RESULTS

All of our species success metrics were significantly related to at least four of the nine traits considered, including both above- and belowground traits (Fig. 1). The abundance measures in the grassland GPs and the occurrence in the EPs were associated with the largest number of traits (Fig. 1). The delta R2 values ranged from 0.02 for the model on occurrence frequency in the native range (i.e. the proportion of occurrences in Euro+Med) to 0.41 for the model on occurrence frequency outside their native range (i.e. the number of occurrences in GloNAF; Fig. 1; Table 1). When we reduced the models to either include only the three aboveground traits or the three best belowground traits, the variation explained by the belowground-trait models was equal or higher than the variation explained by the aboveground-trait models for all species success metrics, except frequency of occurrence in the grassland EPs (Table 1).
Root-tissue density was a significant predictor in all models (Fig. 1). Species with low root-tissue densities were consistently more successful than species with high root-tissue densities across all spatial scales considered (i.e. all linear coefficients were negative and significant; Fig. 1). For occurrence frequency outside the native range, the coefficient of the quadratic term was also significantly negative (Fig. 1), indicating that this success metric was highest for species with intermediate root-tissue densities (Fig. 1, Appendix S9).
Specific leaf area (SLA) was a significant predictor in most models, but the direction of the effect on species success changed with the spatial scale considered (Fig. 1). Occurrence frequencies outside their native range, in their native range, in Germany, and in the grassland GPs and EPs increased with SLA, and sometimes slightly decreased again at higher SLA values. However, the abundance in the GPs decreased with SLA and the abundance in the EPs was highest at intermediate SLA values, although these effects were only marginally significant (Fig. 1, Appendix S9).
Bud-bank size was also a significant predictor in most models, but its effects on species success varied with spatial scale (Fig. 1). Bud-bank size was negatively associated with occurrence frequency of species outside their native range, whereas occurrence frequencies in their native range and in Germany were lowest at intermediate bud-bank sizes (Fig. 1). However, occurrence frequencies as well as abundances in the grassland GPs and EPs increased linearly or asymptotically with bud-bank size (Fig. 1, Appendix S9).
The other traits were only significant predictors in some of the models of species success (Fig. 1). Seed weight had no significant associations with success at the larger spatial scales, but occurrence in Germany was higher for species with lower seed weights. Occurrence frequency and abundances in the GPs and EPs, on the other hand, were highest at higher seed weights (Fig. 1, Appendix S9). Maximum rooting depth was non-linearly positively associated with occurrence frequency outside the native range, and was positively associated with occurrence frequencies in the native range and Germany, but not in the EPs and GPs (Fig. 1, Appendix S9). Root-weight ratio was marginally negatively associated with occurrence frequency outside the native range, with an optimum in the mid-lower range of the trait, which was also the case for occurrence frequency in GPs and abundance in EPs (Fig. 1, Appendix S9). First-order root diameter had no significant effects on any of the occurrence frequencies, but had significant negative effects on abundance in the GPs and EPs (Fig. 1, Appendix S9). Specific root length only had a weak marginally significant effect for occurrence frequency in Germany (Fig. 1, Appendix S9).