at day 1. We also took logarithms to stabilize the error variance. The rescaled log-data is shown in Figure 1(b). 

These curves have a noticeable inflection point around day 15 . This is because in response to hormonal changes occurring prior to pupation, larvae stop eating and start wandering in search of a place to pupate, and so lose body mass. Therefore we fitted warped ANOVA models with a single warping knot at τ 0 = 15 . As spline basis we used cubic B-splines with 7 equispaced knots; this gives a total of 9 basis functions, providing enough flexibility without excessive irregularity. We cons idered several ANOVA models with equal number of components for the main factor and the residual term, ranging from 0 (mean-only model) to 3 components. The resulting parameter estimators were: 

• For p = q = 0 (mean-only model): ˆ Σ = . 013 , ˆ Ω = . 031 , ˆ σ = . 181 . 

• For p = q = 1 : ˆ Σ = . 010 , ˆ Ω = . 035 , ˆ γ = . 323 , ˆ λ = . 128 , ˆ σ = . 138 . 

• For p = q = 2 : ˆ Σ = . 010 , ˆ Ω = . 051 , ˆ γ = ( . 344 , . 021) , ˆ λ = ( . 168 , . 010) , ˆ σ = . 124 . 

• For p = q = 3 : ˆ Σ = . 005 , ˆ Ω = . 035 , ˆ γ = ( . 426 , . 022 , . 005) , ˆ λ = ( . 186 , . 028 , . 012) , ˆ σ = . 121 . 

Overall, it seems that a single principal component is suffic ient to explain amplitude variability, so we chose the model with p = q = 1 . The fitted curves ˆ x$_{ij}$ ( t ) are shown in Figure 2(a) and we see that they provide a good approximation to the data in Figure 1(b). The estimated warping functions ˆ w$_{ij}$ ( t ) are shown in Figure 2(b); the time variability around day 15, which is substantial, is captured well by these curves. The amplitude principal components ˆ φ ( t ) and ˆ ψ ( t ) are shown in Figure 2(c); to facilitate interpretation of the components we plotted ˆ µ ( t ) together with ˆ µ ( t ) ± ˆ φ ( t ) in Figure 2(d). We see that ˆ φ ( t ) and ˆ ψ ( t ) , which are very similar, explain variation in overall mass: individuals with 

