Supplementary Materials for Grazing and ecosystem service delivery in global drylands

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Supplementary Materials for
Grazing and ecosystem service delivery in global drylands
Fernando T. Maestre et al.
Corresponding author: Fernando T. Maestre, ft.maestre@ua.es
Science 378, 915 (2022)
DOI: 10.1126/science.abq4062
The PDF file includes:
Materials and Methods
Figs. S1 to S19
Tables S1 to S28
References
Other Supplementary Material for this manuscript includes the following:
MDAR Reproducibility Checklist
Movie S1

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Materials and Methods
Characteristics of the study sites
We carried out our study in rangelands, defined as “lands carrying natural or semi-natural
vegetation that provide habitat suitable for herds of wild or domestic ungulates” (33), located in
drylands (areas with an aridity index [precipitation/potential evapotranspiration [P/PET] below
0.65, 34) between January 2016 and September 2019. The area of dryland rangelands shown in
Fig. 1 and fig. S1 was obtained from refs. 35 and 36. Field data and plant and soil samples were
gathered at 98 sites located in 25 countries from six continents (Algeria, Argentina, Australia,
Botswana, Brazil, Canada, Chile, China, Ecuador, Hungary, Iran, Israel, Kazakhstan, Kenya,
Mexico, Mongolia, Namibia, Niger, Palestine, Peru, Portugal, South Africa, Spain, Tunisia, and
the United States of America; fig. 1, Movie S1), including remote and traditionally poorly
studied dryland regions. These include the Southeast of Tunisia, the Sechura Desert in Peru, the
Golestan province in Iran, and the West Bank, to name a few. Site selection aimed to capture a
wide range of grazing pressure levels and of the variety of the abiotic (climate, soil type, surface
inclination) and biotic (type of vegetation, total plant cover, species richness) features
characterizing dryland rangelands worldwide, and to be as geographically representative as
possible while keeping the survey logistically feasible.
Standardized climatic data from all the sites were obtained from WorldClim 2.0
(www.worldclim.org), a high resolution (30 arc seconds or ~ 1 km at equator) database based on
many climate observations and topographical data for the 1970-2000 period (37). Aridity index
data were obtained from the Global Aridity Index and Potential Evapotranspiration Climate
Database v2 (38), which uses interpolations based on WorldClim. The range of the aridity index,
mean annual precipitation, and mean annual temperature values covered by the study sites was
0.01 to 0.54, 26 mm/yr to 891 mm/yr, and -1.2 ºC to 29.2 ºC, respectively. All sites experienced
high seasonal variability in rainfall (74.69% ± 34.61%, mean ± SD). The studied sites included
16 of the World Reference Base soil groups (39) and all major soil groups present in drylands
worldwide (40). Surface inclination values ranged between 0º and 31.6º. All sites with a slope
value > 2º were located on SE-SW and NE-NW faces in the Northern and the Southern
Hemispheres, respectively, to minimize the potential effects of different microclimates promoted
by slope aspect, which can be very important in drylands (41–43). Elevation varied between 12
m and 2214 m a.s.l. The sites surveyed encompass a wide variety of representative vegetation
physiognomies, including grasslands, shrublands, savannas, and open woodlands with shrubs
(fig. S2). Perennial plant canopy cover ranged between 0% and 99%. Detailed information about
the location and main environmental characteristics of the study sites can be found in the
database that accompanies this article (doi: 10.6084/m9.figshare.14923065).
Selection of local grazing gradients and characterization of grazing pressure
At each of the 98 study sites, multiple 45 m × 45 m plots were sampled once across a local
grazing gradient (including the effects of vegetation removal and trampling) with different levels
of grazing pressure (low, medium, and high grazing pressure plus another plot in an ungrazed
area whenever possible) by livestock and native herbivores. This gradient approach, which is
frequently used in large-scale studies assessing grazing impacts (44–46), is the most appropriate

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way to capture: i) potential effects of grazing, and the interactions between climate, biodiversity,
and soils, on the provision of ecosystem services and ii) the large amount of environmental
variability/heterogeneity across sites and to minimize this variability within sites.
To determine a grazing gradient within each site, we located plots at different distances from
artificial watering points, which are ponds, impoundments, or drinking troughs that provide
permanent sources of water for livestock and wild herbivores in drylands (45, 47). The distance
to watering points is a valuable proxy of grazing pressure (i.e., sites closer to water are more
heavily grazed; 45, 47–49), and has been widely employed (and validated multiple times) when
assessing the ecological impacts of grazing pressure in drylands worldwide (45, 47–52). To
ensure a correct characterization of the grazing gradient, we also conducted an expert-level
heuristic assessment of plot-level grazing pressure using the best available knowledge, historical
records, and prior information whenever available. While this heuristic assessment of grazing
pressure combined with distance to waterpoints and expert knowledge is somewhat subjective,
each survey team was familiar with current grazing intensities at their plots and sites. In eight of
the 98 surveyed sites, local grazing gradients were established using paddocks grazed at different
intensities, rather than distance to watering points. Nevertheless, all plots were established in
areas representative of the vegetation and soil types found in the site, so the impacts of grazing
pressure could be assessed at each site without confounding factors associated with differences
in climate, soil type or vegetation. This is because plots within each site have identical or similar
climate and parent material, so differences among them are largely due to the different grazing
pressure levels they experience. Selected watering points were separated from other watering
points and/or elements that could alter the movement of mammalian herbivores, such as fences,
by at least 1 km to avoid confounding effects that could influence the impact of distance to water
on the measured ecosystem structural and functional attributes.
Of the 98 sites surveyed, a total of 52 sites had three plots corresponding to three grazing
intensities (low, medium, and high grazing pressure). In addition to these 52 sites, 35 sites had an
additional ungrazed area surveyed (ungrazed, low, medium, and high grazing pressure). In eight
sites, an ungrazed control plus two additional grazing levels (medium and high or low and high
grazing pressure) were surveyed. Finally, in three sites, only two plots could be located because
they lacked low or medium grazing pressure plots. In total, 326 plots of 45 m × 45 m (including
43 ungrazed, 88 low grazing pressure, 97 medium grazing pressure, and 98 high grazing pressure
plots) were surveyed in situ as described in the following sections.
Our study needed to be standardized (so results can be comparable), and thus it was not possible
to capture the wide variation in the size of fields used for managing extensive livestock grazing
across dryland rangelands (53–55). This issue (i.e., a fixed plot size), which is shared by any
global standardized experiment and survey conducted so far (e.g., BIOCOM (18), NutNet (56),
DroughtNet (57), Darkdiv (58)), does not preclude the acquisition of representative results in our
study for four main reasons. First, the spatial resolution [plot area] and actual extent [summed
area of all plots] (sensu ref. 59) at which our field data were gathered (spatial resolution of 2025
m2 and actual extent of 660,150 m2 respectively) is substantially larger than that used in most
ecological and grazing studies conducted so far (59, 60). Furthermore, the potentially represented
area of the surveyed plots at each site (i.e., that covered by these plots and the distance between
them) is much larger (range 1.1 - 6096.7 ha, mean size = 25.8 ha) and resembles that of (small to
medium sized) paddocks typically found across rangeland drylands worldwide (53, 55, 61).

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Second, our plots were in areas representative of their landscapes. In dryland ecosystems such as
those we surveyed, the spatial resolution and size of the plots we used captures information on
key ecosystem properties (e.g., perennial vegetation cover) that are both representative of those
found at larger spatial extents (62) and can be scaled up to larger regions (63). Third, the location
of plots of different grazing pressures within each site captures the spatial heterogeneity in
grazing that is typically found in larger paddocks (64). Finally, paddock size per se may not be a
good proxy for grazing pressure at the scale of our study. For instance, a high density of
herbivores in a small paddock in a subhumid environment could represent a moderate grazing
pressure for that area whereas fewer herbivores in a much larger paddock in an arid landscape
could equate to high grazing pressure for that area. For these reasons, paddock size is not an
attribute that we considered in our study. Certainly, paddock size would be an important
consideration if we were looking at the same number of animals in paddocks of different sizes.
We fully acknowledge that some grazing effects (e.g., on soil properties such as carbon) might
take years to be noticeable (65). We consider that our approach is appropriate since we measured
the response variables in paddocks subjected to grazing for many years. This is one of the
advantages of our observational study vs. experiments that are usually done over short periods of
time. Furthermore, the time needed for some grazing impacts to be noticeable in soil variables is
not a problem to interpret our results because we are comparing the impacts of grazing pressure
on ecosystem services across space, not across time, and because we are controlling for site-
specific effects in our analyses (see “Statistical analyses” section below). This issue would have
been a problem if we had compared, for instance, the impacts of grazing on soil properties in a
single site using a short temporal data series.
Overall, our study focused on the resultant grazing pressure, which is a composite of different
types of herbivores, the location of particular plots within a paddock (close to water, far from
water), the length of time that grazing has occurred, and the type of herbivores, among other
considerations. The resultant signature, assessed as grazing pressure (recent and historic), was
linked to the different ecosystem services measured. In this way the type of grazing (e.g., set
stocking, time-controlled grazing, low risk stocking, transhumance, etc.) is not particularly an
issue because we are using dung and livestock tracks to ensure that our local grazing gradients
are properly characterized (see “Validation of grazing pressure gradients” section below).
Finally, and as shown in fig. S9, our experimental approach successfully captured the full range
of grazing pressure that is typically observed across dryland rangelands worldwide. Our results
are relevant, therefore, to situations where grazing pressure is greater, whether this occurs close
to watering points, or under nomadic systems, or where different densities of animals are
constrained within paddocks. We believe that grazing pressure, rather than the assessment
methodology or how such pressure is created, is the most important aspect when interpreting the
results of our study.
Validation of grazing pressure gradients
Our grazing pressure was not selected a priori, though we would expect that our plots would
represent a gradient in grazing pressure within each site. To confirm that this was the case, we
conducted multiple validation tests of the heuristic value of grazing pressure obtained at each
plot by: i) identifying, counting and weighing the dung or pellets of all herbivores within
quadrats, a standard approach to assess the abundance of livestock and wild herbivores (66–68),

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ii) using livestock density data whenever available, iii) conducting a cluster analysis with
dung/pellet data, and iv) measuring the width and depth of all livestock tracks crossing the plot
to derive a total cross-sectional area of livestock tracks for each site, a surrogate of historic
grazing pressure (69). Results from all validation tests conducted, presented in detail in the
following paragraphs, indicated that dung mass accurately predicted the four-level categorical
assessment of grazing pressure (ungrazed, low, medium, and high grazing pressure; figs. S4-S8).
Increases in grazing pressure (from ungrazed to high grazing pressure) were associated with
livestock density (fig. S6), dung mass (fig. S7) and area/density of livestock tracks (fig. S8).
We first conducted in situ assessments of recent grazing pressure by all herbivores in all plots by
counting and identifying their dung and pellets. The assessment of dung production has been
used widely to evaluate recent grazing pressure and abundance of large mammalian herbivores
(68), such as cattle (67), sheep (66), deer (70, 71) and kangaroos (72). Because our aim was to
investigate the impact of grazing pressure on biodiversity and ecosystem services, we limited our
assessment of herbivory to mammalian, mostly large-bodied herbivores (> 20 kg e.g., Roe deer
Capreolus capreolus). We also included grazing by the European rabbit (Oryctolagus cuniculus)
and hares (Lepus spp.) because these herbivores are typically associated with environments
grazed by livestock. Further, these grazers have been shown to contribute to substantial biomass
reduction in rangelands (73, 74). We acknowledge, however, that smaller-bodied mammalian
herbivores and omnivores, such as the Southern Mountain cavi (Microcavia australis) and birds
such as the Greater rhea (Rhea americana) and Common ostrich (Struthio camelus), also co-
occur with livestock and larger mammalian herbivores. However, we did not record the dung of
these animals in field surveys because their relative grazing effects would be extremely small
compared with livestock and other native herbivores, and because they are not associated with
increases in grazing pressure.
To measure dung and pellets in the field, we placed a 25 m2 (5 m × 5 m) quadrat, within which
was nested a smaller 1 m2 (1 m by 1 m) quadrat, at distances of 10 m and 30 m along each 45 m
transect. Within the larger quadrat we counted the dung of large-bodied herbivores (e.g., giraffe,
cattle, and horses), and in the smaller quadrat the dung or pellets of smaller-bodied herbivores
(e.g., goats, sheep, lagomorphs), and classified it according to the species producing it.
Experienced field operators were familiar with the dung of different herbivores and were,
therefore, able to identify and separate dung in the field. This was particularly important in
locations supporting high herbivore richness such as those from South Africa, where herbivore
richness was the greatest (n = 6). Field guides are available to allow operators to identify dung in
different regions (e.g., antelope spp. in Africa (75) or different herbivores in Australia (76)).
However, it was not possible to successfully separate the dung of sheep and goats, except where
they occurred separately, largely because of the high degree of overlap in dung morphology (77).
To calculate dung/pellet (dung hereafter) mass, we used one of two approaches: i) direct
measurements, or ii) estimates based on dung counts. Some survey teams made direct
measurements of dung by collecting, oven drying and weighing all dung found in the quadrats
and expressed it as a mass per m2 for each plot and herbivore type. Direct measurements of dung
mass are typically used either where dung mass is low, or where the main herbivores do not
produce clearly defined pellets, such as horses (Equus caballus), cattle (Bos spp.), donkeys
(Equus africanus asinus), giraffe (Giraffa camelopardalis), elephants (Loxodonta africana),
buffalo (Syncerus caffer), camels (Camelus sp.), hartebeest (Alcelaphus buselaphus), wildebeest

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(Connochaetes sp.), and zebra (Equus quagga). Alternatively, field surveyors counted dung of
each herbivore in all quadrats but collected it from only a subsample of the quadrats surveyed,
generally four large (25 m2) or small (1 m2) quadrats (depending on herbivore type), to derive
relationships between dung counts and mass for separate herbivore types. This estimation
technique is highly effective for those herbivores that produce pellets, such as goats (Capra
hirca), sheep (Ovis aries), deer (Capreolus capreolus, Cervus elaphus), various antelope species
including Gemsbok (Oryx gazella), Springbok (Antidorcas marsupialis) and Greater kudu
(Tragelaphus strepsiceros), various kangaroos (Osphranter rufus, Macropus spp.), European
rabbit, and the European hare (Lepus sp., table S2). Typical relationships between dung counts
and mass varied among herbivore types and sites, but coefficients of determination were
always > 0.40 (fig. S4). Although in most plots we directly measured the weight of dung, some
sites relied on the calibration between dung count and mass. These ranged from very strong
relationships (e.g., horses in Chile: R2=0.89, P < 0.001, n = 27; cattle in Argentina: R2=0.94, P <
0.001, n = 12) to relatively weak, often due to low sample size (cattle in Hungary: R2=0.43, P =
0.003, n = 17; cattle in New Mexico USA: R2=0.64, P = 0.054, n = 5). Thus, using either direct
assessment of dung mass or estimated measures, we were able to calculate the total oven-dried
mass of dung per hectare for each herbivore as one measure of recent grazing pressure.
As an initial test of the validity of herbivore dung as a measure of recent grazing pressure, we
examined four sites in our study (two from Argentina, one each from Australia and Iran) that
were all grazed by sheep and from which we had data on the mass of dung collected in the field
and empirical data on long-term stocking rates obtained from experimental studies or from
pastoralists or herders. We plotted the total dry mass of dung against livestock density, which
was adjusted to a common scale of dry sheep equivalents (DSE·ha-1); the value of one non-
lactating ewe without a lamb (78). Results for these four sites demonstrate a positive linear
relationship between livestock density (DSE·ha-1) and dung mass (kg·ha-1; fig. S5). Moreover,
experimental studies of sheep grazing in arid South Australia show a strong relationship between
the time that livestock spend grazing and the amount of dung produced (79). Other studies from
Zimbabwe (80), Kenya (81), South Africa (82) and southern Mongolia (83) have linked dung
counts to herbivore grazing pressure. We are confident, therefore, that greater time spent grazing
equates with more livestock dung and thus a greater amount of recent grazing.
We then examined whether the reported grazing pressure (DSE·ha-1) was related to our heuristic
measure of grazing pressure (ungrazed, low, medium, high) using data from the Australian,
Iranian and the combined Argentinian sites described previously (fig. S6). Our results clearly
show a significant increase in grazing pressure along a grazing gradient from ungrazed to high
grazing pressure in Argentina (One-way ANOVA: F3,7 = 4.8, P = 0.04), Australia (F3,10 = 4.51, P
= 0.045) and Iran (F3,7 = 22.3, P = 0.001).
As a final test of the links between our dung measurements and current grazing pressure, we
examined the relationship between the total mass of dung from each study (kg·ha-1) and our
heuristic measure of grazing pressure (ungrazed and low, medium, and high grazing pressure)
using two analyses. First, we tested the relationship between these grazing pressure levels and
dung measurements using a general linear model that considered study sites as a random effect.
Increases in grazing pressure were associated with increasing levels of dung production (F =
37.0, df = 3, P < 0.001, on log10(x+1) data; fig. S7a). Tukey’s post-hoc LSD test indicated a
significant difference among all grazing pressure levels except medium and high, which did not

