Complexity of Septal Surfaces and Suture Lines in Ammonoids : Implications for the Hydrostatic Apparatus and Palaeoecology Using

Complexity of septal surfaces and suture lines in ammonoids – implications for the hydrostatic apparatus and palaeoecology using

modern CT techniques

Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften an der Fakultät für Geowissenschaften der Ruhr-Universität Bochum

vorgelegt von

Robert Lemanis

geboren am 22.06.1989 in New York (Vereinigte Staaten)

Erklärung

„Ich erkläre hiermit an Eides statt, dass ich die vorliegende Arbeit selbständig angefertigt sowie die benutzten Quellen und Hilfsmittel vollständig angegeben habe. Ich habe alle Fakten,

Textstellen und Abbildungen, die anderen Weken dem Wortlaut oder dem Sinn nach entnommen sind, durch entsprechende Zitate gekennzeichnet. Die vorliegende Dissertation wurde in dieser oder ähnlicher Form bei keiner anderen Fakultät oder Hochschule eingereicht.“

Bochum, June 2016

Robert Lemanis

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Publication list of the Dissertation

1. Title: A new approach using high-resolution computed tomography to test the buoyant

properties of chambered cephalopod shells

Authors: R. Lemanis1, S. Zachow2, F. Fusseis3, R. Hoffmann1

Published in Paleobiology in March 2015;

Volume 41(02); Pages 313-329 (chapter 3 of this thesis)

DOI: 10.1017/pab.2014.17

2. Title: The evolution and development of cephalopod chambers and their shape

Authors: R. Lemanis1, D. Korn4, S. Zachow2, E. Rybacki5, R. Hoffmann1

Published in Plos One in March 2016;

Volume 11(3) (chapter 4 of this thesis)

DOI: 10.1371/journal.pone.0151404

3. Title: Comparative cephalopod shell strength and the role of septum morphology on

stress distribution

Authors: R. Lemanis1, S. Zachow2, R. Hoffmann1

Under review in PeerJ (chapter 5 of this thesis)

1Institute of Geology, Mineralogy, and Geophysics, Ruhr-Universität Bochum, Bochum,

Germany

2Department of Scientific Visualization and Data Analysis, Zuse Institute, Berlin, Germany

3School of Geosciences, University of Edinburgh, Edinburgh, U.K.

4Museum für Naturkunde Berlin, Leibniz-Institut für Evolutions- und Biodiversitätsforschung,

Berlin, Germany

5Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum, Potsdam, Germany

The research presented here was funded by the Deutsche Forschungsgemeinschaft, grant number

HO 4674/2-1. The main applicant for this grant was Dr. R. Hoffmann and the co-applicant was

Prof. Dr. S. Zachow.

Author contributions and peer review process

R.L. = Robert Lemanis, R.H. = René Hoffmann, F.F. = Florian Fusseis, S.Z. = Stephan Zachow,

D.K. = Dieter Korn, E.R. = Erik Rybacki.

First Article

R.L. and R.H. conceived of the study design. R.L. performed the specimen segmentations, processed the tomographic data, designed and performed the calculations, wrote the initial draft including making the figures, and implemented reviewer criticisms. R.H. provided comments to drafts of the manuscript. F.F. was involved in gaining access to the synchrotron facility. S.Z. provided the software used and continual technical support. This article was evaluated by two reviewers, Kenneth De Baets and Dieter Korn, and accepted on October

14, 2014.

Second Article

R.L. and R.H. designed the study. R.L. performed the specimen segmentations (the pathologic S. spirula, A. scrobiculatus, and Arnsbergites sp. were segmented by students) processed the tomographic data, wrote the initial draft including making the figures, and implemented reviewer criticisms. R.H. and D.K. provided comments through versions of the manuscript. D.K. provided the Arnsbergites sp. specimen. E.R. performed several computed tomographic scans of specimens used in this study. S.Z. provided the software used and continual technical support. This article was submitted twice to Plos One. The first version of the

v article was rejected after being reviewed by two reviewers, Kenneth De Baets and one anonymous reviewer. R.L., after discussion with R.H., and D.K., submitted a revised version of the article that was submitted on December 16, 2015. This version was reviewed by two reviewers, Christian Klug and one anonymous reviewer, and accepted on February 26, 2016.

Third Article

R.L. processed the tomographic data, created and refined the surface and volumetric meshes, performed the finite element analyses, wrote the initial draft including making the figures, and implemented reviewer criticisms. R.H. provided comments to drafts of the manuscript. S.Z. provided the software used and continual technical support.

Additional information about this thesis

R.L. also contributed to the following publications: Hoffmann et al. 2014 (see references in Chapter 2), Hoffmann et al. 2015 (see references in Chapter 1) and Hoffmann et al. 2015 (see references Chapter 4). An additional project was undertaken as part of the grant that funded this research that resulted in a publication: Lamas-Rodríguez et al. 2015 (see references Chapter 6).

References in this thesis are given at the end of their respective chapters.

Bochum, June 2016

Robert Lemanis

vii

Abstract

Ammonoids are an iconic and highly important fossil group that spans 350 million years and is distributed across the world. The shell of ammonoids has been historically modelled through the use of a number of mathematical descriptors. Investigations into palaeobiological aspects of ammonoids have traditionally been done using these models. This method is capable of recreating the gross morphology of the shell or approximate morphologies of parts of the shell and was used due to the impossibility of modeling the entirety of the shell accurately. The goal of this project is to use computed tomography to create 3D models directly from the original shells and use these models to explore ammonoid palaeobiology.

Tomographic based, empirical models of the shells of the deep sea squid Spirula spirula and the Jurassic ammonite Cadoceras are here constructed and used to calculate buoyancy and hydrostatics. Comparisons with traditional methods demonstrate the inaccuracy of previous volume calculations and the biases in hydrostatic calculations. The volume of the Cadoceras shell reconstructed from mathematical approximation shows a persistent underestimation of shell volume. Hydrostatic analysis identified a progressive bias in the calculation of the center of gravity in which overall hydrostatic stability is overestimated for shorter body chamber forms when calculated using the traditional method. Furthermore, a methodology for the calculation of buoyancy using tomographic data is created and used to show that a hypothetical ammonite could remain in the water column despite a potential, overall negative buoyancy. Despite many unknowns, the swimming mode of an ammonite hatchling was reconstructed and found to be very similar to modern coleoid hatchlings. Hypothesis based on mathematical models of ammonoids should be re-evaluated in light of the improved accuracy afforded by computed tomography.

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The function of the complexly folded septa of ammonoids has long been a controversial topic dominated by investigations based on mathematical approximations. Two methods are here used to investigate physiological and mechanical hypothesis of septal function. Ontogenetic changes in the ratio of chamber surface area to volume are calculated based on tomographic data of extant Nautilus, Allonautilus, Spirula, the Paleozoic ammonoids Arnsbergites, and the

Mesozoic ammonoids Amauroceras, Cadoceras, and Kosmoceras. Previous work has suggested that septal complexity increased the relative inner surface area of the chambers thereby allowing rapid fluid diffusion out of the chambers. Our results reject this hypothesis over most of ontogeny; however, an increase in the relative surface area of the chambers is shown for all tested ammonoids that preserved their early ontogeny. This might reflect adaptations towards an increase in growth in early ontogeny that are coupled with a shift in early ammonoid evolution towards smaller eggs and higher fecundity. We further demonstrate that the increase in complexity increases the curvature of the septal surface that might aid in chamber refilling.

The mechanical function of ammonitic septa is investigated through comparative finite element analysis on the shells of Nautilus, Spirula, and Cadoceras. The entire shell is meshed into finite element models that are subjected to hydrostatic pressure and point loads. The hypothesis that increases in septal complexity should increase shell resistance to hydrostatic pressure is not supported as Spirula, which has the simplest septal morphology, shows the highest resistance to hydrostatic pressure. The use of septal amplitude as a proxy for palaeobathymetry is rejected as increasing septal amplitude is shown to increase the stress due to hydrostatic pressure as opposed to reducing it. Septal amplitude is shown to decrease stress due to point loads indicating a potential anti-predatory function of septal complexity which agrees with the increase in septal curvature that would help compensate for lost shell material.

Kurzfassung

Ammoniten sind sowohl eine ikonische als auch bedeutende Gruppe, deren Geschichte sich über 350 Millionen Jahre erstreckte und deren Fossilien auf der ganzen Welt verbreitet sind.

Die Schale dieser Lebewesen wurde mathematisch auf vielfältige Art und Weise beschrieben, die traditionell in paläobiologischen Untersuchungen Anwendung gefunden haben. Diese Methoden können die Bruttomorphologie der Schale oder die ungefähre Morphologie von Teilen der Schale nachbilden und wurden benutzt, da die exakte Darstellung der gesamten Schale unmöglich gewesen ist. Das Ziel dieses Projekts ist es, Computer Tomographie zu nutzen, um 3D Modelle von originalen Schalen zu erschaffen, mit denen ammonitische Paläobiologie erforscht werden soll.

Auf Tomographien basierte empirische Modelle der Tintenfischgruppe Spirula spirula und des jurassischen Ammonitengenus Cadoceras wurden erstellt, um die Auftriebskraft und

Hydrostatik zu berechnen. Vergleiche mit traditionellen Methoden zeigen auf, dass

Volumenberechnungen ungenau waren und es zu Verzerrungen hydrostatischer Kalkulationen kam. Eine Rekonstruktion der mathematischen Annäherung der Cadocerasschale zeigt, dass das

Schalenvolumen fortdauernd unterschätzt wurde. Hydrostatische Analysen haben eine progressive Verzerrung bei der Berechnung des Gravitationszentrums identifiziert, in denen die hydrostatische Stabilität für kürzere Formen der Körperkammer überschätzt wurde, wenn traditionelle mathematische Verfahren angewendet worden sind. Weiterhin wird eine

Berechnungsmethodologie kreiert, die tomographische Daten nutzt, um zu zeigen, dass ein hypothetischer Ammonit trotz potentieller insgesamt negativer Auftriebskraft, in einer

Wassersäule verharren könnte. Obgleich vieler Unbekannten wurde der Schwimmmodus von

Ammonitenschlüpflingen rekonstruiert. Dieser zeigt sich als vergleichbar mit modernen coleoid

Schlüpflingen.

Die Funktion der komplex gefalteten Septa der Ammoniten ist ein kontrovers debattiertes

Thema, welches von Untersuchungen dominiert ist, die auf mathematischen Annäherungen basieren. Hier wurden zwei Methoden genutzt, um die physiologische und mechanische

Hypothese der septal Funktion zu untersuchen. Ontogenetische Veränderungen werden im

Verhältnis von Kammeroberfläche zu -volumen berechnet, die auf tomographischen Daten existenter Nautilus, Allonautilus, Spirula, paläozoischer Ammoniten Arnsbergites, und den mesozoischen Ammoniten Ameuroceras, Cadoceras und Kosmoceras beruhen. Frühere Arbeiten legen nah, dass die septal Komplexität die relative innere Oberfläche der Kammern erhöht hat und dadurch rapide Flüssigkeitsdiffusion aus den Kammern heraus gewährleistet wurde. Unsere

Resultate widerlegen diese Hypothese größtenteils. Ein Anstieg der relativen Kammeroberfläche kann für alle getesteten Ammoniten nachgewiesen werden, die in ihrer frühen Ontogenese erhalten sind. Dies spiegelt möglicherweise Adaptionen hin zu erhöhtem Wachstum in früher

Ontogenese wieder, die in Verbindung mit einer Verschiebung in der Evolution zugunsten kleinerer Eier und höherer Fruchtbarkeit stehen. Weiterhin demonstrieren wir, dass der Anstieg der Komplexität, der die Krümmung der septal Oberfläche erhöht, möglicherweise das

Wiederbefüllen der Kammer begünstigt.

Die mechanische Funktion der ammonitischen Septa ist durch vergleichende finite

Elementanalyse auf den Schalen der Nautilus, Spirula und Cadoceras untersucht worden. Die gesamte Schale ist in endliche Elementmodelle vernetzt worden, welche hydrostatischem Druck und Punktlast ausgesetzt wurden. Die Hypothese, dass der Anstieg in septal Komplexität den

Schalenwiderstand gegenüber hydrostatischem Druck erhöhen sollte, kann durch die Ergebnisse

xi von Spirula, die die einfachste septal Morphologie vorweisen, nicht befürwortet werden, da sie den höchsten Widerstand gegen hydrostatischen Druck aufweisen. Der Gebrauch einer septal

Amplitude als Stellvertreter für Paläobathymetrie wird verworfen, da gezeigt wird, dass eine ansteigende septal Amplitude die Belastung durch hydrostatischen Druck erhöht und nicht reduziert. Es wird gezeigt, dass die septal Amplitude die Belastung durch Punktbelastung verringert, was auf eine potentielle anti-räuberische Funktion der septal Komplexität hindeutet, die mit dem Anstieg der septal Krümmung übereinstimmt. Dies würde helfen, verlorenes

Schalenmaterial zu kompensieren.

