Statistical analysis
All statistical analyses were conducted using SAS statistical software (SAS Institute 9.0 Inc. 2002). Biomass traits including shoot mass, root mass, total biomass and root:shoot ratio, and morphological traits including main root length, main root diameter, lateral root number and lateral root length were analyzed. To minimize variance heterogeneity, all data were log-transformed before statistical analysis. Three-way ANOVA and ANCOVA were used to evaluate overall effects of growth stage, soil conditions and population density and their interactions on all traits, with total biomass nested in growth stage as a covariate in three-way ANCOVA. Within each soil condition at each stage, effects of density were analyzed by one-way ANOVAs for total mass, and one-way ANCOVAs for all the other traits with total mass as a covariate. For a given trait, it was considered to exhibit apparent plasticity whenever plant size (total biomass) accounted for significant variation in its response to density, and any variation in its expression that was independent of total biomass was considered an indication of true plasticity (after removal of size effects) (McConnaughay and Coleman 1999, Weiner 2004). Multiple comparisons used Least Significant Difference (LSD) method of the General Linear Model (GLM) program in one-way ANCOVA, which also produced adjusted mean values and standard errors.