Combining the Tools of Geometric Morphometrics

Abstract

The greatest strength of the new geometric morphometrics is the system of interrelated multivariate and graphical procedures it offers for a variety of analytic questions involving landmark data. A typical analysis will begin with the conversion of landmark data into a multivariate statistical representation of shape, will continue with a series of broadly familiar multivariate matrix manipulations, and will conclude by inspection of a considerable variety of diagrams that represent the findings in both the space of shape coordinates per se and the space of the two-or three-dimensional image of the organism. The choices under the first heading, the passage to a multivariate representation of shape, include two-point shape coordinates, partial warp scores, and Procrustes residuals. Each of these except the partial warp scores is unsuitable for some subset of the reasonable matrix manipulations; for instance, shape coordinates do not supply sensible principal components analyses, and Procrustes residuals cannot lead to sound canonical variate analyses without modification. The modes of diagramming data include thin-plate splines, partial warp splines and scatters, Procrustes residual scatters, and resistant-fit scatters, among others. Most analyses benefit greatly from exploiting more than one of these.