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.