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Figure S1 The relationship between native and exotic diversity at three spatial scales for 32 grassland sites from four regions.

Figure S2 Scale-dependent responses of diversity to environmental gradients in 32 grassland sites from four regions on two continents.

Figure S3 A scatter diagram showing the strength of the relationship between the average cover of exotic dominants (Table S4) vs. total native plant cover at the 32 study sites.

Table S1 List of study sites.

Table S2 Summary of regional metadata from the four study regions, representing 32 grassland sites on two continents.

Table S3 The most abundant (i.e. dominant) exotic species at each site.

Table S4 Results from ANOVAs conducted to assess the significance of the fixed effects for linear mixed effect models of introduced and native species richness and fixed effects representing climatic conditions, landscape and human influences, primary productivity and non-climatic environmental variability with random intercepts due to site.

Table S5 Regional-level comparisons of significant correlations among species pairs, within 32 grassland sites on two continents.

Table S6 Comparison of significant plot-level negative vs positive pairwise associations for native and exotic species.

Appendix S1 Additional methodological and analytical details.

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