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Acknowledgements

First and foremost, I would like to thank Dr. René Hoffmann for providing me the opportunity to pursue a PhD and his continuous and invaluable support throughout the entire process. I truly appreciate all of the cups of coffee we shared and your efforts to help me advance my scientific career.

Secondly, I thank Jörg Mutterlose and Helmut Keupp for officially supervising my PhD project. Jörg also provided valuable comments and discussion that improved this thesis and are greatly appreciated.

I thank my cooperators at the Zuse Institute, Stefan Zachow and Moritz Ehlke, for their support with the software and availability for any question I might have. I extend thanks to all of my coauthors: Stefan, Florian Fusseis, Dieter Korn, and Erik Rybacki. I give a special thanks to

Dieter whose comments and extensive discussion helped me greatly improve my second paper.

I would like to thank all of the people that have provided us CT scans. Lothar Heuser and

Werner Weber and the technicians from the Knappschaftskrankenhaus Bochum who graciously allowed us free access to their medical facility. Julia Shultz, Erik Rybacki and Hendrik

Wesendonk who provided scans throughout the course of this project.

A special thanks to all of the members of Sedimentology and Palaeontology at the Ruhr

University Bochum who have all greatly improved the quality of time here in Germany. A separate thanks to Cornelia Schäfer who provided extensive support wading through German bureaucracy and Thomas Murad for being a helpful and easy-going housemate. Specific thanks to Kevin Stevens whose many discussions proved interesting and entertaining.

Last but not least, I thank all of my family and loved ones who constantly supported me during this arduous process.

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Table of Contents Erklärung...... ii Publication list of the Dissertation...... iv Abstract ...... viii Kurzfassung ...... x Acknowledgements ...... xiii Chapter Overview ...... xvii Chapter 1. Introduction to Ammonoids...... 1 1. The Ammonoidea, Early Evolutionary History ...... 1 2. Morphology ...... 2 2.1 Soft Body Anatomy ...... 2 2.2 Shell and Septa ...... 7 3. Motivation ...... 10 4. Specimens used in this study ...... 12 References ...... 13 Chapter 2. Introduction to the Methodology ...... 22 1. Computed Tomography ...... 22 1.1 Origins ...... 22 1.2 Contrast in Theory ...... 24 1.3 Contrast in Practice ...... 26 1.4 Computed Tomography Methods ...... 30 2. Finite Element Analysis ...... 32 2.1 Practical FEA ...... 33 References ...... 37 Chapter 3. A New Approach using High-Resolution Computed Tomography to Test the Buoyant Properties of Chambered Cephalopod Shells ...... 40 1. Introduction ...... 42 2. Materials and Methods ...... 46 2.1 Hard Parts and Soft Tissue ...... 48 2.2 Siphuncle ...... 51 2.3 Jaws ...... 51 2.4 Mantle Cavity ...... 52 2.5 Calculations ...... 54

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2.6 Swimming and Sinking ...... 54 3. Results ...... 56 3.1 Cadoceras ...... 56 3.2 Spirula ...... 60 4. Discussion ...... 61 4.1 Model Limitations ...... 61 4.2 Life Habit ...... 65 5. Summary ...... 69 Acknowledgments ...... 70 References ...... 72 Chapter 4. The Evolution and Development of Cephalopod Chambers and their Shape ... 85 1. Introduction ...... 86 2. Material and Methods ...... 90 2.1 Specimens ...... 90 2.2 CT Scanning ...... 91 3. Results ...... 94 3.1 Surface Area/Volume Ratios ...... 94 3.2 Siphuncular Surface vs. Chamber Volume...... 96 4. Discussion ...... 97 4.1 Scaling ...... 97

4.2 Siphuncle and SAS:VC ...... 101 4.3 Curvature ...... 103

4.4 Evolution of high SAC:VC ...... 103 4.5 Septal Complexity ...... 107 4.6 Mechanical resistance and shell internalization ...... 110 5. Conclusions ...... 111 Acknowledgments ...... 113 References ...... 114 Chapter 5. Comparitive Cephalopod Shell Strength and the Role of Septum Morphology on Stress Distribution ...... 125 1. Introduction ...... 127 2. Material & Methods ...... 130 2.1 Specimens and Segmentation ...... 130

2.2 Meshing and Finite Element Modelling ...... 131 2.3 Finite Element Analysis ...... 133 2.4 Pressure Loading ...... 133 2.5 Point Loading ...... 133 2.6 Septal Strength Index...... 134 3. Results ...... 134 3.1 Pressure ...... 134 3.2 Point Force ...... 135 4. Discussion ...... 137 4.1 Pressure and Comparisons with Previous Results ...... 137 4.2 Septal Strength Index...... 140 4.3 Point Force ...... 141 4.4 Septal Complexity and Palaeoenvironment ...... 143 5. Conclusion ...... 143 Acknowledgements ...... 145 References ...... 146 Chapter 6. Conclusions ...... 154 1. Tomographic methods and ammonoid data ...... 154 1.1 Tomographic data and geometric models ...... 155 2. Shell buoyancy and hatchling mode of life ...... 156 3. Function of complex septa ...... 157 4. Outlook ...... 158 References ...... 162 Curriculum Vitae ...... 166

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Chapter Overview

This thesis is divided into 6 chapters:

1. The first chapter serves as an introduction to ammonoids, their evolutionary history and

palaeobiology. We summarize current knowledge about their origins and the evolution of

the clade with an emphasis on the folded septa and their evolutionary function. Proposed

functions of the septa are discussed along with their implications for life-habits and use in

environmental reconstructions.

2. Here we introduce the techniques used in this paper. This chapter is divided into two

parts: computed tomography and finite element analysis. The primary focus of this

chapter is computed tomography as this technique forms the basis for all of the work

presented in this thesis. Therefore, we present an overview of the history of this

technology as well as some theoretics and practical applications. The latter section of this

chapter briefly introduces finite element analysis and covers basic concepts, terminology,

and practical considerations of using this technique, especially in palaeontology.

3. Chapter three reports on the first ever quantitative investigation of ammonoid

palaeobiology using computed tomography. The method and its accuracy are assessed

and used to calculate theoretical hydrostatic and hydrodynamic scenarios. Primarily, CT

data is used to demonstrate the most accurate method to calculate buoyancy of extinct

shelled cephalopods.

4. Chapter 4 focuses on a potential physiological function of complex septa. The role of

septal folds in the efficiency of the buoyancy system are evaluated using high-resolution

surfaces and shape analysis. We propose a new function of folded septa in early ontogeny

as well as a change in function through ontogeny.

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5. Chapter 5 uses finite element analysis to evaluate the common hypothesis of the role of

septa in increasing the mechanical strength of the shell. Two indices proposed in the

literature to help reconstruct palaeobathymetry of ammonoids are called into question and

a complex image of septa and shell strength is demonstrated.

6. The final chapter summarizes the main results of the thesis and discusses the implications

of these findings. Furthermore, avenues of future research are explored.

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Chapter 1

Introduction to Ammonoids

1. The Ammonoidea, Early Evolutionary History

The Ammonoidea (ammonoids) is a group of cephalopods possessing an external shell, which first evolved during the Early Devonian, about 417 Ma, and went extinct at the

Cretaceous/Paleogene boundary, 66 Ma (Kröger et al. 2011; Klug et al. 2015). The first cephalopod that appeared in the fossil record was the Late Cambrian Plectronoceras, around 540

Ma (Yochelson et al. 1973; Kröger et al. 2011). Cephalopod diversity in the modern ocean is dominated by coleoids (e.g., squids, octopuses, and cuttlefish) with Nautilus and Allonautilus being the only living representatives of the Nautiloidea. Nautiloidea, Ammonoidea, and

Coleoidea are the three primary groups that cephalopods can be classified into with only the

Ammonoidea lacking any living representatives (Engeser 1996; Klug et al. 2015). This means that Nautilus and living coleoids are used as analogues for reconstructing the biology and behavior of ammonoids (Jacobs and Landman 1993; Warnke and Keupp 2005).

Ammonoids and coleoids evolved from bactritoid ancestors, who possessed straight instead of coiled shells (Dzik 1981, 1984; De Baets et al. 2012; Ritterbush et al. 2014; Klug et al.

2015; Vinther 2015; Fig. 1). The transition between straight and coiled shells in ammonoids was accompanied by a change in the shape of the initial chamber (protoconch), an increase in coiling

(Fig. 2), the reduction in the size of the embryonic shell (ammonitella), and the increase in the size of adults (De Baets et al. 2012). The latter two point towards a shift in reproductive style indicating that ammonoids may have produced a higher number of smaller eggs compared to nautiloids (De Baets et al. 2012; Ritterbush et al. 2014). These early morphological changes have been tied with potential changes in life-habit. Kröger (2005) and Klug et al. (2010) hypothesized

1 that these changes were driven by increased predation during the evolution of jawed fish and other swimming (nektonic) predators. As the shell coiling increased, the aperture moved to a more horizontal position and the tightly coiled shell would allow for more maneuverable swimming, allowing these forms increased swimming speed (Saunders and Shapiro 1986; Klug and Korn 2004; Klug et al. 2010; Monnet et al. 2011). Here we have a potential shift from a less active life-habit, floating near the sea floor, to a more active life-habit in the water column.

2. Morphology

The morphology of the external shells of fossil cephalopods are well known; however, their soft body anatomy is rarely preserved in part and never preserved in totality (Tanabe et al.

2000; Klug et al. 2008; Lehmann et al. 2015; Polizzotto et al. 2015; Fig. 3). This section will provide a brief overview of the possible soft body anatomy and the general morphology of the shell of ammonoids.

2.1 Soft Body Anatomy

This section will not cover all aspects of ammonoids soft parts. Instead this section shall discuss aspects of the soft body that are directly discussed in later chapters of this thesis or are relevant to consider for discussions of life-habit.

2.1.1 Arms

Looking at Nautilus (Fig. 4), the arms are the exterior most part of the animal. Arms in ammonites are controversial at best considering that no direct evidence of arms is recorded in the fossil record. Older models of ammonoids reconstruct them with numerous arms similar to

Nautilus, which has up to 90 arms (Fukuda 2010). Recent embryological work has revealed that the many arms in Nautilus are a derived feature, with all extant cephalopods possessing an initial ten arm buds (Shigeno et al. 2008). Since both Nautilus and the coleoids both possess ten arm

Figure 1. An evolutionary timeline of Cephalopoda. Stippled lines are hypothetical relationships that lack fossil calibrations. Modified from Kröger et al. (2011). 3

Figure 2. Illustrative view of the change in morphology that accompanied the evolution from straight shelled ancestors to the coiled shell typical of ammonites. The blue sections are the body chamber, the green sections are the shell, and the teal sections are the protoconch. The extent of the body chamber is not known for embryonic forms. Modified from De Baets et al. (2012). buds, it is reasonable to reconstruct ammonoids with ten arms. Klug et al. (2012) present a potential preserved arm crown from a heteromorph ammonite from the Late Cretaceous of

Germany. The imprints in this specimen resembles a retracted arm crown suggesting that ammonoids might have restracted the arms towards or even into the aperture, which would explain the difficulty in finding fossil evidence of such features (Klug and Lehmann 2015).

2.1.2 Jaws

The arms surround the mouth, which in Nautilus and modern coleoids, consists of a chitonous beak (Tanabe and Fukuda 2010). The fossil record of cephalopod beaks begins in the

Late Devonian and potential, preserved mouth parts are reported from ammonoids from the

Lower to Middle Devonian (Nixon 1996). There are multiple occurences of beaks preserved in the body chamber of the shell surrounding the radula (Nixon 1996; Tanabe et al. 2015a).

One curious feature of derived, Mesozoic ammonoids is the occurence of so called aptychi. Aptychi refer to the transformed lower jaws, which superficially resemble the shells of bivalves, composed of organic and mineralized layers (Engeser and Keupp 2002). The aptychi are large structures likely unsuited for powerful biting, their function has been heavily debated

(e.g., Seilacher 1993; Engeser and Keupp 2002; Parent et al. 2014; Lehmann et al. 2015a). The function of the aptychi is not discussed in this thesis; however, the aptychi has to be accounted for in buoyancy calculations and might have been able to move within the body chamber to help resposition the angle of the aperture aiding in certain forms of feeding (Parent et al. 2014).

2.1.3 Digestive Tract

Remnants of the digestive tract, including stomach, crop and oesophagus, have been reported for exceptionally preserved specimens (Nixon 1996; Jäger and Fraaye 1997; Wippich and Lehmann 2004; Keupp 2007; Klug and Jerjen 2012; Klug et al. 2012). Preserved stomach contents give us clues as to what ammonoids preyed upon. Stomach (or crop) contents of modern

Nautilus include pieces of small fish, crustaceans, echinoids, and parts of other Nautilus’ (Saisho and Tanabe 1985; Ward 1987; Saunders and Ward 2010). Klug and Lehmann (2015) summarize stomach contents from ammonoids that include ostracods, forams, crustaceans, jaws of smaller ammonoids, echinoids, gastropods, and sponges.

