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We use three-dimensional (3D) numerical models to examine critical hydrodynamic characteristics of a range of shell shapes found in extinct ammonoid cephalopods. Ammonoids are incredibly abundant in the fossil record and were likely a major component of ancient marine ecosystems. Despite their fossil abundance we lack significant soft body remains, which has made it historically difficult to investigate the potential life modes and ecological roles that these organisms played. By employing numerical tools to study how the morphology of a shell affected an ammonite's hydrodynamics, we can build a foundation for hypothesizing and testing changes in the organism's capabilities through time. To achieve this goal, the study was carried out in two major steps. First, we applied a number of simulation methods to a known problem, the drag coefficient of a half-sphere, to select the most appropriate modeling method that is accurate and efficient. These were further checked against previous experimental results on ammonoid hydrodynamics. Next, we produced 3D models of the ammonoid shells using Blender and Zbrush where each shell model emulated a specific fossil ammonoid, recent Nautilus, or an idealized shell forms created by systematically varying shell inflation and umbilical exposure. We test the hypothesis that both the overall shell inflation and umbilical exposure will increase the drag experienced by a similarly sized ammonoid shell as it moves through water relative to other morphologies. ANSYS FLUENT was employed to execute the study. We further compare our simulation results to published experimental measurements of drag on ammonoid fossil replicas and live Nautilus. The simulation results provide accuracy within an order of magnitude of published values, across the tested range of water flow velocities (1-50 cm/s). The simulated drag measurements demonstrate a first-order sensitivity to shell inflation, with a second-order effect from umbilical exposure. The impact of a larger umbilical exposure (shells that are more evolute) is minimal at low velocities, but substantial at higher velocities. We conclude that the overall shell inflation and umbilical exposure influence an individual shell's drag coefficient, therefore, influence the hydrodynamic efficiency.

A boom in technological advancements over the last two decades has driven a surge in both the diversity and power of analytical tools available to biomechanical and functional morphology research. However, in order to adequately investigate each of these dense datasets, one must often consider only one functional narrative at a time. There is more to each organism than any one of these form-function relationships. Joint performance landscapes determined by maximum likelihood are a valuable tool that can be used to synthesize our understanding of these multiple functional hypotheses to further explore an organism's ecology. We present an example framework for applying these tools to such a problem using the morphological transition of ammonoids from the Middle Triassic to the Early Jurassic. Across this time interval, morphospace occupation shifts from a broad occupation across Westermann Morphospace to a dense occupation of a region emphasizing an exposed umbilicus and modest frontal profile. The hydrodynamic capacities and limitations of the shell have seen intense scrutiny as a likely explanation of this transition. However, conflicting interpretations of hydrodynamic performance remain despite this scrutiny, with scant offerings of alternative explanations. Our analysis finds that hydrodynamic measures of performance do little to explain the shift in morphological occupation, highlighting a need for a more robust investigation of alternative functional hypotheses that are often intellectually set aside. With this we show a framework for consolidating the current understanding of the form-function relationships in an organism, and assess when they are insufficiently characterizing the dynamics those data are being used to explain. We aim to encourage the broader adoption of this framework and these ideas as a foundation to bring the field close to comprehensive synthesis and reconstruction of organisms.

A substantial body of research has been accumulated around ammonoids over several decades. A core aspect of this research has been attempts to infer their life mode from analysis of the morphology of their shells and the drag they incur as that shell is pushed through the water. Tools such as Westermann Morphospace have been developed to investigate and scaffold hypotheses about the results of these investigations. We use Computational Fluid Dynamics (CFD) to simulate fluid flow around a suite of 24 theoretical ammonoid morphologies to interrogate systematic variations within this space. Our findings uphold some of the long-standing expectations of drag behavior; conch inflation has the greatest influence over ammonoid drag. However, we also find that other long-standing assumptions, such as oxyconic ammonoids being the best swimmers, are subject to substantial variation and nuance resulting from their morphology that is not accounted for through simple drag assessment.

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