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\begin{document}

\title{Nutrients and herbivores impact grassland stability across multiple
spatial scales through different pathways}



\author[1]{Q. Q. Chen}%
\author[1]{Shaopeng Wang}%
\author[2]{Eric Seabloom}%
\author[3]{Andrew  MacDougall}%
\author[2]{Elizabeth Borer}%
\author[4]{Jonathan Bakker}%
\author[5]{Ian Donohue}%
\author[6]{Johannes Knops}%
\author[7]{John Morgan}%
\author[3]{Oliver  Carroll}%
\author[8]{Michael Crawley}%
\author[9]{Miguel Bugalho}%
\author[3]{Sally A Power}%
\author[10]{Anu Eskelinen}%
\author[11]{Risto Virtanen}%
\author[12]{Anita Risch}%
\author[13]{Martin Schuetz}%
\author[14]{Carly Stevens}%
\author[15]{Maria Caldeira}%
\author[3]{Sumanta  Bagchi}%
\author[16]{Juan Alberti}%
\author[2]{Yann Hautier}%
\affil[1]{Peking University}%
\affil[2]{University of Minnesota}%
\affil[3]{Affiliation not available}%
\affil[4]{University of Washington}%
\affil[5]{Trinity College Dublin}%
\affil[6]{Xi'an Jiaotong-Liverpool University}%
\affil[7]{La Trobe University}%
\affil[8]{Imperial College}%
\affil[9]{University of Lisbon Centre for Applied Ecology Prof Baeta Neves}%
\affil[10]{German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig}%
\affil[11]{University of Oulu}%
\affil[12]{Swiss Federal Institute for Forest Snow and Landscape Research}%
\affil[13]{Swiss Federal Institute for Forest, Snow and Landscape research}%
\affil[14]{Lancaster University}%
\affil[15]{University of Lisbon}%
\affil[16]{Instituto de Investigaciones Marinas y Costeras (IIMyC; UNMDP-CONICET)}%


\vspace{-1em}



  
  \date{May 19, 2024}


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\selectlanguage{english}
\begin{abstract}
Nutrients and herbivores have independent effects on the temporal
stability of aboveground biomass in grasslands; however, their joint
effects may not be additive and may also depend on spatial scales. In an
experiment adding nutrients and excluding herbivores in 34 globally
distributed grasslands, we found that nutrients and herbivores mainly
had additive effects. Nutrient addition consistently reduced stability
at the local and larger spatial scales (aggregated local communities),
while herbivore exclusion weakly reduced stability at these scales.
Moreover, nutrient addition reduced stability primarily by causing
changes in local community composition over time and by reducing local
species richness and evenness. In contrast, herbivore exclusion weakly
reduced stability at the larger scale mainly by decreasing asynchronous
dynamics among local communities, but also by weakly decreasing local
species richness. Our findings indicate disentangling the influences of
processes operating at different spatial scales may improve conservation
and management in stabilizing grassland biomass.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Grasslands are one of the largest terrestrial ecosystems on Earth
(Suttie et al. 2005). Aboveground biomass production is one of the
important functions in grasslands, providing many essential services to
humanity such as feed for livestock, carbon storage, and climate
mitigation (Bengtsson \emph{et al.} 2019). However, increasing nitrogen
deposition (Galloway \emph{et al.} 2004) and accelerating herbivore
extirpation (Ripple \emph{et al.} 2015; Atwood \emph{et al.} 2020) are
altering aboveground biomass and stable provision (i.e. stability) of
aboveground biomass in grasslands (Hautier \emph{et al.} 2015, 2020;
Bl\selectlanguage{ngerman}üthgen \emph{et al.} 2016; Qin \emph{et al.} 2019; Zhang \emph{et
al.}2019; Borer \emph{et al.} 2020). Stability is a multi-dimensional
concept (Donohue \emph{et al.} 2013; Arnoldi \emph{et al.} 2019); here
we examine temporal invariability, calculated as the mean of aboveground
biomass through time divided by its standard deviation in local
communities (alpha stability) and larger spatial scales (aggregated
local communities; gamma stability). Metacommunity theory clarifies that
alpha stability and asynchronous dynamics among local communities
(spatial asynchrony) determine gamma stability (Wang \& Loreau 2016;
Wang \emph{et al.} 2019).

