Sexual dimorphism in multiple aspects of 3D facial symmetry and asymmetry defined by spatially dense geometric morphometrics

Abstract

Accurate measurement of facial sexual dimorphism is useful to understanding facial anatomy and specifically how faces influence, and have been influenced by, sexual selection. An important facial aspect is the display of bilateral symmetry, invoking the need to investigate aspects of symmetry and asymmetry separately when examining facial shape. Previous studies typically employed landmarks that provided only a sparse facial representation, where different landmark choices could lead to contrasting outcomes. Furthermore, sexual dimorphism is only tested as a difference of sample means, which is statistically the same as a difference in population location only. Within the framework of geometric morphometrics, we partition facial shape, represented in a spatially dense way, into patterns of symmetry and asymmetry, following a two-factor anova design. Subsequently, we investigate sexual dimorphism in symmetry and asymmetry patterns separately, and on multiple aspects, by examining (i) population location differences as well as differences in population variance-covariance; (ii) scale; and (iii) orientation. One important challenge in this approach is the proportionally high number of variables to observations necessitating the implementation of permutational and computationally feasible statistics. In a sample of gender-matched young adults (18-25 years) with self-reported European ancestry, we found greater variation in male faces than in women for all measurements. Statistically significant sexual dimorphism was found for the aspect of location in both symmetry and asymmetry (directional asymmetry), for the aspect of scale only in asymmetry (magnitude of fluctuating asymmetry) and, in contrast, for the aspect of orientation only in symmetry. Interesting interplays with hypotheses in evolutionary and developmental biology were observed, such as the selective nature of the force underpinning sexual dimorphism and the genetic independence of the structural patterns of fluctuating asymmetry. Additionally, insights into growth patterns of the soft tissue envelope of the face and underlying skull structure can also be obtained from the results.

Fig. 1

Method work-flow (AMMI, additive main model and multiplicative interaction).

Fig. 2

Multiple aspect analysis. (A) Two populations differing in location only. Feature to focus on is the sample mean or centroid. (B) Two populations differing in variance-covariance scale only. The feature to focus on is the sample dispersion based on distances from the centroid. (C) Two populations differing in variance-covariance orientation only. The feature to focus on is the sample subspace, represented using eigenvectors and the principal angles between them.

Fig. 3

(A) A non-pivotal D-statistic is computed as a single distance between both groups of observations. (B) A pivotal F-statistic is computed by comparing the within pair-wise distances (solid lines), against the between pair-wise distances (dotted lines) of observations.

Fig. 4

Two-factor anova partitioning of male facial shape variation following an isotropic model (IM) and a distance-based NPMANOVA (D). Throughout the table values are coded as IM/D. P1000 Column: P values using 1000 permutations with * and light green P < 0.05; ** and yellow P < 0.001; dark green not significant (P ≥ 0.05). MS (mean square) is the sum of squares divided by the appropriate degrees of freedom, reflecting the magnitude of the effect. F (F-ratio) is the MS divided by an appropriate error MS, reflecting the relative magnitude or strength of the effect. The interaction term is used as error term for the main effects of individuals and sides and the actual error term is used for the interaction term.

Fig. 5

Two-factor anova partitioning of female facial shape variation following an isotropic model (IM) and a distance-based NPMANOVA. Throughout the table, values are coded as IM/D. P1000 Column: P values using 1000 permutations with * and light green P < 0.05; ** and yellow P < 0.001; dark green not significant (P ≥ 0.05). MS (mean square) is the sum of squares divided by the appropriate degrees of freedom, reflecting the magnitude of the effect. F (F-ratio) is the MS divided by an appropriate error MS, reflecting the relative magnitude or strength of the effect. The interaction term is used as error term for the main effects of individuals and sides and the actual error term is used for the interaction term.

Fig. 6

Sexual dimorphism on the aspect of sample location for the component of symmetry (E) and asymmetry (F). (A) Female symmetric group average. (B) Female directional asymmetry, differences between mean original and reflected configurations amplified five times and visualized onto (A). (A) Male symmetric group average. (B) Male directional asymmetry, differences between mean original and reflected configurations amplified five times and visualized onto (A).

Fig. 7

The effects, a positive morph and a negative morph along the first two principal components in patterns of symmetry [(A) females, (B) males], and asymmetry [(C) females, (D) males].

Fig. 8

Sexual dimorphism for the aspect of sample scale. Distribution of dispersions for the components of symmetry [(A) females, (B) males] and asymmetry [(C) females, (D) males].

Fig. 9

Sexual dimorphism for the aspect of sample orientation for the component of symmetry [(A) D-statistic; (B) F-statistic] and asymmetry [(C) D-statistic; (D) F-statistic].