SKR patterns changed with increasing LUI. We finally repeated this procedure using a set of 300-600 grassland communities (from light to dark grey) and found that the identified LUI-thresholds were robust to the size of the window used.