Phenotypic trajectory analysis
We applied phenotypic trajectory analysis (PTA) to test whether the
magnitude and direction of the multivariate plastic response of the
metabolome to fish kairomones differed among subpopulations. This
technique tests for pairwise differences between groups in multivariate
plasticity (i.e. the phenotypic trajectories) by comparing the magnitude
and the direction of the two-state multivariate reaction norms (Collyeret al. 2007). PTA allows statistical testing for differences in
magnitude and direction of phenotypic change by comparing observed
values to distributions created from random pairs of trajectories
obtained by permutations (Collyer et al. 2007). We compared the
multivariate plasticity using all important metabolite peaks (VIP
> 1) identified by the PLS-DA model including all three
subpopulations.
The detailed methods of the PTA analyses are presented in the
Supplementary Information. Briefly, we tested for differences in the
magnitude and direction of the multivariate metabolomic change among the
subpopulations using an extended R script of Adams & Collyer (Adams &
Collyer 2009) where the statistical model included subpopulation, fish
kairomones and their interaction, and effects of clonal variation. To
visualize the multivariate reaction norms, we conducted a principal
component analysis, and plotted the scores on the first three, varimax
normalized components. Note that these bivariate projection PCA plots
cannot fully reflect the magnitudes and angles of the multivariate
reaction norms as the PTA is conducted in a multi-dimensional trait
space (Collyer et al. 2007).