Body size and allometric variation in facial shape in children

Abstract

Objectives: Morphological integration, or the tendency for covariation, is commonly seen in complex traits such as the human face. The effects of growth on shape, or allometry, represent a ubiquitous but poorly understood axis of integration. We address the question of to what extent age and measures of size converge on a single pattern of allometry for human facial shape.

Methods: Our study is based on two large cross-sectional cohorts of children, one from Tanzania and the other from the United States (N = 7,173). We employ 3D facial imaging and geometric morphometrics to relate facial shape to age and anthropometric measures.

Results: The two populations differ significantly in facial shape, but the magnitude of this difference is small relative to the variation within each group. Allometric variation for facial shape is similar in both populations, representing a small but significant proportion of total variation in facial shape. Different measures of size are associated with overlapping but statistically distinct aspects of shape variation. Only half of the size-related variation in facial shape can be explained by the first principal component of four size measures and age while the remainder associates distinctly with individual measures.

Conclusions: Allometric variation in the human face is complex and should not be regarded as a singular effect. This finding has important implications for how size is treated in studies of human facial shape and for the developmental basis for allometric variation more generally.

Keywords: 3D facial imaging; allometry; face shape; growth; human; morphometrics.

Figure 1

Anatomical Landmarks. 29 landmarks as placed on the 3-D facial photo scans. Corresponds to anatomical descriptions in Table 1.

Figure 2

Thin-plate spline warps of Tanzanian allometric variation. Thin-plate spline warps showing variation across age, centroid size (CS), head circumference (HC), height (HT), and weight (WT). Negative end of the axis of variation is displayed in the left column, while the positive is displayed on the right. Corresponds to Table 4.

Figure 3

Thin-plate spline warps of allometric variation in European-derived North American children. Thin-plate spline warps showing variation across age, centroid size (CS). Negative end of the axis of variation is displayed in the left column, while the positive is displayed on the right.

Figure 4

Thin-plate spline warps for PC 1–5 of Tanzanian and European-derived North American sample. Negative and positive PC scores represented. Color maps represent areas of greatest difference (red) and least difference (blue). Figure corresponds to Table 3.

Figure 5

Facial shape effects by population and sex. A shows the mean face shapes for the Tanzanian and North American samples and the differences between those means as a heatmap. C shows exaggerated morphs for Males and Females. These were calculated as 2.5x the Procrustes distance between the sexes after standardizing for age. D shows the regression of face shape on age by sex.

Figure 6

Three-dimensional morphs showing the facial shape variation that corresponds to each size measure and age (A). The morphs are scaled to 2 standard deviation departures from the mean in each direction. B shows heatmaps that correspond to these morphs.

Figure 7

A) Regression of the conditional variation for each variable against the first PC of the size measures and age. B) Visualization of the correlation matrix for the size measure and age. C) The shape variances explained by each variable for the regressions of the conditional variation.

Figure 8

A shows the shape vectors that correspond to the regressions of face shape on each size measure and age. Some vectors point inwards from the surface of the face. B shows the distributions of angles among resampled vectors. Since all angles are positive, a mean angle of 0 is not possible. The Null distribution shows the expected distribution of angles when the angles between the vectors for the same regression is resamples. The blue line shows the expected mean when the angles are orthogonal (random) while the red line shows 0 (completely parallel).