2.5 | Phenotypic variation
To summarize phenotypic variation of sampled trees in the inland and
coastal sites, we performed principal component analyses (PCA) using the
function prcomp in R 3.3.2. Among the eight traits, the frequency
distributions of the density and size of stellate hairs and the scale
bud number, were skewed. Thus, values of the size, the density + 1, and
the number + 1 were log-transformed. The phenotypic values of the eight
traits were scaled (mean = 0 and variance = 1) and applied to PCA.
Contributions of each principal component (PC) to the total phenotypic
variation and loadings of each trait to the first and second PCs were
obtained. Statistical differences in PC values among taxa were verified
using the function kruskal.test in R 3.3.2.
To evaluate phenotypic plasticity in response to inland and coastal
environments, we plotted the Qd ancestry and the first phenotypic
PC values of individual trees and fitted smoothed lines in each of the
inland and coastal sites using the function lowess with the parameterf = 1 in R 3.3.2. We applied a linear model to the data using the
function lm in R 3.3.2,
y ~ α +
β1x 1 +
β2x 2 +
γx 1x 2,
where y is the first phenotypic PC value,x 1 is the Qd ancestry, andx 2 is 0 in the inland site and 1 in the coastal
site; α is an intercept, β1 and β2 are
coefficients of x 1 and x 2effects, respectively, and γ is a coefficient of their interactions.
Significant γ indicates different slopes between the sites, suggesting
different reaction norms of phenotypic plasticity in response to coastal
environment depending on the Qd ancestry.