2.1.4 The Buoyancy System

The siphuncle is an organic strand, largely containing blood vessels (Fig. 3), that runs from the rear of the soft body through the entirety of the shell to the first formed chamber

(protoconch). The siphuncle serves as the pathway for the diffusion of liquid and gas into and out of the chambers (Denton and Gilpin-Brown 1966). The siphuncle tissue operates through the formation of a hyperosmotic pump, using NaCl gradients to permit diffusion even when the local water pressure prevents simple diffusion, at depths greater than 250 m (Denton and Gilpin-

Brown 1973; Ward et al. 1980; Greenwald et al. 1982, 1984; Jacobs 1996; Tanabe et al. 2000,

2015b; Hoffmann et al. 2015). This morphology has been well studied in Nautilus and preserved structures of the siphuncular epilthelium of Akmilleria support the presence of this system in ammonoids (Tanabe et al. 2000). Newly formed chambers are filled with cameral fluid that are gradually emptied by the siphuncle; however, there will be a point when the fluid is emptied such that it is no longer in contact with the siphuncle (decoupled). Once this happens, fluid transport is dependant upon the pellicle.

Figure 3. Representative cross sections of the siphuncular tissue from the Paleozoic ammonoid Akmilleria

(A), Nautilus (B), and Spirula (C). e = siphuncular epithelium, oc = outer connective tissue, ic = inner connective tissue, a = artery and v = vein. Modified from (Tanabe et al. 2015a).

The pellicle is a sub-micron organic membrane-like structure that covers the hard sheath around the siphuncle as well as the internal walls of the chambers. Denton and Gilpin-Brown

(1966) sawed open a fresh Nautilus and observed this pellicle lining the chambers.

By placing a drop of water upon the pellicle, they noted the fluid was absorbed by the pellicle and spread throughout the surface. When the pellicle was removed the water simply formed a static bead upon the mineral surface. Therefore the pellicle acts as a type of blotting paper, aiding in diffusion and fluid transport after decoupling of the fluid and the siphuncle. Further discussions about the function of the pellicle and implications for ammonoids are discussed in chapter four of this thesis.

2.2 Shell and Septa

The cephalopod shell can be divided into two major parts: the body chamber and the phragmocone. The body chamber is where the animal resides and consists of the shell tube that surrounds the soft tissue. The phragmocone is the buoyancy apparatus and consists of the shell tube that is then divided into a series of internal chambers by the septa (Fig. 4). The shells of ammonoids show a considerable range of overall shape, ranging from spherical to laterally compressed, lenticular (convex lens shaped) forms. Differences in shell shape have been used as proxies for life habit. For example, more spherical shells have been considered planktonic while the lenticular shells have been viewed as fast swimming nekton (Westermann 1996; Ritterbush and Bottjer 2012; Ritterbush 2015). Theoretical hydrodynamics has demonstrated the role of shell morphology on potential life habits by demonstrating a large difference in hydrodynamic efficiency and drag minimization between different shell shapes (Chamberlain 1976, 1981, 1993;

Jacobs 1992, 2001; Jacobs and Chamberlain 1996; Naglik et al. 2015). Furthermore, different

7 shell shapes would be optimized for different hydrodynamic roles, lenticular shells show less drag at high speeds while spherical shells have less drag at slow speeds (Jacobs 1992).

Figure 4. View of the shell of Nautilus (A, C) and the ammonites Cadoceras (B) and Amauroceras (D). A and B are volume renderings of the shell cut to view the internal structures, chamber volumes are colored.

C and D are median sections, D is a median section of a label field consisting of chamber and siphuncle volumes. C includes a schematic diagram of the soft-tissue of Nautilus.

Tendler et al. (2015) analyzed theoretical ammonoid shells and found that morphometric analysis supports the idea of shell shape being a product of several functional constraints such as hydrodynamics, shell economy (minimizing the amount of material needed to build the shell), and fast growth.

The septa of the ammonoid phragmocone are a distinctive and important feature. Only in ammonoids do the septa develop into intricately complex, near fractal structures (Vicencio 1973;

Klug and Hoffmann 2015). The septa of ammonoids are characterized by a folded structure that evolved multiple times over the course of ammonoid evolution and repeatedly after mass extinctions (Bayer and McGhee 1984; Jacobs et al. 1994). If one were to polish away the exterior layers of the shell, a series of lines would become visible on the external surface that show the attachment of the septa to the inner shell wall (Fig. 5). These lines are the suture lines.

Traditionally, investigations of septal complexity have been carried out through analysis of the suture lines (Bayer and McGhee 1984; Saunders 1995; Checa and Garcia-Ruiz 1996; Saunders et al. 1999; Korn et al. 2003; Perez-Claros 2005; Perez-Claros et al. 2007; Yacobucci and Manship

2011).

The unique morphology of ammonitic septa (Fig. 5) coupled with the iterative evolution of this complex structure through time and after mass extinctions (Bayer and McGhee 1984;

Seilacher 1988; Allen 2007) has led to a focus on possible functions of the septa. Septal functions can generally be divided into two categories: physiological and mechanical. Further discussion of the potential function of septa will be done in chapters four and five of this thesis.

Here is a briefly review of some of the proposed functions:

1. Improved respiration, deduced by association with Nautilus as the shape of the septa

reflect the shape of the mantle (Newell 1949)

2. Fluted (folded) septa serve as muscle attachments, specifically for retractor muscles

(Seilacher 1975) or increasing the muscular connection between the soft body and the

septa (Lewy 2002)

3. Increase the size of the pellicle, thereby allowing faster fluid transportation rates in the

chambers (Mutvei 1967; Kröger 2002)

4. Improve the potential for chamber refilling by increasing the overall curvature of the

septal surface (Daniel et al. 1997) thereby allowing greater ability to recover from

predator attacks (Kröger 2002).

5. Improve the mechanical strength of the shell against hydrostatic pressure and predation

(Westermann 1975; Daniel et al. 1997; Hewitt and Westermann 1997; Hassan et al.

2002). The mechanical hypothesis is explored in more depth in chapter five of this thesis.

See Klug and Hoffmann (2015) for additional septal functions not discussed here.

3. Motivation

It has been argued that the evolutionary increase in septal complexity in ammonoids strengthened the shell against water pressure thereby allowing forms with more complex septa to inhabit deeper depths (Hassan et al. 2002). This result was further argued by theoretical calculations modeling curved, planar surfaces that represented septa (De Blasio 2008). Both of these papers stood in opposition to prior results that argued complexly folded septa weakened the shell to water pressure, limiting the habitat depth of forms with complex septa (Daniel et al.

1997).

These results are a manifestation of a long lasting debate in ammonoid palaeobiology centering on the evolution of ammonoids most noticeable feature, the complexly folded septa.

There are several schools of thought related to their function, all of which have implications for palaeoecology and reflect the fundamental importance of septa for palaeobiology making this topic vital in our understanding of ammonoids as animals and our interpretations of the ecological systems they inhabit.

Figure 5. Assorted examples of cephalopod septa and sutures. Representative suture lines are outlined

nd th in red (A-C). D is the ontogenetic sequence of the 2 to 10 septa of Cadoceras (D1-D9). E is a view of the final septum of Nautilus, warmer colors indicate thicker regions of the septa. B is modified from Klug and Hoffmann (2015). 11

The goal of this project is to evaluate proposed functions of ammonitic septa using the latest computed tomographic imaging technology. The shells of cephalopods were scanned and turned into 3D models that form the basis of several projects to evaluate hydrostatics, hydrodynamics, physiology, and mechanics. Using this data, we can evaluate palaeoecologic interpretations of ammonoids and discuss the use of the shell in reconstructing palaeobathymetry.

4. Specimens used in this study

A total of eight specimens ranging from extant Nautilus and Spirula to the Paleozoic goniatite Arnsbergites were modeled during the course of this project (Table 1). The limited number of specimens is due to the segmentation process being very time intensive, one specimen can take up to nine months. Additional information for each specimen is provided in the chapters in which they were used. Data and specimens are archived in the Ruhr Universität-Bochum.

Specimen Stratigraphic Group Age Allonautilus Recent Nautiloidea, scrobiculatus Nautilidae Nautilus pompilius Recent Nautiloidea, Nautilidae Spirula spirula Recent Coleoidea, Spirulidae Spirula spirula Recent Coleoidea, Spirulidae (pathological) Kosmoceras sp. Callovian Ammonoidea, Kosmoceratidae Cadoceras sp. Callovian Ammonoidea, Cadoceratidae Amauroceras sp. Pleinsbachian Ammonoidea, Amaltheidae Arnsbergites sp. Visean Ammonoidea, Goniatitidae

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Chapter 2

Introduction to the Methodology

1. Computed Tomography

1.1 Origins

Wilhelm Röntgen in 1895 discovered, during his research into cathode rays, a curious radiation that recorded a transparent representation of a material upon a photographic plate. He later found that these rays could penetrate human skin and record an image of the underlying bones. The applicability of these new found X-rays to the field of medicine were quickly realized with the first X-ray analysis for medical purposes occurring months after Röntgen’s initial publication (Mamourian 2013).

The first X-ray devices were relatively simplistic in form compared to modern computed tomographic machines. The early machines simply involved an X-ray source opposite a photographic plate and the specimen of interest, generally a part of the body, was placed between the two and exposed for a certain amount of time (Hsieh 2003). These early images had comparatively poor contrast between tissue types due to the wide nature of the static X-ray beam and were not able to resolve spatial relationships (Hsieh 2003; Mamourian 2013). This is simply due to the face that all of the information produced from the interaction of the X-rays and the object being scanned were compressed onto a 2D plate. Attempts to improve contrast between different types of tissues were initially addressed by the development of tomography.

Tomography refers to the placement of the X-ray source and plate on opposite sides of the patient, with the ability to pivot around a common center of rotation. This method permitted a more focused image to be produced of the structures in the plane of rotation while structures out of this plane were blurred (Mamourian 2013).

A major advancement in imaging that led to the eventual development of computed tomography was back-projection. Here X-rays are projected at an object of interest and the final intensity of the X-rays are recorded by a detector opposite the X-ray source. The resulting intensities are back projected along a line that contains intensity information based on X-ray attenuation by the object being scanned (Hsieh 2003; Stock 2008). The object is then turned and the process repeats. Ultimately multiple projections made at different angles and are combined to reconstruct the object of interest (Fig. 1).

Figure 1. A) A group of circular objects (red) scanned at three angles. i-iii are the resulting intensity profiles that are back projected into lines. B) Example of how the intensity profiles are used to reconstruct the original scanned object. The number of lines indicates the degree of absorption. The blue circles are reconstructed objects that do not appear in the original scanned object. Additional profiles taken at different angles would eliminate these false objects. C) A back-projection based reconstruction illustrated as a numeric grid. The numbers of the grid are the additive intensities from the two profiles. Adapted from Stock (2008).

In the latter half of the 20th century, the power of computers was taken advantage of in order to create algorithms based on a form of back-projection. This developed into computed tomography (CT). The first experimental CT device was built by Allan M. Cormack in 1963 while the first clinical CT device was built by Godfrey N. Hounsfield in 1967 (Hsieh 2003;

Mamourian 2013). In honor of his contributions, the unit of attenuation used to reconstruct CT data was named a Hounsfield unit (Mamourian 2013).

1.2 Contrast in Theory

X-ray based imaging technologies, such as computed tomography, operate through the preferential penetration of materials that can be predicted on the basis of the attenuation properties of those materials. The final intensity of measured X-rays used in back-projection can be calculated on the basis of the initial intensity of the X-ray and the attenuation coefficient of the material, or sum of attenuation coefficients of the materials in the path of the X-ray, according to a known relationship (eq. 1; Stock 2008).

I = I0 exp(-µx) eq.1

Io is the initial intensity of the X-ray, x is the thickness of the material, µ is the linear attenuation coefficient of the material and I is the final intensity of the X-ray. This equation is also commonly written in terms of the mass attenuation coefficient (eq. 2).

I = I0 exp((-µ/ρ)ρx) eq.2

ρ is the density of the material, µ/ρ is the mass attenuation coefficient. For compound materials, in which multiple different materials are in the path of the X-ray, a combined attenuation coefficient (µ/ρt) can be easily calculated as a weighted sum (eq. 3; physics.nist.gov/PhysRefData/XrayMassCoef/chap2.html).

µ µ/ρt = ∑ 푤 ( ) eq. 3 푖 푖 휌 푖

The primary mineral component of cephalopod shells is calcium carbonate (CaCO3). We can create a theoretical profile for calcium carbonate using the mass fraction of each element, the mass attenuation of each element (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html) and eq. 3 (Fig. 2).

Figure 2. Theoretical attenuation profile of calcium carbonate. The black arrow points to the absorption edge. This edge would be a vertical line if the calculations were done at a higher resolution in this interval. The absorption edge is a result of the energy of the X-ray photon being equal to the binding energy of an electron (Ganten and Ruckpaul 2006).

