Model structure
Multi-level random effects models were used for all models , using the metafor package . All models had a study-level ID (a unique ID to each primary literature source), with a unique case ID nested within it (each case, regardless of study or GC, was given a unique ID) as random effects. In addition, as the biodiversity metric used in each case resulted in significantly different impacts on the effect size (although, all resulted in a negative impact, Figure S1), the biodiversity metric was used as a crossed-effect within the random effects .
For most of the models, the fixed effects were all structured similarly. For each model, the variable of interest was interacted with body size. The interaction was then tested with a Wald-Type test (‘anova’ function in metafor), and removed if p > 0.01. If the interaction was removed the singular effects were then tested, and removed if p > 0.01. Main effects were retained if the interaction was retained. All models used a compound symmetry variance structure, and were fitted with restricted maximum-likelihood.
Four broad groups of models were created. Firstly, a model was created with the six main GCs (hereafter, ‘main model’), where the six main GCs were the variable of interest, and the entire dataset was used. Secondly, using only the data for one GC at time (i.e., just data relating to climate change), a model was created where the variable of interest was the environmental stressor (Table 1; ‘environmental stressor models’). Not all data for each GC was used in the environmental stressor models, as some environmental stressors had too little to provide robust coefficients. Thirdly, to determine how responses vary across taxonomic groups, the dataset was subset to the four most represented taxonomic groups: Acari, Collembola, earthworms, and nematodes. These were not only well represented across the six GCs, but well distributed across all environmental stressors within the GCs. These four groups were then used as the variable of interest in one model (‘taxonomic model’); however, body size was not included in this model. Finally, to determine if the habitat type influenced the biodiversity response, a model was created using the main six-level GC classification, habitat type, and the interaction between the two (‘habitat model’). Model simplification occurred as previously described.