Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications

Abstract

Approximately two decades after the first pioneering analyses, the study of shape asymmetry with the methods of geometric morphometrics has matured and is a burgeoning field. New technology for data collection and new methods and software for analysis are widely available and have led to numerous applications in plants and animals, including humans. This review summarizes the concepts and morphometric methods for studying asymmetry of shape and size. After a summary of mathematical and biological concepts of symmetry and asymmetry, a section follows that explains the methods of geometric morphometrics and how they can be used to analyze asymmetry of biological structures. Geometric morphometric analyses not only tell how much asymmetry there is, but also provide information about the patterns of covariation in the structure under study. Such patterns of covariation in fluctuating asymmetry can provide valuable insight about the developmental basis of morphological integration, and have become important tools for evolutionary developmental biology. The genetic basis of fluctuating asymmetry has been studied from empirical and theoretical viewpoints, but serious challenges remain in this area. There are many promising areas for further research that are only little explored at present.

Fluctuating Asymmetry of Human Populations: A Review

“…Shape asymmetry, involving either matching symmetry or object symmetry [24][25][26] can be estimated from landmarks or semi-landmarks in either two or three dimensions [25][26][27][28][29][30][31][32], as well as continuous symmetry measures [12,[33][34][35]. Despite the apparent simplicity of fluctuating asymmetry, careless researchers can easily reach erroneous conclusions [8,12,22,23,36].…”

“…Remarkably, these two indices were still in use as recently as 2011 [40], mostly in studies of human dermatoglyphic asymmetry. We recommend indices based on (1) the variance of d, such as the mean absolute deviation [8,12]; (2) the Procrustes distance of geometric mophometrics [25,26,28,41]; (3) dense surface modeling [42]; and (4) continuous symmetry measures [33,35].…”

A Study for Parametric Morphogeometric Operators to Assist the Detection of Keratoconus

“…During this stage, singular points of the posterior surface were identified on each solid corneal model (healthy or keratoconic), and a morphogeometric analysis was performed in the local region [30,31] where curving (caused by progression of keratoconus) manifests gradually.…”

Changes of Fluctuating Asymmetry with Age in Human Fetuses and Young Infants

“…More research with data from different populations might shed more insights in this potential between-population difference. On the other hand, it is also worth noting that the use of FA as a measure of DI has been questioned and may not be correct generally, as outlines in a recent review [14]. Nevertheless, we did find higher FA in fetuses and infants with major abnormalities ( [10] and this study), with severe genetic abnormalities and when several organ systems or patterning processes are affected [5], which does suggest that limb FA does signal developmental perturbations, albeit often only when they are very severe.…”