The ability to resolve different materials can be predicted on the basis of the differences in their mass attenuation coefficient at the energy of the CT. A calcium carbonate shell infilled with calcium carbonate mud will be expected to show very poor contrast due to their mass attenuation coefficients being nearly the same. Though there are ways to enhance this contrast, such as phase contrast tomography, which takes advantage of differences in refractive indices of the materials (Stock 2008; Hoffmann et al. 2014).

Hoffmann et al. (2014), in an effort to improve the reproducibility of segmentation of CT data, experimented with the use of a standard (phantom) to be scanned with a shell of Nautilus pompilius. The standard was of known material with a known volume and a similar mass attenuation as calcium carbonate (Fig. 3). The threshold used to segment the shell would be dictated by the threshold necessary to accurately reconstruct the volume of the standard.

Interestingly, the calcium carbonate crystal turned out to be a poor phantom possibly due to the large thickness of the crystal compared to the relatively thin shell.

Figure 3. The shell of Nautilus pompilius was scanned with three reference bodies. A sphere of silicon oxide, aluminum oxide, and a calcium carbonate crystal. The calculated mass attenuation coefficient profiles are calculated for each of the reference bodies.

1.3 Contrast in Practice

In the final CT scan, the object of interest is resolved into a number of voxels (3D pixels) where each voxel is assigned a value measured in Hounsfield units that is based on the

26 attenuation coefficient of the material. The size of the individual voxels is controlled by the resolution of the scan and is reported throughout this thesis as isotropic voxel size.

It is important to recognize that each voxel can only be assigned a single value. This means that if two or more materials are present within the same space represented by a voxel, the value of that voxel will be determined by a combination of the properties of the materials within this voxel. For instance, the boundary between the shell and the surrounding air will be a gradient going from pure white, 100% shell, to pure black, 100% air. The higher the resolution of the scan, the smaller the voxel size and the better resolved the boundary between materials is visualized (Fig. 4).

Figure 4. Comparison of CT scans of the same shell of Nautilus pompilius and Allonautilus scrobiculatus

(right). One scan (left) was performed with a medical scanner with an isotropic voxel size of 0.5 mm. The second scan (middle) was scanned with a micro-CT device and an isotropic voxel size of 0.175 mm. A. scrobiculatus was scanned using nano-CT and an isotropic voxel size of 0.060 mm. The bottom row shows an enlarged view of the lines on the shell.

This becomes important in quantitative studies using CT data as volumes and surface areas are quite sensitive to resolution. For example, the reconstructed weight of the shell of

Nautilus pompilius (Fig. 3) was calculated to be 65%-72% greater than the true weight using data from a medical scanner while data from a micro-CT scan reconstructed a weight 5%-12% greater than the true weight (Hoffmann et al. 2014). One method that can be used as a demonstration of the effect of resolution on volume data is based around accounting for the partial volume effect

(PVE).

Remember again that every voxel is assigned a single value that ranges, along a grey scale, from white to black. As the voxel values move from white to black, a decreasing percentage of the material of interest will be present within the space represented by each voxel.

The first step towards quantifying CT data is the creation of a label field (sometimes referred to as a mask). The label field requires a definitive boundary be constructed between the object of interest and everything else in the scan. How then is it decided which grey scale values to include in the final label field and which to exclude? This is generally, especially in palaeontology, a subjective choice as no single grey scale value can be chosen to be the correct grey scale value at which to draw the boundary. This fact was the rationale behind the attempt to find a reliable standard that can be used for segmentation as discussed earlier.

The PVE refers to the differences in volume that result when different grey scale values are used as a boundary value in the generation of a label field. The error due to PVE and subsequently the error that is involved in the segmentation process can be roughly estimated by growing and shrinking the final label field by a single voxel layer (Hoffmann et al. 2014;

Lemanis et al. 2016). This is not a definitive calculation of error as the true volume is unknown

(error for CT data should always be reported when possible (Hoffmann et al. 2014; Tajika et al.

2015)), however, it does provide some measure of susceptibility of that particular CT dataset to

PVEs.

1.3.1 Artefacts

There are a range of artefacts that can be present in CT data that have to be accounted for in order to create an accurate model. Common artefacts seen in our data include ring artefacts, streaks, beam hardening, and motion artefacts (Fig. 5). Ring artefacts (Fig. 5A) are a product of the detectors, each pixel will record slightly different values than their neighboring pixels that form streaks in back projected reconstructions and manifest as rings (Vidal et al. 2005). There are several filters and algorithms developed to reduce ring artefacts though they may also result from a fault in the detector that requires fixing or changing devices (Stock 2008). Streaks (Fig.

5B) can result from different phenomenon including beam hardening and photon scatter.

Standard image filters can reduce streaks though they tend to need manual segmentation in order to fully get rid of. Beam hardening is a result of using a polychromatic X-ray and a tendency of a material to attenuate X-rays differentially through their volume causing the outer edges of the specimen to appear brighter than the center (Davis and Elliott 2006). The one way to completely avoid beam hardening is to use a monochromatic X-ray beam, which is only possible using a synchrotron. Motion artefacts (Fig. 5D) result from movement of the specimen (or X-ray source/detector) during the scanning process. This was comparatively rare in the specimens scanned during the course of this project but can be corrected simply by rescanning the specimen.

Figure 5. Examples of artefacts that are seen in our CT data. A) Ring artefacts, visible as concentric rings radiating outward from near the center of the image. B) Streaks, seen as bright, horizontal streaks often occurring near edges and where the septa connect to the shell wall. C) Beam hardening, manifests as a brightening of the outer edge of the specimen while the interior is darker in comparison. D) Motion artefacts look like blurred or doubled parts of the image.

1.4 Computed Tomography Methods

Two CT methods have been mentioned in this chapter so far, medical CT and micro-CT.

Two additional methods will also be discussed, nano-CT and synchrotron tomography. Detailed comparisons between different CT methods and specific devices are given in Hoffmann et al.

(2014; Table 1)

1.4.1 Medical CT

Medical CT is perhaps the most common form of CT devices due to their obvious utility.

These devices are comprised of a moving table where the patient sits, and a large ring structure through which the table moves. The circular structure houses both the X-ray source and the detector that spin around the focal axis, which lies within the patient. Medical devices have certain requirements that limit their utility in palaeontology however. These CT devices are quite large, often requiring a dedicated room, in order to be able to scan an entire person. Furthermore, the energy of the X-rays are limited in order to minimize dosage to the person being scanned.

This limits the penetrative ability of the medical CT devices and limits the maximum resolution of the scans, our scans reached a maximum resolution of 0.5 mm using a medical CT scanner.

1.4.2 Micro-CT

Micro-CT has become an almost staple technique in palaeontology (e.g., Dierick et al.

2007; Suwa et al. 2007; Sutton 2008; Kiel et al. 2010; Abel et al. 2012). The main advantage of micro-CT is the lack of dose limitations. This means X-ray beam energy and exposure time are much higher than conventional medical scanners resulting in improved contrast and higher resolution (Fig. 4). The mechanics of scanning an object are different than medical scanners, the

X-ray source and detector are generally immobile while the object is placed on a rotating stand.

The resolution of micro-CT scans are typically between 1 and 100 microns (Sutton et al. 2013).

1.4.3 Nano-CT

Nano-CT is a direct improvement of micro-CT with improved detectors, resolution and detectability limits (Hoffmann et al. 2014). Like micro-CT, the object is placed on a rotating stage between the X-ray source and the detector (Fig. 6). Nano-CT boasts improved contrast and cleaner images (less artefacts) compared to micro-CT coupled with sub-micron resolution.

1.4.4 Synchrotron Tomography

Synchrotron radiation is emitted by charged particles traveling along a curved path at near the speed of light. Some of this radiation is in the forms of X-rays and can be channeled for tomographic imaging (Balerna and Mobilio 2015). Synchrotrons are housed in large facilities that require a successful project proposal in order to gain access too with access being granted for one or several days. A synchrotron is composed of a linear accelerator that boosts particles into an accelerator (booster) ring and from there into a storage ring (Balerna and Mobilio 2015).

Branching off from the storage ring are numerous beam lines that direct the particle beam to workstations where the specimens are scanned. Synchrotron tomography can achieve the highest resolution of any other technique. Furthermore, high contrast and penetration are achieved through monochromatic, high energy X-rays.

2. Finite Element Analysis

Finite element analysis (FEA) generally refers to a computational implementation of the finite element method. FEA originated as a method of stress analysis in complex engineering problems such as in the fields of aeronautical and nuclear engineering (Cook et al. 2001;

Rayfield 2007). Modern FEA has expanded in scope, being applied to problems such as mantle convection (Zhong et al. 2000), fluid flow (Connor and Brebbia 2013), and electromagnetic induction (Badea et al. 2001).

In palaeontology, FEA is focused on structural applications by calculating the stress and strain in a structure, such as a skull or shell, which results from a predefined loading condition.

The application of FEA in palaeontology has been facilitated by the increasing commonality of computed tomography (Cunningham et al. 2014; Rayfield 2007; Anderson et al. 2012). In

32 practice, FEA is not a particularly difficult method though it does require specialist software. A simple example will be used here to provide a brief introduction into finite element analysis.

Figure 6. Shell of Allonautilus scrobiculatus scanned using nano-CT at the TPW Prüfzentrum, Neuss,

Germany. Overview of the machine (A) with a close up of the specimen stage and X-ray source (B).

2.1 Practical FEA

FEA works by taking a continuous structure and breaking this structure down so it can be represented by numerous simple, geometric shapes. Each of these shapes, in 3D these are typically tetrahedrons, are referred to as elements. The models used in chapter five of this thesis

33 are based on CT data; however, for the example used here we shall skip this step and start with a simple structure. Fig. 7 shows a cube divided into variable numbers of 3D elements. Each of

Figure 7. Four cubes of equal dimensions that have been represented by varying numbers of 3D elements. the cubes in Fig. 7 is referred to as a finite element model. Once a finite element model has been constructed it needs material properties and boundary conditions. Most models in palaeontology are static, linear elastic analyses using isotropic material properties (Fastnacht et al. 2002;

Rayfield 2007; Tseng and Flynn 2015). Static refers to a single load case being applied with no time dependence, i.e., the load does not change with time nor does the response of the object.

FEA can be broadly separated into two categories: linear and non-linear. Linear FEA assumes a linear relationship between the deformation of the object and the force being applied; deflection is minor and elastic (non-permanent) (Cook et al. 2001). The assumptions of linear FEA make modeling simpler and the time necessary to solve the model much shorter. Conversely, non-

34 linear FEA is used to model a much greater diversity loading conditions including scenarios of large deformation, permanent deformation, impact loads (e.g., two cars crashing into each other), and material properties that are load dependent (Cook et al. 2001).

FEA requires the input of material properties. These properties describe how a material reacts to applied stress. In palaeontology, the only material properties usually needed are the elastic constants: Young’s modulus and Poisson’s ratio. Young’s modulus is the relationship between stress and strain of a material and Poisson’s ratio is the ratio between the strain applied in one direction, elongation, and the resulting strain in the perpendicular direction, contraction

(Vincent 1990). The Young’s modulus and Poisson’s ratio of the example cubes is 5 GPa and 0.2 respectively.

Boundary conditions refer to the forces and constraints being applied to the object (Fig.

8). In our example of the cube, constraints are necessary because simply applying a force to one side without a constraint would simply push the cube in 3D space. Constraints prevent such movement, referred to as rigid body motion.

Figure 8. Boundary conditions applied to a cube with 12 elements. The force applied is 1N along the Z- axis. Four constraints against translation are placed along the opposite face.

For each element, explicit solutions for the variables being solved for, e.g., stress, are solved for explicitly at nodes. These results are then interpolated between nodes to create a

35 solution for each element. The element solutions are compiled to represent an approximation of a solution for the continuous surface the finite element models represent. There are numerous types of both 2D and 3D elements; in palaeontology most models use tetrahedral elements.

Tetrahedral elements can come in two common forms: TET4 and TET10. The only difference between these two element types are the number of nodes. TET4 elements have 4 nodes located at the vertices while TET10 elements have 10 nodes located at the vertices and at the midpoints of the edges (Fig. 9). TET10 elements require more time and computational resources than TET4 in order to solve (Chapter 5).

Figure 9. Two cube models composed of TET4 elements (left) and TET10 elements (right). Nodes are the red points.

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Chapter 3

A New Approach using High-Resolution Computed Tomography to Test the Buoyant

Properties of Chambered Cephalopod Shells

Robert Lemanis, Stefan Zachow, Florian Fusseis, and René Hoffmann

Abstract

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

40 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.

