ability of the aligned curves. (This process of aligning curves is variously known as “time warping” or “curve registration” in the Functional Data lit erature.) But evolutionary biolo- gists frequently must make decisions about how to align or register individual curves from a population of individuals. For example, when studying growth curves in a population of animals that undergo metamorphosis from one life history state to another (usually from a non-reproductive larval form to a reproductive adult form), it is not necessarily clear how to align the individual curves. The default choice for most biologists is to align the curves at the date of birth or hatching, but an equally valid choice might be the date of metamorphosis or the peak body mass prior to metamorphosis. For example, Ragland and Carter (2004) chose to align the growth curves of larval salamanders by date of metamor- phosis and then reset the growth period to a fractional scale. Although this approach was effective, it was unsophisticated and ad hoc; more rigorous methods would be beneficial. In this paper we propose a functional ANOVA approach that explicitly models time variability. For simplicity, we consider only the one-way random factor model, but the ideas can be easily extended to more complex ANOVA models. We follow a likelihood- based approach that uses the raw data directly, without pre-smoothing. Therefore the method can be applied to irregularly sampled trajectories, with possibly different starting points and endpoints. The fact that pre-smoothing is not necessary makes the method ap- plicable to longitudinal data, where a smooth latent process is assumed but the observed data themselves are not smooth (Rice, 2004; M¨uller, 2008). The paper is organized as fol- lows: a brief background on random processes is given in Section 2; the warped ANOVA model is presented in Section 3; the asymptotic distribution of the main parameter esti- mators is derived in Section 4; the small sample behavior of the estimators is studied by simulation in Section 5; finally, the beetle growth data is an alyzed in detail in Section 6. 3