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.