Fig. 2: Standardized coefficients and relative importance of the ecological distances between recipient and donor regions on naturalization probability.
a Standardized coefficients of the linear (β₁) and quadratic (β₂) terms of ecological distances, estimated using a multivariate generalized linear mixed-effects model based on 6,931,789 observations of 11,604 alien plant species naturalized across 650 regions. Points represent the standardized coefficients for the linear and quadratic terms of each distance metric, and error bars indicate their 95% confidence intervals (from model-based standard errors); in some cases, the intervals are narrower than the symbols and thus not visible. All standardized coefficients are significantly different from zero (all P values from two-sided Wald z-tests <0.001). No adjustments for multiple comparisons were applied. b Distributions of variable relative importance for each ecological distance, calculated as the combined contributions of their linear and quadratic terms across 999 bootstrap replicates, with each replicate fitted on 5000 randomly selected observations from the complete dataset of 6,931,789 observations. Density plots (top) show the full distribution of relative importance values (%), and boxplots (bottom) show the median (center line), the upper and lower quartiles (box limits), and the largest and smallest values within 1.5× the interquartile range (whiskers); outliers are not shown. Source data are provided as a Source Data file.