In grassland ecosystems, nutrient addition often decreases alpha
stability (Hautier \emph{et al.} 2015; Koerner \emph{et al.} 2016;
Zhang\emph{et al.} 2016; Liu \emph{et al.} 2019), and these effects may
propagate to gamma stability (Zhang \emph{et al.} 2019; Hautier \emph{et
al.} 2020). In contrast, herbivore exclusion has been found to have
positive, neutral, or negative effects on grassland stability, depending
on the herbivore species excluded and spatial scales studied (Halpern
\emph{et al.} 2005; Hautier \emph{et al.} 2015; Blüthgen \emph{et al.}
2016; Ren \emph{et al.} 2018; Ganjurjav \emph{et al.} 2019; Qin \emph{et
al.} 2019; Saruul \emph{et al.} 2019; Liu \emph{et al.} 2021). Effects
of herbivores on stability may be more apparent at the larger spatial
scale because herbivores usually promote vegetation heterogeneity in the
landscape due to selective grazing, trampling, and localized deposition
of urine and dung (Glenn \emph{et al.} 1992; Howison \emph{et al.}
2017). However, to our knowledge, no study has investigated how
nutrients and herbivores jointly regulate grassland stability across
multiple spatial scales.

In contrast to stability, a range of studies have examined the joint
effects of nutrients and herbivores on grassland species richness
(Proulx \& Mazumder 1998; Worm \emph{et al.} 2002; Bakker \emph{et
al.}2006; Hillebrand \emph{et al.} 2007; Alberti \emph{et al.} 2010,
2011; Yang \emph{et al.} 2013; Borer \emph{et al.} 2014b; Beck \emph{et
al.}2015; Koerner \emph{et al.} 2018), community evenness
(Hillebrand\emph{et al.} 2007), community composition (Milchunas \&
Lauenroth 1993; Chase \emph{et al.} 2000; Grellmann 2002; Hartley \&
Mitchell 2005; Alberti \emph{et al.} 2017; Hodapp \emph{et al.} 2018),
and aboveground biomass (Milchunas \& Lauenroth 1993; Chase \emph{et
al.} 2000; Moran \& Scheidler 2002; Alberti \emph{et al.} 2010, 2011;
Borer \emph{et al.}2020). The majority of these studies found strong
interactive effects between nutrients and herbivores. For instance,
herbivores typically decrease species richness at low nutrients or
productivity, while increasing it at higher nutrients or productivity
(Proulx \& Mazumder 1998; Bakker \emph{et al.} 2006; Hillebrand \emph{et
al.} 2007; Borer\emph{et al.} 2014b). Herbivores also can consume extra
aboveground biomass stimulated by nutrient addition particularly when
their abundance is high (Borer \emph{et al.} 2020).

As plant diversity and biomass can impact stability indirectly and
directly, it is likely that nutrients and herbivores also jointly impact
grassland stability. For instance, nutrients or herbivores can
indirectly impact gamma stability by regulating species richness at the
local and larger spatial scales (alpha and beta diversity, respectively)
(Hautier et al. 2015; Zhang et al. 2019; Liang et al. 2020). Although
less often tested, nutrients or herbivores can also impact alpha and
gamma stability through community evenness (Grman \emph{et al.} 2010;
Liang et al. 2020) and community dissimilarity across time and space
(Koerner \emph{et al.} 2016; Zhang \emph{et al.} 2019). Our
understanding of plant diversity (including alpha and beta diversity,
evenness, community dissimilarity across time and space) on stability
are limited because different studies usually focus on different plant
diversity metrics (Grime 1998; Tilman \emph{et al.} 2006; Polley\emph{et
al.} 2007; Grman \emph{et al.} 2010; Hautier \emph{et al.}2015; Koerner
\emph{et al.} 2016). Therefore, it remains unclear which plant diversity
metrics are the major factors mediating the effects of nutrient and
herbivores on alpha and gamma stability. Assessing the relative
contribution of different facets of plant diversity to alpha and gamma
stability can deepen our understanding of the underlying mechanisms for
stability across spatial scales and help prioritize conservation
efforts.

