Statistical analysis
We first predicted the relative contributions of soil invertebrates and microbes across absolute latitude using weighted least square models controlled for the random effects of references. The relative contribution of microbes in each case was calculated as one minus the invertebrate contribution. We then used a natural log-transformed response ratio (LRR) to estimate invertebrate effect size of each observation (Hedges et al. 1999), viz :
\(L\text{RR}\ \)=\(\ln{(K}_{c}\)/\(K_{f})\)
where \(K_{c}\) and \(K_{f}\) are the mean decay rates under invertebrate inclusion and exclusion treatments, respectively.\(LRR>0\) indicates that soil invertebrates contribute positively to forest litter decomposition. The within-study variance (\(v_{i}\)) of each effect size was calculated as:
\begin{equation} v_{i}=\frac{S_{c}^{2}}{n_{c}K_{c}^{2}}\ +\ \frac{S_{f}^{2}}{n_{f}K_{f}^{2}}\nonumber \\ \end{equation}
where \(n_{c}\) and \(n_{f}\) are the sample sizes of invertebrate inclusion and exclusion treatments, respectively, and \(S_{c}\) and\(S_{f}\) are the standard deviations of invertebrate inclusion and exclusion treatments. We calculated the effect size and \(v_{i}\) using the ‘escalc′ function in the R package ‘metafor′ (Xu et al. 2020). We estimated missing\(S_{c}\) and \(S_{f}\) values using random number simulation (10000 repetitions) and estimated the missing\(\ v_{i}\) using the ‘impute_SD′ function in the ‘metagear′ package (Bracken & Sinclair 1992). Invertebrate contributions (%) to forest leaf litter decomposition were calculated as:
Invertebrate contribution (%) = [1 – 1/exp (\(L\text{RR}\))] × 100%
In our meta-data, a single reference usually reported multiple observations, which means the observations are nested in the reference. This nested data structure may cause non-independent response variables. Thus, we applied an inverse variance-weighted hierarchical random-effects model (rma.mv) with a random part (~ 1| reference / observation) to estimate the weighted mean effect size (LRR++) with 95% confidence intervals (Viechtbauer 2010). Confidence intervals not crossing zero indicate significant mean effect sizes. We first estimated the mean invertebrate effect sizes at spatial scales and then performed a driving factor analysis to assess the relationships between moderators and invertebrate effect sizes. For categorical moderators (i.e., region, biome, and realm), we used the hierarchical model to calculate the mean effect sizes at different levels and compared them by employing multiple comparisons using the ‘multcomp′ package (Bretz et al. 2010). For continuous moderators (i.e. termite diversity, earthworm richness, microbial biomass carbon, MAT, MAP, and soil pH), we used mixed-effects meta-regression to assess the relationships between effect sizes and moderators. We also tested the effects of decomposition duration and protocol (mesh vs. chemical) of invertebrate exclusion on invertebrate effect sizes.
We used a Q-statistic to evaluate the heterogeneity of effect sizes, which is based on a chi-squared test. Total heterogeneity (Qt) can be divided into the variance explained by the moderators (Qm) and the residual error variance (Qe). A significant Qm (P < 0.05) indicates that the moderator significantly influences effect sizes (Viechtbauer 2010). Publication bias arises from a preponderance of articles presenting ‘favorable′ results which can impact the reliability of our assessment. We tested the possibility of publication bias using a funnel plot and performed Egger’s regression test to examine, quantitatively, the funnel symmetry (Su et al. 2021). A p value greater than 0.05 for Egger’s test indicates that the result is less affected by publication bias. All analyses were performed in R 4.2.0.