Raw Data for FEA models of the labeled Shells

Raw data for PeerJ manuscript: Comparative cephalopod shell strength and the role of septum morphology on stress distribution.<div><br></div><div>Files include nodal values for displacement magnitude and principal stresses for all models used in the above study.<br><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><h2><br></h2></div><div><br></div></div

Complexity of septal surfaces and suture lines in ammonoids

Die Funktion komplexer Ammonitensepten ist ein kontroverses Thema. Früher genutzte mathematische Modelle, stellen eine unzureichende Annäherung dar. Nun wurden computertomographische empirische Modelle zur Klärung herangezogen. Die physiologische Annahme, Septenkomplexität erhöhe die relative Oberfläche der Kammern, um einen schnellen Flüssigkeitstransport zu gewährleisten, wurde widerlegt. Es wurde gezeigt, dass komplexe Septen helfen höhere Schalenverluste durch schnelleres Rückfluten von Flüssigkeit, zu kompensieren. Die mechanische Hypothese, Septenkomplexität sei eine Anpassung an tiefere Habitate, wurde widerlegt. Vergleichende Finite-Element-Analysen zeigten, dass größere Amplituden zu erhöhter Belastung durch hydrostatischen Druck führen statt diesen zu reduzieren. Bei Punktbelastung jedoch wird auftretender Stress durch komplexe Septen reduziert (Bruchflächen minimiert), was auf eine potenzielle Schutzfunktion der Septenkomplexität gegenüber bezahnten Raubtierattacken deutet

Comparative cephalopod shell strength and the role of septum morphology on stress distribution

The evolution of complexly folded septa in ammonoids has long been a controversial topic. Explanations of the function of these folded septa can be divided into physiological and mechanical hypotheses with the mechanical functions tending to find widespread support. The complexity of the cephalopod shell has made it difficult to directly test the mechanical properties of these structures without oversimplification of the septal morphology or extraction of a small sub-domain. However, the power of modern finite element analysis now permits direct testing of mechanical hypothesis on complete, empirical models of the shells taken from computed tomographic data. Here we compare, for the first time using empirical models, the capability of the shells of extant Nautilus pompilius, Spirula spirula, and the extinct ammonite Cadoceras sp. to withstand hydrostatic pressure and point loads. Results show hydrostatic pressure imparts highest stress on the final septum with the rest of the shell showing minimal compression. S. spirula shows the lowest stress under hydrostatic pressure while N. pompilius shows the highest stress. Cadoceras sp. shows the development of high stress along the attachment of the septal saddles with the shell wall. Stress due to point loads decreases when the point force is directed along the suture as opposed to the unsupported chamber wall. Cadoceras sp. shows the greatest decrease in stress between the point loads compared to all other models. Greater amplitude of septal flutes corresponds with greater stress due to hydrostatic pressure; however, greater amplitude decreases the stress magnitude of point loads directed along the suture. In our models, sutural complexity does not predict greater resistance to hydrostatic pressure but it does seem to increase resistance to point loads, such as would be from predators. This result permits discussion of palaeoecological reconstructions on the basis of septal morphology. We further suggest that the ratio used to characterize septal morphology in the septal strength index and in calculations of tensile strength of nacre are likely insufficient. A better understanding of the material properties of cephalopod nacre may allow the estimation of maximum depth limits of shelled cephalopods through finite element analysis

Ammonoid Buoyancy

The buoyancy of ammonoids is one of the most controversial issues of ammonoid paleobiology. This chapter gives a short historical review about attempts made to clarify the potential function of the cephalopod chambered shell (phragmocone) and ammonoid life habits either as benthic crawler or as free swimmers in the water column. In order to understand efficiency of buoyancy control and the mode of life of the extinct ammonoids decoupling of cameral liquid, process of osmotic pumping including local osmosis, pre-septal gas, and the role of the siphuncle and cameral liquid were discussed extensively. It is accepted that processes like osmotic pumping and local osmosis act in ammonoids due to similar architecture of the extant relatives including the presence of a siphuncle. Additionally, the calculation of buoyancy represents a major task which depends on exact reconstructions of volumes and densities for shell and soft body. With the rise of 3D-imaging techniques the determination of volumes were enhanced and now represent an important step towards more precise buoyancy calculations

Data from: A new approach using high-resolution computed tomography to test the buoyant properties of chambered cephalopod shells

