Linear mixed models
We used LMM, with the same design as in Dawson et al. (2017), as a
baseline for comparison and as an example of the standard analysis in
ecology and evolution (Table S1). The fixed effects were area, sampling
effort (average % native species completeness), gross domestic product
per capita (GDPc), human population density (HPD), mean annual
temperature, mean annual precipitation, and whether the region was
coastal or landlocked. The random effects consisted of the
(subcontinental) TDWG Level 2 regions, nested within TDWG continents
(random intercepts only). We inspected corrected Akaike’s Information
Criterion for all full models, and all models nested within them, to
identify the set of models with the lowest-AIC values, which were
selected for inference. Given that the AIC criterion does not inform
about the goodness of fit of the model (Mac Nally et al., 2018), we also
calculated the marginal R 2 (accounting for
fixed effects) and conditional R 2 (accounting
for both fixed and random effects) following Nakagawa & Schielzeth
(2012). Sampling effort was not included in models explaining alien
fish, reptile, and spider richness because data on native species
inventory completeness were not available for these taxonomic groups
(Dawson et al., 2017). We used the R package nlme (Pinheiro et
al., 2024) to compute the linear mixed models, and MuMIn (Bartoń,
2022) to obtain the marginal and conditionalR2 . Last, we used Pearson correlations and a
principal component analysis, using R packages FactoMineR (Lê et
al., 2008) and factoextra (Kassambara & Mundt, 2020) to examine
the correlations among the predictors and for data visualization to
further interpret the results (see correlation and principal component
analysis in Figs. S3 and S4, respectively).