Study area and sampling design

Sampling was conducted at six holm oak (Quercus ilex L.) dehesa farms located in the province of Cáceres, western Spain. Three of them were used for free-range livestock rearing (farms 1, 2 and 3); in the other three, livestock had been absent long-term, for at least ten years before the beginning of the study (farms 4, 5 and 6). At farms 1-3, we randomly chose eight pairs of oaks per farm in February 2016. Within each pair, one tree was randomly chosen for experimental short-term livestock exclusion and the other one was left as control. To sum up, there were eight trees x three farms without livestock for ten years or more, and eight trees x two treatments x three farms with livestock. Therefore, 72 Q. ilex trees were monitored (N (control) = 24; N (one-year exclusion) = 24; and N (ten-year exclusion) = 24) (Figure 1, Tables S1-2).
In March 2016 (early spring), experimental trees of farms 1-3 were fully enclosed by a fence to avoid livestock grazing beneath their canopies. In April 2017 (spring), we sampled all study trees following the same methodology. We vacuumed 2 m2 of the floor (2900 W vacuum machine) beneath the canopy of each tree: a 1 m2 plot at the northern half of the canopy and 1 m2 at the southern half. Each plot was vacuumed for 30 seconds to sample all the arthropods on the soil surface and on the vegetation. We pooled both samples of each tree and stored them in cardboard boxes that were taken to the laboratory and placed in the fridge at 4 ºC until sorting. By doing this, we preserved the specimens and kept them inactive, thus preventing them flying off during sample cleaning and classification. The content of each box was emptied on a tray and carefully inspected. Plant debris and soil were discarded, and all the arthropods taken and placed in a bottle filled with 96% ethanol. After 5 minutes without finding any new specimen, we considered sample revision as completed.
As livestock effects on arthropods can be mediated by changes in vegetation structure, we measured vegetation density and height beneath the tree canopy while sampling arthropods (raw data available in Table S3). At each tree, we annotated vegetation height at 8 random points with a calibrated rod that we placed vertically on the ground. At each point we registered whether vegetation touched the rod at: ground level, 0-10 cm, 11-25 cm, 26-50 cm, and taller than 50 cm; we also measured the maximum vegetation height (see Muñoz et al., 2009 for a similar sampling procedure).