The chambered shell of modern cephalopods functions as a buoyancy apparatus, allowing the animal to enter the water column without expending a large amount of energy to overcome its own weight. Indeed, the chambered shell is largely considered a key adaptation that allowed the earliest cephalopods to leave the ocean floor and enter the water column. It has been argued by some, however, that the iconic chambered shell of Paleozoic and Mesozoic ammonoids did not provide a sufficiently buoyant force to compensate for the weight of the entire animal, thus restricting ammonoids to a largely benthic lifestyle reminiscent of some octopods. Here we develop a technique using high-resolution computed tomography to quantify the buoyant properties of chambered shells without reducing the shell to ideal spirals or eliminating inherent biological variability by using mathematical models that characterize past work in this area. This technique has been tested on Nautilus pompilius and is now extended to the extant deep-sea squid Spirula spirula and the Jurassic ammonite Cadoceras sp. hatchling. Cadoceras is found to have possessed near-neutral to positive buoyancy if hatched when the shell possessed between three and five chambers. However, we show that the animal could also overcome degrees of negative buoyancy through swimming, similar to the paralarvae of modern squids. These calculations challenge past inferences of benthic life habits based solely on calculations of negative buoyancy. The calculated buoyancy of Cadoceras supports the possibility of planktonic dispersal of ammonite hatchlings. This information is essential to understanding ammonoid ecology as well as biotic interactions and has implications for the interpretation of geochemical data gained from the isotopic analysis of the shell

Chamber volume development, metabolic rates, and selective extinction in cephalopods

Reconstructing the physiology of extinct organisms is key to understanding mechanisms of selective extinction during biotic crises. Soft tissues of extinct organisms are rarely preserved and, therefore, a proxy for physiological aspects is needed. Here, we examine whether cephalopod conchs yield information about their physiology by assessing how the formation of chambers respond to external stimuli such as environmental changes. We measured chamber volume through ontogeny to detect differences in the pattern of chamber volume development in nautilids, coleoids, and ammonoids. Results reveal that the differences between ontogenetic trajectories of these cephalopods involve the presence or absence of abrupt decreases of chamber volume. Accepting the link between metabolic rate and growth, we assume that this difference is rooted in metabolic rates that differ between cephalopod clades. High metabolic rates combined with small hatching size in ammonoids as opposed to lower metabolic rates and much larger hatchlings in most nautilids may explain the selective extinction of ammonoids as a consequence of low food availability at the end of the Cretaceous

Virtual 3D modeling of the ammonoid conch to study its hydrostatic properties

Computed tomography has provided a wealth of biological data that now stands beside a vast, more traditional, morphometric database. By exploiting these two resources, we present a novel methodology to construct intricate, virtual cephalopod shells. As a case of study, we applied this method to Maorites seymourianus using data obtained from a previous work. For this purpose, evaluation of the conch geometry, and the definition of new parameters such as the segment width expansion rate (SWER), segment height expansion rate (SHER), the segment thickness expansion rate (STER), and three indices related, were introduced. The conch geometry of M. seymourianus follows a spiral that can be defined by a polynomial function. While similar to a logarithmic function, a polynomial fit is preferred because it reveals higher values of whorl expansion at the early ontogenetic phase and lower values reaching the adult body chamber. Results on the hydrostatic properties of the virtual models indicate that M. seymourianus would have a near neutral buoyancy, ranging from slightly positive to slightly negative, depending upon parameters that influence organismal mass. Positions of the center of mass and the center of buoyancy indicate that the studied species would have a relatively low hydrostatic stability, estimating a shell orientation of approximately 74–76° with respect to the vertical, with the aperture slightly inclined downwards relative to the horizontal plain.Fil: Moron Alfonso, Daniel Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Geológicas; ArgentinaFil: Peterman, David J.. Wright State University; Estados UnidosFil: Cichowolski, Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Geológicas; ArgentinaFil: Hoffmann, René. Ruhr Universität Bochum; AlemaniaFil: Lemanis, Robert E.. Technische Universität Dresden.; Alemani

Supplementary Tables

CT derived volume, buoyancy, and hydrostatic data for a Cadoceras and reconstructed Spirula hatchling

Specimen Data and Tomographic Scan Meta-Data.

<p>Specimen Data and Tomographic Scan Meta-Data.</p

Chamber surface area to chamber volume ratio (A) and siphuncular surface area to chamber volume ratio (B) plotted against cumulative chamber volume.

<p>While both shell diameter and cumulative volume are proxies for size, volume is a more accurate basis for comparison due to the heteromorphic morphology of the shell of <i>Spirula</i>, possessing a whorl interspace that artificially inflates shell diameter. Regardless both graphs show that ammonoids possess a relatively high surface area to volume ratio in early ontogeny.</p