morphometrics

Morphometrics, or morphometric analysis, is the quantitative study of the form of organisms and structures, focusing on size and shape. It encompasses methods that compare morphology across individuals, populations, or taxa, with the goal of identifying patterns of variation, similarity, and allometry. Morphometrics can be applied to biological structures ranging from bones and teeth to leaves and skulls, as well as to non-biological shapes.

Traditional morphometrics relies on linear measurements, angles, and ratios, often analyzed with univariate or multivariate statistics. Geometric morphometrics, by contrast, captures shape more comprehensively by using the Cartesian coordinates of homologous landmarks or the outline of a structure, and analyzes them after alignment to remove non-shape variation.

Typical workflow: data collection via landmarks or outlines, digitization, alignment and scaling using Procrustes superimposition, size is summarized as centroid size, shape variation is studied with principal components analysis or other multivariate methods, and allometry can be explored by regressing shape on size. Phylogenetic considerations may be incorporated.

Applications include taxonomy, systematics, and phylogeography; functional and developmental biology; paleoanthropology and paleontology; botany; and forensic anthropology. Geometric morphometrics helps visualize shape change and quantify subtle differences not captured by traditional measurements.

Common software packages include MorphoJ and the TPS series for landmark-based analyses, and the R packages geomorph and Momocs for flexible, script-based workflows. Data sharing and standardization have aided reproducibility in recent decades.

Limitations include dependence on landmark homology, measurement error, missing data, and sample size constraints. Results can be sensitive to the choice of landmarks, preprocessing steps, and the phylogenetic structure of the sample, requiring careful interpretation and validation.