2.4 Data analysis
Bivariate
analysis with ordinary least-squares linear regression (OLR) and
quadratic regression (QR) were used to quantify how
hypocotyl
trait values varied with latitudinal gradients and biotic/abiotic
factors. Because of high correlations among most hypocotyl traits
(r > 0.36, P < 0.001), we performed
a principal component analysis
(PCA) with multiple traits using the ‘princomp’ function in R 4.1.3 (R
Core Team 2022), and used the two
first PC axes to represent the hypocotyl traits.
To evaluate how environmental factors, maternal plants or inherent
factors explained variation in
hypocotyl traits, we used a
nested analysis of variance (ANOVA) coupled with variance partitioning
techniques (Martin et al., 2017). We carried out linear mixed model
(LMM) for PC1 and RTD by using the ‘lme’ function in ‘nlme’ R package
(Pinheiro, Bates, & R Core Team, 2022). In each model, all nested
levels (i.e. site > genealogy > within
[individual]) were entered as sequential random effects and the
intercept was the only estimated fixed effect. We then used the
‘varcomp’ function in the ‘ape’ R package (Paradis et al., 2004) to
calculate the variance components associated with each nested level.
To quantify how hypocotyl traits were affected by climatic factors,
oceanic factors, and maternal performance, we implemented LMMs using the
‘lme’ function in the R package ‘nlme’. The fixed-effect terms included
the climatic, oceanic and maternal variables. To account for additional
variation potentially caused by some missing site-specific effects
(e.g., other environmental factors), and that caused by other maternal
effects uncaptured by aboveground biomass, we treated sampling site and
tree genealogy as random factors. All variables were standardised before
the modelling, such that each variable had a mean of zero and a standard
deviation of one. To reduce the adverse influence of multicollinearity,
we removed multicollinear variables until the variance inflation factors
(VIFs) of all variables in the model were less than three (Ouyang et
al., 2019). Both primary and
quadratic
mixed models were considered, and only the better fitted model was
showed (based on the Akike information criteria). We calculated the VIF
using the R package ‘car’ (Fox & Monette, 2019). The
pseudo-R2 was calculated using the function
‘r.squaredGLMM’ in the R package ‘MuMIn’ (Bartoń, 2022), to represent
the variance explained by the fixed effect in the LMM. The effect sizes
of fixed factors were measured by the regression coefficients in the
LMM.
Structural equation modelling (SEM) was used to disentangle direct and
indirect effects of all predictive factors on hypocotyl traits. After
standardising all variables, multicollinear variables were removed based
on VIF. We first considered a full model that included all variables and
all reasonable pathways. Non-significant pathways were then sequentially
removed, unless the pathways were biologically informative. The removing
and adding of pathways were repeated until bothPχ 2-test ≥ 0.05 (that is, no
significant difference between model predictions and the observed data)
and root mean square error of approximation (RMSE) < 0.08 were
reached (Wu et al., 2022). The SEM was performed using the ‘lavaan’ R
package (Rosseel, 2012).