Externally shelled cephalopods with coiled, planispiral conchs were ecologically successful for hundreds of millions of years. These animals displayed remarkable morphological disparity, reflecting comparable differences in physical properties that would have constrained their life habits and ecological roles. To investigate these constraints, self-propelling, neutrally buoyant, biomimetic robots were 3D-printed for four disparate morphologies. These robots were engineered to assume orientations computed from virtual hydrostatic simulations while producing Nautilus-like thrusts. Compressed morphotypes had improved hydrodynamic stability (coasting efficiency) and experienced lower drag while jetting backwards. However, inflated morphotypes had improved maneuverability while rotating about the vertical axis. These differences highlight an inescapable physical tradeoff between hydrodynamic stability and yaw maneuverability, illuminating different functional advantages and life-habit constraints across the cephalopod morphospace. This tradeoff reveals there is no single optimum conch morphology, and elucidates the success and iterative evolution of disparate morphologies through deep time, including non-streamlined forms.

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Theoretical 3D models were digitally reconstructed from a phragmocone section of Baculites compressus in order to investigate the hydrostatic properties of the orthoconic morphotype. These virtual models all had the capacity for neutral buoyancy (or nearly so) and were highly stable with vertical syn vivo orientations. Body chamber lengths exceeding approximately 40% of the shell length cause buoyancy to become negative with the given modeled proportions. The distribution of cameral liquid within the phragmocone does not change orientation and only slightly influences hydrostatic stability. The mass of cameral liquid required to completely reduce stability, permitting a non-vertical static orientation, would cause the living cephalopod to become negatively buoyant. A concave dorsum does not significantly change the mass distribution and results in a 5° dorsal rotation of the aperture from vertical. The restoring moments acting to return neutrally buoyant objects to their equilibrium position were investigated using 3D-printed models of Nautilus pompilius and Baculites compressus with theoretically equal masses and hydrostatic stabilities to their virtual counterparts. The N. pompilius behaved as an underdamped harmonic oscillator during restoration due to its low hydrostatic stability and drag relative to the B. compressus model. In contrast, the B. compressus model more quickly returns to its equilibrium position without oscillating (overdamped system). The thrust required to overcome such a large restoring moment was explored using several extant cephalopod analogues. Significant angles of displacement were only achieved with coleoid-like thrusts, which were unrealistically high despite the probable similarities in their locomotor design. These maximum bursts of thrust may have been too energetically expensive and would preclude an unusual form of locomotion in a non-vertical orientation. These results suggest baculitids and other orthocones with similar hydrostatic stabilities probably lived a nektic to quasiplanktic mode of life with a primarily vertical orientation and mobility.

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Heteromorphs are ammonoids forming a conch with detached whorls (open coiling) or non‐planispiral coiling. Such aberrant forms appeared convergently four times within this extinct group of cephalopods. Since Wiedmann's seminal paper in this journal, the palaeobiology of heteromorphs has advanced substantially. Combining direct evidence from their fossil record, indirect insights from phylogenetic bracketing, and physical as well as virtual models, we reach an improved understanding of heteromorph ammonoid palaeobiology. Their anatomy, buoyancy, locomotion, predators, diet, palaeoecology, and extinction are discussed. Based on phylogenetic bracketing with nautiloids and coleoids, heteromorphs like other ammonoids had 10 arms, a well‐developed brain, lens eyes, a buccal mass with a radula and a smaller upper as well as a larger lower jaw, and ammonia in their soft tissue. Heteromorphs likely lacked arm suckers, hooks, tentacles, a hood, and an ink sac. All Cretaceous heteromorphs share an aptychus‐type lower jaw with a lamellar calcitic covering. Differences in radular tooth morphology and size in heteromorphs suggest a microphagous diet. Stomach contents of heteromorphs comprise planktic crustaceans, gastropods, and crinoids, suggesting a zooplanktic diet. Forms with a U‐shaped body chamber (ancylocone) are regarded as suspension feeders, whereas orthoconic forms additionally might have consumed benthic prey. Heteromorphs could achieve near‐neutral buoyancy regardless of conch shape or ontogeny. Orthoconic heteromorphs likely had a vertical orientation, whereas ancylocone heteromorphs had a near‐horizontal aperture pointing upwards. Heteromorphs with a U‐shaped body chamber are more stable hydrodynamically than modern Nautilus and were unable substantially to modify their orientation by active locomotion, i.e. they had no or limited access to benthic prey at adulthood. Pathologies reported for heteromorphs were likely inflicted by crustaceans, fish, marine reptiles, and other cephalopods. Pathologies on Ptychoceras corroborates an external shell and rejects the endocochleate hypothesis. Devonian, Triassic, and Jurassic heteromorphs had a preference for deep‐subtidal to offshore facies but are rare in shallow‐subtidal, slope, and bathyal facies. Early Cretaceous heteromorphs preferred deep‐subtidal to bathyal facies. Late Cretaceous heteromorphs are common in shallow‐subtidal to offshore facies. Oxygen isotope data suggest rapid growth and a demersal habitat for adult Discoscaphites and Baculites. A benthic embryonic stage, planktic hatchlings, and a habitat change after one whorl is proposed for Hoploscaphites. Carbon isotope data indicate that some Baculites lived throughout their lives at cold seeps. Adaptation to a planktic life habit potentially drove selection towards smaller hatchlings, implying high fecundity and an ecological role of the hatchlings as micro‐ and mesoplankton. The Chicxulub impact at the Cretaceous/Paleogene (K/Pg) boundary 66 million years ago is the likely trigger for the extinct...