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).