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).