Size, shape, and form: concepts of allometry in geometric morphometrics

Abstract

Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould–Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley–Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.

Genome of the Tasmanian tiger provides insights into the evolution and demography of an extinct marsupial carnivore

“…Each species was assigned to a general diet type (carnivore, herbivore, insectivore, omnivore; Supplementary Table 4), and the relative effects of size (represented by centroid size) and diet on cranial shape were compared. Given the extensive range of body sizes in our data set, centroid size was log-transformed prior to analysis 63 . Due to the non-independence of related species 64 , tests were also run in a phylogenetic context using our mammalian supertree ( Supplementary Fig.…”

Anyone with a Long-Face? Craniofacial Evolutionary Allometry (CREA) in a Family of Short-Faced Mammals, the Felidae

“…However, even in closely related species, large differences in size are typically accompanied by differences in shape, because of allometry, or the covariation of size and shape (Klingenberg 2016). Allometry, although it may not always be present, is a pervasive aspect of morphological variation in mammals and many other animals.…”

“…Thus, contrary to simple TMM (Marcus 1990) measurements, such as condylo-basal length, centroid size provides an overall estimate of size, but not one that can be unequivocally and simply referred to a specific feature. However, it is the most used metric in PGMM allometric analyses (Klingenberg 2016), as it relates precisely to the same anatomical landmarks used to estimate shape.…”

The Future of Forensic Biology

“…Currently, the most commonly used form of morphometric methods are Generalized Procrustes method (GPA), Euclidean Distance Matrix Analysis (EDMA), Principal Components Analysis (PCA) and 3D imaging methods (µMRI and µCT) [30]. One of the major aspect of morphometrics is allometric measurements which compares size of the body parts in relation to the size of the organism [31]. Allometry is also a prominent feature of contour variation for multifarious morphological traits such as craniofacial shape [30].…”