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.