Results
Two very different analytical techniques (HP and RF) to measure variable importance, but which each deal explicitly with variable intercorrelations, generally provided similar rankings of predictors (Table 1, Fig. 2A–1D and Figs. S5–S7), in contrast to regression coefficients of LMM (Table 1, Fig. 2E–1F and Fig. S8). HP and RF suggested that GDPc and HPD were the most important predictors for plants (Fig. 2A and 1C), whereas LMM suggested that HPD and area were the most influential (Fig. 2E). For birds, the variable importance techniques suggested that GDPc was the most important predictor, after controlling for sampling effort (Fig. 2B); by contrast, LMM suggested that area and HPD were more influential (Fig. 2F). The results for other taxa were similar: LMM tended to highlight the effects of area, HPD, and temperature whereas the other techniques attributed more importance to GDPc (Table S2, Figs. S5–S8).
Results for HP also showed that much of the variation explained was shared among predictors, but this differed among taxa; the individual contribution was generally higher for temperature and precipitation and lower for socioeconomic variables, latitude, and area (Fig. 2, Figs. S5 and S9). The correlations among predictors (Figs. S3 and S4) were relatively low (|r | always < 0.41), which and helped us to understand these unique contributions and the contrasting results above. Most predictors were intercorrelated but coastal (vs landlocked mainland) region, precipitation, HPD, and sampling effort had the weakest correlations and GDPc the strongest with the other predictors (Figs. S3 and S4). In agreement, beta weights were more different from zero for HPD and sampling effort (and secondarily, precipitation) in contrast to the two other techniques, whereas GDPc had beta weights closer to zero because it was more correlated to many predictors, despite having high relative importance and unique contributions (Fig. 2, Fig. S8).
HP and RF analyses including both absolute and relative measures (Fig. 3, Figs. S9–S12) suggested that human economic indicators (GDP and GDPc) are generally much more important than human population size and density to explain alien species richness. Specifically, HP indicated that, except for mammals, the total GDP of a region is more important than its human population and that GPDc is more important than human population density (Fig. 3, Fig. S9). HP also showed that absolute measures (i.e. GDP and HP) are more important than their relative counterparts (GDPc and HPD), except for mammals and birds (Fig. S9). Conditional variable importance of random forests, which are not constrained by collinearity issues, suggested that GDPc is more important than GDP to explain alien species richness (Fig. S11).
Although some independent contributions were small, most were significant for both LMM and HP analyses (Tables 1 and Fig. S2). The orderings of conditional (Fig. 2, Figs. S6 and S10) and unconditional (Figs. S7 and S11) RF measures of variable importance were similar. Climatic features differed markedly among taxa; increasing temperature is associated with greater alien richness of ants, amphibians, reptiles, birds, mammals, but has the opposite association with plants and fish; the richness of alien ants, plants, and spiders is positively related to precipitation but is not so for other taxa. Socioeconomic variables were more consistent and always displayed positive associations with richness (Fig. S12).