Data analysis
Linear mixed-effects models were used to investigate the effects of
aridity, grazing, haying and their interaction on plant species richness
and ecosystem functions. First, we tested the response of plant species
richness to the fixed effects of aridity (as a continuous, linear
predictor), grazing (as a binary predictor: 0 = no grazing or 1 =
grazing), and haying (as a binary predictor: 0 = no haying or 1 =
haying). These models included the two-way interactions between aridity
and grazing or haying. None of the sites had both grazing and haying,
and thus the models did not include the grazing × haying interactions. A
random intercept was included for each site. The fixed effects model
structure is shown in Table 1. Second, we tested the response of
aboveground biomass and soil organic C to these same predictors, and
also included plant species richness (continuous, linear predictor) and
its interaction with aridity as fixed effects (see model structure in
Table 1). The sites were classified into three land-use types
(exclosure, grazing, or haying), and land-use was divided into the two
factors grazing (yes or no) and haying (yes or no).
Piecewise structural equation modelling (SEM) was used to examine if
aridity and land-use affect aboveground plant biomass and SOC through
changes in plant species richness (Lefcheck 2016). SEM was performed
with the specification of a conceptual model of hypothetical
relationships, based on a priori and theoretical knowledge (Grace
2006). The initial model included the paths from aridity, grazing, and
haying to plant species richness, aboveground biomass, and SOC, and from
species richness to aboveground biomass and SOC. According to
modification indices, the correlation between grazing and haying was
added to the model. Results of linear mixed-effects models showed that
there were significant interaction effects between aridity and grazing
on species richness and between aridity and haying on aboveground
biomass. The paths from aridity × grazing to species richness and from
aridity × haying to aboveground biomass were added to the SEM model. The
path from aridity × haying to aboveground biomass was not significant,
and it was removed from the model. Grazing is binary (0 = no or 1 =
yes), haying is binary (0 = no or 1 = yes), and the aridity x grazing
interaction is the product of aridity and grazing. The Akaike
information criterion (AIC) and Shipley’s test of d -separation
were used to evaluate the fit of the models (Grace 2006; Lefcheck 2016),
and the final test of d-separation (Fisher’s C = 4.51, P =
0.11) showed a good model fit. Response variables were log transformed
to meet linear model assumptions where appropriate. Linear mixed-effects
models and SEM were conducted using the “lme” and “piecewiseSEM”
packages in R 4.0.2 (R Development Core Team 2013; Lefcheck 2016;
Pinheiro & Sarkar 2016).