Data from: Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry

Morphometric studies often consider parts with internal left-right symmetry, for instance, the vertebrate skull. This type of symmetry is called object symmetry and is distinguished from matching symmetry, in which two separate structures exist as mirror images of each other, one on each body side. We explain a method for partitioning the total shape variation of landmark configurations with object symmetry into components of symmetric variation among individuals and asymmetry. This method is based on the Procrustes superimposition of the original and a reflected copy of each landmark configuration and is compatible with the two-factor ANOVA model customary in studies of fluctuating asymmetry. We show a fully multivariate framework for testing the effects in the two-factor model with MANOVA statistics, which also applies to shapes with matching symmetry. We apply the new methods in a small case study of pharyngeal jaws of the Neotropical cichlid fish Amphilophus citrinellus. The analysis revealed that the symmetric component of variation in the pharyngeal jaws is dominated by the contrast between two alternative trophic morphs in this species and that there is subtle but statistically significant directional asymmetry. Finally, we provide some general recommendations for morphometric studies of symmetric shapes.

形态测量学研究常聚焦于具有内部左右对称性的躯体结构，例如脊椎动物头骨。此类对称性被称为物体对称性（object symmetry），与匹配对称性（matching symmetry）存在本质区别：匹配对称性指躯体两侧各存在一个互为镜像的独立结构。本文提出一种方法，可将具有物体对称性的标志点（landmark）构型的总形状变异拆解为个体间对称变异与不对称变异两个组分。该方法基于对每个标志点构型的原始形态与其镜像复本进行普氏叠加（Procrustes superimposition），且兼容于波动不对称（fluctuating asymmetry）研究中通用的双因素方差分析模型。我们构建了一套完整的多变量分析框架，可借助多变量方差分析（MANOVA）统计量对双因素模型中的效应开展检验，该框架同样适用于具有匹配对称性的形状数据。我们将该新方法应用于一项小型案例研究，分析对象为新热带慈鲷Amphilophus citrinellus的咽颌。分析结果表明，该物种咽颌的对称变异组分主要由两种不同营养型态之间的差异主导，同时存在微弱但具有统计学显著性的方向不对称（directional asymmetry）现象。最后，我们为对称形状的形态测量学研究提供了若干通用建议。