2.3 Statistical analysis
Dry mass content (DMC) of each sample was calculated as:
DMC=\(\frac{W_{\text{FS}}-W_{\text{DS}}}{W_{\text{FS}}}\),
where WFS and WDS are
fresh weight and dry weight, respectively. We multiplied the total fresh
weight of each tissue by the corresponding DMC to obtain the dry biomass
of every individual tree. A power-law function was used to describe the
scaling relationship between trunk D and H or branch
diameter (d ) and length (L ):
y = β x α ,
where y represents H or L , x representsD or d , β is the normalization constant, andα is the scaling exponent (Niklas 1994). To stabilize the
variance, data were log-transformed as
log(y)=log(β )+a log(x) (Niklas 1994). Similar to previous
statistical analyses (Zhang et al. 2016; Sun et al. 2019),
standard major axis (SMA) regression of the log-transformed data was
used to determine the numerical value of scaling exponents (a )
and normalization constants (β ) (Smith 2009).
The
heterogeneity of scaling exponent was significantly, when the 95 %
confidence intervals did not overlap. One-way analyses of variance
(ANOVA) with least significant difference (LSD) fisher multiple
comparisons was used to test differences in biomass, growth rates, and
leaf mass per branch. In addition, the Benjamini-Hochberg method was
used for p -value correction. All statistical analyses were
performed using the statistical software environment R (version 3.6.0)
(R Core Team 2019); SMA regression was performed using the packagesmatr (version 3.4-8) (Warton et al. 2012). All tests for
heterogeneity were based on p < 0.05.