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differ significantly. When dung data were separated into livestock and wild herbivores (fig. S1),
this pattern was reproduced for livestock species but not for wild herbivores, as their dung mass
did not increase among the different grazing levels evaluated. These results further suggest that
increases in grazing pressure along our local grazing gradient were largely driven by livestock,
and not by wild herbivores. Second, we performed a cluster analysis validation. In this analysis,
we first standardized the dung density values by dividing them by the maximum dung density
found within each site. Standardization yielded a value ranging from 1 (maximum density within
a site) to 0 (minimum possible dung density). We then performed a cluster analysis, using the
Elbow method (84), to identify the optimum number of clusters that can be obtained using dung
data only. This analysis identified four clusters as being optimum, which is consistent with our
assignment of four categorical classes under the expert-derived heuristic method (fig. S7b). To
test the veracity and accuracy of this clustering approach, we assigned clusters to the plots based
on the mass of dung (labeled U, L, M and H in fig. S7c) and compared the match with the
classification made by individual experts (ungrazed and low, medium, and high grazing
pressure). Total accuracy of expert assignment was 39.2%, with a significant association
between dung-based and expert-based grazing levels (χ2 = 95.05, df= 9, P < 0.001). Low
accuracy was driven mainly by a similarity among low and ungrazed plots, which are not well
distinguished in terms of dung clusters. When this process was repeated without ungrazed plots,
the match between expert-based assignment and dung-based assignment increased to 53.2% (fig.
S7d; χ2 = 46.01, df = 4, P < 0.001). For this reduced analysis, the greatest mismatch between
expert-based and dung-based approaches occurred under medium grazing pressure plots, which
sometimes had dung levels close to high grazing pressure and others close to low grazing
pressure plots (fig. S7d).
The dung data gathered across all our plots showed a very wide range of variation (fig. S9),
suggesting that our survey effectively captured a large range in grazing pressure levels. The
comparison of these dung data with those obtained from the literature (including studies
assessing a wide range of grazing pressure, from ungrazed to very high grazing, in drylands from
Australia, China and Kenya) shows how the range of variation reported in these studies is very
similar to that observed in our survey (fig. S9).
We also used the size and density of livestock tracks as a measure of historic grazing by
livestock. These tracks are semi-permanent landscape features that are formed when livestock
traverse the same path to and from water (85). These compacted tracks are clearly visible over
many decades, and tracks become wider and deeper as the pressure of livestock grazing
increases. The density and size of livestock tracks are therefore useful indicators of the history of
livestock grazing (48, 68). These tracks, however, fail to form or persist on sandy soils, which
lack the compaction created by trampling (86), so historic grazing could not be assessed at all
sites.
To assess the level of historic grazing pressure, we measured the width and depth of all livestock
tracks crossing each of the 45 m transects to derive a total cross-sectional area of tracks for each
site. These values were then scaled to a total area per 100 m of transect. We also calculated the
total number of tracks per 100 m of transect (fig. S8). Using a general linear model that
considered study site as a random effect, we found a strong and significant difference in the area
of livestock tracks among the four levels of grazing pressure (ungrazed and low, medium, and
high grazing pressure; F3,163 = 14.95, P < 0.001 on log10(x+1)-transformed data; fig. S8). For

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track density, we found a significant difference in density between ungrazed and the three levels
of grazing pressure (F3,166 = 9.28, P < 0.001; log10(x+1)-transformed data).
Overall, the comprehensive analyses conducted showed very similar trends, irrespective of
whether we used dung mass as a measure of recent grazing pressure, track area/density as a
measure of long-term grazing pressure or the expert heuristic site classification. This gives us a
high degree of confidence that the grazing gradients we observed are true gradients in grazing
pressure, and thus were well-suited to achieve the objectives of our study. Furthermore, the range
of variation in dung mass observed across the surveyed sites was very similar to that observed in
previous studies carried out in multiple dryland regions (fig. S9), suggesting that our survey
successfully captured the full range of grazing pressure levels that is typically observed in grazed
drylands across the globe.
Vegetation and soil sampling
Vegetation and soil surveys were conducted following a standardized sampling protocol,
described in full in ref. 87. The coordinates and elevation of each 45 m × 45 m plot were
recorded in situ with a portable Global Positioning System and were standardized to the WGS84
ellipsoid for visualization and analyses. We located four 45 m transects oriented downslope
within each plot, spaced 10 m apart across the slope, for the vegetation surveys. To minimize
potential impacts of seasonal variability within and across sites, vegetation and soil surveys took
place just after the main vegetation growth period and in the peak of the dry season, respectively.
This ensured that the data obtained across sites were as standardized and comparable as possible.
When required by local authorities, permissions were obtained for conducting field work. Our
study did not involve handling or collection of endangered species.
Perennial plant presence and cover were measured in each transect using the line-point intercept
method (88). Specifically, we surveyed points located every 20 cm for a total of 225 points per
transect (900 points per plot). Also, we placed 25 contiguous quadrats (1.5 m × 1.5 m) in each
transect (100 quadrats per plot) and visually estimated the cover of each perennial vascular plant
present as the percentage of the quadrat covered (0-100). The cover for each species was
calculated as the sum of the species cover for all quadrats. In addition, all identified species per
plot were classified into three functional categories associated with their life strategy/biological
type: forbs, grasses, and woody species. The cover of each category was calculated as the
proportion of total vegetation cover (sum of the cover for all species) that was associated with
that category (e.g., covergrass = sum [cover of all grass species]/sum [cover all species]). We
restricted our study to perennial plants because they are instrumental in maintaining the
functioning of drylands (18, 89). Moreover, annual plant composition in drylands shows high
intra- and inter-annual variability (89, 90). Thus, we did not survey annual species to avoid
confounding effects in the differences in plant species richness among study sites caused
primarily by the timing of sampling.
We measured maximum plant height, specific leaf area, and leaf dry mass content (LDMC) on
21,106 individuals from 1,918 species, and foliar nitrogen content on 2,570 individuals from
1,034 species following standard protocols (91). Maximum plant height (in m) measures the
height of a plant from the ground up to the highest leaves belonging to the vegetative part of the
plant. Specific leaf area (cm²·g-1) was calculated as the ratio between leaf area (cm2) and dry leaf

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mass (g), while LDMC (unitless) was estimated as the ratio between oven-dry and water-
saturated fresh mass of leaves. The selected traits were measured on the tallest individual of each
perennial plant species present in 20 quadrats randomly selected among the 100 quadrats
surveyed at each plot (5 quadrats per transect). For each selected plant individual, we sampled
the youngest mature and undamaged leaves at the top of the plant (sampled leaf surface was
always > 2 cm²). Leaves were then stored in moistened plastic bags and brought to the laboratory
for rehydration. Leaf area was quantified on each individual by taking photographs of the
collected leaves and analyzing them using the freeware ImageJ (92)
(https://imagej.nih.gov/ij/index.html; see ref. 87 for additional details on the procedure
followed). Leaf fresh and dry mass were obtained by weighing before and after oven drying at 60
ºC for 48 h. To obtain foliar nitrogen content, leaves were grouped by species within each plot
for chemical analysis. Then, oven-dried leaves were ground in a homogenizer (Precellys® 24;
Bertin Technologies, Montigny-le-Bretonneux, France) and analyzed for total nitrogen on a
EuroEA3000 elemental analyser (EuroVector, Pavia, Italy).
Soils were sampled using a stratified random procedure. At each plot, five 50 cm × 50 cm
quadrats were randomly placed under the canopy of the dominant (in terms of % cover)
perennial vegetation element and in open areas devoid of perennial vegetation (10 quadrats in
total). A composite topsoil sample consisting of five 145 cm3 soil cores (0-7.5 cm depth) was
collected from each quadrat, bulked, and homogenized in the field. After field collection, the soil
samples were taken to the laboratory, where they were sieved (2 mm mesh). Once sieved, a
fraction was air-dried for one month and stored for physico-chemical analyses; another was
immediately frozen at -20 ºC for microbial analyses (depending upon the availability of a freezer
close to the field site). Dried plant and soil samples, and frozen soil samples from all the
countries were shipped to the laboratory of Rey Juan Carlos University in Móstoles (Spain).
These shipments were carried out according to national and international regulations; exporting
permits were obtained for each country (when required) and importing permits to Spain were
obtained for every shipment by the Spanish Ministry of Agriculture, Fisheries and Food. Once in
the laboratory, we created a composite soil sample per microsite (vegetated and open areas) and
plot using equal amounts of all the replicate soil samples collected in the field. All the laboratory
analyses were carried out on these composite samples (two composite samples per plot, 648
samples in total), either at Rey Juan Carlos University or in other laboratories. By doing so,
every variable was analyzed in the same laboratory by the same personnel and using the same
protocol.
Soil properties measured
Soil pH was measured in all the soil samples with a pH meter, in a 1: 1 soil to water (w:v)
suspension. Soil texture (sand, clay, and silt content) was measured according to ref. 93. The
three textural variables measured (sand, clay, and silt) were highly intercorrelated at both open
(Spearman ρsand-silt = -0.969, P < 0.001; Spearman ρsand-clay = -0.796, P < 0.001; Spearman ρsilt-clay
= 0.677, P < 0.001) and vegetated (Spearman ρsand-silt = -0.987, P < 0.001; Spearman ρsand-clay = -
0.851, P < 0.001; Spearman ρsilt-clay = 0.766, P < 0.001) microsites. Thus, we selected just one of
these fractions (sand), to use in our data analyses because this fraction is less prone to
measurement errors given the method used (93). These physico-chemical properties widely
differed among the 326 plots surveyed: sand content and pH ranged from 14% to 99% and from
3.73 to 9.93, respectively.

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Characterization of above- and belowground biodiversity
Plant diversity - The total plant species richness of each plot was calculated as the total number
of perennial plant species found using at least one of the survey methods (transects or quadrats).
Plant species richness was highly correlated with other diversity metrics such as Shannon’s and
Simpson’s indices (r > 0.65, P < 0.001), so we focused on species richness for this study because
it represents the most widely studied component of biodiversity to date (23, 94–96), and shows
positive relationships with ecosystem functions related to multiple ecosystem services in global
drylands (18).
Herbivore diversity - We used data from the in situ dung/pellet survey (see “Validation of
grazing pressure gradients” section above) to estimate the richness of domestic and wild
mammalian herbivores present at each site as described above. Across all sites, we recorded a
total of 31 different herbivores (table S2), ranging in body size from the European rabbit
encountered in Europe, Australia, and the Americas (~1.2 kg) to the African elephant in Namibia
(~2,500 kg). Dung/pellet data were not available from 26 plots, so the final data set for herbivore
richness includes 300 plots.
Belowground diversity - To quantify belowground diversity, we measured the richness of soil
bacteria, fungi, protists, and invertebrates by amplicon sequencing on the 16S and 18S rRNA
genes, respectively. Soil DNA was extracted from 0.5 g of defrosted soil samples from vegetated
microsites using the Powersoil® DNA Isolation Kit (Mo Bio Laboratories, Carlsbad, CA, USA)
according to the instructions provided by the manufacturer. The extracted DNA samples were
frozen and shipped to the Next Generation Genome Sequencing Facility of the University of
Western Sydney (Australia). There, they were defrosted and analyzed using the Illumina MiSeq
platform. Prokaryotic 16S and eukaryotic 18S rRNA genes were amplified using the 341F/805R
(97) and Euk1391f/EukBr (98, 99) primer sets, respectively. Raw reads quality control, merging
and chimera detection were performed using USEARCH (100), and phylotypes (i.e., ASVs) were
identified at the 100% identity level using UNOISE3 (101, 102). Representative sequences of the
ASVs were annotated against the SILVA-132 SSU database for bacteria, and SILVA LSU (103)
and PR2 (104) databases for eukaryotes, respectively. The ASV abundance tables were generated
using QIIME (105), and then rarefied at 10,000 (16S rRNA gene) and 2,000 (18S rRNA gene)
reads per sample to ensure even sampling depth before diversity calculation. Frozen samples
were obtained for 80 sites encompassing 264 of the 326 plots surveyed. The amplification
procedure failed for some samples, leaving the total number of plots available for belowground
diversity analyses to 242. The richness of soil bacteria, fungi, protists, and invertebrates were
scaled using the Z-score transformation and averaged to obtain a synthetic index of belowground
diversity (106).
Assessment of ecosystem services
In all plots, we measured a total of 36 ecosystem variables linked to nine ecosystem services
(four regulating, two supporting, and three provisioning services; see table S1). The four
regulating ecosystem services assessed were: i) water regulation, measured using soil porosity
and water holding capacity, ii) soil carbon storage, evaluated by measuring soil organic carbon
stocks, iii) organic matter decomposition, quantified using five soil extracellular enzyme
activities related to the degradation of organic matter (β-glucosidase, phosphatase, cellobiase, β-

12
N-acetylglucosaminidase and xylanase) and measurements of soil carbon and nitrogen
mineralization and microbial biomass, and iv) erosion control, assessed by measuring total plant
cover, soil aggregation, and the stability of soil macro-aggregates (aggregates >250 µm). The
two supporting ecosystem services evaluated included: i) aboveground plant biomass and its
temporal stability, estimated using the average plant biomass (APB) measured using satellite
data and the inverse of the CV of APB, and ii) soil fertility, evaluated using multiple proxies of
soil nutrient availability (contents of total N, NH4+, NO3-, dissolved organic N, total P, K, Cu,
Mg, Fe, Mn, and Zn). The three provisioning services included: i) forage quantity, estimated as
the biovolume of perennial grasses and forbs, ii) forage quality, evaluated using the SLA, the
LDMC, and the leaf nitrogen content of perennial grasses and forbs weighted by their relative
cover, and iii) wood quantity, quantified using the biovolume of woody vegetation. These soil
and vegetation variables have often been used as proxies of the ecosystem services evaluated
(107–112), which are essential for sustaining dryland livelihoods and their livestock (15, 113,
114). A detailed description of how each ecosystem service was quantified is given below.
Aboveground plant biomass and its temporal stability. This service, which is particularly
important for extensive livestock production that is dependent upon native forage (115–117),
was quantified using two variables: the average APB and the inverse of the coefficient of
variation (CV) of APB during the 1999-2019 period. To quantify APB, we used the Normalized
Difference Vegetation Index (NDVI), obtained using images from the Landsat 7 Enhanced
Thematic Mapper Plus (ETM+) sensor (118). Multiple studies have shown that NDVI is a good
proxy of APB, particularly in areas with sparse vegetation such as drylands (119-121). Since the
removal of vegetation by grazing changes the amount of photosynthetically active biomass, it
also modifies NDVI accordingly (122). In a similar way, NDVI may also be affected by
differences in APB that may depend on species composition (123). However, NDVI has been
found to be a good proxy of APB in dryland rangelands subject to different grazing levels (123,
124). Finally, the resolution of Landsat data is 30 m x 30 m/pixel, thus it is suitable for
quantifying NDVI at our plots, which have a size of 45 m x 45 m. Indeed, Landsat data have
been frequently used to quantify NDVI in field plots of a size similar to that used in our study
(125, 126).
Landsat ETM+ images (pixel size of 30 m x 30 m) were atmospherically corrected using the
Landsat Ecosystem Disturbance Adaptive Processing System (126), and included a cloud,
shadow, water, and snow mask produced using the C Function of Mask, and a per-pixel
saturation mask (127). The NDVI was calculated as:
  󰇛 󰇛󰇜
󰇛 󰇛󰇜
where RNIR and Rred are the spectral reflectance near-infrared (0.77–0.90 μm) and in the red
(0.63–0.69 μm) bands of Landsat ETM+. The NDVI calculation produces values between -1 to
1, where positive values indicate areas with vegetation, and negative values are typically areas
devoid of vegetation cover, such as bare soil. Using NDVI data, we calculated the mean NDVI
(NDVI) and its variability (128) as:
  


13
 NDVICV
where n is the number of NDVI data available with the above quality criteria (n = 141,863) and
NDVICV is the coefficient of variation of NDVI for the 1999-2019 period.
It is worth highlighting that we considered the average value of 20 years when evaluating APB,
perhaps the most dynamic variable among those used to quantify the ecosystem services
measured. This makes variation in APB across sites/plots due to the different sampling years
among the 3.7 yr window of our survey unlikely to have biased our results and conclusions.
Dryland rangeland vegetation dynamics, and consequently livestock production and human
livelihoods, are highly sensitive to changes in both average APB and its yearly variability (see
ref. 129 and references therein). Thus, we used NDVI and the inverse of  to
quantify a synthetic index of APB and its temporal stability. The inverse of the coefficient of
variation is commonly used when estimating the temporal stability of a given ecological variable
(130–133). For our calculations, we scaled and averaged NDVI and 1/
observed within each plot. A high value of this service is indicative of productive and stable
dryland ecosystems, something that is highly valued by dryland inhabitants and makes these
ecosystems more functional (134) and less prone to degradation (135).
Forage quantity. This service was quantified using the biovolume of grasses and forbs present at
each plot, a variable often used as a proxy for forage available for livestock in drylands (136–
139). The biovolume of each plot was calculated by multiplying the average cover of each
species across all quadrats in a plot and the averaged maximum plant height of each species (m),
obtained from field measurements, and then grouped and summed by plant life form (grasses and
forbs). This metric is provided in m3·m-2.
Forage quality. This ecosystem service was quantified using the specific leaf area (SLA), leaf
dry mass content (LDMC) and leaf nitrogen content of grasses and forbs and weighted by their
relative abundance within each plot. Both SLA and LDMC are functional markers describing one
of the major axes of plant diversification observed in terrestrial systems (140). They discriminate
between acquisitive and conservative growth strategies associated with leaf nutrient contents
(141). The nitrogen content of plant leaves is commonly used to estimate leaf protein contents
(142–145) and is strongly linked to the nutritive value of forage plants (146–148). Overall, these
three plant traits are good proxies for plant palatability -leaves with higher SLA and lower
LDMC are more palatable than leaves with low SLA and high LDMC (149)- and nutritional
content, and thus for forage quality (149–157).
To measure this service, we first averaged individual SLA, leaf nitrogen and LDMC
measurements at the species level. We then quantified plot-level estimates of these variables by
calculating, for grasses and forbs, the community mean trait (Mean j) values as:



where pi and Ti are the relative abundance and the trait value of species i in plot j, respectively.
We then calculated the leaf water content (LWC) as 1 / LDMC.

