Comparison between the strengths of trait dissimilarity and hierarchy on spatial patterns
As the absolute trait distances of individual traits used in this study generally had negative effects on pairwise spatial associations, which supports environmental filtering or hierarchical competition (Fig. 1d), we compared the strengths between trait hierarchy and trait dissimilarity on pairwise spatial associations by simultaneously including explanatory predictors of both absolute and hierarchical trait distances in equation (2) to distinguish these two mechanisms. For the 80 focal species in this study, we found that LA, WD, and Hmax consistently showed stronger trait hierarchy effects on pairwise spatial associations than trait dissimilarity effects for more focal species across different summary statistics and spatial scales (Fig. 3 and Fig. S2-S6). For SLA and WDMC under situations where we observed negative relationships between trait dissimilarity and spatial associations, the strengths of trait hierarchy did not vary significantly from the strengths of trait dissimilarity effects (Fig. 3 and Fig. S3, Fig. S4 and Fig. S6).
The relationship betweenthe magnitude that trait hierarchy effect outcompetes trait dissimilarity effect and the abundance of focal species
Overall, LA, WD and Hmax showed stronger trait hierarchy effects than trait dissimilarity effects on their pairwise spatial associations for the 80 focal species. For LA and WD, we observed a positive relationship between the magnitude that trait hierarchy effects outcompete trait dissimilarity effects (MHD) and the abundance of each focal species, while for the trait of Hmax, the MHD decreased with the abundance of focal species (Fig. 4).