positive pc scores tend to have trajectories above the mean and individuals with negative pc scores tend to have trajectories below the mean. The similarity between ˆ φ ( t ) and ˆ ψ ( t ) has a biological explanation: the main factor of the ANOVA model represents the genetic contribution of the father, while the residual term represents the genetic contribution of the mother together with environmental factors (see e.g. Heckman, 2003, sec. 3). For a population in Hardy-Weinberg equilibrium, the genetic contribution of both parents is identical, so the ˆ φ$_{k}$ ( t ) s and the ˆ ψ$_{k}$ ( t ) s will be similar if the environmental factors are not very strong. Supporting this result is the fact that Irwin and Carter (2013) showed that most of the phenotypic variance was explained by genetic effects in most parts of the growth curve. The amplitude principal components reveal a very interesting biological result that was not apparent in the original analysis of the raw data in Irwin and Carter (2013): very little variation in amplitude exists at the inflection point at day 1 5 (Figure 2(c) and 2(d)). This indicates that the beetles have a target peak mass that is reached prior to entry into the wan- dering phase, which suggests that the target peak mass must be reached before pupation can begin, and that selection for that peak mass (or a related physiological trait) may occur. Interestingly the warping functions shown in Figure 2(b), as well as the original analysis in Irwin and Carter (2013) demonstrate there is substantial variation at the age at which peak mass is reached. In combination these two results provide a basis for future exper- iments investigating physiological mechanisms, genetic underpinnings and evolutionary implications of size and age of peak mass. The variance ratios for the amplitude and warping components are ˆ h$_{z}$ = . 72 and ˆ h$_{w}$ = . 23 , with respective asymptotic standard deviations . 15 and . 13 . The bootstrap distributions of ˆ h$_{z}$ and ˆ h$_{w}$ are shown in Web Appendix D; the bootstrap standard deviations are . 20 and . 16 respectively, not far from the asymptotic values, but the Normal approximation is more accurate for the transformations arcsin √ ˆ h$_{z}$ and arcsin √ ˆ h$_{w}$ . The 90% asymptotic 20