Here, we used a globally coordinated grassland experiment, Nutrient
Network (NutNet) (Borer \emph{et al.} 2014a) to assess (1) the joint
effects of nutrient addition and herbivore exclusion on the temporal
stability of aboveground biomass at the local and larger spatial scales
(i.e. alpha and gamma stability); (2) the relative contribution of
different facets of plant diversity in mediating the responses of alpha
and gamma stability to nutrients and herbivores. We hypothesized that
(1) nutrient addition decreases alpha and gamma stability, while
herbivore exclusion worsens these decreases particularly at sites with
high grazing intensity; (2) Nutrient addition decreases gamma stability
via reducing alpha stability, which is regulated by all facets of plant
diversity. Herbivore exclusion decreases gamma stability not only via
alpha stability but also via spatial asynchrony, because herbivores
often increase vegetation heterogeneity in the landscape (i.e. spatial
community dissimilarity).

\textbf{Material and methods}

\textbf{Experimental Design}

We replicated a factorial combination of nutrient addition and herbivore
exclusion by fencing at 34 sites, which were part of the Nutrient
Network distributed experiment (NutNet; Borer et al. 2014a). These sites
were the subset of sites that met the following criteria: (1) 5 years of
post-treatment; (2) 3 blocks; (3) each block containing a factorial
design of nutrient addition and herbivore exclusion by fencing. A block
typically spreads over 320 m\textsuperscript{2}, and all three blocks
typically spread over \textgreater{}1000 m\textsuperscript{2}. These
sites spanned a broad envelope of climate and included a wide range of
grassland types such as montane, alpine, semiarid grasslands, prairies,
old fields, pastures, savanna, tundra, and shrub-steppe (Table S1).

In each block at each site, two plots were fertilized with nitrogen (N),
phosphorus (P), potassium (K), and micronutrients (Fe, S, Mg, Mn, Cu,
Zn, B, and Mo in combination). Nutrients were added annually before the
start of the growing season at rates of 10
gm\textsuperscript{-2}y\textsuperscript{-1}. N was supplied as
time-release urea ((NH\textsubscript{2})\textsubscript{2}CO) or ammonium
nitrate (NH\textsubscript{4}NO\textsubscript{3}), there were no
detectable differences between these N sources on plant biomass or
diversity (Seabloom \emph{et al.} 2015). P was supplied as triple
superphosphate
(Ca(H\textsubscript{2}PO\textsubscript{4})\textsubscript{2}), and K as
potassium sulfate (K\textsubscript{2}SO\textsubscript{4}). The
micronutrient mix was applied once at the start of the experiment at a
rate of 100 g m\textsuperscript{-2}. Two plots (one in ambient
conditions and the other receiving nutrient addition) were enclosed with
fences to test the effects of herbivore exclusion (excluding mammalian
herbivores \textgreater{} 50 g) on plant communities. Fences were around
230 cm tall, and the lower 90 cm were covered by 1cm woven wire mesh. To
further exclude digging animals such as voles, an additional 30 cm
outward-facing flange was stapled to the soil. Four strands of barbless
wire were strung at similar vertical distances above the wire mesh. Six
of the 34 sites deviated from this fence design (Table S2). Wild
herbivores such as rodents, lagomorphs, ungulates, marsupials are
present at all sites, while domestic herbivores such as sheep, yak,
goats, and cattle are also present at a few sites (Table S2). Further
details on the design are available in Borer et al. (2014b).

\textbf{Sampling protocol}

All NutNet sites followed standard sampling protocols. A 1×1m subplot
within each 5×5 m plot was permanently marked and sampled annually at
peak biomass. The number of species, species identity, and their covers
were recorded. Species cover (\%) was estimated visually for all species
in the subplots. Aboveground biomass was measured adjacent to the
permanent subplot, by clipping all aboveground biomass within two 1 ×
0.1 m strips (in total 0.2 m\textsuperscript{2}), which were moved each
year to avoid resampling the same location. For shrubs and subshrubs
occurring in strips, we collected all leaves and current year's woody
growth. Biomass was dried at 60 °C (to constant mass) before weighing to
the nearest 0.01 g. Dried biomass was multiplied by 5 to estimate grams
per square meter. At some sites with strong seasonality, cover and
biomass were recorded twice per year to include a complete list of
species and follow typical management procedures at those sites. For
those sites, the maximum cover for each species and total biomass were
used in the following analyses. The taxonomy was adjusted within sites
to ensure consistent naming over time. Specifically, when individuals
could not be identified as species, they were aggregated at the genus
level but referred to as ``species'' for simplicity.

