Quantification of ontogenetic allometry in ammonoids

Ammonoids are well-known objects used for studies on ontogeny and phylogeny, but a quantification of ontogenetic change has not yet been carried out. Their planispirally coiled conchs allow for a study of "longitudinal" ontogenetic data, that is data of ontogenetic trajectories that can be obtained from a single specimen. Therefore, they provide a good model for ontogenetic studies of geometry in other shelled organisms. Using modifications of three cardinal conch dimensions, computer simulations can model artificial conchs. The trajectories of ontogenetic allometry of these simulations can be analyzed in great detail in a theoretical morphospace. A method for the classification of conch ontogeny and quantification of the degree of allometry is proposed. Using high-precision cross-sections, the allometric conch growth of real ammonoids can be documented and compared. The members of the Ammonoidea show a wide variety of allometric growth, ranging from near isometry to monophasic, biphasic, or polyphasic allometry. Selected examples of Palaeozoic and Mesozoic ammonoids are shown with respect to their degree of change during ontogeny of the conch.