We obtained regional species-distribution data as regional invasiveness measures, for vascular plants for 18 regions in total, on six continents (Table 1). The regions ranged from countries to whole continents (Table 1). The data were obtained largely from online national databases, floras and published literature (see Table 1). Data for the grid-cell occupancy of species in the Czech Republic were obtained from the working database CzechFlor, held at the Institute of Botany, Academy of Sciences of the Czech Republic, Průhonice. The species included in regional datasets were considered at least to be casual (sensu Richardson et al. 2000, Pyšek et al. 2004), naturalised (sensu Richardson et al. 2000, Pyšek et al. 2004) or weed/invasive species (Table 1). For Europe, and all European countries, only species introduced after AD 1500 (‘neophytes’) were included.

The number of alien species per region varied from 221 (China) to 3, 682 (North America; Table 1). There was no significant correlation between region area and the number of species included (Spearman’s ρ = -0.117, 95% CI = -0.6376, 0.4615, p = 0.644). Region areas were obtained from atlas sources. For regions with non-grid cell distribution units, atlas sources were also used to calculate the mean average area of distribution unit per region, and these values were used as a measure of resolution (Table 1). The largest region was North America (USA + Canada), which also had the coarsest resolution of distribution; the smallest of the 18 regions was New Jersey (Table 1).

Data on the number of habitats/communities and the median abundances of species within those habitats were obtained from vegetation-plot data for the Czech Republic and Montana. Both datasets used originally included native and alien plant species that were present in each plot; however, we excluded the native species for our purposes and included all aliens for Montana and all neophytes for the Czech Republic. The dataset used for the Czech Republic was from Chytrý et al. (2005); it included a stratified selection of over 20, 000 vegetation plots from the Czech National Phytosociological Database (Chytrý and Rafajová 2003: GIVD code EU-CZ-001, Dengler et al. 2011); these plots varied in size according to vegetation type (see Chytrý et al. 2005, for details) and contained species-cover records determined according to the Braun-Blanquet or Domin scale (van der Maarel 1979). These plots were classified into 32 habitat types based upon EUNIS Habitat Classification (Davies and Moss 2003; Chytrý et al. 2005). We calculated three metrics from this dataset: (i) the number of habitats occupied by a species, (ii) the average median cover of species across habitats occupied, and (iii) the maximum median habitat cover (i.e. the habitat with the highest median cover). Median covers per habitat were calculated using vegetation plots where a species was present and average median covers per habitat were calculated across habitats where a species was present. The median cover from the habitat with the highest median cover for a species was used as the maximum median cover. For Montana, data were downloaded from VegBank (http://vegbank.org/vegbank/index.jsp , accessed 03/02/2011; GIVD code NA-US-002; Dengler et al. 2011), which included 6, 251 vegetation plots (also varying in size depending on vegetation type).The same three metrics were calculated as for the Czech plot data (except ‘number of communities’ replaced ‘number of habitats’). The community data in VegBank followed definitions outlined by the guidelines for describing associations and alliances of the US National Vegetation Classification (Jennings et al. 2009). Species cover in plots was measured as percentage of total area. A total of 175 and 158 species were included in the final datasets for the Czech Republic and Montana, respectively.

The Global Compendium of Weeds is the most comprehensive list of weedy and invasive species to date (Randall 2002), and whilst it is not exhaustive, it is still global in scale, and draws on records from all six inhabited continents, and also oceanic islands. We used the GCW to generate two invasiveness measures for species present in each regional dataset. First, all references to a species were counted. Second, the number of GCW areas was counted (11 in total) within which a species was referenced as occurring. These GCW areas were Africa, Europe, North America, Central America, South America, Australasia, Central Asia, South Asia, Middle East, South-East Asia and Pacific Islands (including Hawai’i; see Table S1 in Appendix for further details; Dawson et al. 2011). Additionally, a number of references included within the GCW only record species as ‘introduced’, which may not indicate that the species has established, or is invasive. Thus, these two invasiveness measures were recalculated, including only those references explicitly referring to species that were weedy, naturalised or invasive (i.e. species were weeds, noxious or environmental weeds, naturalised, invasive alien/exotic, exotic/alien of ecological/conservation concern; these references are hereafter referred to as ‘weed only’ references). References exclusively citing weeds of agriculture were not included as ‘weed only’ references.