\textbf{Grazing intensity}

Following Borer \emph{et al.} (2020) and Anderson \emph{et al.} (2018),
we quantified grazing intensity from vertebrate herbivores at each site
using a herbivore index. Specifically, herbivore species
(\textgreater{}2 kg) that consume grassland biomass were documented at
each site by site PIs, and each species was assigned an importance value
from 1 (present, but low impact and frequency) to 5 (high impact and
frequency). An index value was calculated for each site as the sum of
herbivore importance values for all herbivores.

\textbf{Plant diversity metrics} \textbf{and stability across scales}

Following Hautier et al. (2020), we treated each 1
m\textsuperscript{2}subplot as a ``community'' and the replicated
subplots within a treatment across blocks within a site as the ``larger
scale'' sensu Whittaker (1972) (see an illustration in Fig. S1). Plant
diversity metrics used in this study included alpha diversity, beta
diversity, Pielou's evenness, and community dissimilarity metrics. Alpha
diversity is the average number of species (i.e. species richness)
recorded in the three subplots in each treatment at each site. Beta
diversity is calculated as gamma diversity/alpha diversity (i.e.
multiplicative beta diversity), where gamma diversity is the total
number of species recorded in three subplots in each treatment at each
site. Pielou's evenness was calculated as H/ln (S), where H is Shannon's
diversity index, and S is alpha diversity.

We calculated community dissimilarity (temporal and spatial community
dissimilarity) using Bray--Curtis dissimilarity metrics based on cover
data. Note that some researchers also refer to temporal and spatial
community dissimilarity as temporal and spatial beta diversity (e.g.
Chalcraft \emph{et al.} 2008; Dornelas 2014). Community dissimilarity
can arise from two concurrent processes, namely abundance gradients and
balanced variation in abundance (Baselga 2017). Abundance gradients
arise from a simultaneous increase or decrease in the cover of all
species, reflecting changes in the total cover. Balanced variation
arises from replacement among species (i.e. decreases in the cover of
some species are compensated for by increases in other species),
reflecting changes in the relative cover. Temporal and spatial community
dissimilarity may impact gamma stability via alpha and spatial
asynchrony respectively, and their impact may depend on the driving
processes (see Fig. S2 for more details). Therefore, we also look at
which process is driving temporal and spatial community dissimilarity,
and their impact on alpha and gamma stability. Temporal community
dissimilarity of each treatment was calculated as dissimilarity of a
community through the 5-year experiments and averaged over 3 blocks.
Similarly, spatial community dissimilarity of each treatment was
calculated as dissimilarity of 3 blocks in each treatment each year and
averaged over the experimental years. Temporal/spatial community
dissimilarity and the partitioning of it into abundance gradients and
balanced variation were done using the function ``beta.multi.abund''
from the R package betapart with the index.family of ``Bray'' (Baselga
\& Orme 2012).

Stability at a given spatial scale was calculated as temporal
invariability: \(\frac{\mathbf{\mu}}{\mathbf{\sigma}}\) , where \selectlanguage{greek}μ \selectlanguage{english}and \selectlanguage{greek}σ \selectlanguage{english}are the mean and
standard deviation of aboveground biomass over the experimental years.
Alpha stability was the stability of aboveground biomass averaged over
three subplots in each treatment at each site; gamma stability was the
stability of total aboveground biomass in three subplots in each
treatment at each site (Wang et al. 2019; Hautier et al. 2020). Biomass
was not detrended because no clear trends were shown over the 5-year
experiment in most sites (Fig. S3). Also, previous studies using NutNet
data show that treatment effects (i.e. nutrient addition) on stability
are quantitatively the same with or without detrending (Hautier \emph{et
al.} 2020). Spatial asynchrony was calculated as 1/\selectlanguage{greek}φ, φ
\selectlanguage{english}=\(\frac{\sum_{i,j}w_{\text{ij}}}{\left(\sum_{i}\sqrt{w_{\text{ii}}}\right)^{2}}\), where w\textsubscript{ij} is the temporal
covariance of aboveground biomass between local communities i and j, and
w\textsubscript{ii} is the temporal variance of aboveground biomass of
local community i. These variables were calculated using the function
``var.partition'' (Wang\emph{et al.} 2019).