1. Introduction

Ammonoids are among the most widely utilized fossil groups—having been applied in nearly all disciplines of paleontological study (see Ritterbush et al. 2014) from stratigraphy (e.g.,

Meister and Piuz 2013; Moreno-Bedmar et al. 2013) to geochemistry (Moriya et al. 2003;

Lukeneder et al. 2010; Kruta et al. 2014), evolutionary dynamics (e.g., Monnet et al. 2011; De Baets et al. 2012; Korn et al. 2013), paleoecology (Tanabe 1979, 2011), functional morphology (e.g.,

Ward and Westermann 1976; Reyment 1980; Ritterbush and Bottjer 2012), and biomechanics

(Daniel et al. 1997; Hassan et al. 2002). Despite this robust research history the commonly proposed primary function of the ammonite phragmocone, to serve as a hydrostatic apparatus allowing the animal to enter the water column (Teichert 1967; Crick 1988), has been subject to continuing controversy. General interpretations of ammonite life habits view these animals as planktonic/nektonic (i.e., pelagic) though a few have argued for a benthic life habit (e.g., Klinger

1981; Shigeta 1993; Ebel 1999; Westermann 2013). Ammonite hatchlings are generally considered to be planktonic largely on the basis of facies analysis of shell occurrences and comparisons with modern cephalopod hatchlings (De Baets et al. 2012; Ritterbush et al. 2014). Prior buoyancy calculations of juvenile shells have argued for a nektobenthic lifestyle (Shigeta 1993) or a benthic mode of life for hatchlings and early juveniles (Wetzel 1959). In this paper we develop a novel method of buoyancy calculation utilizing quantitative computed tomography that can be used to test the function and buoyant properties of the cephalopod phragmocone and hypotheses of life habits.

Ammonoids are ectocochleate cephalopods (i.e., possessing an external shell) and thus often compared to the only extant ectocochleate cephalopod the nautilus, though they are more closely related to the coleoids: squids, octopuses, cuttlefish, and Spirula (Engeser 1996; Warnke and Keupp

2005; Kröger et al. 2011). The first attempt to deduce ammonite life habits based on the

42 morphological similarity with Nautilus was done in the seventeenth century by Robert Hooke, who correctly postulated that Nautilus could alter its buoyancy by regulating the water to gas ratio in the chambers of the shell and extended this interpretation to ammonites (fide Derham 1726; Denton and

Gilpin-Brown 1973; Davis 2010). Nautilus, however, should not be considered the ideal model organism to understand the mode of life of ammonites, owing to differences in reproduction style and phylogenetic distance (Jacobs and Landman 1993; Ritterbush et al. 2014), as well as the observation that ammonites are a morphologically diverse group whereas the modern Nautilus shows highly limited shell morphology (Jacobs and Landman 1993; Warnke and Keupp 2005;

Mutvei and Dunca 2007; Wright 2012). Kröger (2002) showed that the buoyant properties of the

Nautilus shell and an ammonite shell are quantifiably different by calculating the capacity of the shell to tolerate shell loss. It is therefore necessary to establish a reliable framework within which accurate buoyancy calculations can be performed on any variety of cephalopod shells.

Initial attempts to theoretically quantify the volume of a planispiral shell were the equations of Moseley (1838), which were based on the calculation of the volume of coiled cones. Moseley never applied these equations to actual shells; this was later done by Raup and Chamberlain (1967), who modified the equations to make them more amenable to calculations involving measurements from actual specimens. Trueman (1941) avoided applying Moseley’s equations in favor of a simplified approach inspired by Thompson (1917), in which the shell volume was calculated by using a modified form of the equation for the volume of a cone. Trueman (1941) noted that his equation and those of Moseley assume that the cross-section of the cone changes in a uniform manner, which is a deviation from true ammonite growth patterns. Heptonstall (1970) revised an oversight in Trueman’s equations and then calculated ammonite densities by using more accurate cephalopod shell densities (Trueman used the density of pure aragonite for the density of the shell,

43 which led to notable error in the buoyancy calculations of both Trueman (1941) and Currie (1957).

Further quantitative study of the volumetrics of the shell through mathematical methods and implications for the life habits of extinct ammonoids and nautiloids were the topics of numerous publications in the following decades; for comprehensive discussions of this topic, see Westermann

(1996, 1999), Jacobs and Chamberlain (1996), Westermann and Tsujita (1999), and Ritterbush et al.

(2014).

Ebel (1983) attempted to calculate the buoyant properties of the shell by using cones with idealized geometric base areas (triangular and trapezoidal) and argued for the benthic-crawler model of ammonite life habits (Ebel 1990, 1992, 1999). Additional calculations by Rein (1999), for

Ceratites, have been used to argue for negatively buoyant (i.e., benthic) life habit. Dietl (1978) argued for a benthic life habit for Spiroceras on the basis of high shell variability. Delanoy et al.

(1991) calculated a negative buoyancy for the heteromorph ammonite Moutoniceras. These conclusions have been duly criticized, especially the calculations of Ebel (1983), by Westermann

(1993, 1996) and Kröger (2001) for unclear and incorrect calculation methodology or by claiming their results fall within the range of error of neutral buoyancy. Shigeta (1993) focused on calculating the buoyancy of Cretaceous ammonite hatchlings and attempted to correct the assumption of isometric shell growth and a circular whorl cross-section assumed in the calculations of Moseley (1838) and Trueman (1941) by dividing the shell into separate components and measuring the volume of these components separately. Shigeta (1993) used these calculations to argue for an initially planktonic life habit transitioning to a nektobenthic life habit for larger juveniles, and Tanabe et al. (1995) also applied this method to Carboniferous ammonoid hatchlings.

Ammonites were highly abundant and widespread in Paleozoic/Mesozoic seas and therefore knowing the life habits of ammonites is vital to understanding the biology and predator-prey

44 interactions with contemporaneous animals (e.g., Sato and Tanabe 1998; Rieppel 2002). Functional studies of both the hydrostatics and the hydrodynamics of the shell assume that adult ammonites lived in the water column (Chamberlain 1976; Klug and Korn 2004; Ritterbush et al. 2014). Existing buoyancy calculations have relied on simplification of shell geometry through mathematical modeling or creating casts or physical models, approaches that lose information about the internal features of the shell or fine external shell features. To achieve more accurate buoyancy calculations, we apply X-ray computed tomography (CT) to create 3-D data sets of true specimens whose physical properties, including shell and phragmocone volume, can be directly quantified. Hoffmann et al. (2014) tested this method on the extant Nautilus, which has a known nektobenthic lifestyle

(Ward et al. 1977), and found that with sufficient resolution buoyancy can be reasonably calculated.

We transfer this method to higher-resolution scans of a Cadoceras sp. and the earliest chambers of the shell of a Spirula spirula, which has been argued to be an analogue for some aspects of ammonite paleobiology (Warnke and Keupp 2005), in order to test mode-of-life hypotheses and establish a methodology for calculating the buoyancy of adult ammonites.

The first application of computed tomography in paleontology dates back to the 1980s; since then, CT has been frequently applied to questions of functional morphology in the fossil record

(Abel et al. 2012; Cunningham et al. 2014; Hoffmann et al. 2014). For an extensive review of the application of CT techniques in paleontology and an introduction to a generalized methodology see

Sutton et al. (2013), and for technical and theoretical background information concerning CT see

Stock (2008). Lehmann (1932) was the first to apply X-rays to create stereo images of the internal structures of ammonites. Recent applications of tomography to ammonites has been limited to destructive (grinding tomography), low-resolution techniques (Naglik et al. 2014; Tajika et al. 2014)

45 to study the morphometrics and function of the shell, or high-resolution computed tomography to study discrete parts of the animal such as the radula (Kruta et al. 2011; Tanabe et al. 2012).

Quantitative CT-based studies of ammonites have not yet been performed, largely because it is difficult to differentiate the carbonate shell from the often-carbonate rock matrix or infill. The lack of a strong difference between the absorption properties of the shell and the surrounding material can make differentiating them nearly impossible in conventional CT data sets (Naglik et al. 2014).

For this reason we chose as our subject a hollow ammonite, a Cadoceras sp. hatchling, which we scanned with high-resolution synchrotron micro-tomography (SRµCT). Wetzel (1959) suggested that ammonite hatchlings would be benthic, though this claim was challenged by House (1985), who supported a planktonic life habit for hatchlings even with the protoconch as the only empty chamber.

A planktonic mode of life for ammonoid hatchlings is supported by the occurrence of embryonic and juvenile shells in dysoxic sediments that are characterized by the absence of benthic fauna, as well as by comparisons to similarly sized modern cephalopod paralarvae, which are planktonic

(Landman et al. 1996a; De Baets et al. 2012; Ritterbush et al. 2014). The hatchling phase is a distinct ontogenetic state in the development of ectocochleate cephalopods discernible by the nepionic constriction, which marks the end of the embryonic shell (ammonitella) (Fig. 1A).

2. Materials and Methods

The internal shell of Spirula spirula, collected from Fuerteventura, was scanned at the

GeoForschungsZentrum (GFZ) Potsdam, using the Phoenix Nanotom-s at 70 keV. This data set is composed of 1880  1880  1900 slices with an isotropic voxel size of 8.747 µm and a file size of

13 GB. The full shell has a diameter of 17.75 mm.

The shell of a hatchling Cadoceras sp. was scanned at the Advanced Photon Source (APS) at

Argonne National Laboratory, using phase contrast tomography at 27.2 keV and a sample-detector

46 distance of 300 mm, with an isotropic voxel size of 0.74 μm, resulting in a data set with 2048  2048

 1948 slices and a file size of 32 GB. The hatchling shell has a diameter of 0.98 mm. Both data sets are archived at the Ruhr Universität Bochum. CT slices, volume renderings, and segmented models are shown for Cadoceras (Fig. 1A–C) and Spirula (Fig. 1D–F).

Figure 1. Computed tomographic slice of the juvenile Cadoceras sp. (A; black arrow indicates the terminal extent of the ammonitella) and Spirula spirula (D). 3-D model of Cadoceras (B) and the first whorl of Spirula (E). Reconstructed 3-D model of Cadoceras showing a cross-section of the interior of the shell and the septa in red (C). Selected shell and first three chambers used in the buoyancy calculations of a potential Spirula hatchling (F).

The data sets were analyzed in Avizo Fire (version 7.0, Visualization Science Group) and

Amira (Zuse Institute Berlin), whereby the shell material was isolated using the automatic threshold tool provided and, where necessary, manually corrected. Most of these manual corrections were necessary in the Cadoceras data set, owing to diagenetic alterations largely in the form of secondary calcite growth on the inner and outer surfaces of the shell and septa (Fig. 2 A,B). The Spirula data

47 set required minimal manual corrections except in regions where the shell material was very thin, or where the shell features, mainly the siphuncle, were damaged and the irregular geometry had to be manually corrected.

We corrected for the secondary calcite in the hatchling Cadoceras by using the “shrink” feature in Avizo, which shrinks the selected region by one voxel layer while preserving the original geometry. Direct measurements of the entire hatchling shell wall of Cadoceras are not reported in the literature; however, Drushchits et al. (1977) measured the thickness of the nepionic ridge of a

Cadoceras to be 40 m. After shrinking, the measured thickness of the nepionic ridge of our

Cadoceras hatchling was 35-37m. Measurements by Landman et al. (1996a) of ammonitella thicknesses for the heteromorph ammonite Baculites are between 2 and 8 m. In our specimen the original selection thickness, without corrections for the secondary calcite growth, was nearly 30 m; reselected thickness ranges from <1 to 12 m.

2.1 Hard Parts and Soft Tissue

The shell and chamber volumes of both specimens were segmented as separate materials.

The soft-body model of Cadoceras was assumed to be equal to the entire volume of the body chamber (an overestimation; see below for a mathematical correction for this assumption); however, because it is unknown how many chambers the hatchling Cadoceras possessed and because the extent of the body chamber changes through development (Trueman 1941), we modeled six scenarios. The initial scenario models the hatchling with the protoconch as the only empty chamber and the rest of the volume of the ammonitella taken up completely by the soft body; this scenario is the commonly assumed condition for hatchling ammonoids (Shigeta 1993; Landman et al. 1996a).

Subsequent scenarios added additional chambers, with the final scenario modeling the protoconch and five additional chambers (Fig. 2C, D). The additional chambers are modeled in order to examine

48 the influence of the ratio of shell, soft body, and air on buoyancy. Findings of ammonitella with more than one septa are reported by Bandel (1982) and Kulicki and Wierzbowski (1983). It is unclear if these actually represent ammonite hatchlings, though variation in the number of septa in

Sepia hatchlings has been observed (Bandel and Boletzky 1979); see Landman et al. (1996) for a more thorough discussion of this topic. All chambers are modeled as being completely empty (i.e., filled with gas only and no cameral fluid or gel [Landman et al. 1996a]). The weight of the gas is presumed to have ignorable effect on the weight calculation.

Estimates of soft-body volume of Spirula are based on geometric relationships between the shell diameter and the dorsal/ventral mantle length and breadth reported in the measurements of

Bruun (1943), who recorded the diameter of the shell, length of the dorsal mantle, and mantle breadth as percentages of the ventral mantle length in juvenile specimens from the Indo-Pacific and

Atlantic Oceans. Specimens show a range of relationships between these parameters; we use the most extreme relationships (highest and lowest percentages) to calculate minimum and maximum estimates for the soft-body volume. We present three scenarios for the hatchling Spirula: the internal shell with one, two, and three chambers. Each chamber, together with the corresponding section of the siphuncle, is extracted as a separate structure in the CT data, and dimensions of the soft body are calculated from the diameter of the single-, double-, and triple-chambered shell.