We used Spearman’s rank correlation to assess the association between regional distribution data and GCW invasiveness measures, because (i) we did not expect relationships to be linear and (ii) data were skewed and sometimes included outliers. Whilst Spearman’s rank correlation is robust to the presence of outliers compared to the product-moment correlation, it can still be affected by heteroscedasticity, and by outliers when they are large in number (Bin Abdullah 1990). To ensure that estimates of Spearman’s rho coefficients were robust, we used a resampling-with-replacement bootstrapping procedure (with 9999 sample replicates) in order to calculate 95% confidence intervals (bias-corrected). Confidence intervals not overlapping zero indicate that the correlation between a regional distribution and GCW invasiveness measure is significantly greater than zero. However, the numbers of species within regions are large, and the precision with which one can estimate a correlation coefficient increases with sample size. Thus, even weak correlations are likely to be estimated accurately and differ significantly from zero. Therefore, the strength of the correlations themselves is of greater relevance to this study than whether or not the correlations differ significantly from zero.

Coefficients and confidence intervals were calculated for correlations between distribution data of each region and one of the two GCW-invasiveness measures: (i) the total number of GCW references, (ii) the number of GCW areas a species was recorded in. This was repeated for (iii) the number of ‘weed only’ category references, and (iv), the number of GCW areas according to ‘weed only’ category references. In all cases, to avoid non-independence of GCW-derived invasiveness and regional distribution measures, references in the GCW from the area containing the target region considered were always excluded (see Table S1 for description of GCW areas). For example, for correlations involving the German and European regional distribution data, all references of species from Europe were excluded in the calculation of the GCW measures. Similarly, for the data from China, all references from East Asia were excluded, as were all references from North America, when Canadian provinces and USA states were analysed.

We used the random effects meta-analysis approach outlined by Gurevitch and Hedges (1999) to analyse the relationship between correlation coefficient strength and region area or resolution. A Pearson’s rank correlation test of area and resolution (both log transformed) revealed that regional areas and resolution were strongly and significantly correlated (Pearson’s R = 0.806, 95% CI = 0.531, 0.927, df = 15, P < 0.0001), and so they were considered individually. Australia was excluded from the analyses involving resolution, as the distribution units for Australia were point records.

First, we transformed Spearman’s rho coefficients (ρ) from the correlations between regional distributions and GCW measures, using Fisher’s Z transformation:

The variance associated with each Z-transformed coefficient was calculated as:

where n equals the sample size. This transformation has the benefit of stabilising the variance of the correlation coefficients, reducing heteroscedasticity. We wanted to analyse these transformed coefficients meta-analytically, and to do so, Gurevitch and Hedges (1999) recommend a random-effects approach, to account for random variation that occurs between effect sizes (transformed coefficients in this study). This requires estimation of not only within-region coefficient variances, but also between-region coefficient variances (Gurevitch and Hedges 1999). To achieve this, we ran a fixed effects linear regression model, with Z-transformed correlation coefficients as the effect sizes, and area or resolution (ln-transformed) as the explanatory variable. The between-region variance in coefficients was then extracted and added to the within-region variances (Gurevitch and Hedges 1999). The inverse of these summed within- and between-region variances was then used as weightings per region in a second linear regression model (the actual meta-analysis). Because of the relatively low sample size (17/18 regions), the second linear regression model was bootstrapped with 999 replicates (where the region coefficients were randomly sampled with replacement), and bias-corrected 95% confidence intervals were inspected to assess the significance of slopes (confidence intervals containing zero indicate that the relationship between correlation strength and region area/resolution is not significantly different from zero). This meta-analytical procedure was conducted for coefficients with each of the GCW-derived invasiveness measures per region.