\textbf{Statistical analyses}

All the analyses were performed in R v.3.6.3 (R core team, 2020). We
used linear mixed-effects models from the R package ``nlme''
(Pinheiro\emph{et al.} 2017) to account for the nested structure of the
data. We looked at the treatment effects on each plant diversity metric
and stability using the R syntax: lme (y \textasciitilde{} nut*fen,
random= \textasciitilde{}1\textbar{}site). Alpha stability, spatial
asynchrony, and gamma stability were log-transformed to improve
normality and homogeneity of variance. To look at whether the effects of
herbivore exclusion and its interaction with nutrient addition on
stability increase as grazing intensity increases, we rerun the above
models but adding the herbivore index as a covariate in the models.

We built a structural equation model (SEM) using the function ``psem''
from the R package piecewiseSEM (Lefcheck 2016) to evaluate the direct
and indirect effects of nutrient addition, herbivore exclusion, and
their interaction on alpha and gamma stability. An initial model (Fig.
S4) was built based on prior knowledge (Grman \emph{et al.} 2010;
Wilcox\emph{et al.} 2017; Zhang \emph{et al.} 2019; Hodapp \emph{et al.}
2018; Gilbert \emph{et al.} 2020). Rationales for each link in the
initial SEM are summarized in Table S2. To fit the SEM, we used the
function ``lme'' with site as the random effect when the component
models tested only the treatment effects, and we used function ``lm''
when the component models tested the relative contribution of both
treatments and plant diversity metrics to stability to take into account
the diversity gradient among sites. Alpha stability, spatial asynchrony,
and gamma stability were log-transformed to improve normality and
homogeneity of variance. Several studies suggest that abiotic variables
such as rainfall, temperature, and soil parameters impact grassland
stability (Zelikova \emph{et al.} 2014; Garc\selectlanguage{ngerman}ía-Palacios\emph{et al.}
2018; Zhang \emph{et al.} 2018; Gilbert \emph{et al.}2020). We,
therefore, performed another SEM including temporal variability in water
balance and spatial variability in soil chemistry following Gilbert
\emph{et al.} (2020) to test the robustness of our results. See online
supplementary text for more details.

We further analyzed which component (abundance gradients or balanced
variation) of temporal community dissimilarity was more related to alpha
stability and which component of spatial community dissimilarity was
more related to spatial asynchrony. We fitted ``lm'' models where alpha
stability was the response variable, temporal community dissimilarity
(or each of its components), and its interaction with treatments as the
explanatory variables. We fitted similar models for spatial asynchrony.
We define that an effect is marginally significant when
0.05\textless{}p\textless{}0.1, while significant when p\selectlanguage{english}[?]0.05.

\textbf{Results}

Nutrient addition and herbivore exclusion had no significant interactive
effects on any variables measured except for spatial asynchrony (Fig.
1). That is, herbivore exclusion decreased spatial asynchrony under
ambient conditions but not under fertilized conditions. Although
nutrient addition and herbivore exclusion had no significant interactive
effects on gamma stability, herbivore exclusion reduced gamma stability
by 11 \% on average compared with that of the control under the ambient
conditions. Additionally, under the ambient conditions, the effects of
herbivores on spatial asynchrony and gamma stability tended to be more
apparent at sites where herbivore index was higher (Fig. S5). Nutrient
addition alone decreased alpha diversity and evenness, but it did not
affect beta diversity. Nutrient addition increased temporal community
dissimilarity by increasing temporal balanced variation and decreasing
temporal abundance gradients, whereas it decreased spatial abundance
gradients. Moreover, nutrient addition decreased alpha stability and
marginally decreased gamma stability. Similarly, herbivore exclusion
decreased alpha diversity and evenness, but it did not affect beta
diversity. Herbivore exclusion increased spatial community dissimilarity
by increasing spatial balanced variation, and it also marginally
increased temporal balanced variation. Herbivore exclusion had no
significant effects on alpha and gamma stability, but marginally reduced
spatial asynchrony (Fig. 1; see Table S3 for test statistics).