Accurate buoyancy calculations depend on many considerations in addition to the volume of the shell and soft body (Kröger 2002). Variation in extant cephalopod shell density forces the consideration of a range of ammonite shell densities. Measured shell density of Spirula and density values reported by Bruun (1943) yield a reasonable minimum shell density of 2.5 g/cm³ and a maximum shell density of 2.7 g/cm³. Measured densities of the shell of Nautilus and reported shell densities of the externally shelled ammonites show similar variation (2.7 g/cm³ [Greenwald and

Ward 2010]; 2.62 g/cm³ [Okamoto 1988]; 2.5958 g/cm³ [Ebel 1983]; 2.65 g/cm³ [Westermann

2013]); therefore we extract a suitable minimum and maximum value, which are the same minimum and maximum values used for Spirula.

Figure 2. Two CT slices showing the original shell material of Cadoceras (A) and the labeled and reduced shell in yellow (B). The shell shows growth of secondary calcite on the shell wall and septa, which would overestimate the shell thickness (inset). We corrected for this by using the “shrink” feature in Avizo. The length of the body chamber and the number of chambers a hatchling ammonite would possess are unknown; therefore we model six scenarios. The first scenario models the protoconch as the only empty chamber and the body length (in dark brown) extends from the end of the ammonitella back to the protoconch (C). The last scenario models the protoconch and five additional chambers (D). Intermediate scenarios model the animal with the protoconch and one through four additional chambers. 50

The soft-body density is also variable as the body is composed of multiple tissue types, which have varying densities. The average soft-body density is, like the shell, represented by a minimum and maximum, of 1.05 g/cm³ and 1.07 g/cm³ respectively (1.06 g/cm³ [Greenwald and

Ward 2010]; 1.068 g/cm³ [Heptonstall 1970]; 1.055 g/cm³ [Longridge et al. 2009]; 1.05-1.07 g/cm³

Ward and Westermann 1977]). Potential soft-body densities are the same for Spirula and

Cadoceras.

The pellicle is a thin tissue layer lining the inner surface of the phragmocone that assists in the removal of cameral liquid (Denton and Gilpin-Brown 1966). The volume of the pellicle is estimated by taking the surface area of the chamber volumes and multiplying it by the thickness, here taken as 0.5 µm. The pellicle is treated as soft tissue in terms of density.

2.2 Siphuncle

The siphuncle is a small but notable volume of soft body and, in the form of septal necks, shell volume. The septal necks of Spirula extend through an entire chamber, from septum to septum, and are well preserved, allowing easy recognition of the siphuncle volume although no soft tissue is present. The septal necks and siphuncle volume are segmented with the same method as the shell and chambers. The siphuncle, as expected, is not preserved in Cadoceras, nor does the specimen seem to possess septal necks; however, the spaces through which the siphuncle would have passed through the septa (siphuncular foramina) are preserved and allow us to trace the estimated dimensions of the siphuncle. The siphuncle of Cadoceras is therefore separated into a series of linked cylinders through each chamber. The height and radius of each cylinder is taken as the minimum and maximum extent of chamber width and siphuncular passage respectively (Table 1).

2.3 Jaws

The jaws are a potentially significant weight especially in Cadoceras and other aptychus-

51 bearing ammonites. Aptychi are typically composed of various layers of organic and calcareous materials (Engeser and Keupp 2002); the structure and composition of the juvenile aptychus of

Cadoceras is unknown, so we present a range of possible values. The volume of the aptychus is calculated in two ways: the minimum as the cross-sectional area of the aperture (Kröger 2002) and the maximum as equal to the volume of the final septum. According to Hewitt et al. (1993) the density of the aptychus is between chitin (1.655 g/cm³) and calcite (2.71 g/cm³); we use these two density values as minimum and maximum estimates.

The jaws of the juvenile Spirula have an unknown volumetric relationship with the rest of the body and are therefore estimated as a volume equal to the final septal volume. The density is taken as that of chitin because Spirula lacks the calcareous plates of Nautilus jaws (Kruta et al.

2014). The smallest and largest potential jaw volumes are averaged together, thereby providing a constant volume for each Spirula scenario; this has no significant effect on the buoyancy calculation.

2.4 Mantle Cavity

The assumption that 100% of the body chamber volume would have been soft body is an oversimplification and overestimation of the soft-body structure, as noted by Kröger (2002). The mantle cavity is the most notable and important body chamber modification. The mantle cavity in

Nautilus is 15% of the total body chamber volume and would have been filled largely with seawater, excluding the gills (Chamberlain 2010). The extent of the ammonite mantle cavity is unknown; thus

Nautilus is used as a reference and 15% of the relative body chamber volume is subtracted and treated as a volume of seawater.

Table 1. Volume data for Cadoceras and Spirula

Specimen Component Volume (cm3) Min/Max Density (g/cm3) Min/Max Cadoceras sp. Ammonitella 4.9354E-05 2.5/2.7 Protoconch 6.73596E-05 “ Chamber 1 3.94319E-06 Chamber 2 6.81996E-06 Chamber 3 9.14975E-06 Chamber 4 1.2699E-05 Chamber 5 1.58107E-05 Septa 1 2.63207E-07 “ Septa 2 6.36807E-07 “ Septa 3 9.10622E-07 “ Septa 4 1.10741E-06 “ Septa 5 1.57367E-06 “ Body Chamber 1 0.00019627 1.05/1.07 Body Chamber 2 0.000192063 “ Body Chamber 3 0.000184606 “ Body Chamber 4 0.000174546 “ Body Chamber 5 0.00016074 “ Body Chamber 6 0.000143355 “ Siphuncle 2 1.14321E-07/1.77666E-07 “ Siphuncle 3 1.04310E-07/1.69543E-07 “ Siphuncle 4 1.13507E-07/2.21698E-07 “ Siphuncle 5 1.51543E-07/2.45982E-07 “ Siphuncle 6 1.75659E-07/2.38389E-07 “ Pellicle 1.73E-06 “ Aptychus 2.34085E-08/1.74710E-06 1.655/2.71 Spirula spirula Shell 1 2.88317E-05 2.5/2.7 Shell 2 5.9473E-05 “ Shell 3 0.000106066 “ Chamber 1 2.88317E-05 Chamber 2 2.97924E-05 Chamber 3 4.47395E-05 Body 1 3.34998E-5/0.00144 1.05/1.07 Body 2 0.00075/0.00890 “ Body 3 0.00173/0.01909 “ Siphuncle 2 8.48879E-07 “ Siphuncle 3 1.85307E-06 “ Jaw 3.62447E-06/8.11656E-06 1.655

The size of the mantle cavity of a juvenile Spirula and its geometric relationships with other body shape parameters are unknown; however, Spirula is known to be capable of retracting its head

53 and tentacles into the mantle cavity (Bruun 1943). The length and diameter of the head and tentacles in relation to the ventral mantle length are not noted by Bruun (1943), so our calculations of soft- body volume assume the animal has retracted its head and tentacles into the mantle cavity, completely filling the mantle cavity volume with soft tissue.

2.5 Calculations

Buoyancy calculations traditionally involve the calculation of effective weight, the weight of the animal underwater, or density. Using the volume data derived from the CT scans and the above quoted density values, we can calculate the mass of each section of the animal (shell and soft body) as (mass=volume*density) and then convert that into weight (weight=mass*acceleration due to gravity). Buoyancy is the difference between the total weight of the animal and the buoyant force; the buoyant force is equal to the weight of displaced fluid such that the volume of fluid is equal to the total volume of the object that displaces that fluid (in this case the total volume of

Cadoceras/Spirula). We use the standard density of seawater, 1.0275 g/cm³, to calculate the buoyant force. Then, dividing the total mass by the total volume, we can calculate the total density of the animal, which we can compare with the seawater density to determine buoyancy.

2.6 Swimming and Sinking

Investigations of buoyancy should take into account the ability of motile animals to generate forces to counteract potential sinking due to negative buoyancy. Many nektonic and planktonic animals exhibit slight negative buoyancy, including sharks (e.g., Wilga and Lauder 2002), diatoms

(e.g., Raven and Waite 2004), and Nautilus (Ward et al. 1977). The swimming capability of ammonites is a subject of significant speculation (Jacobs 1992; Chamberlain 1993; Parent et al.

2014); however, Chamberlain (1981) used the hydrodynamics of Nautilus (the only empirical hydrodynamic model for ectocochleate cephalopods) and the stability (S) of Raup (1967) to estimate

54 swimming velocity:

−1 −1 −1 −1 푉 = (2푚푔푆푠푖푛(휃)휌 퐴 퐶퐷 ((푥⁄푑) − 푆푠푖푛(휃)) )^ 1⁄2 (1) where V is the swimming velocity, m is the total mass of the animal, g is the gravitational acceleration, S is stability, θ is the angle of rotation (10° for Nautilus [Chamberlain 1981]), ρ is the density of seawater, A is the reference area (shell volume^[2/3] for ectocochleate cephalopods), CD is the coefficient of drag (a range of hypothetical values are used corresponding to a range of

Reynolds numbers), x is the moment arm of thrust (estimated for each scenario), and d is the shell diameter.

Stability is defined as the ratio between the distance between the center of buoyancy

(coincident with the center of volume) and the center of mass of the soft body to the shell diameter

(Raup 1967; Raup and Chamberlain 1967). Trueman (1941) first investigated these quantities in ammonites and defined the center of buoyancy and the center of mass as the two main parameters, and considered a third parameter, which he called the center of gravity (the center of mass of the soft body and shell) too difficult to determine empirically. Later studies would follow this trend, using the center of buoyancy and the center of mass instead of the center of gravity (Okamoto 1996;

Westermann 1999; Parent et al. 2014). With Avizo, all three parameters can be calculated. We calculate the stability of Raup (1967) and compare the differences between the center of mass and the center of gravity.

The swimming velocity is compared with the sinking velocity to test whether the animal would have been capable of overcoming negative buoyancy. The equation for sinking velocity (eq.

2) is a slightly modified form of the terminal velocity equation, corrected for the effect of buoyancy:

푉 = (2(퐹푏 − 퐹푔)/퐶퐷휌퐴)^ 1⁄2 . (2)

Fg is the force of gravity (weight), and Fb is the buoyant force; thus, Fb−Fg is the effective weight of

55 the animal or the buoyancy. If the swimming velocity is greater than the sinking velocity then the animal would have been able to enter the water column (though potentially only for discreet periods of time) despite being negatively buoyant.

3. Results

3.1 Cadoceras

Volume data for the constituent parts of the ammonite are given in Table 1. The buoyancy calculations (Fig. 3A) show a range of buoyancy values across the six potential scenarios from -2.47

 10-7 N to 3.57  10-7 N (Table 2). The Cadoceras hatchling displays a slight negative buoyancy for both minimum and maximum estimates of shell and soft-body volume, aptychi density and volume, and siphuncle volume in the first two scenarios (the protoconch and the protoconch plus one additional chamber). The formation of the third chamber is when near-neutral/slight positive buoyancy is attained under minimum estimates though maximum estimates only attain positive buoyancy with the fifth chamber. The variation of aptychus volume doesn’t make an effective difference in the buoyancy calculation (i.e., shift from negative to positive buoyancy) except in the third minimum scenario in which a near-neutral negative buoyancy becomes slightly positive with a decrease in the aptychus volume. Density calculations show the same results, near-neutral/positive buoyancy (density equal to or greater than seawater respectively) is reached between the third and fifth chamber.

The effect of the pellicle on the buoyancy calculation is minimal and does not shift any buoyancy result to positive or negative. The change in buoyancy is, at most, slightly less than 0.08% depending on scenario and density.

Tanabe (1975) notes that the weight of the septa ranges between 2% and 6% of the shell weight, based on measurements made by Trueman (1941) of several ammonite genera.

