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).