Eigenshape

Eigenshape refers to a concept often encountered in the field of geometric morphometrics, a technique used to quantitatively analyze and compare biological shapes. In essence, an eigenshape is a standardized representation of a shape that captures its fundamental variations. It is derived through a process that often involves Procrustes analysis, where homologous landmarks on different specimens are aligned and scaled to remove differences due to position, orientation, and size.

Once specimens are aligned, the variation in landmark positions is analyzed using principal component analysis (PCA). The resulting principal components represent directions of maximum variance in the shape space. Each principal component, when visualized, depicts a particular mode of shape variation. The term "eigenshape" is sometimes used to describe these principal component axes or modes of variation themselves, as they are analogous to eigenvectors in linear algebra, representing fundamental directions of transformation.

By examining the relative contributions of each eigenshape (i.e., the variance explained by each principal component), researchers can identify the most significant ways in which a population or group of organisms varies in shape. Low-order eigenshapes typically represent major, common shape differences, while higher-order eigenshapes capture more subtle or specific variations. Understanding these eigenshapes allows for statistical comparisons between groups and the identification of evolutionary or developmental patterns related to shape.