14
The community mean trait values for SLA, nitrogen content and LWC were scaled and averaged
to obtain a synthetic index of leaf palatability and nutritional value. This index was then
multiplied by the cover of grass and forb species to obtain plot-level estimates of forage quality.
A high value of this service corresponds to plots dominated by grass and forb species
characterized by high SLA, high nitrogen content and low LDMC, a marker of a high forage
quality (149, 150, 153, 158).
Wood quantity. To quantify this ecosystem service, we used the biovolume of woody vegetation,
which is frequently used as a proxy for fuelwood and wood resources available for construction
and other uses in dryland areas (159–161). The biovolume of woody species was quantified
following the same procedure described for grasses and herbs above (but using data from woody
species).
Organic matter (OM) decomposition. To quantify this ecosystem service, we measured five soil
extracellular enzyme activities related to the degradation of OM [β-glucosidase, phosphatase,
cellobiase, β-N-acetylglucosaminidase and xylanase], soil C and nitrogen mineralization, and
microbial biomass. These variables are either direct measurements of OM decomposition (e.g., C
and N mineralization) (162–165) or are involved in the degradation of compounds such as
sugars, chitin, cellulose, and hemicellulose (soil enzymatic activities) (166, 167). Therefore, they
are good proxies for the capacity of a given ecosystem to decompose OM and return available
nutrients from organic sources to the soil (168).
The activity of phosphatase was measured by determination of the amount of p-nitrophenol
(PNF) released from 0.5 g soil after incubation at 37 ºC for 1 h with the substrate p-nitrophenyl
phosphate in MUB buffer (169) (pH 6.5). The activity of β-glucosidase was assayed according to
ref. 170, following the procedure for phosphatase, but using p-nitrophenyl-β-D-glucopyranoside
as substrate and Trishydroxymethyl aminomethane instead of NaOH. The activities of β-N-
acetylglucosaminidase, cellobiase and xylanase were measured from 1 g of soil using
fluorometry as described in ref. 171.
Carbon mineralization rate (µg CO2-C·g-1 dry soil·day-1) was measured as CO2 evolved after 48
h of incubation at 25 ºC and 60% of water holding capacity in soil samples from each plot. We
waited 48 h to make sure that an equilibrium in the soil atmosphere was reached after disruption
and water adjustment to achieve 60% of WHC (172). We measured soil CO2 exchange by
placing 10.5 g of each soil sample inside a 30 mL plastic jar with a tightly sealed lid connected to
a portable, closed-chamber soil respiration system (EGM-4, PP systems, MA, USA) during 60 s.
We monitored CO2 concentration every second and fitted these data to a linear model (R2 > 0.95
in all cases). Afterwards, the ideal gas law equation was used to convert and calculate the net
CO2 increase (ppm) to mass of C (m) in the headspace of the jar:
     
 
where P (atm) and V (L) are, respectively, the air pressure and the known headspace volume in
the jar, M is the atomic mass of carbon (g mol−1), R is the universal gas constant (0.08206 ATM
l mol−1 K−1) and T is the temperature (oK) at the measurement time. The headspace volume in

15
the jar (L) was measured as the total volume of the jar minus the volume of the soil. The mass of
CO2 evolved from each flask was calculated according to ref. 173 and expressed as µg CO2-C s-
1. Finally, we expressed soil carbon mineralization on a dry mass basis (µg CO2-C g-1 soil day-1).
Potential N mineralization rate was measured by determination of total K2SO4-extractable NO3-
before and after soil incubation in the laboratory at 80% of water holding capacity and 30 ºC for
14 days (174).
Soil microbial biomass was assessed using an automated O2 micro-compensation system (175)
by substrate-induced respiration, i.e., the respiratory response of microorganisms to glucose
addition (176). To saturate catabolic microbial enzymes, 4 mg glucose g-1 dry soil was added as
aqueous solution to the soil samples. Prior to the measurement, and to prevent a respiration peak
due to water addition, the dry soil samples were rewetted 24 h before so that they reached 40%
water holding capacity. The final measurements were done at 60% water holding capacity by
adding a specific amount of water and glucose to reach 4 mg glucose g-1 soil dry weight. The
mean of the three lowest hourly measurements was taken as the maximum initial respiratory
response (MIRR) – a period where microbial growth has not started - to calculate microbial
biomass C. Microbial biomass C (mg C·g-1) was calculated as 38 × MIRR (ml O2 g-1 dry soil)
according to ref. 177. All these measurements were conducted at 20 °C in an air-conditioned
laboratory using the same analytical devices.
Soil extracellular enzyme activities related to the degradation of organic matter, soil carbon and
nitrogen mineralization, and microbial biomass were scaled and averaged to obtain a synthetic
index of OM decomposition.
Soil carbon storage. We used organic soil C stocks as a proxy for this ecosystem service (108,
110). We did so because soil organic C is a major terrestrial C reservoir and a major sink of
atmospheric CO2 (178–181). Soil organic C stocks were calculated as the product of soil organic
C concentration, bulk density, and sampling depth. Organic C concentration was determined on
ball-milled soils by dry combustion, gas chromatography and thermal conductivity detection
Thermo Flash 2000 NC soil analyzer (ThermoFisher Scientific, Waltham, Massachusetts, USA),
after removing carbonates by acid fumigation (182). Bulk density was measured at each plot
following the cylindrical core method (183). Changes in grazing pressure did not affect bulk
density across the plots surveyed (Tukey’s HSD test, P > 0.85).
Soil fertility. We quantified this ecosystem service by measuring the contents of total N, NH4+,
NO3-, dissolved organic N, total P, K, Cu, Mg, Fe, Mn, and Zn, which are commonly used
indicators of soil fertility because they are strongly related to plant growth and productivity in
drylands (184–187). Total N was determined on ball-milled soils by dry combustion, gas
chromatography and thermal conductivity detection using a Thermo Flash 2000 NC soil
analyzer. Dissolved organic N, ammonium and nitrate concentrations were measured from a
subsample of a K2SO4 0.5 M soil extracts in a ratio 1:5 (soil: K2SO4). Soil extracts were shaken
in an orbital shaker at 200 rpm for 1 h at 20 ºC and filtered to pass a 0.45-µm Millipore filter
(188). The filtered extract was kept at 4 ºC until colorimetric analyses, which were conducted
within the 24 h following the extraction. Ammonium concentration was directly estimated by the
indophenol blue method using a microplate reader (189). Nitrate was first reduced to NH4+-N
with Devarda alloy, and its concentration was determined by the indophenol blue method.

16
Dissolved organic N was first oxidized to NO3--N with K2S2O8 in an autoclave at 121ºC for 55
min (173), then reduced to NH4+-N with Devarda alloy, and its concentration was determined by
the indophenol blue method. Total P, K, Mg, Fe, Mn, Cu and Zn were extracted by open-vessel
nitric-perchloric acid wet digestion, re-suspended in water, and measured by inductively coupled
plasma optical emission spectrometry (190, 191) with a Perkin Elmer Optima 4300 DV (Perkin
Elmer, Waltham, Massachusetts, USA).
The different nutrient concentrations were scaled and averaged to obtain a synthetic index of soil
fertility.
Erosion control. We quantified this ecosystem service by measuring perennial plant cover, soil
aggregation and the water stability of soil aggregates. The cover of perennial vegetation is
strongly (and negatively) related to soil erosion in drylands (192–195), and is a variable
commonly used as a proxy of erosion control (196–198). Soil aggregation and the water stability
of soil aggregates are good proxies for erosion control, as they largely determine the resistance of
soils to erosive forces (199–204) and are strongly linked to soil quality (205–208).
The cover of perennial vegetation (in %) was derived from the transects (line-point intercept
data) laid out at each plot (see “Vegetation and soil sampling” section above). Soil aggregation
was determined by measuring both the mean weight diameter of the whole sample and the water
stability of the macro-aggregate fraction > 250 µm. Each sample was passed through a stack of
sieves (1 mm, 212 µm, 53 µm, <53 µm) to separate the sample into five fractions of decreasing
particle size. The fraction weights were used to calculate the mean weight diameter (in mm) as:
MWD = 


where  is the mean diameter of size fraction i and  is the weight of the fraction i standardized
by the overall sample mass. Water stability of aggregates was tested following a modified
protocol from ref. 209. Following the MWD measurements, samples were carefully mixed, and
4.0 g placed on small sieves of 250 µm mesh size. Samples were first wetted through capillary
wetting before being introduced to the sieving machine (Agrisearch Equipment, Eijkelkamp,
Giesbeek, Netherlands). They were then moved vertically for 3 min in deionized water to
separate samples into their water-stable and water-unstable fractions. The water-stable fraction
was then washed to extract sand particles and organic debris (i.e., the coarse matter fraction).
The percentage of water-stable aggregates was calculated as follows:
WSA (%) = (water stable fraction-coarse matter) / (4.0 g-coarse matter) *100.
Perennial vegetation cover, soil aggregation and the water stability of soil aggregates were scaled
and averaged to obtain a synthetic index of erosion control.
Water regulation. This ecosystem service was quantified by assessing the soil water holding
capacity (the amount of water that a given soil can hold), and soil porosity (the percentage of the
soil volume occupied by pore spaces). Water holding capacity is relevant to many aspects of soil
water management (210), is an important determinant of aboveground primary productivity in
rangelands (211) and is linked to essential water-related ecosystem services such as plant-water

17
provision (212). Soil porosity is also an important physical variable that controls multiple key
soil hydrological properties, including infiltration and water storage capacity (213–216).
To measure water holding capacity, we weighed 10 g of dry soil per sample and added them to a
funnel with moist filter paper. We then added 10 mL of deionized water to each sample and
covered every funnel with parafilm to avoid evaporation. The soils were allowed to drain for 24
h into a test tube. After 24 h, we weighed the soils to calculate their water holding capacity.
Soil porosity was estimated as 1 - (Db/Dp), where Db and Dp are bulk density and particle
density, respectively (217). Bulk density was estimated for every plot as described above (see
description of the soil carbon storage ecosystem service). Particle density was estimated using a
constant value of 2.65 g/cm3, a typical value used when estimating soil porosity and/or soil
particle properties in soils such as those surveyed here (218–222).
All soil-based analyses were conducted with dry samples, as commonly carried out with global
surveys conducted in drylands and mesic ecosystems (18, 223–226). Previous studies have
shown that in drylands such as those we studied, air drying, and further storage of soils does not
appreciably alter functions such as those studied here (227, 228). It is also important to note that
our sampled soils would have remained dry for a large portion of the year (229–232), and that
most samples were collected when the soil was in this very dry state. Thus, the potential bias
induced by our drying treatment is expected to be minimal.
For all soil variables used to quantify ecosystem services, we first obtained a plot-level estimate
from samples collected under the canopy of vegetation and on bare ground devoid of vascular
vegetation (18). These estimates were obtained using a weighted average of the values observed
in bare ground and vegetated areas, weighted by their respective cover at each plot (quantified
using the line-point intercept survey). All the ecosystem services were standardized between 0
and 1 before statistical analyses to facilitate the comparison between them.
Soil aggregate stability analyses were carried out at the laboratories of the Institute of Biology at
Free University Berlin (Germany). Microbial biomass and C mineralization analyses were
conducted in the laboratories of the Institute of Biology at Leipzig University (Germany). C
mineralization, soil organic C and total N, P, K, Mg, Fe, Mn, Cu and Zn analyses were
conducted at the laboratories of the Institute of Agricultural Sciences-CSIC (Madrid). The rest of
analyses were carried out at the laboratory of the Biology and Geology Department, Rey Juan
Carlos University (Móstoles, Spain).
Statistical analyses
Our overarching objectives were to evaluate the relationships between grazing pressure and the
capacity of drylands to deliver key ecosystem services and to evaluate how grazing pressure
interacts with climate, biodiversity, and soil properties, which are known to impact the delivery
of ecosystem services across drylands worldwide. To do so, we used linear mixed effect models
to evaluate how grazing pressure relates to ecosystem services, accounting for the effects of key
climatic variables, soil properties, and biodiversity. Site was considered as a random factor
(random effect: 1|site) allowing model intercept to vary among sites since plots belonging to the
same site correspond to a local grazing gradient that has been repeated across the 98 sites

18
surveyed. Grazing was treated as a continuous variable in all models ranging 0 to 3 (0 =
ungrazed, 1 = low grazing pressure, 2 = medium grazing pressure, and 3 = high grazing
pressure). As grazing gradients were nested within sites, we also considered an alternative
approach with a random effect nesting grazing within site (random effect: grazing|site) allowing
both intercepts and slopes to vary across sites. However, this approach may lead to model
overfitting and singularity in some cases, i.e., a form of multicollinearity that often occurs when
using mixed models (233, 234). Our results were robust to the approach employed (either 1|site
or grazing|site) as both provided very similar results (see tables S13-S18). Thus, we only present
and discuss in the main text results from the simplest approach considering site as a random
factor (random effect: 1|site). Other predictors were fixed in our models; the rationale for using
them is described below. We conducted all statistical analyses using the statistical software R
v.4.0.5 (235).
Predictors included in ecosystem service models - We used MAT, MAP, and rainfall seasonality
(coefficient of variation of 12 monthly rainfall totals; RASE) obtained from WorldClim 2.0 (37)
to characterize the climate of all plots surveyed. We selected these variables because they: i) are
important drivers of plant diversity in drylands (236, 237), ii) are key predictors of the global
variation observed in dryland ecosystem functioning and stability (134, 236, 238), and iii)
describe largely independent features of climate across the study sites (bivariate correlations had
r < 0.4 in all cases). We did not consider temperature seasonality (standard deviation of monthly
temperatures * 100) because it was highly correlated with MAT in our dataset (r = 0.79). We
considered quadratic terms for MAT and MAP because: i) we sampled global abiotic gradients
for these variables (e.g., ranging from cold environments with freezing temperatures to hyper-
arid and hot regions), and ii) ecosystem responses to changes in climate do not necessarily
change linearly along global drylands (239).
We selected for our analyses soil variables (sand content and pH) measured in samples from
open areas to ensure that their effects on the ecosystem services measured were as independent
from those of organisms as possible. Soil sand content plays a key role in controlling water
availability, the performance and community structure of perennial vascular plants and soil
microorganisms, and ecosystem functioning in drylands (18, 240–243). Soil pH is also a major
driver of plant and soil diversity in drylands (19, 237, 244). A quadratic term was considered for
pH in all models.
While biodiversity is sometimes viewed as a supporting service (245), we consider it in our study
as a driver of ecosystem functioning and associated services across dryland ecosystems (18, 23,
95, 134, 236, 238, 246, 247). We thus included in our framework the richness of perennial plants
occurring in each of the 326 studied plots. We also considered the diversity of soil organisms
(bacteria, fungi, protists, and invertebrates) known to influence ecosystem functions linked to
key ecosystem services, such as OM decomposition and soil carbon storage (19, 107, 248). We
then considered in our analyses the richness of mammalian herbivores in each plot, which has
been shown to largely impact vegetation and ecosystem functioning in drylands (25, 249, 250).
Finally, we included in our models a series of covariates that may influence the relationship
between grazing and ecosystem services. We considered the latitude and longitude of our study
sites, as well as their elevation and topography (slope angle) in our analyses to control for these
potential confounding effects. We used the sine and cosine of the longitude to avoid any bias due

