Geometric morphometrics in ammonoids based on virtual modelling

Abstract

Linear morphometrics is the most widely applied technique to study the variation of the conch morphology in ammonoids and other ectocochleate cephalopods. However, because this method frequently relies upon a few linear measurements, it lacks the explanatory power to accurately characterize the shape of the whorl cross-section, which is instead discussed solely in descriptive terms, e.g., elliptical, triangular, or subquadrate. Here, we introduce a landmark-based geometric morphometric approach to study ammonoid whorl cross-sections, derived from the regularly used morphometric parameters in cephalopods. This new technique uses virtual modelling to generate semilandmark configurations and virtual models of whorl cross-sections. We applied it to study 50 ammonoid specimens belonging to 48 genera exhibiting a wide range of morphologies and ages. Results indicate that this new method is appropriate to describe the shape of ammonoid whorl cross-sections, allowing us to construct a morphospace showing several biological patterns (e.g., clustering and homeomorphy), and complex morphological transformations that, in some cases, correlate with evolutionary tendencies described by previous authors. Further, this technique can be used to generate the basic segment required for the elaboration of the virtual models employed in hydrostatic and hydrodynamic studies.

The intriguing shapes of the ammonoid whorl

“…Results of this work are congruent with previous morphological trends observed on the ammonoid WP and the general conch morphology showing close similarities to other morphospaces (Saunders et al, 2004;Korn and Klug, 2012;McGhee, 2012;Ritterbush and Bottjer, 2012;Tendler et al, 2015;Gerber, 2017). In this regard, the rates of variance and the transformations obtained for the principal components agreed with previous results (Morón-Alfonso et al, 2021) indicating that most of the WP variation is summarised by the first three principal components (around 87%). Here we provide a more extensive depiction of this morphospace showing representations of the predicted morphologies and their possible variations .…”

“…The geometric morphometric methodology used here was described by Morón-Alfonso et al (2021). It employs a basic landmark configuration derived from the morphometric parameters that is translated from virtual models of the selected samples using a subdivision surface algorithm (Figure 1).…”

“…Abbreviations: ah, aperture height; dm, diameter; iz, imprint zone; wh, whorl height, ww, whorl width. B-E) Geometric morphometric model to study the whorl shape presented in Morón-Alfonso et al (2021). B) Basic virtual model (grey area) showing the corresponding configuration based on 18 semi-landmarks.…”

Morphometric analysis of the Late Cretaceous Placenticeras of Alabama, USA: sexual dimorphism, allometry, and implications for taxonomy

“…The accretionary growth of ammonoid shells records their ontogenetic trajectories, which are often studied via precisely located cross sections of individual shells (a "longitudinal sampling strategy," in the terminology of Cock [1966], Klingenberg et al [1996], and Korn [2012]). Although this method reveals the full ontogenetic trajectory for sampled individuals and provides cross sections that are suitable for landmark-based approaches (e.g., Bischof et al 2021;Morón-Alfonso et al 2023), it is a difficult, time-consuming, and destructive process, and often prohibitively reduces the number of specimens that can be analyzed (for both practical and taphonomic reasons; Naglik et al 2015;Korn 2012). In this study, we use a more flexible sampling strategy (a "mixed longitudinal approach" in the terminology of Cock [1966]), which allows the inclusion of many additional specimens and avoids destructive sampling of museum specimens while still providing information on ontogeny.…”