Relationships between pairwise spatial associations and trait dissimilarity and hierarchy
The pairwise spatial associations (estimated as SES ofgij(r ) and Dij (r ), represented as zij below) was modeled as a function of trait dissimilarity and trait hierarchy between speciesi and j , in a linear mixed model using the ‘lmer’ in the R package ‘lme4’ (Bates, Mächler, Bolker, & Walker, 2015), in which the focal species were treated as random intercept allowing intercepts to vary among each focal species and we used each explanatory predictor as random slopes to evaluate the effects of each predictor on spatial associations for different focal species. The model takes the general form:
\(z_{\text{ij}}=a+a_{i}+\sum_{m=1}^{n}{\left(b_{m}\ +b_{\text{im}}\right)x_{\text{mij}}+\varepsilon_{\text{ij}}}\), (2)
where zij represents the spatial associations between species i and species j with the focal speciesi , xmij represents themth explanatory predictors of trait distance (with n predictors in total), which could either be absolute or hierarchical trait distances, a is the fixed intercept andbm is fixed slope of themth explanatory predictor for the overall regression, while ai is the random intercept for the focal species i and bim is the random slope for the mth explanatory predictor for the focal species i .
We first exclusively applied the absolute trait distances of six individual traits: LA, SLA, LDMC, WD, WDMC and Hmax in equation (2) to evaluate the effects of absolute trait distances on the pairwise spatial associations to distinguish the assembly mechanisms of limiting similarity (Fig. 1c) and environmental filtering or hierarchical completion (Fig. 1d). If absolute trait distances have positive effects on pairwise spatial associations, it suggests functionally similar species tend to be spatially repulsive and indicates the operation of competition via limiting similarity in the forest (Fig. 1c). If absolute trait distance have negative effects on pairwise spatial associations, it indicates functionally similar species tend to co-occur together, presumably caused by either environmental filtering or hierarchical competition (Fig. 1d) that needs to be further tested. In addition, we also applied absolute trait distances estimated by multiple traits separately to equation (2) to test the effects of trait dissimilarity on pairwise spatial association because of the collinearity between absolute trait distances of individual and multiple traits.
To further test the mechanisms of environmental filtering and hierarchical competition when absolute trait distances have negative effects on pairwise spatial associations (Fig. 1d), we simultaneously included variables of both absolute and hierarchical trait distances and tested the relative importance of absolute and hierarchical trait distances in explaining the pairwise spatial associations by comparing the absolute values of the coefficients of the absolute trait distances and their corresponding hierarchical trait distances for each focal species. To do this, we compared the differences in the 95% confidence intervals of the coefficients (absolute values) of each absolute trait distance and its corresponding hierarchical trait distance for each focal species and we then grouped species into three categories, which are (1) hierarchical trait distances had stronger effects, (2) absolute trait distances had stronger effects and (3) hierarchical trait distances had comparable effects to absolute trait distances.