Klingenberg Christian Peter, Barluenga Marta, Meyer Axel
Department of Biology, University of Konstanz, Germany.
Evolution. 2002 Oct;56(10):1909-20. doi: 10.1111/j.0014-3820.2002.tb00117.x.
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.
形态测量学研究通常会考虑具有内部左右对称的部分，例如脊椎动物的头骨。这种对称类型被称为物体对称，它与匹配对称不同，在匹配对称中，两个独立的结构作为彼此的镜像存在，分别位于身体的两侧。我们解释了一种方法，用于将具有物体对称的地标配置的总形状变化划分为个体间对称变化和不对称的成分。该方法基于每个地标配置的原始副本和反射副本的普氏叠加，并且与波动不对称研究中常用的双因素方差分析模型兼容。我们展示了一个完全多变量的框架，用于使用多元方差分析统计量检验双因素模型中的效应，该框架也适用于具有匹配对称的形状。我们将新方法应用于新热带丽鱼科鱼类柠檬慈鲷咽颌的一个小型案例研究中。分析表明，该物种咽颌变化的对称成分主要由两种不同食性形态之间的差异主导，并且存在细微但具有统计学意义的方向不对称。最后，我们为对称形状的形态测量学研究提供了一些一般性建议。