One potential reason for correlation strength varying between regions could be due to the fact that smaller regions are more likely to have dissimilar, idiosyncratic sets of species compared to the larger regions. To test this, Spearman’s rho correlations were conducted between region size (area) and the proportion of species within a region with zero references from elsewhere outside the target region. A negative correlation with region area would be expected, if smaller regions tend to have more idiosyncratic species not found elsewhere. A bootstrapped, bias-corrected 95% confidence interval (9999 replicates; confidences intervals are hereafter referred to as ‘95% CI’) was used to assess significance of the correlation, as above.

For the vegetation-plot data from the Czech Republic and Montana, the same analytical procedure was used as for the individual regional-scale distribution correlations with GCW invasiveness measures. All analyses were conducted using R 2.14.0 (R Development Core Team 2011).

When all GCW references were considered, the correlation between the number of GCW references and regional distribution measures was significantly different from zero for all regions except Germany (Fig. 1). Spearman’s rho coefficients ranged from 0.091 (Germany) to 0.523 (California). Despite the significance of the correlations, all of them were far from a 1:1 relationship. Only one region (California) had a correlation strength above 0.5 with this GCW invasiveness measure; the majority of regions (13) had correlation coefficients <0.4 (Fig. 1). When the number of GCW areas recording a species was used as the GCW invasiveness measure, the majority of regions (14) had correlation coefficients slightly (but not significantly) lower than when the number of references was used (Fig. 1). When ‘weed only’ category references were considered, the correlations between the number of GCW references or GCW areas and regional distributions were similar in strength overall to those obtained when all references were considered (Fig. S2). Correlation strength was also high (>0.4) for North America and Australia (Fig. 1), which are the two regions most over-represented by references in the GCW, suggesting that the GCW is a reasonable correlate of regional alien plant distribution independently of the reference bias for these two regions. The proportion of species per region with zero references outside the target region was not significantly correlated with region area (ρ=0.170; bootstrapped, bias-corrected 95% CI= -0.4137, 0.6390).

In the meta-analyses, the strength of correlation between GCW-derived invasiveness and regional distributions was significantly and positively related to the area of the target region (Fig. 2a), when the number of references was considered (β_ln(area)=0.035, 95% CI= 0.012, 0.054). A similar significant, positive relationship with area was observed for the number of GCW areas occupied (β_ln(area)=0.041, 95% CI= 0.023, 0.059; Fig. 2a).

The strength of correlation between regional distribution and GCW invasiveness was also related to resolution of distribution units; correlation strength increased with increasing average area of distribution units (Fig. 2b). The relationship between resolution and correlation strength was similar whether the number of references (β_{ln(resolution)}=0.032, 95% CI= 0.015, 0.048) or the number of GCW areas was used (β_{ln(resolution)}=0.033, 95% CI= 0.013, 0.049; Fig. 2b). The relationships between area or resolution and correlation strength were similar when ‘weed only’ references were used, but less variation in coefficient strength was explained by area, than when all references were used (Fig. S3).

In the Czech Republic, the number of habitats occupied by a species was significantly correlated with GCW invasiveness measures, and the correlation was strongest when number of ‘weed only’ references was used; however, none of the coefficients were >0.3 (Table 2, Table S4). In comparison, correlation strength for the same set of species was always greater (although not significantly) when the number of occupied 11 × 12 km grid cells in the Czech Republic was considered (Table 2). Maximum median cover in a habitat was not significantly correlated with the number of references or the number of GCW areas occupied (Table 2). Results were similar when ‘weed only’ references were used, except average median cover in a habitat for the Czech Republic was significantly and negatively correlated (ρ= -0.15) with the number of GCW areas recording a species (Table S4).

In Montana, the number of plant communities occupied by a species was significantly correlated with the number of GCW references and the number of GCW areas (Table 2). The correlation coefficients for the same set of species were not significant when the number of Montana counties occupied was considered (Table 2). Average median cover in a community was not significantly correlated with the number of GCW references or the number of GCW areas (Table 2). The maximum median cover of species in a habitat for Montana was significantly and positively correlated (ρ= 0.19) with the number of ‘weed only’ references (Table S4).