1)Analyses based on all (sub)plots
Prior to data analyses all variables were Z-score standardized to avoid
the difference in dimension among variables. To examine Questions
1~3, we explained biomass, productivity and their
stability (S_B, S_P) with two groups of variables as follows: 1)
Biodiversity, including eight variables depicting the richness, evenness
and divergence of species, functional and phylogenetic diversity, as
mentioned above; 2) Stand factors, including stand density and
DBHmax.
In addition to bivariate analyses, we used model selection based on
modified Akaike information
criterion (AICc) to obtain the most parsimonious model, so as to
identify the major factors affecting ecosystem functions and stability.
Model selection was conducted with the “dredge” function in the MuMIn
package of R, which select the optimal model based on both the lowest
AICc value and the least number of predictors (Bartoń 2016). To evaluate
the relative importance for variables retained in the models, we
calculated Chi-square values for mixed-effect models (400, 800, and 1200
m2 subplots), while F-value for models of the 2500
m2 plots. The 400, 800 and 1200 m2subplots were split from the 2500 m2 plots, and thus
were statistically not fully independent among subplots within a same
plot. Consequently, for these subplots we used mixed-effect models with
plot as a random effect, which were then submitted to the MuMIn package
for model selection. Mixed-effect model analyses were implement with the
R package “nlme”. For the 2500 m2 plots, ordinary
multiple regression was used. However, because of the limited sample
size (10 plots), a maximum of seven predictors were allowed by the model
selection procedure with the MuMIn package. As a result, we selected
five out of eight diversity indices (i.e. species richness and evenness,
PSR, PSV and Fric), which showed stronger correlations with the four
response variables, to be used in the initial models of the 2500
m2 plots (together with stand density and
DBHmax).