19
to intrinsic circularity of longitude in the statistical models (i.e., Longitude (sin) and Longitude
(cos) hereafter, respectively) (237). All the predictors considered were weakly correlated (table
S3).
Model selection procedure - We considered a full model for each ecosystem service i as:
lmer (ecosystem servicei ~ (1|site) + latitude + longitude (sin) + longitude (cos) + slope +
elevation + MAP*grazing + MAT*grazing + RASE*grazing + MAP² + MAT² + sand*grazing +
pH*grazing + pH² + Biodiversity*grazing).
Using this full model considering all predictors, we ran a model averaging procedure to select the
set of predictors that best explained variations in ecosystem services. To do this, we applied a
multimodel inference procedure using the "MuMIn" R package (251). This method allowed us to
create a set of models with all possible combinations of the initial variables, which were fitted
using a Maximum Likelihood procedure (252) and sorted according to the Akaike Information
Criterion (AIC). The AIC of each model was then transformed to ΔAIC, which is the difference
between AIC of each model and the minimum AIC obtained. We retained all models with an
AIC difference (ΔAIC) < 2, which we defined as best-fitting models.
During the model selection procedure, we maintained site as a random factor in all models and
kept model covariates (latitude, longitude [sine and cosine], slope, and elevation) to account for
their potential confounding effects on ecosystem services. We also forced the model selection
procedure to retain the main effect when an interaction was selected in the final best-fitting
model (i.e., the model with the lowest AIC value). We did so for two reasons: i) we used
continuous variables to model interactions, and ii) two independent variables x and y (e.g.,
grazing and other predictor) will be correlated with the interaction term xy. By including x, y, and
xy, we evaluated how much the interaction involving grazing can explain beyond what grazing
does as a main effect. Similarly, when a quadratic term was selected for a given predictor, we
retained the linear term in the best-fitting model.
For each service, we finally averaged predictor estimates selected across best-fitting models
(those models selected within a ΔAIC < 2) using the conditional averaging approach in the
function model.avg from the "MuMIn" R package. We fitted all models with the R package
"lme4" using the LMER function (253). The full results of the model averaging procedure,
including model estimates, standard errors, P values, variable importance values, and variance
inflation factors, are available in tables S13-S15.
All predictors were standardized before analyses using the Z score to interpret parameter
estimates on a comparable scale. Response variables were log-transformed when necessary to
normalize data distribution prior to analyses to meet the assumptions of the tests used, i.e.,
normal distribution of residuals. For each model, we inspected the distribution of residuals and
checked for the presence of potential outliers using the Cook’s distance in the function romr.fnc
from the package "LMERConvenienceFunctions" (254). If outliers were detected, they were
removed as they may bias model estimates. Models were then rerun using the same model
averaging procedure. Across the nine services considered, we detected the presence of nine, eight
and four outliers for water regulation, soil fertility, and aboveground plant biomass and its
temporal stability, respectively, representing 0.007% of the whole data set. We also tested for

20
model multicollinearity using Variance Inflation Factors, checked the distribution of residuals,
and tested for the presence of spatial autocorrelation in the residuals using Moran tests (255,
256). Multicollinearity and spatial autocorrelation were absent in model residuals for all response
variables considered (tables S13-S15).
For each service, we calculated the relative importance of each predictor in the model selection
procedure using the sum of weights calculated for each predictor. This sum was calculated using
the sw function from the "MuMIn" R package (251). This function uses Akaike’s weights to
define the relative importance of each predictor across the final set of best-fitting models (i.e.,
those with a ΔAIC < 2 from the best-fitting model) by summing the Akaike weights values of all
models that include the predictor of interest, considering the number of models in which each
predictor appears. Predictor importance is proportional to the number of times a given predictor
(and its interactions with other predictors) was selected in the final set of best-fitting models, and
ranges from 0 (when a given predictor is not selected in any of the best-fitting models) to 100
(when a given predictor was selected in all of the best-fitting models). The relative importance of
predictors was also averaged across the nine ecosystem services measured to compare their
overall importance on ecosystem service delivery (Fig. 2).
Finally, and to ensure the robustness of our results, we repeated all analyses described above but
considering dung mass and livestock track area instead of our continuous variable of grazing
pressure (from ungrazed [0] to high grazing pressure [3]). Data of dung mass and livestock track
areas were scaled within each site prior to analyses to reflect local grazing gradients. Dung mass
provided very similar results to those obtained using our continuous variable for all services
except for wood quantity and APB and its temporal stability (tables S19-S21). Interestingly, the
analyses conducted with track area well explained those two services and in a similar way to our
continuous gradient (tables S22-S24). Therefore, our results are not only robust to the approach
employed to characterize the grazing gradient, but also show that our local grazing gradient
encompasses complex effects of grazing on ecosystem services such as short- and long-term
effects. Because of this, we only present and discuss in the main text results from the approach
considering grazing as a continuous variable ranging from 0 (ungrazed) to 3 (high grazing
pressure).
Use of biodiversity data in our statistical models - We considered the richness of perennial
plants, mammalian herbivores (herbivore richness) and belowground organisms as biodiversity
predictors in our models. While data for plant species richness were available for the 326 plots
surveyed, herbivore richness and belowground diversity data were available for 300 and 242
plots, respectively. Because models with a different number of observations cannot be compared
using AIC, we conducted a model preselection procedure to select the best set of biodiversity
predictors to be included in the model selection procedure described above. To do so, we
considered a subset data of 242 plots where both belowground diversity and plant species
richness were available. We compared a full model including both belowground diversity and
plant species richness together to a model including plant richness only. If models including
belowground diversity showed lower AIC values, we considered the subset of 242 plots to
perform the model selection procedure. If the best models only included plant species richness,
we considered the full data set of 326 plots to perform the model averaging procedure. We
performed the same preselection for the data subset that includes the 300 plots with both plant
and herbivore richness information. If mammalian herbivore richness improved model quality

21
compared to models with plant species richness only, we considered the subset data with
herbivore richness for the model selection procedure. If herbivore richness did not improve
model AIC, we considered the full data set with plant species richness only. Results of the model
pre-selection procedure are available in table S25 for analyses using 1|site as random effect, in
table S26 for analyses using grazing|site as random effect, and in tables S27 and S28 for analyses
using dung mass and livestock tracks as surrogates of grazing pressure, respectively.
Plotting the interactive effect of grazing with climate, soils, and biodiversity- We graphically
represented the results from best fitting models (tables S13-S15) in two different ways. First, we
used model partial residuals to show how each predictor influenced ecosystem services
according to all grazing pressure levels evaluated (Fig. 3, figs. S13-S15). Second, we calculated
the predicted values for each service in each site at low and high grazing pressure levels using
model estimates of best-fitting models. Predictions were made using observed variability
between sites in plant species richness, mean annual temperature (MAT), and rainfall seasonality
(RASE); all other parameters were fixed at their mean value. Then we calculated the predicted
effect of grazing at each site as the difference between high and low grazing pressures using a
log response ratio [lnRR; Predicted lnRR = ln (predicted service at high grazing
pressure/predicted service at low grazing pressure)]. Finally, we plotted the relationships
between the effect of grazing pressure (Predicted lnRR) and ecosystem services across sites and
along the global gradient of abiotic conditions and plant species richness surveyed (Fig. 4).
Indirect effect of grazing on ecosystem services - We also tested whether grazing could impact
ecosystem services through indirect pathways. We did so because grazing may not only impact
ecosystem services through direct and interactive effects but also through indirect pathways, e.g.
if grazing affected local species richness or soil conditions in our models. To explore these
potential indirect effects of grazing, we conducted a confirmatory path analysis, a form of
structural equation modeling (257), using a d-sep approach (258, 259). This approach is based on
an acyclic graph that depicts the hypothetical relationships among predictors (links represented
by arrows) and independence claims among variables (missing links), where the latter are tested
using the C statistic. Based on the correlation matrix of our predictors (table S3), we tested the a
priori model that grazing pressure does not have indirect effects on ecosystem services through
changes in soil properties and biodiversity (fig. S10). Please note that we did not test indirect
effects of grazing mediated by plant cover because this variable was used in the calculation of
erosion control (see the “Assessment of ecosystem services” section), and thus we could not
include it as a predictor of ecosystem services in the d-sep analyses. These analyses had the
following steps (259): i) we express the hypothesized relationships between the variables in the
form of a directed acyclic graph (fig. S10). In our case, we hypothesized that there was no
linkage between grazing and plant species/herbivore richness and between grazing and soils; ii)
we list each of the k pairs of variables in the graph that do not have an arrow between them. This
list defines the missing links in our path analyses; iii) we test each missing link by comparing the
models with and without the missing links; each link was tested using linear mixed models
similar to those explained in the “Model selection procedure” section above. When a P value is
not significant it means that there is an independence between a given pair of variables (i.e., they
are not related); and iv) we finally combined the k probabilities using the C statistic (257) and
compared the resulting C value to a chi-squared distribution with 2k degrees of freedom. The
path model is valid when the result of this test is not significant (P > 0.05).

22
Model formulas employed to test each missing link, C statistics and significance test for each
path analysis are available in tables S4-S12. Standardized path coefficients were calculated
following ref. 260 to measure the direct, and indirect effect of predictors for each service. For all
services evaluated, we did not detect any indirect effect of grazing through changes in soil
properties or richness conditions (fig. S11 and tables S4-S12). These results indicate that grazing
pressure impacted the different ecosystem services measured only through direct and interactive
effects.

23
Fig. S1. Box plots of the mass of dungs of livestock (a) and wild (b) herbivores for the four
levels of grazing pressure evaluated. Boxes show the median, 25th and 75th percentiles. Distinct
lowercase letters indicate significant differences (p < 0.05) between grazing pressure levels
(Tukey’s HSD test). The total number of plots used for these analyses was 300.

24
Fig. S2. Examples of the vegetation present at plots surveyed in the USA (a, b), Spain (c), Kazakhstan (d), Mongolia (e),
Ecuador (f), Namibia (g), Kenya (h), Australia (i) and Argentina (j). The background map represents the extent of dryland
rangelands. The aridity index (AI) is calculated as precipitation/potential evapotranspiration. See Materials and Methods for the AI
and rangeland area data sources used.

25
Fig. S3. Range of environmental conditions covered by the surveyed drylands. Bivariate
relationships between key environmental variables (mean annual temperature and mean annual
precipitation and soil pH and organic carbon) are shown in panels A and B. Panels C-E show the
spatial distribution of the Mahalanobis distance regarding the environmental characteristics
covered (<0.975 Chi-squared threshold for outliers) by the surveyed drylands. To obtain these
panels, we determined how much the parameter space of the predictors (e.g., mean annual
temperature, soil organic carbon, elevation) differed from that of global drylands (261). We used
the Mahalanobis distance of any multidimensional point to the center of the known distribution
(calculated based on the 98 locations from the original dryland dataset) (262–264) For panel C
we considered the spatial coverage of climatic conditions (number of dimensions = 7; mean
annual temperature, mean annual precipitation, temperature seasonality, precipitation
seasonality, temperature mean diurnal range, aridity index and evapotranspiration) using data
from refs. 37 and 38. For panel D, we considered the spatial coverage of soil conditions (number

26
of dimensions = 5; nitrogen, carbon, soil texture [% of clay and silt], soil pH and C/N ratio)
using data from ref. 263. For panel E, we considered the overall environmental coverage
(number of dimensions = 14; vegetation [NDVI], elevation, nitrogen, carbon, soil texture [% of
clay and silt], soil pH, C/N ratio, mean annual temperature, mean annual precipitation,
temperature seasonality, precipitation seasonality, temperature mean diurnal range, aridity index,
and evapotranspiration).

27
Fig. S4. Relationship between the number of dung/pellets of grazing animals and their mass
(g) for six surveyed sites from Argentina, Algeria, Ecuador, Palestine, and South Africa.
Each data point represents data from a quadrat surveyed in the field. Antelope records are from
Namibia (n = 6), Botswana (n = 7) and South Africa (n = 16). Kudu records are from Namibia (n
= 13) and South Africa (n = 5).

28
Fig. S5. Relationships between livestock density and oven-dried mass of dung for four of
the surveyed countries where we had access to long-term livestock density data. Each data
point represents a plot.

29
Fig. S6. Mean (± SE) livestock density, adjusted to a common scale of dry sheep
equivalents, observed in ungrazed and low, medium, and high grazing pressure plots in
Argentina (n = 15), Australia (n = 11) and Iran (n = 11). Different lowercase letters indicate
significant (P < 0.05) differences between grazing pressure levels using a linear model (One-way
ANOVA).

30
Fig. S7. Results of a cluster analysis of dung/pellet data. (a) Box plots of average dung mass
(kg·ha-1) for the four levels of grazing pressure evaluated. Boxes show the median, 25th and 75th
percentiles. Distinct lowercase letters indicate significant (p < 0.05) differences between grazing
pressure levels (Tukey’s HSD test); (b) Plot of within-group sum of squares in relation to the
number of clusters. The optimal number of clusters is that from which additional clusters results
in similar variance explained (here four clusters); (c) Mosaic plots illustrating the results of
contingency tables between pre-inspection level of grazing pressure (ungrazed to high) in
relation to the post-inspection assessment of dung mass on the four clusters identified in (b)
above. Panel (c) uses all the classifications, but panel (d) is based on the three-group cluster.
Edge length is proportional to the number of cases, and thus the area of each square is
proportional to the degree of match between the two methods of classifying grazing pressure.
Colour of mosaics represents over (blue) or under (red) representation of each combination of
classifications, measured as Pearson’s residuals obtained from chi-squared tests. For a perfect
match, the diagonal of these mosaics (ungrazed-ungrazed; low-low; medium-medium; high-high)
should exhibit significant overrepresentation and the other either non-significance or
underrepresentation. The overall match, i.e., the sum of high to high, medium to medium, low to
low and ungrazed to ungrazed, is 37.3% in panel c; and 51.3% in panel d. Plot level accuracy is
calculated as correct matches (low-low, high-high, medium-medium, ungrazed-ungrazed)
divided by the total of plots classified as each grazing level according to expert classification.
The total number of plots used for these analyses was 300.

31
Fig. S8. Box plots of the area (a) and density (b) of livestock tracks for the four levels of
grazing pressure evaluated. Boxes show the median, 25th and 75th percentiles. Distinct
lowercase letters indicate significant differences (p < 0.05) between grazing pressure levels
(Tukey’s HSD test). The total number of plots used for these analyses was 232.

32
Fig. S9. Comparison of the amount of dung from livestock and native herbivores found
across the surveyed plots (Current study) and in other surveys conducted in dryland
rangelands from Australia, Kenya and China encompassing a wide variation in grazing
pressure. Data from Australia and China come from refs. 266 and 267, respectively; data from
Kenya come from refs. 268 and 80.

33
Fig. S10. A priori model used to evaluate direct and indirect effects of grazing pressure
through changes in soil properties and biodiversity on the ecosystem services studied. Our a
priori path model considers that grazing does not have indirect effects through changes in soil
properties and biodiversity (null hypothesis). We explicitly tested conditional independence
claims (“missing links”) using a confirmatory path analysis (13). These independence claims
(dashed lines), include potential indirect effects of grazing on ecosystem services mediated by
biodiversity and soil parameters. We considered quadratic effects for mean annual precipitation
(MAP), mean annual temperature (MAT) and soil pH. Sand = sand content, and RASE = rainfall
seasonality.
Ecosystem service
(Y)
Climate
MAP (X1)
MAT (X2)
RASE (X3)
Soil parameters
Sand (X5)
pH (X6)
Plant richness (X7)
Herbivore richness (X8)
Belowground diversity
(X9)
Grazing (X4)

34
MAP (X1)
MAT (X2)
RASE (X3)
Grazing (X4)
Sand (X5) R²m=0.31
R²c= 0.89
pH (X6)R²m=0.62
R²c= 0.92
Carbon storage (Y)
R²m=0.77
R²c= 0.94
Plant rich (X7)R²m=0.41
R²c= 0.85
Herb rich (X8)R²m=0.06
R²c= 0.19
Cstatitic = 30.32
df =30
P value = 0.45
X5 = -0.22x1+ 0.15x1²
0.38x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.18x2- 0.20x2²
Y = 0.01x4
Y = 0.17x7 +
0.06x8
a)
n = 300
MAP (X1)
MAT (X2)
RASE (X3)
Sand (X5) R²m=0.25
R²c= 0.89
pH (X6)R²m=0.69
R²c= 0.93
Organic matter
decomposition (Y)
R²m=0.75
R²c= 0.89
Plant rich (X7)R²m=0.45
R²c= 0.87
Below div (X8)R²m=0.35
R²c= 0.60
Y = 0.08x7 +
0.06x8
Grazing (X4)
Y = 0.03x4
Cstatitic = 30.79
df =30
P value = 0.42
b)
n = 242
X5 = -0.25x1+ 0.22x1²
0.33x2+ 0.13x2²
X6 = -0.69x1+ 0.11x1²
-0.08x2- 0.17x2²
MAP (X1)
MAT (X2)
RASE (X3)
Sand (X5) R²m=0.25
R²c= 0.89
pH (X6)R²m=0.69
R²c= 0.93
Erosion control (Y)
R²m=0.53
R²c= 0.91
Plant richness (X7)
R²m=0.45
R²c= 0.87
Y = 0.02x7
Grazing (X4)
Y = 0.01x4
X5 = -0.25x1+ 0.22x1²
0.33x2+ 0.13x2²
X6 = -0.69x1+ 0.11x1²
-0.08x2- 0.17x2²
Cstatitic = 27.92
df =22
P value = 0.20
c)
n = 242