The SEM clarified the direct and indirect effects of nutrient addition,
herbivore exclusion, and their interaction on stability at the local and
larger spatial scales (Fig. 2). Nutrient addition and herbivore
exclusion alone influenced gamma stability through different pathways.
Nutrient addition decreased gamma stability by decreasing alpha
stability, but not spatial asynchrony. The negative effect of nutrient
addition on alpha stability was mediated by decreased alpha diversity,
evenness, and increased temporal community dissimilarity. Moreover,
temporal community dissimilarity was the primary factor by which
nutrient addition decreased alpha and gamma stability, contributing ca.
50 \% of the decline in stability. In contrast, herbivore exclusion
weakly decreased gamma stability by decreasing spatial asynchrony,
although it also had a weak negative effect on alpha stability by
decreasing alpha diversity (Fig. 2). A decrease in spatial asynchrony
with herbivore exclusion was counteracted by its positive interaction
with nutrient addition. Spatial asynchrony was positively correlated
with beta diversity but not with spatial community dissimilarity. The
effects of herbivore exclusion and the interactive effects of nutrient
addition and herbivore exclusion on spatial asynchrony were not mediated
by beta diversity or spatial community dissimilarity. Results were
generally robust to the inclusion of environmental factors (see
supplementary text and Fig. S6).

The variation in temporal community dissimilarity was mainly driven by
temporal balanced variation, which was negatively correlated with alpha
stability (slope and 95 \% confidence intervals (CI): -0.68, CI =
{[}-1.12, -0.24{]}; Fig. 3A). In contrast, temporal abundance gradients
only accounted for a small portion of temporal community dissimilarity
and were unrelated to alpha stability (-0.50, CI = {[}-1.78, 0.77{]}).
The variation in spatial community dissimilarity was mainly driven by
spatial balanced variation, which was unrelated with spatial asynchrony
(-0.02, CI = {[}-0.24, 0.21{]}). In contrast, spatial abundance
gradients only accounted for a small portion of spatial community
dissimilarity but were negatively correlated with spatial asynchrony
(-0.86, CI = {[}-1.71, -0.01{]}).

\textbf{Discussion}

Based on a globally coordinated experiment in grasslands, our analysis
demonstrates that (1) nutrient addition and herbivore exclusion mainly
had additive effects, with nutrient addition consistently reducing
stability at the local and larger spatial scales, while herbivore
exclusion weakly reduced stability at both scales; (2) nutrient addition
reduced stability primarily by increasing temporal community
dissimilarity and decreasing species richness and evenness. In contrast,
herbivore exclusion reduced gamma stability mainly by reducing spatial
asynchrony, but also weakly by decreasing local species richness.
Temporal and spatial community dissimilarity was mainly attributed to
balanced variation (i.e. change in relative abundance among species but
not total abundance in communities across time or space), pointing at
the importance of turnover driven by species replacement in determining
grassland stability.

In contrast to our hypothesis 1, our analysis provides weak support for
interactive effects of nutrients and herbivores on stability across
spatial scales and other plant community properties (additive for plant
diversity and stability but a synergistic effect for spatial
asynchrony). Previous analyses using different subsets of NetNut data
looking at the joint effects of nutrient and herbivores on species
richness and aboveground biomass also found weak interactive effects
(Borer \emph{et al.} 2014b, 2020). Several non-exclusive processes may
explain the lack of the interactive effects of nutrients and herbivores
found here. First, relatively low grazing intensity at many sites.
Indeed, we found that the effects of herbivores on spatial asynchrony
and gamma stability tended to be more apparent at sites with high
grazing intensity under the ambient conditions (Fig. S5). Second,
duration of the current experiment may not be long enough to capture
changes in plant communities (Chen \emph{et al.} 2019, 2020).
Borer\emph{et al} . (2020) found that the interactive effects of
nutrient addition and herbivore exclusion on aboveground biomass became
stronger using 8-10 years post-treatment data compared with those using
2-4 years post-treatment data. Third, the effects of nutrients and
herbivores on plant communities may act at different spatial scales,
where nutrient addition influences local communities and herbivores
modulate spatial heterogeneities (see next paragraph). Consistent with
previous analyses (Zhang \emph{et al.} 2019; Hautier \emph{et al.}
2020), our results show that the negative effects of nutrient addition
alone cascaded to larger spatial scales. Herbivore exclusion alone had
weak negative effects on stability at the two scales investigated.
Again, this may be due to low grazing intensity at many sites (Table
S1).

