Structural equation model
As the same metrics are used in multiple hypotheses, we utilised a piecewise structural equation modelling approach. The ’base’ model was constructed through linear models developed from the relationships assumed in hypotheses 1-5 (Figure 2). Mean abundance was log-transformed to meet the assumptions of the linear model. We noted relationships with species richness -> synchrony, and synchrony -> community stability were non-linear, a quadratic term included in these models was significant but produced an overall model with a higher AIC and with qualitatively similar results for all other relationships. Therefore, we retain the simpler model with all relationships modelled as linear. For the models predicting species richness and abundance, it was necessary to account for other unmeasured biogeographic differences between the countries (Settele et al.2008). As categorical variables are challenging to interpret in a structural equation approach, we modelled unmeasured spatial correlation using Generalized Least Squares (GLS) with an exponential spatial correlation structure.
In addition to the base model, we included some additional correlated errors between observed variables not accounted for in the main models. Initially, we included a dependency between mean abundance and species richness due to possible differences in site quality, as it may be that high-quality sites are more species-rich and abundant than expected given climatic niche position. However, this was not significant correlation and was removed for parsimony. Tests of directed separation were then used to assess dependencies in the model (Shipley 2000). This identified five missing dependencies in the model, three of these were added as paths as they predicted one of the response variables in the model (mean niche volume -> species richness, mean niche volume -> log mean abundance, niche overlap –> log mean abundance). However, the other two relationships were fitted with correlated errors as they were not dependent variables, and were likely a statistical consequence of increases in species richness; these were that increased species richness predicted lower niche-overlap and greater niche-mismatch.
The piecewise structural model analysis was conducted using the piecewiseSEM R package (Lefcheck 2016) and the GLS was fitted using nlme (Pinheiro et al. 2019). All analyses were conducted in R 3.6.1 (R Core Development Team, 2019).