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).