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

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. These orientations were aided by the obliquity of the shell’s ribs, which were parallel to former positions of the aperture during life. 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 deviates from this 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.

. This condition also depends upon 108 shell thickness and the densities assigned to each component of the living animal, which have 109 been somewhat variable in previous research [39,41]. 110 Previous studies have demonstrated that heteromorph ammonoids may have been able to 111 achieve much different life orientations than their planispiral counterparts [20,29,[34][35][36][37][38][39][42][43][44][45]. 112 These living cephalopods would have assumed some static orientation when their centers of 113 buoyancy and mass were vertically aligned [41,46,47] (Fig 1). The difficulty to which these 114 living cephalopods could deviate from their static orientation depends on hydrostatic stability, 115 which is proportionate to the separation between the centers of buoyancy and mass [20]. High stability would have reduced the influence of external forms of energy on orientation, but would 117 have simultaneously made it more difficult for the living cephalopod to self-modify its 118 orientation [36]. 119 The directional efficiency of movement (thrust angle) depends upon the relative position [20]. This method for virtual reconstruction is favorable for Nipponites because specimens of this 149 genus are rarely found complete; discouraging destructive sampling techniques like serial 150 grinding tomography. Computed tomography (CT) scans of such specimens also lack contrasts 151 of X-ray attenuation factors to distinguish the shell from its surrounding materials [52]. 152 However, each of these tomographic techniques can provide very accurate measurements of 153 hydrostatic properties and volumes when the specimens are adequate for imaging [52][53][54][55][56][57][58][59]. remarkable degree of preservation. Most of the ontogeny is preserved for this specimen with 158 minimal matrix on the inside (Fig 2A). However, two portions had to be virtually reconstructed; 159 1) the crushed ~5 cm section of the adoral-most body chamber, and 2) the earliest crioconic 160 whorls that are partially embedded in a remnant of the original concretion. These two portions of 161 the shell were reconstructed (Fig 2B)   Nature and Science) MP35490 (Fig 3), producing a mesh denoting the entire shell without septa.  (Table 1). C, Extruded 182 septa generated from the suture pattern. D, Extruded shell and septa models unified together to 183 produce a single, manifold 3D mesh of the entire shell. (black) and septa (grey) as a function of whorl height. Measurements were recorded from 186 specimen NMNS PM35490 and used to define thickness in the virtual model.   (Fig 3). These final septa ( Fig 2C) were merged with the extruded, external shell to produce a 218 single, manifold 3D mesh of the entire, septate shell ( Fig 2D).
Where V wd and ρ wd are the volume and density of the water displaced, V sb and ρ sb are the volume 255 and density of the soft body, V sh and ρ sh are the volume and density of the shell, ρ cl is the density 256 of cameral liquid, ρ cg is the density of cameral gas, and V ct is the total cameral volume of the 257 phragmocone. A soft body density of 1.049 g/cm 3 is preferred based on the measurement of  The total center of mass is weighted according to each material of unique density (i.e., the 263 soft body, shell, cameral liquid, and cameral gas in the current study). Each individual center of 264 mass for the soft body, shell, cameral liquid, and cameral gas were computed in MeshLab [75]    Rotational thrust angles (θ tr ) were measured between the thrust vector (perpendicular to 288 the aperture) and the rotational axis ( Fig 1C). A rotational thrust angle of 90° would allow pure 289 rotation to take place, while angles of 0° and 180° would result in translational movement.

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The unknown soft body can produce errors in buoyancy calculations depending upon its 293 total volume. By comparing the soft body used herein with a soft body that terminates at the 294 aperture, there is only a 0.5% difference in Φ. Similarly, the mass distribution is not significantly 295 different between either model (a 0.7 % difference in S t ).

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Because the body chamber ratio was variable on measured specimens, this ratio was 297 manipulated by removing one septum and adding one septum to the terminal stage model with a 298 body chamber ratio of 42%. Removing one septum increases the total body chamber ratio to 299 46%. This change yields a 16% increase in Φ (to 84.6%) and a 7% increase in S t (to 0.0786).

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Adding one septum decreases the body chamber ratio to 37%. Yielding a 10% decrease in Φ (to 301 65.7%) and an 8% decrease in S t (to 0.0676). These changes suggest that small error (~10%) in 302 body chamber ratio would not significantly alter calculations of buoyancy or the characteristics 303 of the mass distribution. Small deviations from the ideal body chamber ratio took place (   the juvenile criocone phase, Φ decreases and stabilizes at its lower values (Fig 7). Hydrostatic 323 stability (S t ) follows a similar decreasing trend and does not significantly oscillate (Fig 7). These fashion throughout ontogeny, ranging between approximately -11 and 99 degrees (Fig 7).

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Apertural orientations significantly turned downwards are not observed. The juvenile criocone 329 phase has apertural angles of about 70°, followed by complex oscillations as the alternating U-330 shaped bends develop. Afterwards, there is some degree of regularity in orientation, mostly 331 exhibiting horizontal and diagonally upwards directions (Fig 7).  thrust is produced normal to the aperture (Fig 9). While the normalized lever arm lengths seem to 370 decrease during ontogeny, sufficient torques for rotation can only be produced when the rotational thrust angle is high. Furthermore, the x-component of the normalized lever arm is not 372 significantly lower than the total normalized lever arm during ontogeny, suggesting that the 373 subhorizontal declination of the total lever arms would still provide significant rotational 374 movement in ontogenetic stages after the crioconic phase (Fig 9). Hydrostatic simulations reveal that Nipponites mirabilis had the capacity for neutral 388 buoyancy throughout its ontogeny, retaining some amount of cameral liquid in the shell to 389 compensate for residual buoyancy (Fig 7). These results support the buoyancy calculations of ontogenetic stages (Fig 7). These observed orientations may have accommodated a lifestyle of would be about 10° less (downward) for many of the examined ontogenetic stages (Fig 8). The Complex heteromorphy in an evolutionary context 468 Okamoto [78] suggests that Nipponites originated from the nostoceratid, Similarly, throughout the late Turonian and Coniacian, a larger degree of uncoiling takes place 491 for specimens found in successively younger strata [78]. These specimens cluster into three 492 distinguished morphotypes [78] that may have become more stable and adept at rotation as they Nipponites contrast with those of its probable ancestor, Eubostrychoceras [78]. These differences 531 in morphology along with the hydrostatic analyses in the current study infer that the seemingly 532 convoluted coiling scheme of Nipponites represents unique adaptive solutions to several 533 hydrostatic constraints, rather than random morphological aberration.