Affine Transformations as a Model of Virtual Form Change for Generating Morphospaces

Abstract

Affine change might be used to seek general patterns of variation or to envisage new ways of describing and evaluating form change. In this paper, we assume a theoretical perspective and show a strategy for generating affine morphospaces (ordered collections of affine-transformed images of a base form), by means of a new computer program called D’ARCYGRAPH. We propose the use of affine transformations as models of change that might induce the search for new explanations based on the constraints imposed by the properties of affine change, that is, their invariants.

We introduce a technique to elaborate affine morphospaces; as an example, we build the morphospace of pelvic girdles generated by using as a base form the pelvis of Deinonychus antirrhopus (Dinosauria, Theropoda). We explore possible transformation paths from this base form, which is considered to be the closest sister group of the major clade Ayes. A discussion of the type of variables (called “dispositionals”) that can be used and explained by the affine model is provided. We conclude that it is possible to build an affine trend that simulates the fossil record transition, Theropoda—Aves, according to these dispositional variables.

Also, we introduce an interactive strategy for the superimposition of forms, without any automatic optimality criteria. A comparison with other superimposition methods, based on tridactyl dinosaur footprints is discussed.