Statistical analysis
All statistical analyses were conducted using SAS statistical software
(SAS Institute 9.0 Inc. 2002). All traits were used in analyses
(abbreviations see Table 1). All data were log-transformed except for
petiole angles and branch angles (square root-transformed) to minimize
variance heterogeneity before statistical analysis. Three-way ANOVA and
ANCOVA were performed to evaluate the overall effects of growth stage,
soil condition and population density and their interactions on all
traits, with total mass 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 ANOVA for total mass, and one-way
ANCOVA for all the other traits with total mass as a covariate. Adjusted
mean values of traits produced from multiple comparisons by LSD method
of the General Linear Model (GLM) program in ANCOVAs were used in
calculation of plasticity.
The plasticity in traits was evaluated with the revised simplified
Relative Distance Plasticity Index (RDPIs), for its
strong statistical power in tests of differences in plasticity
(F. Valladares, Sanchez-Gomez, & Zavala,
2006). For a given trait, its RDPIs values in response
to high and medium densities relative to low density (H-L
RDPIs and M-L RDPIs) were calculated
as:
RDPIs = (X – Y )/(X + Y )
where X was the adjusted mean trait value at high or medium
density, and Y was the mean value at low density. Both the level and
degree of plasticity (relative plasticity and absolute plasticity) in
traits were calculated as REL RDPIs and ABS
RDPIs respectively.
Phenotypic canalization was evaluated by coefficient of variation (CV)
for a given trait, calculated as the standard deviation divided by mean
value of the trait. Phenotypic integration was estimated with the number
of significant correlations of a trait with other traits (NC; p
< 0.05) and coefficient of integration (CI)
(Cheverud, Rutledge, & Atchley, 1983).
Correlations among traits were evaluated by Pearson Correlation
Coefficients (PCC) produced by PROC CORR
(Gianoli & Palacio-López, 2009). CI for
traits was computed as:
I =
[∑(λ -1)2/(n 2-n )]1/2
where n is the number of traits andλ is an eigenvalue of the
correlation matrix of the normalized data.
Both Correlation and regression analyses were applied to qualify and
quantify the relationships between phenotypic plasticity
(RDPIs) and phenotypic canalization (CV) or integration
(NC) at different densities for plants in each soil conditions at each
stage. Results of correlations and regressions were also analyzed with
three-way ANOVA to access effects of population density, soil conditions
and growth stage and their interactions; and one-way ANOVA for effects
of density on these relationships in each soil conditions at each stage.