Confirming our hypothesis 2, nutrients and herbivores impacted gamma
stability via different pathways. Nutrient addition reduced alpha and
gamma stability probably because nutrient addition intensified
interspecific competition within local communities, causing a decline in
alpha diversity, a decrease in evenness, and an increase in temporal
community dissimilarity. Moreover, increased temporal community
dissimilarity contributed to decreased alpha and gamma stability as much
as the combined effects of decreasing alpha diversity and evenness. This
confirms previous results showing a stronger contribution of temporal
community dissimilarity to alpha stability compared to alpha diversity
(Koerner \emph{et al.} 2016). In contrast, herbivore exclusion weakly
decreased gamma stability primarily by decreasing spatial asynchrony,
and weakly by decreasing alpha diversity. It suggests that the effects
of herbivores may be more apparent at the larger spatial scale probably
by impacting vegetation heterogeneity, particularly in aboveground
biomass (Glenn \emph{et al.} 1992; Howison \emph{et al.} 2017). Our
results suggest that maintaining stability from nutrient addition and
herbivore exclusion in grasslands needs to focus on different processes
across spatial scales.

Additionally, nutrient addition decreased alpha and gamma stability via
increasing temporal balanced variation, while its negative effect on
temporal abundance gradients does not translate into changes in
stability. In contrast, the effects of herbivore exclusion on spatial
asynchrony and gamma stability were not related to spatial community
dissimilarity, which is consistent with previous analyses
(Wilcox\emph{et al.} 2017; Zhang \emph{et al.} 2019). Community
dissimilarity across time is commonly used as an index of compositional
stability (Hillebrand \emph{et al.} 2018; Hillebrand \& Kunze 2020;
White \emph{et al.} 2020) and higher compositional stability has been
suggested to lead to higher biomass stability (Allan \emph{et al.}
2011). Thus, the relationship between compositional stability and
biomass stability may depend on the spatial scale considered. This
necessitates looking at multidimensional stability (Donohue \emph{et
al.} 2013). As cover is usually easier to measure in the field and less
destructive compared with biomass harvesting, many researchers evaluate
stability based on total cover (i.e. mean of total cover through time
divided by its standard deviation; e.g. Post 2013; Beck \emph{et al.}
2015; Bluthgen\emph{et al.} 2016; Wilcox \emph{et al.} 2017). Our
results suggest that using cover data to calculate stability may fail to
capture changes induced by balanced variation. For instance, two
communities (in different years or places) can differ markedly in
biomass due to species replacement even when their total cover remains
the same (Fig. S2E). As a result, a cover-based metric of stability may
overestimate ecosystem stability relative to its biomass-based
counterpart (Fig. S7). That said, community dissimilarity (and its
partitioning) serves as a useful index to predict biomass stability, but
spatial scales need to be considered.

In this study, we regarded aggregated local communities within
treatments across blocks as ``larger spatial scale'' following previous
analyses (Chalcraft \emph{et al.} 2008; Wilcox \emph{et al.} 2017;
Zhang\emph{et al.} 2019; Hautier \emph{et al.} 2020). However, subplots
belonging to different treatments within blocks are closer to each other
compared with subplots belonging to the same treatments across blocks
(i.e. larger spatial scale), thus dispersal may be stronger for subplots
within blocks than the larger spatial scale used here and dispersal may
bias the results. We argue that dispersal may not influence our results
for two reasons. First, blocks typically spread within a relatively
small area at each site (around 1000 m\textsuperscript{2}), thus all
subplots within sites may be connected by dispersal (Zhang \emph{et
al.}2019). Second, we found that subplots belonging to different
treatments within blocks had relatively higher spatial community
dissimilarity (0.61 average across sites) than those belonging to the
same treatments across blocks (0.55, 0.58, 0.53, 0.57 for control,
fence, NPK, and NPK+fence). This suggests that treatments are the
dominant filter for plant community assembly.

