2.4 Statistical analyses
We performed two main analyses in this study. First, one-way ANOVA combined with a multiple comparisons test (least significant differences, LSD) was used to test the differences in the fraction of total plant biomass allocated to shoots (the shoot mass fraction, SMF), the fraction of total plant biomass allocated to roots (the root biomass fraction, RMF), and the R/S among the different species and densities. Second, standard major axis (SMA) regression analyses were conducted to explore the allometric relationships of biomass between shoots and roots at different densities. A likelihood ratio test was used to indicate the heterogeneity of the scaling exponents at different densities and their difference from 1 (Warton et al., 2012). The data were log10-transformed before the SMA regression analysis. The differences in the SMF, RMF and R/S among the six species were analysed based on the pooled data from all five planting densities. The pooled data were subjected to a Kolmogorov-Smirnov test to examine whether they conformed to a normal distribution; if they did not, a log10 transformation was performed. Before using ANOVA to study the effect of density on the biomass allocation in each species, the data from the individuals in each planting pot were averaged; therefore, the data presented in the figures are averages based on three replicates. In addition, differences in the ANPP and BNPP fractions and ratios for the different functional groups (annualsvs perennials, C3 vs C4) at the global scale were analysed using a mixed model and compared with the results of this experiment. All analyses in this study were performed in R 4.0.2 (R Core Team, 2020).