The Truss: Body Form Reconstructions in Morphometrics

The truss: body form reconstruction in morphometrics. Syst. Zool., 31:113–135.—In principle, any measured distances between landmarks of a form may serve as characters for morphometric analyses. Systematic studies typically are based on a highly biased and repetitious sample of these. But collections of landmarks and the distances among them must be homologous from form to form for comparisons to be meaningful, and an adequate character set should at least permit the full reconstruction of the original configuration of landmarks. We describe a geometric protocol for character selection, the truss network, which enforces systematic coverage of the form and which exhaustively and redundantly archives the landmark configuration. Reconstruction of the form from truss measures provides Cartesian coordinates for landmarks and allows estimation of, and compensation for, measurement error. Samples of forms may be averaged and standardized to one or more common reference sizes by regression of measured distances on a composite measure of body size, followed by reconstruction of the form using distance values predicted by the regression functions at some standard body size. Principal component loadings of distance measures may be indicated directly on the truss network to display patterns of within-group allometry or between-group shape differences. Because the truss enforces use of cross measurements, discrimination among groups may be enhanced. Composite mapped forms are useful in biorthogonal analyses of differences in shape because they allow the comparison of averaged forms among samples. Certain patterns of principal component loadings are concordant with, and provide an initial sampling of, the biorthogonal grids for these deformations.