Investigation of simulated tectonic deformation in fossils using geometric morphometrics

Tectonic deformation is an important part of the taphonomic histories of many fossils. Although the effects of deformation, and methods to remove those effects, have been a subject of inquiry for over a century, systematic testing under known parameters has never been used to determine how the effects of deformation and the performance of retrodeformation techniques might vary. Comparative studies of morphology depend on the accurate estimation of variance-covariance structure, so an understanding of the effects of retrodeformation on covariance structure is important in assessing the utility of these methods. Here we address these issues by using geometric morphometric simulations. Nondeformed data sets were generated from specimens of the extant turtle Emys inarmorata, which were known by definition to be nondeformed, and which possess a known ontogenetic signal. Deformation was simulated by applying a combination of uniform shear and uniform compression/dilation to the data. Data were retrodeformed by reflection and averaging of bilaterally symmetric landmarks, use of a principal components analysis to identify a deformation component of shape variation, and removal of the affine component of shape variation among specimens. Deformation increased the amount of variance in the data, as well as altering the variance structure. However, low to moderate levels of deformation did not prevent the confident recovery of the known ontogenetic signal in some cases. The tested retrodeformation techniques did not work well. They either removed too little or too much variance from the data, and provided little improvement in variance structure. Retrodeformation often did not improve our ability to extract the ontogenetic signal from the data, and in some cases introduced an artifactual relationship between size and shape. All of the scrutinized methods showed some properties, such as reducing variance or producing visually appealing images of specimens, that could make them appear to be working in cases where the correct biological signal is not known. This emphasizes the need for simulation testing in the development and evaluation of retrodeformation techniques.