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.