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.