35
MAP (X1)
MAT (X2)
RASE (X3)
Grazing (X4)
Sand (X5) R²m=0.28
R²c= 0.90
pH (X6)R²m=0.61
R²c= 0.92
Water regulation (Y)
R²m=0.63
R²c= 0.92
Plant richness (X7)
R²m=0.40
R²c= 0.86
X5 = -0.21x1+ 0.17x1²
0.34x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.17x2- 0.20x2²
Cstatitic = 22.18
df =22
P value = 0.44
d)
n = 312
Y = 0.005x7
MAP (X1)
MAT (X2)
RASE (X3)
Grazing (X4)
Sand (X5) R²m=0.31
R²c= 0.89
pH (X6)R²m=0.62
R²c= 0.92
Plant biomass &
stability (Y)
R²m=0.55
R²c= 0.92
Plant rich (X7)R²m=0.41
R²c= 0.85
Herb rich (X8)R²m=0.06
R²c= 0.19
Cstatitic = 30.32
df =30
P value = 0.44
X5 = -0.22x1+ 0.15x1²
+0.38x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.18x2- 0.20x2²
Y = 0.02x7 +
0.01x8
e)
n = 296
Y =0.006x4x7
+0.006 x4x8
MAP (X1)
MAT (X2)
RASE (X3)
Grazing (X4)
Sand (X5) R²m=0.28
R²c= 0.90
pH (X6)R²m=0.61
R²c= 0.91
Soil fertility (Y)
R²m=0.62
R²c= 0.95
Plant richness (X7)
R²m=0.40
R²c= 0.86
X5 = -0.21x1+ 0.17x1²
0.34x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.17x2- 0.20x2²
Cstatitic = 23.30
df =24
P value = 0.50
Y = 0.02x4
f)
n = 320

36
MAP (X1)
MAT (X2)
RASE (X3)
Grazing (X4)
Sand (X5) R²m=0.28
R²c= 0.90
pH (X6)R²m=0.61
R²c= 0.91
Forage quantity (Y)
R²m=0.27
R²c= 0.77
Plant richness (X7)
R²m=0.40
R²c= 0.86
X5 = -0.21x1+ 0.17x1²
0.34x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.17x2- 0.20x2²
Cstatitic = 29.46
df =30
P value = 0.49
Y = -0.25x4
g)
Y = 0.48x7
n = 326
MAP (X1)
MAT (X2)
RASE (X3)
Sand (X5) R²m=0.31
R²c= 0.89
pH (X6)R²m=0.62
R²c= 0.92
Forage quality (Y)
R²m=0.23
R²c= 0.89
Plant rich (X7)R²m=0.41
R²c= 0.85
Herb rich (X8)R²m=0.06
R²c= 0.19
Cstatitic =32.45
df =34
P value =0.54
X5 = -0.22x1+ 0.15x1²
0.38x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.18x2- 0.20x2²
Y = 0.14x7 +
0.01x8
h)
n = 277
Grazing (X4)
MAP (X1)
MAT (X2)
RASE (X3)
Sand (X5) R²m=0.28
R²c= 0.90
pH (X6)R²m=0.61
R²c= 0.91
Wood quantity (Y)
R²m=0.28
R²c= 0.86
Plant richness (X7)
R²m=0.40
R²c= 0.86
X5 = -0.21x1+ 0.17x1²
0.34x2+ 0.16x2²
X6 = -0.66x1+ 0.12x1²
-0.17x2- 0.20x2²
Cstatitic = 24.48
df =24
P value = 0.43
i)
Y = 0.27x7
Grazing (X4)
n = 326

37
Fig. S11. Results of the conditional path analyses to test for indirect effects of grazing
pressure. The panels show selected path models linking climate (blue arrows), soil (orange
arrows), biodiversity (green arrows), and grazing (yellow arrows) with soil carbon storage (a),
organic matter decomposition (b), erosion control (c), water regulation (d), soil fertility (e),
aboveground plant biomass and its temporal stability (f), wood quantity (g), forage quantity (h),
and forage quality (i). For each arrow, we indicated the equations associated with each
significant path. Since all predictors were Z-scored prior analyses, coefficient paths represent
effect sizes. We included grazing interactive effects when selected in the final best models (see
supplementary tables S13-S15) represented by circle-ended arrows. Plant biomass & stability =
aboveground plant biomass and its temporal stability, Sand = sand content, Plant rich = plant
species richness, Herb rich = mammalian herbivore richness, Below div = belowground
diversity, MAT = mean annual temperature, RASE = rainfall seasonality, and MAP = mean
annual precipitation.

38
Fig. S12. Relative importance of predictors (grazing pressure, climate, biodiversity, and soil
variables, and their interactions) of ecosystem services selected in best-fitting models.
Importance is quantified as the sum of the Akaike weights of all models that included the
predictor of interest, considering the number of models in which each predictor appears. It is
proportional to the number of times a given predictor (and its interactions with other predictors)
was selected in the final set of best-fitting models (13). In the case of biodiversity, predictor
importance considers the number of models that includes at least one biodiversity proxy (plant
species richness, mammalian herbivore richness or belowground diversity). Full details on model
results, including the number of best-fitting models, are available in tables S13-S15. Plant
biomass & stability = aboveground plant biomass and its temporal stability, Grazing = grazing
pressure, Herb rich = mammalian herbivore richness, Below div = belowground diversity MAT
= mean annual temperature, RASE = rainfall seasonality, and MAP = mean annual precipitation.
R²
0.55
0.27
0.23
0.77
0.75
0.62
0.28
0.53
0.63
Supporting
Provisioning
Regulating
ECOSYSTEM SERVICES
99.1 90.5 89.7 88.6 84.1 66.3 33.0 11.1
Predictor importance averaged across services
Plant biomass & stability
Soil fertility
Erosion control
Water regulation
Forage quality
Organic matter decomposition
Soil carbon storage
Forage quantity
Wood quantity
Importance (%)
010050
61.2 40.5 37.0 32.1 20.4 19.2 9.4 7.6 0.0

39
Fig. S13. Predicted responses of regulating ecosystem services to climate, sand content, and plant species richness at different
levels of grazing pressure. Dots show partial residuals and lines show model fits (using partial regressions) for each significant
predictor in the final best models (ΔAIC < 2, 13). Climatic, soil, and biodiversity predictors are represented in blue, brown, and green,
Soil carbon storage
OM decomposition
Erosion control
Water regulation
Partial residuals
Y = α1MAP***
+ α2MAP²* Y = α1pH * Y = α1Sand***
Y = α1 PR***
Y = α1HR*
Y = α1GR + α2RASE***
+ α3RASE × GR°
Y = α1GR *+α2MAP***
Y = α1GR*
+ α2pH **+ α3pH²**
Y = α1GR* + α2MAT***
+ α3MAT²***
+ α4MAT × GR*
Y = α1GR*+ α2RASE***
Y = α1GR* + α2PR**
Y = α1GR*
+ α1BD**
Y = α1GR*
+α1Sand***
Y = α1GR**+ α2MAP***
Y = α1GR**+ α2RASE*
Y = α1GR**+ α2pH **+ α3pH²° Y = α1GR ** + α2Sand*** Y = α1GR** + α2DPR**
Y = α1MAP*** Y = α1MAT*** NS Y = α1pH+ α2pH²° Y = α1Sand***
Y = α1GR** + α2MAT* + α3MAT²**
+ α4MAT × GR*
Y = α1GR + α2PR+ α2PR x GR**

40
respectively. When significant main or interactive effects of grazing were observed in the final set of best models, we plotted
predictions for the four levels of grazing pressure separately. The darkest dots represent partial residuals at high grazing pressure plots,
while the brightest dots represent partial residuals at ungrazed plots. Similarly, the darkest lines represent model fits for high grazing
pressure plots, the brightest lines represent model fits for ungrazed plots. In both cases, the colour increases from lightest to darkest in
this order: ungrazed, low grazing pressure, medium grazing pressure, and high grazing pressure. Details on model parameters are
available on tables S13-S15. OM = organic matter, NS = non-significant predictors, GR = grazing pressure, MAP = mean annual
precipitation, MAT = mean annual temperature, RASE = rainfall seasonality, Sand = sand content, pH = soil pH, PR = plant species
richness, HR = mammalian herbivore richness, and BD = belowground diversity. Significance of predictors as follows: º P < 0.10, *,
P < 0.05; **, P < 0.01; ***, P < 0.001.

41
Fig. S14. Predicted responses of supporting ecosystem services to climate, sand content, and plant species richness at different
levels of grazing pressure. Plant biomass & stability = aboveground plant biomass and its temporal stability. Remainder of legend as
in fig. S13.
Plant biomass & stability Soil fertility
Y = α1MAP*
Y = α1pH ***+ α2pH²**
Y = α1MAT+ α2MAT²*** Y = α1GR + α2RASE +
α3RASE × GR*NS
Y = α1GR + α2PR* + α3PR ×
GR°Y = α1GR + α2HR*+ α3
HR ×GR°
Y = α1GR** +α1pH* + α2pH²*
+ α4pH × GR
Y = α1GR**+ α2MAP***
+ α3MAP²*
Y = α1GR**
+α2MAT***+ α3MAT²**
Y = α1GR** + α2Sand***
+ α3Sand × GR*NS
Y = α1GR** +α2RASE**
Partial residuals

42
Fig. S15. Predicted responses of provisioning ecosystem services to climate, sand content, and plant species richness at
different levels of grazing pressure. Remainder of legend as in fig. S13.
Partial residuals
Forage quantity Forage quality
Wood quantity
Y = α1GR**+α2MAP** Y = α1GR*+α2MAT° Y = α1GR**+ α2Sand
+ α3Sand × GR*
Y = α1GR** + α2PR***
NS NS NS NS
Y = α1GR*** + α2PR***
NS
Y = α1GR* + α2MAT
+ α3MAT²**
Y = α1GR* + α2RASE*
NS
Y = α1GR** + α2HR
+ α3HR ×GR*
Y =α1GR*+ α1MAP***+
α2MAP²**
Y = α1GR*+ α2Sand
+ α3Sand × GR*
NS NS
Y = α1GR* + α2PR*+ α3DPR× GR***

43
Fig. S16. Geographical variation in the effect of grazing on each ecosystem service
measured across global drylands. For each of the 98 sites surveyed, we plot the effect of
grazing predicted by model parameters along the wide climatic and plant species richness
gradients evaluated. This effect was calculated using the predicted response ratio (lnRR) at each
site, calculated as the lnRR between model predictions at high vs. low grazing pressure levels
(see “Statistical analyses” section) and considering site parameters. These parameters included
plant and mammalian herbivore richness, belowground diversity, mean annual temperature and
rainfall seasonality; all other parameters were fixed at their mean value (see full model
parameters in tables S13-S15). See fig. S12 for the meaning of the symbols depicting each
ecosystem service.
Predicted lnRR

44
Fig. S17. Variation in the effect of grazing on each ecosystem service measured across
global climatic, soil, and plant richness gradients in the drylands surveyed. For each service,
we plot the effect of grazing predicted by model parameters for the 98 sites surveyed along the
wide climatic and plant species richness gradients evaluated. This effect was calculated using the
predicted response ratio (lnRR) at each site, calculated as the lnRR between model predictions at
high vs. low grazing pressure levels (see “Statistical analyses” section) and considering site
parameters. These parameters included plant species richness (PR), mammalian herbivore
richness (HR), belowground diversity, mean annual temperature (MAT), mean annual rainfall
(MAP) and rainfall seasonality (RASE); all other parameters were fixed at their mean value. We
plot significant interactions for each service in each panel (see full model parameters in tables
S13-S15). See fig. S12 for the meaning of the symbols depicting each ecosystem service. Graz =
grazing and Sand = sand content.
Predicted lnRR
Graz × MAT
Graz × MAT
Graz × RASE Graz × MAT
Graz × PR
Graz × PR
Graz × RASE
Graz x HR
Graz × Sand
Graz × PR
Graz × Sand
Graz × Sand

45
Fig. S18. The effects of increased grazing pressure on ecosystem services vary across
contrasting environmental contexts. While increases in grazing pressure reduce forage
quantity and quality and enhance soil fertility regardless of climatic conditions, such increases
interact with temperature, rainfall seasonality and/or plant species richness to determine multiple
ecosystem services. Panel A shows the situation in dryland areas with high temperature, rainfall
seasonality and/or plant species richness. Panel B shows the situation in dryland areas with low
temperature, rainfall seasonality and/or plant species richness. OM = organic matter and Plant
biomass & stability = aboveground plant biomass and its temporal stability. This figure is based
on results shown in Fig. 2 and figs. S13-S15 and S17.
AB

46
Fig. S19. Geographical variation in the effect of grazing on ecosystem services when only
climate (A) and both climate and plant richness (B) are considered. This effect was
calculated using the predicted response ratio (lnRR) at each site, calculated as the lnRR between
model predictions at high vs. low grazing pressure levels. The climatic parameters selected
(mean annual temperature [MAT] and rainfall seasonality [RASE]) interacted with grazing.
Diversity components used include plant species and mammalian herbivore richness. For
simplicity, we averaged the grazing effect at the site level across all services. The size of dots is
proportional to the species richness observed at each site. Predicted grazing effects using climatic
parameters ranged from neutral to mostly positive for most sites (a). When we accounted for the
effects of plant and mammalian herbivore richness in addition to those of climate (b), grazing
effects became negative according to model predictions in sites with a low plant species richness
(small dots in b) while it remained positive in sites with a high plant and herbivore species
richness (large dots in b). These results show that biodiversity both limits negative and promotes
positive impacts of increasing grazing pressure on ecosystem services across global drylands.
Predicted lnRR
A
B

47
Table S1. Ecosystem variables used to quantify regulating, supporting, and provisioning ecosystem services.
Type
Ecosystem service
Ecosystem variable
Units
Regulating
Water regulation
Soil water holding capacity
%
Soil porosity
%
Soil carbon storage
Soil organic C stock
kg C·m-2 soil
Organic matter decomposition
Activity of β-glucosidase
µmol PnP·g soil-1·h-1
Activity of phosphatase
µmol PnP·g soil-1·h-1
Activity of cellobiase
nmol MUF·g soil-1·h-1
Activity of β-N-acetylglucosaminidase
nmol MUF·g soil-1·h-1
Activity of xylanase
nmol MUF·g soil-1·h-1
Soil carbon mineralization
µg CO2-C·g soil-1·day-1
Soil nitrogen mineralization
mg N·kg soil-1·day-1
Soil microbial biomass
µg C mic·g soil-1
Erosion control
Perennial plant cover
%
Mean weight diameter of soil aggregates
mm
Stability of macro-aggregates >250 µm
%
Supporting
Soil fertility
Total N content
g N·kg soil-1
NH4+ content
mg N·kg soil-1
NO3- content
mg N·kg soil-1
Dissolved organic N content
mg N·kg soil-1
Total P content
mg P·kg soil-1
K content
mg K·kg soil-1
Cu content
mg Cu·kg soil-1
Mg content
mg Mg·kg soil-1
Fe content
mg Fe·kg soil-1

48
Mn content
mg Mn·kg soil-1
Zn content
mg Zn·kg soil-1
Aboveground plant biomass and its
temporal stability
Average aboveground plant biomass
[APB]
Unitless
Inverse of the CV of APB
Unitless
Provisioning
Wood quantity
Biovolume of woody vegetation
m3·m-2
Forage quantity
Biovolume of grasses
m3·m-2
Biovolume of forbs
m3·m-2
Forage quality
Specific leaf area of grasses
cm²·g-1
Specific leaf area of herbs
cm²·g-1
Foliar nitrogen content of grasses
%
Foliar nitrogen content of herbs
%
Leaf dry matter content of grasses
Unitless
Leaf dry matter content of herbs
Unitless

49
Table S2. Mammalian herbivores recorded at the sites surveyed and the number of sites where
the different species were found.
Family/Subfamily
Animal
Type
Number of
sites
Antelope
Gemsbok
Oryx gazella
14
Roe deer
Capreolus capreolus
8
Steenbok
Raphicerus campestris
7
Common duiker
Sylvicapra grimmia
6
Red deer
Cervus elaphus
5
Greater kudu
Tragelaphus strepsiceros
4
Springbok
Antidorcas marsupialis
3
Hartebeest
Alcelaphus buselaphus
3
Gazelle
Gazella spp.
2
Blue wildebeest
Connochaetes taurinus
2
Waterbuck
Kobus ellipsiprymnus
1
Rodents
South African
Springhare
Pedetes capensis
4
Macropod
Kangaroo
Macropus spp., Osphranter
rufus
5
Leporids
Rabbit
Oryctolagus cuniculus
33
Hare
Lepus sp.
11
African savanna hare
Lepus victoriae
5
Equine
#Horse
Equus caballus
34
#Donkey
Equus asinus
8
Common zebra
Equus quagga
4
Grevy's zebra
Equus grevyi
3
Suidae
Common warthog
Phacochoerus africanus
1
Bovinae
#Cattle
Bos taurus, Bos indicus
58
African buffalo
Syncerus caffer
1
Camelids
Dromedary
Bactrian camel
Camelus dromedarius
Camelus bactrianus
2
1
Guanaco
Lama guanicoe
2
Ovids
#Sheep
Ovis aries
57
Caprids
#Goat
Capra hirca
35
Giraffid
Giraffe
Giraffa camelopardalis
5
Elephantidae
Elephant
Loxodonta africana
1
#livestock species

