A model of developmental canalization, applied to human cranial form.

Developmental mechanisms that canalize or compensate perturbations of organismal development (targeted or compensatory growth) are widely considered a prerequisite of individual health and the evolution of complex life, but little is known about the nature of these mechanisms. It is even unclear if and how a "target trajectory" of individual development is encoded in the organism's genetic-developmental system or, instead, emerges as an epiphenomenon. Here we develop a statistical model of developmental canalization based on an extended autoregressive model. We show that under certain assumptions the strength of canalization and the amount of canalized variance in a population can be estimated, or at least approximated, from longitudinal phenotypic measurements, even if the target trajectories are unobserved. We extend this model to multivariate measures and discuss reifications of the ensuing parameter matrix. We apply these approaches to longitudinal geometric morphometric data on human postnatal craniofacial size and shape as well as to the size of the frontal sinuses. Craniofacial size showed strong developmental canalization during the first 5 years of life, leading to a 50% reduction of cross-sectional size variance, followed by a continual increase in variance during puberty. Frontal sinus size, by contrast, did not show any signs of canalization. Total variance of craniofacial shape decreased slightly until about 5 years of age and increased thereafter. However, different features of craniofacial shape showed very different developmental dynamics. Whereas the relative dimensions of the nasopharynx showed strong canalization and a reduction of variance throughout postnatal development, facial orientation continually increased in variance. Some of the signals of canalization may owe to independent variation in developmental timing of cranial components, but our results indicate evolved, partly mechanically induced mechanisms of canalization that ensure properly sized upper airways and facial dimensions.