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).