Growth and Allometry in Modern Morphometrics: Review

In traditional shape analysis, linear distance, angles and ratios of measurements are used in multivariate statistical analyses. The challenge in any analysis of growth is to extend quantitative description and to explore aspects of the biology of a given organism, such as the genetic basis of morphogenesis, the phylogenetic underpinnings of developmental patterns, or the role of hormones, teratogens, dietary elements, and other environmental variables on the growth process. It is important to define the growth process with mathematical equations that include biologically meaningful parameters. Size has several different meanings such as length, area, volume, and even the linear combinations of different measured quantities. However, in statistical shape analysis, size is obtained by a specific approach, which provides the geometrical information of an object. Allometry theory was developed as a result of shape variations that occur with the growth of an organism’s different parts or organs at different rates. As the idea of size and shape has been one of the most controversial subjects in traditional morphometrics, allometry (relationship between size and shape) plays an important role in the development of statistical shape analysis. The quantities used in traditional morphometrics for size are highly correlated with shape. Thus, many different methods have been proposed for size correction. However, because of disagreement regarding relevant methods of size correction, researchers have investigated different methods for the analysis of shape data. Today, new geometrical morphometric approaches are being used extensively to explore and model growth and allometry.