Meta-analysis and structural equation modelling
We tested the effects of the moderators on Hedges’ d effect sizes using
meta-regression approach (linear models), conducted using metaforpackage (version 2.1-0) (Viechtbauer, 2010) implemented in R environment
(R Development Core Team, 2019). Prior to the analyses, we inspected
outliers through diagnostic plots (Cook’s distance). We also visually
inspected normality of the residuals using normal quantile–quantile
(Q–Q) plots; our models presented appropriate behaviour in terms of
residuals and outliers. Overall effect size was obtained through
random-effects models, and the moderators were examined through
mixed-effects models (Viechtbauer, 2010). Such mixed-effect models were
obtained using a restricted maximum likelihood (REML) estimator,
assuming a random variation among replicates within a treatment (control
or experimental), and fixed variation among treatments. The moderator
effects were estimated using Cochran’s Q-test with model fitting throughmods argument to ignore the intercept and rma function
(Viechtbauer, 2010). Effect sizes were considered statistically
significant if their 95% confidence intervals did not overlap with 0.
Piecewise structural equation models (pSEM ) were used to test
direct and indirect effects of latitude and underlying climatic
components (PC1temperature and
PCIprecipitation) (Romero et al ., 2018) on the
Hedges’ d effect size for predators and herbivores; for this, we used
the piecewiseSEM package in R (Lefcheck, 2016), and evaluated
model fits using Shipley’s test of d-separation through Fisher’s C
statistics (Lefcheck, 2016).