Our results---based on 34 grasslands across four continents---advance
our knowledge in that (1) nutrients and herbivores mainly have additive
effects on stability in grasslands; (2) nutrients and herbivores impact
stability across multiple spatial scales through different pathways,
wherein turnover driven by species replacement is more important than
species richness in determining grassland stability. Our results point
to the need to reduce nitrogen deposition while preserving or
reintroducing herbivores to ensure the stable provisioning of grassland
biomass. More importantly, our results highlight that maintaining
grassland stability in the face of increasing nutrient addition and
herbivore extirpation requires a multi-scale framework to disentangle
the influences of processes operating at different scales to guide
conservation and management practices.

\textbf{Acknowledgments}

This work was supported by the National Natural Science Foundation of
China (31988102). This work was generated using data from the Nutrient
Network (http://www.nutnet.org) experiment, funded at the site-scale by
individual researchers. Coordination and data management have been
supported by funding to E. Borer and E. Seabloom from the National
Science Foundation Research Coordination Network (NSF-DEB-1042132) and
Long Term Ecological Research (NSF-DEB-1234162 and NSF-DEB-1831944 to
Cedar Creek LTER) programs, and the Institute on the Environment
(DG-0001-13). We also thank the Minnesota Supercomputer Institute for
hosting project data and the Institute on the Environment for hosting
Network meetings. Nitrogen fertilizer was donated to the Nutrient
Network by Crop Production Services, Loveland, CO. We thank Maowei Liang
for helpful discussion.

\textbf{Competing interests}

The authors declare no competing interests.

\textbf{Data availability}

Data will be made publicly available upon acceptance on the Dryad
Digital Repository.

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\textbf{Figures}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig. 1. The average response of plant communities (n = 34) to
nutrient addition, herbivore exclusion by fencing, and their
interaction.} Values show means of raw data, error bars are bootstrapped
95\% confidence interval. See Table S3 for test statistics. Asterisks
indicate significance of treatment effects: * P\textless{}0.1; **
P\textless{}0.05; *** P\textless{}0.001. TCD: temporal community
dissimilarity; TAG: temporal abundance gradients; TBV: temporal balanced
variation in abundance; SCD: spatial community dissimilarity; SAG:
spatial abundance gradients; SBV: spatial balanced variation in
abundance.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Fig. 2. Direct and indirect effects of nutrient addition,
herbivore exclusion by fencing, and their interaction on stability at
the local (i.e. alpha stability) and larger spatial scales (i.e. gamma
stability).} Model fit the data well (Fisher's C = 34.08, P = 0.368,
d.f. = 32, N = 136). Boxes represent measured variables and arrows
represent relationships among variables. The displayed numbers are
standardized path coefficients. Width of the arrows indicates the
strength of the pathways. Line color represents positive (black),
negative (red) path coefficients. Grey arrows and numbers show
correlated errors. Asterisks indicate significant paths: *
P\textless{}0.1; ** P\textless{}0.05; *** P\textless{}0.001. See Table
S4 for R\textsuperscript{2} for each component model. Alpha stability,
spatial asynchrony, and gamma stability were on the log scale to improve
normality and homogeneity of variance. TCD: temporal community
dissimilarity; SCD: spatial community dissimilarity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Fig. 3. Relationships between alpha stability and temporal
community dissimilarity and its components (A); spatial asynchrony and
spatial community dissimilarity and their components (B).} Solid lines
show significant relationships, dashed lines show non-significant
relationships. Lines are linear model fits across treatments, because
the interaction is not significant. See Table S5 for test statistics.
Different shapes represent different treatments (square:
Control.Control; circle: Control.Fenced; triangle: Fertilized.Control;
Diamond: Fertilized.Fenced). TCD: temporal community dissimilarity; TAG:
temporal abundance gradients; TBV: temporal balanced variation in
abundance; SCD: spatial community dissimilarity; SAG: spatial abundance
gradients; SBV: spatial balanced variation in abundance.

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