Describing Ammonite shape using Fourier analysis

Abstract

A number of geometrical methods for comparing shapes have been developed recently. This paper explores two approaches for analyzing the morphological variation of some invertebrate fossil characteristics such as rib pattern and whorl section shape: (1) landmarks analysis (Procrustes methods), (2) mathematical modeling by Fourier analysis. The morphometric analysis has been applied to a faunal sequence of Graphoceratidae (Ammonitina) taken in the central High Atlas. In the first stage of analysis, we used landmarks to describe shapes. This calculation is done through the “Procrustes” program whose results generate phenetic trees with a typically morphological significance and whose nodes convey some degrees of morphological similarities among the different taxa analyzed. In the second stage of describing ammonite shape, a new approach will offer us a valuable morphologic descriptor by modeling the whorl section. It allows for transcription in the form and an equation will be used for descriptive variables which represent necessary data for an analysis in principal components. Factorial planes then correspond to morphological space within which the analyzed individuals are distributed. In this way, it is possible to determine the groups for which whorl section morphologies show similarities. These two morphometric techniques offer a valuable tool for the analysis and comparison of morphologies for both rib shape and whorl section. This allows one not only to analyze morphological diversity in Graphoceratidae with more reliability, but also to highlight the most important convergences among the analyzed taxa.