50
Table S3. Correlation matrix among all studied predictors (n = 326). We show Spearman
correlation coefficients for correlations involving grazing pressure and Pearson correlation
coefficients for the rest of predictors. Graz = grazing pressure, Plant rich = plant species
richness, Herb rich = mammalian herbivore richness, Below Div = belowground diversity, MAT
= mean annual temperature, RASE = rainfall seasonality, and MAP = mean annual precipitation.
Graz
Graz
1
MAP
MAP
0.006
1
MAT
MAT
0.03
0.17
1
RASE
RASE
0
-0.12
0.23
1
Sand
Sand
0.02
-0.14
0.28
0.21
1
Soil
pH
Soil pH
-0.005
-0.56
-0.33
-0.03
-0.25
1
Plant
rich
Plant rich
-0.03
0.28
-0.17
-0.19
-0.08
-0.20
1
Herb
rich
Herb rich
0.17
-0.09
-0.09
0.12
0.09
-0.10
0.12
1
Below
div
Below div
-0.20
0.32
-0.07
-0.28
0.23
-0.28
0.21
-0.05
1

51
Table S4. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for soil carbon storage. We modeled each link using linear mixed models. Model types (lmer = linear mixed effect regression;
glmer = generalized mixed effect regression) and formula are provided for each link. In each model, we controlled for the latitude,
cos_longitude, sin_longitude, elevation, and slope (covariables), and used the site as a random factor (see “Statistical analyses”
section). We present all independent claims considered in the model, provide the P value of each independent claim, and the P value
of the different path analyses. Variables: X1 = mean annual rainfall, X2 = mean annual temperature, X3 = rainfall seasonality, X4 =
Grazing, X5 = Sand, X6 = PH, X7 = plant species richness, X8 = mammalian herbivore richness, X9 = belowground diversity. Y =
ecosystem service, and Cov = covariables. Value of C statistic (P value) = 30.70 (0.42), df = 30
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.16
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.20
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.68
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.79
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.89
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.98
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.28
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.96
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.56
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.68
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.11
12
(X8,X2)|{Cov,X1,X6}
X7 ~ Cov+ X1+X6+X2
glmer (poisson)
||X2
=
0
0.26
13
(X8,X3)|{Cov,X1,X6}
X7 ~ Cov+ X1+X6+X3
glmer (poisson)
||X3
=
0
0.59
14
(X8,X4)|{Cov,X1,X6}
X7 ~ Cov+ X1+X6+X4
glmer (poisson)
||X4
=
0
0.02
15
(X8,X5)|{Cov,X1,X6}
X7 ~ Cov+ X1+X6+X5
glmer (poisson)
||X5
=
0
0.43

52
Table S5. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for organic matter decomposition. Value of C statistic (P value) = 30.79 (0.42), df = 30. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.15
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.36
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.51
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.84
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.12
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.48
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.10
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.09
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.57
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.45
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.33
12
(X9,X3)|{Cov,X1,X2,X7}
X9 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X7+X3
lmer
||X3
=
0
0.94
13
(X9,X4)|{Cov,X1,X2,X7}
X9 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X7+X4
lmer
||X4
=
0
0.84
14
(X9,X5)|{Cov,X1,X2,X7}
X9 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X7+X5
lmer
||X5
=
0
0.89
15
(X9,X6)|{Cov,X1,X2,X7}
X9 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X7+X6
lmer
||X6
=
0
0.22

53
Table S6. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for erosion control. Value of C statistic (P value) = 27.08 (0.20), df = 22. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.15
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.36
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.51
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.84
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.12
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.48
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.10
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.09
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.57
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.45
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.33

54
Table S7. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for water regulation. Value of C statistic (P value) = 22.18 (0.44), df = 22. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.06
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.41
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.79
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.93
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.65
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.82
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.08
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.40
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.62
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.74
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.09

55
Table S8. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for soil fertility. Value of C statistic (P value) = 23.30 (0.50), df = 24. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.06
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.41
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.79
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.93
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.65
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.82
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.08
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.40
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.62
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.74
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.09
12
(Y,X7|{Cov,X1,X2,X3,X4,
X5,X6}
Y ~ Cov+
X1+I(X1^2)+X2+I(X2^2)+X3+X5+I(X5^2)+X6+X4+X4:X5+
X4:X6+X7
lmer
||X7
=
0
0.57

56
Table S9. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for aboveground plant biomass and its temporal stability. Value of C statistic (P value) = 30.30 (0.44), df = 30. Remainder of
legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.16
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.20
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.68
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.79
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.89
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.98
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.28
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.96
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.56
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.68
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.11
12
(X8,X2)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X2
glmer (poisson)
||X2
=
0
0.26
13
(X8,X3)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X3
glmer (poisson)
||X3
=
0
0.59
14
(X8,X4)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X4
glmer (poisson)
||X4
=
0
0.02
15
(X8,X5)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X5
glmer (poisson)
||X5
=
0
0.43

57
Table S10. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for wood quantity. Value of C statistic (P value) = 24.48 (0.43), df = 24. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.06
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.43
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.79
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.93
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.65
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.82
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.08
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.40
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.62
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.75
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.09
12
(Y,X6)|{Cov,X1,X2,X3,X4,X5,X7}
Y ~Cov+X1+I(X1^2)+X2+I(X2^2)+X3
+X5+X7+X4+X4:X5+X4:X7+X6+I(X6^2)
lmer
||X6
=
0
0.31

58
Table S11. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for forage quantity. Value of C statistic (P value) = 29.46 (0.49), df = 30. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.06
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.41
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.78
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.93
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.65
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.82
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.08
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.40
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.62
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.74
11
(X7,X6)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.09
12
(Y,X1)|{Cov,X4,X5,X7}
Y ~ Cov+ X4+X5+X7+X1
lmer
||X1
=
0
0.50
13
(Y,X1)|{Cov,X4,X5,X7}
Y ~ Cov+ X4+X5+X7+X2
lmer
||X2
=
0
0.21
14
(Y,X1)|{Cov,X4,X5,X7}
Y ~ Cov+ X4+X5+X7+X3
lmer
||X3
=
0
0.40
15
(Y,X1)|{Cov,X4,X5,X7}
Y ~ Cov+ X4+X5+X7+X6
lmer
||X6
=
0
0.60

59
Table S12. Conditional independence claims applied in the different hypotheses of the d-sep model implied by the hypothesized path
models for forage quality. Value of C statistic (P value) = 32.45 (0.54), df = 34. Remainder of legend as in table S4.
Link
D-sep independence claims
Formula
Model
H0
P value
1
(X3,X2)|{Cov}
X3 ~ Cov + X2
lmer
||X2
=
0
0.16
2
(X4,X1)|{Cov}
X4 ~ Cov + X1
lmer
||X1
=
0
0.20
3
(X4,X2)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.68
4
(X4,X3)|{Cov}
X4 ~ Cov + X3
lmer
||X3
=
0
0.79
5
(X5,X3)|{Cov,X1,X2}
X5 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3
lmer
||X3
=
0
0.89
6
(X6,X3)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X3
lmer
||X3
=
0
0.98
7
(X5,X4)|{Cov,X1,X2}
X5 ~Cov+ X1+I(X1^2)+X2+I(X2^2)+X4
lmer
||X4
=
0
0.28
8
(X6,X4)|{Cov,X1,X2,X5}
X6 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X5+X4
lmer
||X4
=
0
0.96
9
(X7,X4)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X4
lmer
||X4
=
0
0.56
10
(X7,X5)|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X5
lmer
||X5
=
0
0.68
11
(X7,X6|{Cov,X1,X2,X3}
X7 ~ Cov+ X1+I(X1^2)+X2+I(X2^2)+X3+X6
lmer
||X6
=
0
0.11
12
(X8,X2)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X2
glmer
(poisson)
||X2
=
0
0.26
13
(X8,X3)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X3
glmer
(poisson)
||X3
=
0
0.59
14
(X8,X4)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X4
glmer
(poisson)
||X4
=
0
0.02
15
(X8,X5)|{Cov,X1,X6}
X8 ~ Cov+ X1+X6+X5
glmer
(poisson)
||X5
=
0
0.43
16
(Y,X3)|{Cov,X1,X2,X4,X5,X7,X8}
Y ~ Cov+ X1+X2+X5+X7+X8+X4+X4:X5+X4:X8+X3
lmer
||X3
=
0
0.66
17
(Y,X6)|{Cov,X1,X2,X4,X5,X7,X8}
Y ~ Cov+ X1+X2+X5+X7+X8+X4+X4:X5+X4:X8+X3
lmer
||X6
=
0
0.52

60
Table S13. Results of the model selection procedure for regulating ecosystem services using site as a random effect (random intercept,
1|site). The best models for each ecosystem service and biodiversity proxy are shown. We indicate marginal and conditional R², the
number of observations (n), predictor estimates, standard errors and P values, the number of times each predictor was selected in the
set of best models (n), predictor importance based on sum of weights (Imp.), variance inflation factors (VIF), and the results of Moran
tests for spatial autocorrelation. These tests were performed with the residuals of the models at different spatial scales (using the 10,
20, and 50 closest plots); their results show no evidence for spatial autocorrelation. The VIF values obtained were below 10 in all
cases, hence multicollinearity was not problematic (269). pH = soil pH, and Sand = soil sand content. Results of the model selection
procedure for regulating ecosystem services using grazing nested within site as a random effect (random intercept, Grazing|site) are
available in table S16. Results of model preselection based on AIC are available on table S25.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.136 ± 0.046 0.003 1.42 0.082 ± 0.031 0.008 1.41 0.014 ± 0.013 0.261 1.32 -0.009 ± 0.013 0.476 1.42
Longitude (cos) 0.026 ± 0.042 0.547 1.20 -0.008 ± 0.029 0.772 1.30 0.007 ± 0.012 0.547 1.22 -0.010 ± 0.011 0.354 1.15
Longitude (sin) -0.018 ± 0.046 0.699 1.33 0.053 ± 0.031 0.083 1.44 0.028 ± 0.012 0.025 1.37 0.013 ± 0.012 0.287 1.30
Elevation -0.349 ± 0.048 <0.001 1.55 -0.187 ± 0.033 <0.001 1.79 - 0.008 ± 0.013 0.555 1.55 -0.038 ± 0.012 0.002 1.55
Slope 0.045 ± 0.030 0.130 1.18 0.012 ± 0.022 0.584 1.24 0.009 ± 0.007 0.186 1.16 0.004 ± 0.007 0.542 1.13
Mean annual precipitation (MAP) 0.398 ± 0.055 <0.001 6 1.00 2.01 0.164 ± 0.040 <0.001 4 1.00 2.97 0.055 ± 0.017 <0.001 6 1.00 2.33 0.048 ± 0.013 <0.001 15 1.00 2.00
MAP² -0.067 ± 0.029 0.023 6 1.00 1.32 -0.029 ± 0.022 0.181 1 0.28 1.75 -0.017 ± 0.008 0.038 5 0.89 1.68 -0.012 ± 0.008 0.118 8 0.54 1.40
Mean annual temperature (MAT) -0.448 ± 0.064 <0.001 6 1.00 2.86 - 0.317 ± 0.046 <0.001 4 1.00 3.17 - 0.046 ± 0.018 0.013 6 1.00 2.85 -0.064 ± 0.014 <0.001 15 1.00 2.80
MAT² -0.252 ± 0.044 <0.001 6 1.00 2.49 -0.160 ± 0.033 <0.001 4 1.00 2.98 -0.039 ± 0.013 0.002 6 1.00 2.64 0.010 ± 0.009 0.286 3 0.18 2.34
Rainfall seasonali ty (RASE) 0.214 ± 0.052 <0.001 6 1.00 1.96 0.132 ± 0.040 <0.001 4 1.00 2.42 0.041 ± 0.016 0.013 6 1.00 2.33 0.012 ± 0.012 0.327 3 0.17 2.00
pH -0.099 ± 0.046 0.032 6 1.00 1.95 -0.099 ± 0.037 0.008 4 1.00 2.72 -0.023 ± 0.012 0.051 5 0.89 1.90 0.000 ± 0.011 0.992 4 0.22 1.75
pH² -0.038 ± 0.024 0.111 4 0.62 1.29 -0.061 ± 0.023 0.008 4 1.00 1.62 -0.011 ± 0.007 0.093 3 0.53 1.31 -0.010 ± 0.005 0.074 4 0.22 1.19
Sand content -0.337 ± 0.037 <0.001 6 1.00 1.35 -0.179 ± 0.026 <0.001 4 1.00 1.41 -0.046 ± 0.009 <0.001 6 1.00 1.24 -0.114 ± 0.009 <0.001 15 1.00 1.28
Plant richness 0.177 ± 0.037 <0.001 6 1.00 1.36 0.085 ± 0.027 0.002 4 1.00 1.64 0.023 ± 0.008 0.004 6 1.00 1.33 0.005 ± 0.008 0.544 15 1.00 1.29
Herbivore richness 0.065 ± 0.025 0.011 6 1.00 1.16
Belowground diversi ty 0.062 ± 0.020 0.002 4 1.00 1.28
Grazing presure (Graz) 0.011 ± 0.015 0.474 6 1.00 1.11 0.031 ± 0.012 0.010 4 1.00 1.05 - 0.009 ± 0.003 0.003 6 1.00 1.07 -0.005 ± 0.003 0.141 15 1.00 1.05
Graz × MAP 0.010 ± 0.013 0.405 1 0.16 1.12
Graz × MAT -0.034 ± 0.015 0.024 6 1.00 1.25 -0.026 ± 0.013 0.048 3 0.82 1.09 -0.007 ± 0.003 0.040 6 1.00 1.04 0.004 ± 0.003 0.232 4 0.25 1.08
Graz × RASE -0.027 ± 0.014 0.059 4 0.62 1.09
Graz × pH -0.010 ± 0.016 0.560 1 0.10 1.22
Graz × Sand content -0.010 ± 0.015 0.492 1 0.10 1.12 -0.004 ± 0.003 0.237 2 0.29 1.07 0.002 ± 0.003 0.518 2 0.10 1.07
Graz × Plant richness -0.011 ± 0.004 0.003 15 1.00 1.02
Graz × Herbivore richness
Graz × Belowground dive rsity
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.93
Moran test: n = 10, p = 0.99; n = 20, p = 0.98; n = 50, p = 0.87
n = 300
n = 242
n = 242
Moran test: n = 10, p = 0.98; n = 20, p = 0.91; n = 50, p = 0.79
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.91
n = 317
Water regu lation
R²c = 0.91
R²m = 0.63
R²c = 0.92
R²m = 0.53
Erosion con trol
Soil carb on storage
Organic mat ter decomposition
R²m = 0.77
R²c = 0.94
R²m = 0.75
R²c = 0.89

61
Table S14. Results of the model selection procedure for supporting ecosystem services using site as a random effect (random
intercept, 1|site). The best models for each ecosystem service and biodiversity proxy are shown. See table S17 for model results using
grazing pressure nested within site (random slope and intercept, grazing|site). Plant biomass & stability = aboveground plant biomass
and its temporal stability. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.045 ± 0.013 0.001 1.37 -0.014 ± 0.026 0.589 1.35
Longitude (cos) -0.014 ± 0.012 0.259 1.17 0.010 ± 0.024 0.672 1.12
Longitude (sin) -0.006 ± 0.014 0.642 1.32 0.008 ± 0.025 0.763 1.29
Elevation 0.004 ± 0.014 0.766 1.44 -0.099 ± 0.026 <0.001 1.48
Slope -0.009 ± 0.007 0.216 1.18 0.003 ± 0.013 0.819 1.14
Mean annual precipitation (MAP) 0.033 ± 0.014 0.018 21 1.00 1.81 0.132 ± 0.029 <0.001 6 1.00 1.84
MAP² 1.35 -0.033 ± 0.015 0.030 6 1.00 1.47
Mean annual temperature (MAT) 0.028 ± 0.019 0.133 21 1.00 2.67 -0.171 ± 0.036 <0.001 6 1.00 2.69
MAT² -0.065 ± 0.013 <0.001 21 1.00 2.31 -0.071 ± 0.024 0.003 6 1.00 2.25
Rainfall seasonality (RASE) 0.025 ± 0.015 0.104 16 0.78 1.92 0.083 ± 0.030 0.006 6 1.00 1.91
pH -0.068 ± 0.011 <0.001 21 1.00 1.70 0.043 ± 0.020 0.028 6 1.00 1.57
pH² 0.014 ± 0.005 0.009 21 1.00 1.22 -0.023 ± 0.010 0.015 6 1.00 1.17
Sand content ± -0.206 ± 0.017 <0.001 6 1.00 1.24
Plant richness 0.020 ± 0.009 0.026 21 1.00 1.25 0.015 ± 0.015 0.305 6 0.15 1.23
Herbivore richness 0.013 ± 0.006 0.027 20 0.97 1.21
Belowground diversity
Grazing presure (Graz) -0.001 ± 0.003 0.843 19 0.92 1.20 0.016 ± 0.005 0.003 6 1.00 1.05
Graz × MAP 0.003 0.003 0.357 1 0.03 1.55 0.008 ± 0.006 0.137 1 0.16 1.67
Graz × MAT -0.005 ± 0.003 0.120 9 0.44 1.29 -0.006 ± 0.006 0.356 1 0.14 1.24
Graz × RASE 0.006 ± 0.003 0.074 10 0.51 1.16 -0.004 ± 0.005 0.503 1 0.11 1.11
Graz × pH 0.004 ± 0.003 0.281 2 0.07 1.73 -0.011 ± 0.006 0.064 4 0.68 1.82
Graz × Sand content -0.014 ± 0.006 0.014 6 1.00 1.28
Graz × Plant richness 0.006 ± 0.004 0.110 11 0.53 1.20
Graz × Herbivore richness 0.006 ± 0.003 0.059 15 0.73 1.17
Graz × Belowground diversity
Plant biomass & stability
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.93
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.87
n = 296
n = 320
Soil fertility
R²m = 0.56
R²c = 0.92
R²m = 0.62
R²c = 0.95