Table 2. Buoyancy Results

Spirula spirula Ventral Mantle Scenario Min Max 1 6.86081E-07 1.0627E-08 2 1.04807E-06 -2.6193E-06 3 1.62472E-06 -6.1403E-06 Dorsal Mantle 1 6.8026E-07 -2.5297E-09 2 1.01455E-06 -2.0085E-06 3 1.5533E-06 -6.3017E-06 Average 1 3.4361E-07 2 -8.12933E-07 3 -2.316E-06 Cadoceras sp. Cross Section - Min Aptychus 1 -7.08222E-08 -2.0041E-07 2 -3.40886E-08 -1.6349E-07 3 2.56777E-08 -1.0442E-07 4 1.05564E-07 -2.5347E-08 5 2.18992E-07 8.70522E-08 6 3.57328E-07 2.24179E-07 Last Septa - Max Aptychus 1 -9.91487E-08 -2.468E-07 2 -6.24151E-08 -2.0988E-07 3 -2.64879E-09 -1.5081E-07 4 7.72375E-08 -7.1734E-08 5 1.90665E-07 4.06652E-08 6 3.29002E-07 1.77793E-07 Cadoceras Total Density 1 1.050677556 1.092954866 2 1.038713628 1.080930656 3 1.019248085 1.061690879 4 0.993229577 1.03593751 5 0.956286855 0.999329651 6 0.911231399 0.954668083

Figure 3. Results of the buoyancy calculation for

Cadoceras (A) and Spirula (B). The scenarios for

Cadoceras correspond to the number of

chambers/different lengths of the body chamber (see

Methods and Fig. 2). The data lines correspond to

minimum and maximum estimations of volumes and

densities used to calculate buoyancy. Here we

differentiate between the shell, soft tissue (soft body

and siphuncle), and aptychus: “MinSST-MinA”

corresponds to the minimum estimations of shell and

soft tissue densities and volumes along with the

minimum estimates for aptychus volume and

density. A, B, C, D are the four negative buoyancy

values used in the analysis of swimming and sinking

velocities in Figure 4A. The body volume of Spirula

was calculated using the ventral or dorsal mantle

length. The Spirula hatchling is modeled with one,

two and three chambers, each corresponding to

different dimensions of the soft body.

Our hatchling Cadoceras possesses a septal weight equivalent to 0.53%, 1.82%, 3.66%,

5.91%, and 9.10% of the ammonitella weight with one to five septa respectively. Shigeta (1993) uses several ratios to calculate buoyancy: shell thickness is 2% of the whorl height, the septal angle is a consistent 27, the surface area of a septum is three times the whorl cross-section, and septum thickness is 2% of whorl height. Direct measurements of the Cadoceras hatchling reveal notable

58 deviations from these ratios. Shell thickness is 6–9% of whorl height, expanding to 11% at the primary varix, with an average of 9%. The septal angle ranges between 20.2 and 28.9, with an average of 22.6. The septal surface area ranges from 11 to 20 times the whorl cross-section. Septal thickness is 2–3% of whorl height, with an average of 2.8%. Comparison of the protoconch volume using the method of Shigeta (1993), modeling the protoconch as the sum of parts of three ellipsoids, and the CT data show an error between 22.1% and 34.5%. This method consistently overestimated the volume of the protoconch. This range arises because the protoconch is not perfectly symmetrical and thus the radius for the ellipsoid changes slightly.

Raup and Chamberlain (1967) re-derived the equations of Moseley (1838) in terms of common shell parameters (eq. 3) and the equation used by Trueman (1941) in terms of the same shell parameters (eq. 4).

−3휃/2휋 푉 = (2/3)휋(퐾푅푎/ln⁡(푊))(1 − 푊 ) (3)

2 2 푉 = (1/3)(퐾푅푎)(((4휋 / ln(푊) ) + 1)^1/2) . (4)

W is the whorl expansion rate, K is the area of the aperture, Ra is the distance between the coiling axis and the center of gravity of the aperture, and θ is the radians per revolution. Both equations give similar estimates of volume, 19431106.76 m3 and 19571712.54 m3, respectively (the true volume is 49354020 m3). Both equations underestimate the true volume of shell material by about 2.5 times and have an error of 60%.

The maximum swimming speed and the potential minimum (respiratory) swimming speed are calculated using the equation of Chamberlain (1981) and the observation by O’dor et al. (1990) that the respiratory velocity of an adult Nautilus is roughly 20% of the maximum swimming speed.

Under all tested CD the minimum swimming speed (respiratory velocity) is consistently lower than the sinking speed whereas the maximum swimming speed is higher except for the most negatively

59 buoyant result for scenario 1 (Fig. 4A).

Discrepancy between the positions of the center of mass (center of the soft body) and the center of gravity (center of the shell and soft body) increase with decreasing length of the body chamber (Fig. 5A). The position of the center of gravity is less sensitive to changes in body chamber length relative to the center of mass (Table 3). Stability for Cadoceras (calculated with the center of mass) ranges from 0.13 with the protoconch and five additional chambers (Fig. 5B) to 0.03 when the body chamber extends back to the protoconch (Fig. 5C). Nautilus has a stability around 0.09 (Parent et al. 2014). Stability values can be used for evaluating potential swimming capability, with increasing stability favoring greater swimming ability; Figure 4C shows this in the hatchling

Cadoceras, with increasing swimming speed coupled with increasing stability though not in a simple linear manner.

Sinking and swimming speeds can be used to model a simple scenario of a hatchling ammonite moving vertically in the water column and the number of jet cycles (pulses per second) necessary to ascend and maintain constant position in the water column (maintenance jetting).

Figure 4B shows that to overcome a negative buoyancy of 0.07 µN (1A) Cadoceras would need to jet at 1.34 pulses per second to maintain a constant position in the water column. To overcome a negative buoyancy of 0.2 µN (1C) Cadoceras would require about 28 pulses per second.

3.2 Spirula

Minimum and maximum assumptions both show an initial positive buoyancy with only the protoconch (Fig. 3B). Minimum estimates show an asymptotic decrease in buoyancy with the addition of the second and third chamber; however, maximum estimates show a near-linear decrease in buoyancy, and buoyancy becomes negative with the formation of the second chamber.

Table 3. Stability Values for Cadoceras

X Y Z Center of Volume 869.92438 803.5387 677.63147 Center of Mass Scenario 1 892.58258 816.12671 658.27264 Scenario 4 926.00525 842.86145 656.08667 Scenario 5 971.93958 887.77264 694.10406 Center of Gravity Scenario 1 887.4345559 815.8047509 672.3184676 Scenario 4 902.8615561 828.2852798 671.5084683 Scenario 5 920.7362682 846.3495696 688.2841546 Stability Final Value Scenario 1 0.03235145 Scenario 4 0.071801957 Scenario 5 0.13331843 Distance between Center of Mass and Distance (µm) the Center of Gravity Scenario 1 15.77 Scenario 4 32.12 Scenario 5 66.16

4. Discussion

4.1 Model Limitations

Original ammonite shell density is unknown, and could have been variable among ammonite groups as is shell density among existing cephalopods (Mutvei 1983). It is reasonable then to model a range of potential densities where the range is derived from the densities of cephalopods that phylogenetically bracket ammonites (i.e., Nautilus and coleoids) (Ritterbush et al. 2014). Small density differences seem to exist between the shell and septa in Nautilus, one study noted a small

Figure 4. A, The sinking and swimming velocities

calculated for the negatively buoyant Cadoceras (using

four negative buoyancy values, A–D) when the body

chamber extends back to the protoconch (scenario 1).

Sinking velocity is calculated via terminal velocity,

swimming velocity is calculated via Chamberlain (1981),

and respiratory velocity is 20% of the swimming velocity

(O’dor et al. 1990). B, The change in position of

Cadoceras in the water column (for scenario 1A), starting

in an arbitrary position, through time based on the

swimming/sinking velocities and the number of jet pulses

per second. The changes in position are considered under

the simplification that movement is strictly vertical. C,

The relationship between increasing stability (ratio of the

distance between the center of mass and the center of

buoyancy to the total diameter of the shell) and velocity.

density difference between the outer shell and septa: 2.57g/cm3 and 2.51 g/cm3, respectively

(Hoffmann and Zachow 2011). Our analysis makes no distinction in density between the shell wall

62 and the septa because this difference would be minimal and the results would fall within the range covered by the minimum and maximum density calculations.

The aptychus is a significant unknown in this analysis, so we could only estimate its size and density. Moreover, nothing is known about the characteristics of the aptychus in a hatchling, and thus the sequence of development of the embryological jaws is speculative. Likewise, the relative volume of the jaws for the hatchling Cadoceras is unknown and only rough estimations could be made. The effect of the jaws relative to the shell and soft body is small, however, as can be seen in

Figure 3A.

Like the shell, the density of the soft body of ammonites is unknown but can be estimated reasonably through phylogenetic bracketing. Also like the shell, the density of the constituent parts would vary (i.e., different tissues would have different densities). Therefore we model the soft body as a single density and vary that density between a minimum and maximum value. The range between minimum and maximum value should include the slight tissue density differences.

Additional aspects of the soft body also should be addressed. The volumes of the siphuncle and pellicle are small in comparison to the rest of the chamber and thus make a minimal difference to the final buoyancy calculation. The final soft-body consideration is how to account for the tentacles. The soft-body volume is taken as the volume of the body chamber, which would undoubtedly have accounted for most of the soft body. The hyponomic sinus has been documented in Devonian ammonoids at the edge of the post-embryonic shell, suggesting that the soft body extended to the edge of the aperture (House 1965, 1996). No modification to the calculations were made for additional material that may have been outside of the body chamber, i.e., the tentacles or the yolk (Boletzky 2002). Because no preserved tentacles have been found (Klug et al. 2012;

Ritterbush et al. 2014), the morphology of the tentacles is unknown, and therefore it is unreasonable to speculate. Also unknown is whether the ammonite hatchlings possessed a yolk.

The volume of the soft body of Spirula is not constrained by a body chamber and estimations of the volume had to be based on the relationships reported by Bruun (1943). The negative buoyancy trend seen for Spirula with maximal estimates for density and volume could represent an overestimation of the growth of the body volume relative to shell size caused by the poor understanding of the relative proportions of the hatchling animal. The animal had to be modeled as if the head had retracted into the mantle cavity because the length and volume of the head and tentacles relative to the mantle size are unknown (Chun 1915; Bruun 1943). The siphuncular tube is preserved in Spirula, however, so its volume is directly quantifiable. As in Cadoceras, the jaw apparatus in Spirula is unknown and we estimated its volume in the same way as the volume of the

Cadoceras aptychus.

Beyond the estimations of certain physical parameters, there are additional potential sources of error that have to be addressed. One is the state of preservation of the shell. Although the conch was “hollow,” secondary calcite crystals had formed along the inner and outer surface of the shell and septa. Owing to the high quality of the SRµCT data, we were able to identify these calcite deposits as well as the boundary between the shell and these secondary calcite deposits. Although diagenesis is corrected for (see Methods section) it is possible that further diagenetic alteration affected the geometry of the shell in imperceptible ways, though how this would affect the volume calculations is unknown but unlikely to be very appreciable. The transition from aragonite to calcite during diagenesis of the shell may also alter the shell volume by a small amount (Reyment 1958).

A source of error that is inevitable to some degree in quantitative tomographic work is the partial volume effect (PVE). CT images (see Fig. 1A,D) are constructed from voxels (three

64 dimensional pixels), which are assigned a single value represented by a shade ranging from black to white depending on the material properties of the materials present in the volume of that voxel.

Because each voxel is constrained to a single value if two or more materials are present in the volume represented by that voxel, the shade of the voxel will be an average of the material properties of all materials within that volume. The boundary between two materials, in this case the shell (white) and air (black), is represented by a gray gradient indicating a decreasing presence of the material of interest and an increasing volume of air present within the voxel. How this boundary condition is included in the segmentation can alter the final volume calculation. The effect of the

PVE on different scan methods has been tested using the shell of Nautilus by Hoffmann et al.

(2014). The PVE is minimized in our data through the use of high-resolution SRµCT and Nano-CT, in which only the first whorl of Spirula was in the field of view in order to maximize the resolution.

4.2 Life Habit

The modeling of variable body lengths in Cadoceras presents an opportunity to study the effect of body length on stability. As the distance between the center of mass and the center of buoyancy increases so too does the stability. Nautilus has a stability of about 0.09, brevidomic ammonoids have a stability of 0.05, and mesodomic ammonoids have a stability of 0.03 (Parent et al. 2014). As the length of the body chamber decreases the stability of the animal increases, which can be seen in Cadoceras. It is interesting to note, however, that because the center of mass of ammonites is typically calculated using only the soft body and ignoring the shell, the resulting stability is artificially high for shorter body chambers, compared to ammonoids with body chambers extending back a full whorl (Fig. 5A).

Figure 5. 3-D models with the calculated centers of buoyancy, mass, and gravity. The blue diamond is the center of buoyancy, the dark blue dots are the center of mass, and the green squares are the center of gravity.

B and C show the difference in life position of the hatchling depending on the length of the body chamber

(Fig. 2C, D). Ammonite stability is often calculated using the center of buoyancy and the center of mass of the soft body. The center of gravity takes into account the shell and the distribution of septa. A shows the difference in position of the center of mass of the soft body and the center of gravity for three different body chamber lengths. The closer the center of gravity/mass is to the center of buoyancy, the longer the body chamber. As the length of the body chamber decreases the discrepancy between the center of mass and the center of gravity increases.

The buoyancy calculation shows that the hatchling Cadoceras achieves neutral buoyancy between the third and fifth chamber depending largely on the density of the shell and the soft body, and on the volume and density of the aptychus. Depending on the number of chambers and the way chambers were added after hatching, either the hatchling possessed neutral buoyancy immediately after emerging from the egg or there was a shift in life habit early in ontogeny. The buoyancy calculation itself only models the animal floating in a still column of water and only tests whether the buoyant force generated by the animal is capable of overcoming the animal’s weight. Further calculations are necessary to integrate the potential swimming forces the animal could generate and wave motion (which would likely be more important for sub-millimeter hatchlings than for adult

66 animals). We do not factor into these calculations any liquid that might have been in the protoconch

(Landman et al. 1996a) ; it is possible that the protoconch would have been emptied of liquid and filled with gas after hatching (Rouget and Neige 2001).

