Statistical analysis
To detect the effects of the shrub on herbaceous plants in response to increased precipitation and N enrichment, statistical analyses were conducted at three levels (species, groups of species, and community). For the RII at the community level, linear mixed effect models were carried out to detect the effect of watering and N fertilization on RII biomass and richness of the whole herbaceous community. Watering and N fertilization treatments were used as fixed variables, and block as a random variable.
At the species level, to assess the relationships between functional traits (height and LDMC) and species RII in all treatments, we conducted a redundancy analysis (RDA) using mean species RII in each of the nine treatments as dependent variable and the two functional traits (height and LDMC) as independent (constraining) variables. We excluded four species that occurred in fewer than three of the 72 plots (three watering levels × three N fertilization levels × four replications × two types of quadrats). The automatic stepwise model building method (using permutation testing with 999 steps) was used to evaluate whether the independent variable was a significant predictor. A cluster analysis (Ward’s method; Murtagh & Legendre, 2014) was then conducted to separate species into groups with similar responses to the effect of the shrub and functional trait values, according to the two rows of species RDA scores.
At the group level, we pooled species biomass values within groups and calculated the biomass in open patches and the RII biomass of each cluster group in each replicate of each of the nine treatments. Then, general linear models were performed to assess the effect of watering and N fertilization treatments on biomass in the open plots andRII biomass of each cluster group. We also used a one-way ANOVA model for testing the differences in mean height and LDMC among cluster groups of species. Species traits were not weighed by species abundances since species have been sampled in different patches within the community and abundances could vary among patches. Additionally, our goal was not to assess the community-level functional diversity but the effect of divergence in species functional traits within communities on the responses of herbaceous species to the dominant neighbour along environmental treatments.
All analyses were performed using the R software, v.3.5.1 (R Core Team, 2014). One-sample t -tests were conducted to test the significance of RII values from zero. Biomass data were log transformed since they were not normally distributed. We used the lme4 and lmerTest packages to conduct linear mixed effect model (Kuznetsova et al. , 2017), and the vegan package to conduct the RDA (Dixon et al. , 2003).