Figure Legends
Figure 1 . Conceptual framework to illustrate hypotheses of this study. (a) and (b) respectively show spatial associations of repulsion and attraction between two species at coarse spatial scale. (c) and (d) show the predicted relationships between pairwise spatial associations and absolute trait distance under different processes of community assembly: (c) limiting similarity, if absolute trait distance has positive effects on pairwise spatial associations; and (d) environmental filtering or hierarchical competition, if absolute trait distance has negative effects on pairwise spatial associations. In the case of (d), if absolute trait distance has stronger effects on pairwise spatial association than hierarchical trait distance, we infer that environmental filtering mainly drives the co-occurrence pattern (e); if the hierarchical trait distance has stronger effects on pairwise spatial associations than absolute trait distance, the effect of hierarchical competition is thought to drive the co-occurrence pattern (f). Abbreviation: SA= pairwise spatial associations.
Figure 2 . Effects of absolute trait distances on the pairwise spatial associations in equation 2 that only includes the absolute trait distances as explanatory predictors. The left panels show coefficients of each variable of absolute trait distances with variance. The right panels present percentages of the 80 focal species whose spatial associations are positively (brown circles), negatively (blue circles) and non-significantly (gray circles) correlated with each variable of absolute trait distances. The panels from Row 1-6 represent the results for spatial associations assessed by bivariate pair-correlation function (gij (r ), pcf) across different spatial scales at r = 5 m, 30 m and 50 m and bivariate distribution function of nearest neighbor (Dij (r )) atr = 5 m, 30 m and 50 m, respectively. Abbreviation: LA=leaf area, SLA=specific leaf area, LDMC=leaf dry matter content, WD=wood density and Hmax=maximum height, abdist means absolute trait distance.
Figure 3. Comparison between the strengths of hierarchical and absolute trait distances on spatial associations for the 80 foal species. The strengths of hierarchical and absolute trait distances were respectively given by the absolute values of the coefficients of the variables of hierarchical and absolute trait distances of different functional traits in the full model of equation 2. Each circle represents one focal species. Brown, blue and gray circles respectively represent that hierarchical trait distances had stronger, weaker and non-significantly different effects on the pairwise spatial associations relative to their corresponding absolute trait distances. The results presented here are for spatial associations assessed by bivariate pair-correlation function (gij (r ), pcf) atr =50 m.
Figure 4. The relationships between the abundance of focal species and the magnitude that the effects of trait hierarchy outcompete trait dissimilarity (MHD). MHD was given by the differences in the coefficients (absolute values) of hierarchical trait distances of each trait and their corresponding coefficients (absolute values) of absolute trait distances in the full model of equation 2. Each circle represents one focal species. Brown, blue and gray circles respectively represent that hierarchical trait distances of had stronger, weaker and non-significantly different effects on the spatial associations relative to their corresponding absolute trait distances. The results presented here are for spatial associations assessed by bivariate pair-correlation function (gij (r ), pcf) at r =50 m.
Figure 1