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...

The seemingly aberrant coiling of heteromorphic ammonoids suggests that they underwent more significant changes in hydrostatic properties throughout ontogeny than their planispiral counterparts. Such changes may have been responses to different selective pressures at different life stages. The hydrostatic properties of three species of Didymoceras (D. stevensoni, D. nebrascense, and D. cheyennense) were investigated by creating virtual 3D models at several stages during growth. These models were used to compute the conditions for neutral buoyancy, hydrostatic stability, orientation during life, and thrust angles (efficiency of directional movement). These properties suggest that Didymoceras and similar heteromorphs lived low-energy lifestyles with the ability to hover above the seafloor. The resultant static orientations yielded a downward-facing aperture in the hatchling and a horizontally facing aperture throughout most of the juvenile stage, before terminating in an upward direction at maturity. Relatively high hydrostatic stabilities would not have permitted the orientation of Didymoceras to be considerably modified with active locomotion. During the helical phase, Didymoceras would have been poorly suited for horizontal movement, yet equipped to pirouette about the vertical axis. Two stages throughout growth, however, would have enhanced lateral mobility: a juvenile stage just after the formation of the first bend in the shell and the terminal stage after completion of the U-shaped hook. These two more mobile phases in ontogeny may have improved juvenile dispersal potential and mate acquisition during adulthood, respectively. In general, life orientation and hydrostatic stability change more wildly for these aberrantly coiled ammonoids than their planispiral counterparts.

Nipponites is a heteromorph ammonoid with a complex and unique morphology that obscures its mode of life and ethology. The seemingly aberrant shell of this Late Cretaceous nostoceratid seems deleterious. However, hydrostatic simulations suggest that this morphology confers several advantages for exploiting a quasi-planktic mode of life. Virtual, 3D models of Nipponites mirabilis were used to compute various hydrostatic properties through 14 ontogenetic stages. At each stage, Nipponites had the capacity for neutral buoyancy and was not restricted to the seafloor. Throughout ontogeny, horizontally facing to upwardly facing soft body orientations were preferred at rest. These orientations were aided by the obliquity of the shell's ribs, which denote former positions of the aperture that were tilted from the growth direction of the shell. Static orientations were somewhat fixed, inferred by stability values that are slightly higher than extant Nautilus. The initial open-whorled, planispiral phase is well suited to horizontal backwards movement with little rocking. Nipponites then deviated from this bilaterally symmetric coiling pattern with a series of alternating U-shaped bends in the shell. This modification allows for proficient rotation about the vertical axis, while possibly maintaining the option for horizontal backwards movement by redirecting its hyponome. These particular hydrostatic properties likely result in a tradeoff between hydrodynamic streamlining, suggesting that Nipponites assumed a low energy lifestyle of slowly pirouetting in search for planktic prey. Each computed hydrostatic property influences the others in some way, suggesting that Nipponites maintained a delicate hydrostatic balancing act throughout its ontogeny in order to facilitate this mode of life.

The spatial scaling of 77 hemisutures from 65 species of Cretaceous heteromorphic ammonites was quantified with the fractal box‐counting method. Fractal dimensions within Baculites compressus did not significantly differ between adult hemisutures; however, the juvenile suture of this species did exhibit a significantly lower fractal dimension. This suggests that variation in sutural complexity between explicitly adult ontogenetic stages may not contribute to significant noise in comparisons between other species/morphotypes. High‐spired, three‐dimensionally coiled heteromorphs with a larger degree of septal asymmetry exhibit higher fractal dimensions in outer whorl hemisutures than inner whorl hemisutures due to their elongation and improved space occupation over a larger whorl surface. Three‐dimensionally coiled ammonites also have higher fractal dimensions on average (mean Db = 1.45) with respect to their 2‐D coiled counterparts (mean Db = 1.38). All ammonites in this study exhibit a positive trend between sutural complexity and shell size (proxied by whorl height). These relationships suggest that septal frilling is constrained by shell morphology and whorl section geometry during septal morphogenesis. This, in turn, influences the scaling, space‐filling properties and scaling limits of ammonitic suture patterns. Sutural/septal complexity is also found to positively influence the amount of liquid retained in marginal septal recesses. However, as these septa approach larger scales, less cameral liquid is retained per septal mass. This may further explain the positive relationship between sutural complexity and shell size.