62
Table S15. Results of the model selection procedure for provisioning ecosystem services using site as a random effect (random
intercept, 1|site). The best models for each ecosystem service and biodiversity proxy are shown. See table S18 for model results using
grazing pressure nested within site (random slope and intercept, grazing|site). Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.033 ± 0.111 0.767 1.40 0.096 ± 0.064 0.135 1.33 0.331 ± 0.224 0.141 1.38
Longitude (cos) 0.154 ± 0.106 0.147 1.16 -0.005 ± 0.056 0.930 1.11 -0.009 ± 0.203 0.966 1.13
Longitude (sin) 0.026 ± 0.107 0.811 1.30 0.032 ± 0.063 0.612 1.32 -0.140 ± 0.216 0.520 1.29
Elevation 0.036 ± 0.111 0.746 1.55 0.059 ± 0.060 0.329 1.30 -0.182 ± 0.229 0.428 1.50
Slope 0.111 ± 0.074 0.136 1.12 0.000 ± 0.030 0.992 1.15 0.099 ± 0.122 0.417 1.13
Mean annual precipitation (MAP) -0.055 ± 0.100 0.585 1 0.07 1.61 -0.189 ± 0.061 0.002 9 1.00 1.35 0.797 ± 0.238 0.001 12 1.00 1.86
MAP² 0.057 ± 0.035 0.107 5 0.58 1.41 -0.359 ± 0.135 0.008 12 1.00 1.40
Mean annual temperature (MAT) -0.139 ± 0.130 0.285 2 0.19 2.67 -0.123 ± 0.065 0.061 7 0.79 1.85 0.240 ± 0.308 0.439 12 1.00 2.63
MAT² -0.130 ± 0.083 0.119 1 0.10 2.27 -0.037 ± 0.044 0.404 2 0.17 1.36 -0.553 ± 0.211 0.009 12 1.00 2.21
Rainfall seasonal ity (RASE) -0.086 ± 0.102 0.402 1 0.09 1.92 0.497 ± 0.256 0.054 11 0.93 1.92
pH -0.047 ± 0.091 0.609 1 0.07 1.82 -0.218 ± 0.182 0.233 5 0.34 1.64
pH²
Sand content 0.162 ± 0.088 0.067 8 0.81 1.26 0.064 ± 0.040 0.116 9 1.00 1.21 0.112 ± 0.153 0.466 9 0.76 1.25
Plant richness 0.486 ± 0.083 <0.001 10 1.00 1.33 0.146 ± 0.037 <0.001 9 1.00 1.20 0.275 ± 0.141 0.052 12 1.00 1.26
Herbivore richness 0.012 ± 0.026 0.650 9 1.00 1.17
Belowground dive rsity
Grazing presure (Graz) -0.254 ± 0.035 <0.001 10 1.00 1.02 -0.044 ± 0.014 0.002 9 1.00 1.14 -0.106 ± 0.053 0.045 12 1.00 1.02
Graz × MAP -0.009 ± 0.015 0.559 1 0.08 1.12 0.067 ± 0.059 0.259 4 0.26 1.17
Graz × MAT
Graz × RASE 0.084 ± 0.056 0.134 6 0.49 1.09
Graz × pH
Graz × Sand content -0.016 ± 0.036 0.662 1 0.07 1.02 -0.031 ± 0.014 0.025 9 1.00 1.15 0.124 ± 0.054 0.023 9 0.76 1.07
Graz × Plant richness -0.041 ± 0.038 0.275 2 0.19 1.01 -0.012 ± 0.015 0.423 2 0.17 1.11 0.196 ± 0.059 <0.001 12 1.00 1.16
Graz × Herbivore richness -0.035 ± 0.014 0.010 9 1.00 1.14
Graz × Belowground dive rsity
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.91
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.89
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.87
n = 326
n = 277
Wood quantity
R²m = 0.28
R²c = 0.86
n = 326
Forage quan tity
Forage qual ity
R²m = 0.27
R²c = 0.77
R²m = 0.23
R²c = 0.89

63
Table S16. Results of the model selection procedure for regulating ecosystem services using grazing pressure nested within site
(random slope and intercept, grazing|site). The best models for each ecosystem service and biodiversity proxy are shown. Results of
model preselection based on AIC are available on table S26. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.134 ± 0.046 0.004 1.42 0.083 ± 0.030 0.007 1.40 0.016 ± 0.012 0.202 1.35 -0.008 ± 0.012 0.538 1.45
Longitude (cos) 0.024 ± 0.042 0.572 1.20 -0.010 ± 0.029 0.737 1.30 0.009 ± 0.011 0.440 1.22 -0.011 ± 0.011 0.327 1.17
Longitude (sin) -0.027 ± 0.046 0.556 1.33 0.054 ± 0.030 0.079 1.45 0.032 ± 0.012 0.008 1.37 0.012 ± 0.012 0.311 1.31
Elevation -0.348 ± 0.048 <0.001 1.54 0.015 ± 0.021 0.473 1.83 0.010 ± 0.007 0.141 1.55 0.003 ± 0.007 0.697 1.64
Slope 0.045 ± 0.030 0.133 1.17 -0.183 ± 0.033 <0.001 1.25 - 0.009 ± 0.012 0.474 1.15 -0.038 ± 0.012 0.002 1.15
Mean annual precipitation (MAP) 0.396 ± 0.055 <0.001 9 1.00 2.06 0.167 ± 0.042 <0.001 4 1.00 2.95 0.054 ± 0.016 0.001 14 1.00 2.33 0.049 ± 0.013 <0.001 15 1.00 2.08
MAP² -0.071 ± 0.029 0.015 9 1.00 1.35 -0.031 ± 0.021 0.150 2 0.45 1.72 -0.015 ± 0.008 0.055 14 1.00 1.70 - 0.013 ± 0.007 0.093 9 0.62 1.35
Mean annual temperature (MAT) -0.448 ± 0.063 <0.001 9 1.00 2.90 -0.311 ± 0.046 <0.001 4 1.00 3.15 -0.049 ± 0.018 0.007 14 1.00 2.94 -0.062 ± 0.014 <0.001 5 0.29 2.89
MAT² -0.251 ± 0.044 <0.001 9 1.00 2.50 -0.155 ± 0.033 <0.001 4 1.00 2.97 -0.040 ± 0.012 0.001 14 1.00 2.67 0.012 ± 0.010 0.205 15 1.00 2.41
Rainfall seasonali ty (RASE) 0.216 ± 0.052 <0.001 9 1.00 1.98 0.126 ± 0.040 0.002 4 1.00 2.40 0.041 ± 0.016 0.011 14 1.00 2.35 0.013 ± 0.012 0.277 3 0.17 1.97
pH -0.100 ± 0.046 0.029 9 1.00 1.95 -0.098 ± 0.037 0.009 4 1.00 2.70 -0.022 ± 0.011 0.051 14 1.00 1.91 0.002 ± 0.011 0.888 6 0.34 1.90
pH² -0.039 ± 0.024 0.101 6 0.64 1.30 -0.056 ± 0.023 0.015 4 1.00 1.56 -0.011 ± 0.007 0.087 7 0.54 1.34 -0.011 ± 0.006 0.050 6 0.34 1.20
Sand content -0.337 ± 0.038 <0.001 9 1.00 1.35 -0.183 ± 0.026 <0.001 4 1.00 1.42 -0.044 ± 0.009 <0.001 14 1.00 1.28 -0.113 ± 0.009 <0.001 15 1.00 1.35
Plant richness 0.176 ± 0.037 <0.001 9 1.00 1.37 0.086 ± 0.027 0.001 4 1.00 1.66 0.024 ± 0.008 0.003 14 1.00 1.34 0.006 ± 0.008 0.477 15 1.00 1.36
Herbivore richness 0.059 ± 0.026 0.022 9 1.00 1.14
Belowground diversi ty 0.058 ± 0.020 0.003 4 1.00 1.25
Grazing presure (Graz) 0.011 ± 0.016 0.479 9 1.00 1.10 0.032 ± 0.012 0.008 4 1.00 1.04 -0.009 ± 0.003 0.005 14 1.00 1.06 -0.004 ± 0.003 0.178 15 1.00 1.04
Graz × MAP
Graz × MAT -0.033 ± 0.016 0.043 7 0.84 1.26 -0.027 ± 0.013 0.048 2 0.68 1.04 - 0.006 ± 0.004 0.080 8 0.62 1.12 0.004 ± 0.003 0.263 3 0.18 1.11
Graz × RASE -0.029 ± 0.016 0.068 7 0.77 1.10
Graz × pH -0.014 ± 0.017 0.434 1 0.08 1.19
Graz × Sand content -0.017 ± 0.017 0.313 3 0.23 1.14 -0.005 ± 0.003 0.128 8 0.53 1.08 0.002 ± 0.003 0.606 1 0.04 1.13
Graz × Plant richness -0.011 ± 0.004 0.003 15 1.00 1.05
Graz × Herbivore richness
Graz × Belowground dive rsity
Moran test: n = 10, p = 0.99; n = 20, p = 0.98; n = 50, p = 0.87
Moran test: n = 10, p = 0.97; n = 20, p = 0.90; n = 50, p = 0.82
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.91
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.91
R²c = 0.91
R²m = 0.63
R²c = 0.92
n = 300
n = 242
n = 242
n = 317
R²m = 0.77
R²c = 0.94
R²m = 0.75
R²c = 0.89
R²m = 0.53
Soil carb on storage
Organic mat ter decomposition
Erosion con trol
Water regu lation

64
Table S17. Results of the model selection procedure for supporting ecosystem services using grazing pressure nested within site
(random slope and intercept, grazing|site). The best models for each ecosystem service and biodiversity proxy are shown. Results of
model preselection based on AIC are available on table S26. Plant biomass & stability = aboveground plant biomass and its temporal
stability. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.042 ± 0.014 0.002 1.36 -0.018 ± 0.026 0.499 1.39
Longitude (cos) -0.015 ± 0.013 0.238 1.17 0.015 ± 0.023 0.506 1.09
Longitude (sin) -0.006 ± 0.014 0.668 1.32 -0.002 ± 0.025 0.942 1.29
Elevation 0.006 ± 0.014 0.691 1.45 -0.106 ± 0.025 <0.001 1.43
Slope -0.009 ± 0.007 0.219 1.19 0.003 ± 0.013 0.834 1.14
Mean annual precipitation (MAP) 0.035 ± 0.014 0.012 13 1.00 1.86 0.133 ± 0.028 <0.001 3 1.00 1.92
MAP² -0.006 ± 0.008 0.433 1 0.06 1.42 -0.036 ± 0.015 0.016 3 1.00 1.42
Mean annual temperature (MAT) 0.029 ± 0.019 0.133 13 1.00 2.67 -0.179 ± 0.036 <0.001 3 1.00 2.86
MAT² -0.063 ± 0.013 <0.001 13 1.00 2.29 -0.075 ± 0.024 0.002 3 1.00 2.33
Rainfall seasonality (RASE) 0.027 ± 0.015 0.079 9 0.71 1.92 0.087 ± 0.030 0.004 3 1.00 1.96
pH -0.065 ± 0.011 <0.001 13 1.00 1.66 0.043 ± 0.020 0.030 3 1.00 1.72
pH² 0.012 ± 0.005 0.022 13 1.00 1.23 -0.023 ± 0.010 0.020 3 1.00 1.19
Sand content -0.195 ± 0.017 <0.001 3 1.00 1.29
Plant richness 0.019 ± 0.009 0.030 13 1.00 1.24
Herbivore richness 0.012 ± 0.006 0.028 11 0.87 1.16
Belowground diversity
Grazing presure (Graz) -0.001 ± 0.004 0.859 11 0.82 1.15 0.018 ± 0.006 0.004 3 1.00 1.03
Graz × MAP
Graz × MAT -0.005 ± 0.004 0.160 3 0.24 1.27 -0.007 ± 0.007 0.339 1 0.23 1.27
Graz × RASE 0.004 ± 0.004 0.260 3 0.18 1.16 -0.007 ± 0.006 0.236 1 0.30 1.12
Graz × pH 0.003 ± 0.004 0.356 1 0.06 1.72 -0.016 ± 0.007 0.015 3 1.00 1.21
Graz × Sand content -0.020 ± 0.006 0.001 3 1.00 1.12
Graz × Plant richness 0.004 ± 0.004 0.253 3 0.18 1.20
Graz × Herbivore richness 0.007 ± 0.003 0.030 11 0.82 1.12
Graz × Belowground diversity
Soil fertility
Plant biomass & stability
n = 296
n = 320
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.88
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.92
R²m = 0.55
R²c = 0.94
R²m = 0.62
R²c = 0.95

65
Table S18. Results of the model selection procedure for provisioning ecosystem services using grazing pressure nested within site
(random slope and intercept, grazing|site). The best models for each ecosystem service and biodiversity proxy are shown. Results of
model preselection based on AIC are available on table S26. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P va lue n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.035 ± 0.112 0.756 1.40 0.096 ± 0.064 0.135 1.33 0.343 ± 0.224 0.128 1.38
Longitude (cos) 0.177 ± 0.105 0.093 1.16 0.000 ± 0.057 0.996 1.11 -0.010 ± 0.203 0.961 1.13
Longitude (sin) 0.064 ± 0.113 0.574 1.30 0.023 ± 0.063 0.718 1.31 -0.138 ± 0.216 0.526 1.29
Elevation -0.007 ± 0.115 0.951 1.53 0.067 ± 0.060 0.265 1.34 -0.193 ± 0.229 0.402 1.50
Slope 0.160 ± 0.074 0.031 1.12 0.000 ± 0.031 0.993 1.14 0.097 ± 0.121 0.425 1.13
Mean annual precipitation (MAP) -0.060 ± 0.099 0.545 1 0.07 1.62 -0.198 ± 0.062 0.002 15 1.00 1.39 0.796 ± 0.235 0.001 11 1.00 1.86
MAP² 0.060 ± 0.035 0.087 11 0.72 1.46 -0.359 ± 0.135 0.008 11 1.00 1.40
Mean annual temperature (MAT) -0.197 ± 0.132 0.139 5 0.45 2.74 -0.121 ± 0.065 0.063 11 0.77 1.88 0.253 ± 0.310 0.416 11 1.00 2.64
MAT² -0.149 ± 0.083 0.073 4 0.35 2.27 -0.041 ± 0.044 0.352 1 0.06 1.36 -0.547 ± 0.211 0.010 11 1.00 2.21
Rainfall seasonal ity (RASE) -0.098 ± 0.102 0.340 1 0.09 1.95 0.493 ± 0.257 0.056 11 1.00 1.92
pH -0.084 ± 0.096 0.380 2 0.16 1.81 -0.213 ± 0.182 0.243 4 0.29 1.64
pH²
Sand content 0.192 ± 0.091 0.035 10 0.92 1.26 0.069 ± 0.042 0.101 13 0.86 1.23 0.118 ± 0.153 0.443 8 0.75 1.26
Plant richness 0.468 ± 0.083 <0.001 11 1.00 1.36 0.143 ± 0.038 <0.001 15 1.00 1.21 0.283 ± 0.141 0.046 11 1.00 1.26
Herbivore richness 0.017 ± 0.027 0.522 12 0.83 1.14
Belowground dive rsity
Grazing presure (Graz) -0.262 ± 0.042 <0.001 11 1.00 1.01 -0.040 ± 0.016 0.015 15 1.00 1.11 -0.105 ± 0.053 0.046 11 1.00 1.02
Graz × MAP 0.066 ± 0.059 0.260 3 0.22 1.17
Graz × MAT 0.038 ± 0.044 0.386 1 0.07 1.09 0.010 ± 0.016 0.553 1 0.04 1.19
Graz × RASE 0.085 ± 0.056 0.129 5 0.46 1.09
Graz × pH
Graz × Sand content -0.030 ± 0.016 0.063 10 0.67 1.14 0.124 ± 0.054 0.022 8 0.75 1.07
Graz × Plant richness -0.036 ± 0.043 0.407 2 0.14 1.07 -0.018 ± 0.017 0.317 2 0.10 1.15 0.197 ± 0.059 0.001 11 1.00 1.16
Graz × Herbivore richness -0.036 ± 0.015 0.018 12 0.83 1.11
Graz × Belowground dive rsity
Forage quan tity
Forage qual ity
Wood quantity
R²c = 0.86
n = 326
n = 277
n = 326
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.90
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.91
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.88
R²m = 0.27
R²c = 0.83
R²m = 0.23
R²c = 0.91
R²m = 0.28

