Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: hydrodynamic analyses of restoring moments from 3D-printed, neutrally buoyant models

Abstract

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.

The balancing act of Nipponites mirabilis (Nostoceratidae, Ammonoidea): Managing hydrostatics throughout a complex ontogeny

“…The unique shell of this genus raises questions regarding how its changes in coiling may reflect the modification of syn vivo hydrostatic properties. Such a tactic was suggested for other morphologies of heteromorph ammonoids [17,19,20,[34][35][36][37][38][39]. These physical properties are vital to understand if Nipponites was a benthic crawler, a planktic drifter, an active swimmer, or just an atypical genus with a morphology that was not detrimental for survival or reproduction.…”

The balancing act ofNipponites mirabilis(Nostoceratidae, Ammonoidea): managing hydrostatics during a complex ontogenetic trajectory

“…While the hydrostatic stability index slightly decreases throughout ontogeny, the computed values are all larger than the extant Nautilus (~0.05 [40]), suggesting that living Nipponites probably was not able to significantly modify its own apertural orientation (in terms of its vertical orientation). The highest stability in ectocochleates seem to occur for the orthocones, especially those without cameral deposits [36,40]. Lower stability values should occur for morphotypes with larger body chambers that wrap around the phragmocone (e.g., serpenticones [6,47,49]).…”

“…That is, most of the soft body is still distributed below the phragmocone, lowering the center of mass relative to the center of buoyancy and increasing hydrostatic stability. In most cases, uncoiling of the shell seems to generally increase hydrostatic stability compared to planispiral ectocochleates [20,36,37,39,45,76].…”

“…Heteromorph ammonoids, however, were very diverse, disparate, and successful throughout the Cretaceous [45,79–81]. Furthermore, the coiling schemes of several morphotypes of heteromorph ammonoids suggest that they exploited unique solutions to manage the physical properties that constrained their modes of life by modifying their shells to serve primarily as specialized hydrostatic devices [36–39]. The hydrostatic simulations of the current study reveal that the coiling of Nipponites , which seems biologically absurd, does in fact confer an advantage for specific syn vivo orientations and with rotational capabilities.…”

“…This depends upon the body chamber to phragmocone ratio. If the phragmocone (the chambered portion of the shell) is too small, the living cephalopod would not be able to compensate for its organismal weight and it would become negatively buoyant [34,36,40]. This condition also depends upon shell thickness and the densities assigned to each component of the living animal, which have been somewhat variable in previous research [39,41].…”