Evolution of shape in oligocene and mioceneNotocarinovalva (Ostracoda, Crustacea): A multivariate statistical study

Largely due to L. F. Bookstein, geometric morphometrics has been developed as an amalgamation of techniques drawn from mathematical statistics, non-Euclidean geometry and computer graphics, applied to labelled points (landmarks) and the biological images upon which they are registered. A tool of fundamental importance is the method of interpolation known as the thin-plate spline. Bookstein's sample-oriented procedure of relative warps, applied to data composed of coordinate pairs observed on eight landmarks on three samples of two species of fossil marine ostracods (bivalved microcrustacean),Notocarinovalva airella andN. yulecartensis, separated in time, is used to obtain weight matrices, which, when appropriately partitioned, constitute the familiar data matrices of multivariate statistical analysis. Standard multivariate statistical analysis of samples may be carried out in the tangent space to shape space at the Procrustes average shape. Linear discriminant function scores were used for assessing, approximately, the evolutionary relevance of shape change and change in size (based on standard distance measures) in the species from the upper and lower Oligocene and lower middle Miocene of Victoria, Australia. The findings indicate that a small, though consistent, change in non-uniform shape of the carapace has taken place. The analysis indicates that the evolution in shape of the carapace could have been caused by random genetic drift in moderately large populations, tempered by weak selection.