Trend‐surface analysis of transformation grids

Abstract

Computer methods are described for trend‐surface analysis of D'Arcy Thompson transformation grids, illustrated by data on skulls and jaws of hominoids. In comparing two diagrams the following steps are required. First, corresponding points on each diagram are marked, and their co‐ordinates are recorded. Second, the diagrams are scaled and fitted to give the best possible fit; this gives measures of size and shape difference. Third, the displacements of each point relative to its partner on the other diagram are subjected to trend‐surface analysis. The displacements are analysed in terms of linear, quadratic, cubic and higher order trends. Fourth, the differences based on the trends alone can now be estimated. The results on the illustrative examples are discussed, together with the difficulties in applying such methods. The nature of taxonomic (phenetic) affinity is also discussed, with suggestionsfor measuring different components of this concept. The techniques show promise for a wide variety of taxonomic and morphological applications.