A STATISTICAL-METHOD FOR BIOLOGICAL SHAPE COMPARISONS

Biological shape data combine 2 sorts of information: geometric location and biological homology. The link between these 2 is the landmark, a set of biologically corresponding points located in all the forms of a series. Analysis of shapes as configurations of landmarks proceeds most effectively by D''Arcy Thompson''s (1917, 1942) method of transformations. In this tradition, shape change is not the arithmetical difference of distances, angles and ratios measured on shapes separately; rather, it is a mensurand in its own right, the geometrical deformation taking the Cartesian coordinate space of one form onto that of another in accord with biological homology. This article reviews the statistical description of mean biological form-changes viewed in this way, and introduces linearized significance tests for mean shape change and mean size change. Examples are presented that test cephalometric data in 3 scientific contexts: comparison of groups of biological shapes observed once each; characterization of mean difference in a matched design (i.e., mean growth in 1 group observed twice); and description of mean differences in growth between groups of shapes each observed twice.