66
Table S19. Results of the model selection procedure for regulating ecosystem services using dung mass as a proxy of grazing
pressure. Results of model preselection based on AIC are available on table S27. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.148 ± 0.048 0.002 1.59 0.095 ± 0.036 0.008 1.47 0.010 ± 0.013 0.422 1.55 - 0.010 ± 0.013 0.451 1.60
Longitude (cos) 0.024 ± 0.042 0.568 1.24 0.015 ± 0.034 0.668 1.47 0.007 ± 0.011 0.534 1.21 -0.020 ± 0.011 0.063 1.16
Longitude (sin) -0.035 ± 0.045 0.439 1.26 0.007 ± 0.036 0.854 1.40 0.025 ± 0.012 0.037 1.25 0.000 ± 0.012 0.969 1.20
Elevation -0.331 ± 0.047 <0.001 1.53 -0.158 ± 0.037 <0.001 1.77 -0.009 ± 0.012 0.465 1.45 -0.039 ± 0.012 0.001 1.37
Slope 0.022 ± 0.031 0.472 1.19 -0.009 ± 0.024 0.703 1.25 0.007 ± 0.007 0.313 1.19 0.007 ± 0.008 0.378 1.16
Mean annual precipitation (MAP) 0.393 ± 0.055 <0.001 11 1.00 2.09 0.175 ± 0.044 <0.001 9 1.00 3.07 0.051 ± 0.013 <0.001 12 1.00 1.87 0.039 ± 0.012 0.002 13 1.00 2.05
MAP² -0.059 ± 0.029 0.041 10 0.93 1.37 -0.028 ± 0.024 0.238 2 0.18 1.78 -0.017 ± 0.007 0.018 12 1.00 1.45 -0.006 ± 0.007 0.379 1 0.07 1.36
Mean annual temperature (MAT) -0.392 ± 0.070 <0.001 11 1.00 3.56 -0.283 ± 0.063 <0.001 9 1.00 4.21 -0.042 ± 0.020 0.041 11 0.91 3.44 -0.064 ± 0.013 <0.001 13 1.00 1.79
MAT² -0.222 ± 0.049 <0.001 11 1.00 3.08 -0.142 ± 0.046 0.002 9 1.00 4.10 -0.025 ± 0.012 0.040 8 0.71 2.89
Rainfall seasonali ty (RASE) 0.228 ± 0.050 <0.001 11 1.00 1.83 0.119 ± 0.046 0.010 9 1.00 2.45 0.024 ± 0.013 0.065 9 0.77 1.79 0.008 ± 0.011 0.456 3 0.19 1.28
pH -0.106 ± 0.044 0.017 11 1.00 1.86 -0.080 ± 0.040 0.046 9 1.00 2.36 -0.020 ± 0.009 0.036 12 1.00 1.57 - 0.014 ± 0.011 0.219 3 0.25 1.73
pH² -0.020 ± 0.025 0.410 3 0.19 1.18 -0.048 ± 0.025 0.053 7 0.83 1.25 -0.007 ± 0.006 0.221 1 0.08 1.14
Sand content -0.371 ± 0.038 <0.001 11 1.00 1.37 -0.203 ± 0.029 <0.001 9 1.00 1.36 -0.049 ± 0.008 <0.001 12 1.00 1.30 -0.118 ± 0.010 <0.001 13 1.00 1.38
Plant richness 0.187 ± 0.038 <0.001 11 1.00 1.48 0.061 ± 0.032 0.059 7 0.81 1.78 0.022 ± 0.008 0.006 12 1.00 1.36 0.010 ± 0.009 0.301 13 1.00 1.34
Herbivore richness 0.060 ± 0.025 0.015 11 1.00 1.10
Belowground diversi ty 0.079 ± 0.024 0.001 9 1.00 1.34
Grazing presure (Graz) -0.003 ± 0.015 0.861 9 0.82 1.07 0.010 ± 0.012 0.415 4 0.44 1.05 -0.007 ± 0.003 0.021 12 1.00 1.07 0.000 ± 0.004 0.970 13 1.00 1.09
Graz × MAP 0.025 ± 0.016 0.119 5 0.45 1.97 0.003 ± 0.003 0.385 2 0.13 1.97 -0.005 ± 0.004 0.214 3 0.21 1.25
Graz × MAT -0.032 ± 0.015 0.033 9 0.82 1.25 -0.025 ± 0.013 0.052 3 0.35 1.03 0.004 ± 0.003 0.229 3 0.24 1.37 -0.007 ± 0.004 0.065 9 0.72 1.34
Graz × RASE -0.015 ± 0.015 0.326 2 0.16 1.13 -0.004 ± 0.003 0.121 5 0.41 1.17 0.006 ± 0.004 0.085 2 0.12 1.18
Graz × pH 0.017 ± 0.019 0.376 1 0.07 1.18 -0.002 ± 0.003 0.543 1 0.05 1.98
Graz × Sand content -0.013 ± 0.016 0.420 1 0.07 1.24 -0.008 ± 0.003 0.013 12 1.00 1.49 0.007 ± 0.004 0.064 8 0.67 1.35
Graz × Plant richness -0.037 ± 0.016 0.020 9 0.82 1.24 -0.020 ± 0.012 0.105 2 0.21 1.07 -0.002 ± 0.003 0.486 1 0.05 1.21 -0.011 ± 0.004 0.006 13 1.00 1.19
Graz × Herbivore richness
Graz × Belowground dive rsity
Water regu lation
R²c = 0.91
R²m = 0.70
R²c = 0.92
Soil carbo n storage
Organic mat ter decomposition
R²m = 0.79
R²c = 0.94
R²m = 0.79
R²c = 0.92
R²m = 0.54
Erosion con trol
Moran test: n = 10, p = 0.99; n = 20, p = 0.98; n = 50, p = 0.87
Moran test: n = 10, p = 0.99; n = 20, p = 0.97; n = 50, p = 0.78
n = 265
n = 183
n = 265
Moran test: n = 10, p = 0.97; n = 20, p = 0.93; n = 50, p = 0.72
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.91
n = 253

67
Table S20. Results of the model selection procedure for supporting ecosystem services using dung mass as a proxy of grazing
pressure. Results of model preselection based on AIC are available on table S27. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF
Latitude 0.037 ± 0.016 0.024 1.52 -0.016 ± 0.030 0.591 1.53
Longitude (cos) -0.019 ± 0.014 0.168 1.17 0.010 ± 0.026 0.701 1.19
Longitude (sin) -0.017 ± 0.015 0.256 1.23 -0.009 ± 0.028 0.761 1.24
Elevation 0.019 ± 0.014 0.188 1.35 -0.104 ± 0.028 <0.001 1.42
Slope -0.006 ± 0.008 0.419 1.16 0.024 ± 0.014 0.093 1.17
Mean annual precipitation (MAP) 0.046 ± 0.016 0.005 7 1.00 1.84 0.086 ± 0.027 0.001 7 1.00 1.81
MAP² -0.012 ± 0.009 0.149 3 0.43 1.48 -0.014 ± 0.016 0.365 2 0.21 1.59
Mean annual temperature (MAT) 0.054 ± 0.022 0.015 7 1.00 3.42 -0.189 ± 0.044 <0.001 7 1.00 3.38
MAT² -0.038 ± 0.015 0.009 7 1.00 2.74 -0.090 ± 0.029 0.002 7 1.00 2.78
Rainfall seasonality (RASE) 0.020 ± 0.016 0.230 2 0.30 1.71 0.091 ± 0.031 0.003 7 1.00 1.74
pH -0.059 ± 0.012 <0.001 7 1.00 1.59 0.019 ± 0.020 0.347 2 0.22 1.41
pH² 0.013 ± 0.005 0.014 7 1.00 1.11
Sand content 0.006 ± 0.010 0.526 2 0.18 1.22 -0.232 ± 0.018 <0.001 7 1.00 1.25
Plant richness 0.036 ± 0.017 0.033 7 1.00 1.22
Herbivore richness
Belowground diversity
Grazing presure (Graz) -0.002 ± 0.003 0.605 1 0.09 1.04 0.013 ± 0.006 0.026 7 1.00 1.07
Graz × MAP 0.018 ± 0.006 0.002 7 1.00 1.22
Graz × MAT 0.005 ± 0.006 0.401 1 0.11 1.32
Graz × RASE
Graz × pH
Graz × Sand content -0.010 ± 0.006 0.088 4 0.61 1.29
Graz × Plant richness -0.019 ± 0.006 0.001 7 1.00 1.14
Graz × Herbivore richness
Graz × Belowground diversity
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.99
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.88
n = 260
n = 257
Soil fertility
R²m = 0.56
R²c = 0.93
R²m = 0.65
R²c = 0.96
Aboveground plant biomass and its temporal stability

68
Table S21. Results of the model selection procedure for provisioning ecosystem services using dung mass as a proxy of grazing
pressure. Results of model preselection based on AIC are available on table S27. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VIF Est. Std Er. P value n I mp. VIF Est. Std Er. P va lue n Imp. VIF
Latitude 0.049 ± 0.119 0.683 1.17 0.135 ± 0.064 0.037 1.51 0.084 ± 0.267 0.753 1.55
Longitude (cos) 0.144 ± 0.116 0.216 1.18 -0.028 ± 0.061 0.652 1.08 0.036 ± 0.231 0.878 1.21
Longitude (sin) 0.164 ± 0.121 0.175 1.10 0.009 ± 0.064 0.890 1.21 -0.162 ± 0.250 0.520 1.25
Elevation -0.044 ± 0.122 0.718 1.30 0.082 ± 0.063 0.195 1.24 -0.069 ± 0.250 0.782 1.44
Slope 0.143 ± 0.088 0.104 1.14 0.009 ± 0.036 0.806 1.14 0.048 ± 0.141 0.735 1.13
Mean annual precipitation (MAP) -0.107 ± 0.140 0.447 11 0.92 1.85 -0.204 ± 0.065 0.002 14 1.00 1.39 0.870 ± 0.279 0.002 7 1.00 1.87
MAP² -0.114 ± 0.079 0.152 4 0.28 1.29 0.066 ± 0.038 0.084 9 0.67 1.44 -0.274 ± 0.147 0.064 5 0.76 1.43
Mean annual temperature (MAT) -0.061 ± 0.074 0.414 2 0.11 1.69 -0.074 ± 0.389 0.850 7 1.00 3.43
MAT² ± -0.778 ± 0.267 0.004 7 1.00 2.87
Rainfall season ality (RASE) 0.037 ± 0.060 0.546 1 0.05 1.24 0.656 ± 0.275 0.018 7 1.00 1.77
pH -0.194 ± 0.123 0.116 2 0.81 1.80 -0.272 ± 0.200 0.176 3 0.40 1.55
pH² 0.117 ± 0.067 0.081 1 0.33 1.13
Sand content 0.176 ± 0.102 0.087 11 0.02 1.31 0.049 ± 0.047 0.299 4 0.22 1.26 0.117 ± 0.175 0.507 1 0.10 1.27
Plant richness 0.518 ± 0.100 <0.001 16 1.00 1.29 0.169 ± 0.042 <0.001 14 1.00 1.20 0.460 ± 0.171 0.007 7 1.00 1.29
Herbivore richness -0.163 ± 0.071 0.022 16 1.00 1.10 -0.031 ± 0.030 0.314 14 1.00 1.14
Belowground dive rsity
Grazing presure (Graz) -0.102 ± 0.042 0.015 16 1.00 1.07 -0.015 ± 0.016 0.346 14 1.00 1.07 -0.063 ± 0.060 0.296 2 0.24 1.04
Graz × MAP 0.062 ± 0.041 0.134 4 0.44 1.09 0.025 ± 0.016 0.118 7 0.51 1.05
Graz × MAT
Graz × RASE
Graz × pH ± 11 0.33 1.75
Graz × Sand content
Graz × Plant richness 0.035 ± 0.043 0.416 1 0.02 1.12 0.020 ± 0.016 0.219 3 0.22 1.13
Graz × Herbivore richness - 0.070 ± 0.043 0.108 10 0.52 1.11 -0.047 ± 0.017 0.005 14 1.00 1.16
Graz × Belowground dive rsity
Wood quantity
R²m = 0.32
R²c = 0.86
n = 265
Forage quantity
Forage quality
R²m = 0.26
R²c = 0.76
R²m = 0.20
R²c = 0.88
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.90
Moran test: n = 10, p = 0.99; n = 20, p = 0.99; n = 50, p = 0.86
Moran test: n = 10, p = 0.99; n = 20, p = 0.98; n = 50, p = 0.83
n = 258
n = 245

69
Table S22. Results of the model selection procedure for regulating ecosystem services using livestock tracks as a proxy of grazing
pressure. Results of model preselection based on AIC are available on table S28. Remainder of legend as in table S13.
Est. Std Er. P value n Imp. VI F Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VIF Est. Std Er. P value n Imp. VI F
Latitude 0.165 ± 0.053 0.002 1.78 0.108 ± 0.046 0.020 1.96 0.029 ± 0.016 0.069 1.23 - 0.006 ± 0.015 0.668 1.69
Longitude (cos) 0.005 ± 0.042 0.911 1.20 -0.002 ± 0.031 0.936 1.35 -0.001 ± 0.014 0.948 1.24 -0.014 ± 0.012 0.232 1.05
Longitude (sin) -0.061 ± 0.053 0.252 1.55 -0.035 ± 0.045 0.431 1.87 -0.005 ± 0.018 0.783 1.32 -0.029 ± 0.014 0.049 1.32
Elevation -0.290 ± 0.054 <0.001 1.82 -0.098 ± 0.041 0.016 2.63 0.019 ± 0.018 0.284 1.62 -0.024 ± 0.013 0.066 1.23
Slope 0.040 ± 0.029 0.171 1.19 0.004 ± 0.025 0.873 1.34 0.011 ± 0.008 0.160 1.18 0.007 ± 0.009 0.425 1.14
Mean annual precipitation (MAP) 0.414 ± 0.060 <0.001 3 1.00 2.17 0.120 ± 0.050 0.017 7 1.00 4.03 0.035 ± 0.018 0.056 16 0.75 2.37 0.046 ± 0.017 0.006 3 1.00 2.08
MAP² -0.039 ± 0.032 0.227 1 0.29 1.38 -0.029 ± 0.025 0.251 2 0.22 2.09 -0.010 ± 0.011 0.353 2 0.06 1.63 -0.018 ± 0.009 0.038 3 1.00 1.33
Mean annual temperature (MAT) -0.310 ± 0.079 <0.001 3 1.00 3.00 -0.168 ± 0.070 0.016 5 0.72 4.12 - 0.065 ± 0.018 <0.001 3 1.00 1.84
MAT² - 0.234 ± 0.062 <0.001 3 1.00 2.17 -0.150 ± 0.054 0.006 5 0.72 3.07
Rainfall seasonali ty (RASE) 0.096 ± 0.056 0.086 3 1.00 1.75 0.118 ± 0.054 0.030 6 0.81 2.31
pH -0.084 ± 0.045 0.066 3 1.00 1.81 -0.103 ± 0.045 0.023 7 1.00 2.75 -0.033 ± 0.016 0.040 21 0.96 1.85 0.000 ± 0.013 0.970 3 1.00 1.80
pH² -0.043 ± 0.022 0.052 2 0.77 1.21 - 0.063 ± 0.031 0.042 5 0.77 1.52 -0.013 ± 0.008 0.110 10 0.47 1.14 - 0.008 ± 0.007 0.260 1 0.26 1.16
Sand content -0.364 ± 0.039 <0.001 3 1.00 1.41 -0.221 ± 0.029 <0.001 7 1.00 1.40 -0.035 ± 0.010 0.001 22 1.00 1.18 - 0.107 ± 0.011 <0.001 3 1.00 1.33
Plant richness 0.096 ± 0.038 0.012 3 1.00 1.46 0.036 ± 0.035 0.314 1 0.12 2.40 0.023 ± 0.011 0.035 19 0.87 1.50
Herbivore richness 0.076 ± 0.023 0.001 3 1.00 1.10
Belowground diversi ty 0.074 ± 0.025 0.004