Specimens of Nautilus caught in the wild exhibit some degree of negative buoyancy that the animal can overcome and remain in the water column (Ward et al. 1977). It is possible some ammonites also would have exhibited this type of behavior, and therefore simply calculating a slight negative buoyancy (e.g., Ebel 1990) is insufficient to regulate the animal to a benthic life habit without considering the potential forces the animal could generate to counteract this negative buoyancy (i.e., swimming). To demonstrate this we compared the potential swimming speed to the potential sinking speed and found that within the possible range of swimming and sinking speeds, the juvenile could have overcome potential negative buoyancy if it had hatched with an insufficient number of chambers to allow neutral or positive buoyancy (Fig. 3A).

The calculation of the swimming speed of a hatchling Cadoceras is hypothetical, the equation of Chamberlain (1981) was formulated and tested using an adult Nautilus, and the relationship between the swimming capabilities of an adult and a hatchling Nautilus are unknown. It should also be noted that the hatchling Cadoceras lives at low Reynolds numbers (both sinking and swimming speed were calculated at Reynolds numbers around 1), entering a realm where inertial forces begin to lose their importance, viscous forces dominate drag (Jacobs and Chamberlain 1996;

LaBarbera 2008), and propulsive methods such as jet-driven motion become less efficient. Squid hatchlings, with a length of around 1 mm, face a similar propulsive problem (Staaf et al. 2014).

Squid paralarvae are negatively buoyant and compensate for this continual downward motion through periodic jet pulses, resulting in what can be referred to as hop-and-sink behavior also seen in other negatively buoyant zooplankton (Haury and Weihs 1976). The calculated sink/swim data

(Fig. 4A) of the hatchling Cadoceras potentially fits with a similar “hopping” swimming mode of juvenile squids if the hatchling was negatively buoyant.

Squid paralarvae have been shown to swim at an average speed of 0.00268 m/s, with a range of 0.00146 m/s to 0.00484 m/s (Bartol et al. 2009). Staaf et al. (2014) measured sinking speed of paralarvae at around 0.0046 m/s. Thus, in terms of sinking velocities the order of magnitude and range for squid hatchlings are similar to those of the hatchling Cadoceras (Fig. 4A). Figure 4B shows that Cadoceras would need roughly 1.34 pulses per second with a negative buoyancy of

0.071µN (and 2.11 pulses per second with 0.099µN) to maintain a constant position in the water column (maintenance jetting); the observed jet frequency of squid hatchlings during maintenance jetting is 2.13 Hz (Staaf et al. 2014). Jet frequency during swimming in adult Nautilus is, on average, 1.67 pulses per second with an observed maximum of 2.67 pulses per second (Ward 1987).

Scenario 1C would force Cadoceras to maintain 28 pulses per second for maintenance jetting, a number likely far too high for the animal to accommodate and thus under this scenario Cadoceras would not be able to maintain a position in the water column. It should be noted that ammonite soft parts are rarely preserved and their physiology is unknown and therefore any reconstruction of swimming speed is speculative (Ritterbush et al. 2014). Comparison to coleoid paralarvae may be more appropriate than comparison to baby Nautilus in terms of the lifestyle of the hatchling, owing to the differences in total diameter; a Nautilus hatchling has a shell diameter of around 26 mm—two orders of magnitude larger than the embryonic shell diameter of ammonites (Arnold et al. 2010; De

Baets et al. 2012). Under the majority of estimations and tested scenarios results recover near- neutral/positive buoyancy and negative buoyancy that can be countered by motion; this indicates that hatchling Cadoceras was most plausibly planktonic, which fits well with the recovery of ammonitella in anoxic conditions, i.e., black shale (Mapes and Nützel 2009) and comparisons with

68 similarly sized cephalopod hatchlings (e.g., Calow 1987). A planktonic mode of life would aid in rapid and global dispersion via ocean currents, which has been proposed as one mechanism for survival after mass extinctions (Ward and Bandel 1987; Harries et al. 1996; Tajika and Wani 2011;

De Baets et al. 2012, Ritterbush et al. 2014). The achievement of a planktonic life habit in the hatchling ammonite, coupled with the potential mass spawning behavior (Manger et al. 1999;

Walton et al. 2010; De Baets et al. 2012; Ritterbush et al. 2014), could lead to early and rapid dispersal. It is interesting to note that simple hydrodynamic models of current dispersal of chokka squid paralarvae show that slight negative buoyancy mitigates wave action and could allow paralarvae to stay close to their hatching location (Martins et al. 2013). This could be beneficial if they hatch in nutrient-rich waters.

5. Summary

The application of very high-resolution SRµCT demonstrates the utility of computed tomography to high-precision calculations of ammonite buoyancy and the integration of buoyancy results to potential swimming velocities in order to test hypotheses of ammonite life habits. This CT method allows shell volume to be considered without loss of inherent biological variability or fine details that would necessarily be eliminated through mathematically based modeling. A Cadoceras hatchling could achieve neutral/positive buoyancy provided the ammonitella had three to five chambers (including the protoconch), whereas the Spirula hatchling had positive/neutral buoyancy with just the protoconch, though it may have hatched with two to three septa (Lukeneder et al.

2010). However, minimum estimations of shell and soft tissue densities indicate that the Cadoceras hatchling had sufficient swimming power to enter the water column with just the protoconch.

The high resolution of this method and flexibility of digital tomographic data enables the accounting and assessment of minute, sub-micron details; the assessment of relationships in the size,

69 area, and volume of the shell components; and the modification of shell parameters and morphology in order to test functional hypotheses.

Some have contested, on the basis of recovery of negative buoyancy values, that ammonites were benthic organisms (Wetzel 1959; Ebel 1990; Rein 1999; Delanoy et al. 1991); however, we have demonstrated here that calculation of negative buoyancy is insufficient to deem an ammonite benthic, because swimming capacity can operate to overcome the gravitational force acting on negatively buoyant animals.

Ammonites are a very diverse and long-lived group and the heteromorph ammonites

(heteromorph refers to the non-planispiral shell) show great shell disparity; there is no necessary reason that all heteromorphs must conform to the same life habit. Indeed the speculated modes of life of heteromorphs are diverse, from sessile and mobile benthic animals (Diener 1912; Klinger

1981; Monks and Young 1998; Shevyrev 2005), nektobenthic organisms with persistent negative buoyancy (Higashiura and Okamoto 2012), and burrowers (Frech 1915), to rapid swimmers

(Matsumoto and Obata 1962; Westermann 2013). Provided suitable specimens, this CT method can be used to determine the fundamental capacity of the ammonite phragmocone to provide sufficient buoyancy as to allow a planktonic or nektonic mode of life. The insight provided through this method expands our understanding of ammonite paleobiology—specifically, how ammonites might have interacted with their environment—as well as having implications for the interpretation of geochemical data derived from ammonite shells (Ritterbush et al. 2014).

Acknowledgments

This project was funded by the Deutsche Forschungsgemeinschaft (grant number HO

4674/2-1). The authors would like to thank M. Ehlke (Zuse Institute, Berlin) for help with visualization and data management. We also thank X. Xiao (Advanced Photon Source, Argonne

National Laboratory, Lemont, Illinois, U.S.A.) and E. Rybacki (Deutsches Geoforschungs Zentrum,

Potsdam) for scanning assistance. We greatly appreciate the assistance of V. Mitta (Paleontological

Institute of the Russian Academy of Science, Moscow) for assistance during fieldwork. We thank K.

De Baets (Friedrich-Alexander Universität Erlangen Nürnberg, Germany) and D. Korn (Museum für

Naturkunde, Berlin) for their helpful reviews.

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Chapter 4

The Evolution and Development of Cephalopod Chambers and their Shape.

Robert Lemanis, Dieter Korn, Stefan Zachow, Erik Rybacki, René Hoffmann

Abstract

The Ammonoidea is a group of extinct cephalopods ideal to study evolution through deep time. The evolution of the planispiral shell and complexly folded septa in ammonoids has been thought to have increased the functional surface area of the chambers permitting enhanced metabolic functions such as: chamber emptying, rate of mineralization and increased growth rates throughout ontogeny. Using nano-computed tomography and synchrotron radiation based micro-computed tomography, we present the first study of ontogenetic changes in surface area to volume ratios in the phragmocone chambers of several phylogenetically distant ammonoids and extant cephalopods. Contrary to the initial hypothesis, ammonoids do not possess a persistently high relative chamber surface area. Instead, the functional surface area of the chambers is higher in earliest ontogeny when compared to Spirula spirula. The higher the functional surface area the quicker the potential emptying rate of the chamber; quicker chamber emptying rates would theoretically permit faster growth. This is supported by the persistently higher siphuncular surface area to chamber volume ratio we collected for the ammonite Amauroceras sp. compared to either S. spirula or nautilids. We demonstrate that the curvature of the surface of the chamber increases with greater septal complexity increasing the potential refilling rates. We further show a unique relationship between ammonoid chamber shape and size that does not exist in S. spirula or nautilids. This view of chamber function also has implications for the evolution of the internal shell of coleoids, relating this event to the decoupling of soft-body growth and shell growth.

1. Introduction

Cephalopods are a group of marine mollusks that evolved in the Cambrian from a monoplacophoran-like ancestor (Runnegar and Pojeta 1974; Lee et al. 2003; Kröger et al. 2011;

Landing and Kröger 2012); the earliest known cephalopod is the Late Cambrian Plectronoceras

(Yochelson et al. 1973; Vinther 2015). Basal cephalopods possess a phragmocone that is distinct from other mollusk shells (conch) by the division into discrete chambers (Fig. 1). The chambers are separated by mineralized partitions called septa that allows the shell to function as a buoyancy device. The multi-chambered, aragonitic cephalopod shell is a key adaptation that allows the animal to dwell in the water column without constantly expending energy

(Westermann 1999; Westermann and Tsujita 1999). A thin organic strand, called the siphuncle, runs through all phragmocone chambers and connects this with the rear of the soft body that sits in the body chamber. Liquid and gas diffuse into and out of the chambers through the siphuncle and thereby allows for buoyancy adjustments (Denton and Gilpin-Brown 1966, 1973). The siphuncle was supported by the connecting pellicle, a thin (sub-micron) proteinaceous structure composed of conchiolin that covers the inner surface of each chamber which stores and transports liquid to the siphuncle [9].

The evolution of the chambered cephalopod shell allowed for a life-habit in the water column facilitated by neutral buoyancy; this led to the diversification of the cephalopods that can be classified into three major groups: “Nautiloidea”, Ammonoidea, and Coleoidea (Engeser

1996; Kröger et al. 2011). Nautiloidea are represented by the two extant genera: Allonautilus and

Nautilus, referred to collectively as nautilids. Ammonoidea, which originated from the Bactritida about 417 million years ago during the Early Devonian and went extinct at the end of the

Cretaceous (Landman et al. 2015) , have been one of the prime groups to study evolutionary

86 biology through geologic time (Newell 1949; Seilacher 1988; Boyajian and Lutz 1992; Lehmann et al. 2015).

Nautilids and ammonoids possess external shells. However, the coleoids that also originated from Bactritida, evolved an internal shell that was highly reduced or completely lost in the majority of derived taxa (Kröger et al. 2011). Recently, the ammonoids and the bactritids have been considered as stem group coleoids (Kröger et al. 2011; Vinther 2015). Coleoids comprise the majority of Recent cephalopod diversity; only the sepiids and the deep sea squid

Spirula spirula have retained a mineralized phragmocone. S. spirula is the only extant coleoid with a fully developed spiral phragmocone (Clarke and Trueman 2013). The shells of

Nautiloidea, Ammonoidea, and Coleoidea show characteristic differences both in their overt morphology and in the morphology of their septa. The septa of S. spirula are semi-hemispherical structures (Fig. 1A, 1B) similar to the septa of most of the nautiloids (Fig. 1C, 1D). However, the fossil record is replete with more complicated septal structures in nautiloids that show variable degrees of foldings turning their septa into multilobate structures (Crick 1988; Westermann

1999).

Septal complexity reached its apex in the ammonoids (Fig. 1E), more specifically in the

Jurassic and Cretaceous ammonites that show highly complex folded septa (Fig. 1F, 1G, 1H).

Ammonoids show a persistent, iterative evolutionary trend towards increasing septal complexity

(Klug and Hoffmann 2015; Polizzotto et al. 2015). The most common explanation of this evolutionary trend is either mechanical (Hassan et al. 2002) or physiological (Kröger 2002). This paper focuses on potential physiological drivers for the morphological evolution of cephalopod phragmocone chambers. The morphology of these chambers are influenced by three variables: shell wall morphology, septal morphology, and septal spacing. While tomographic data does

87 present an opportunity to test mechanical hypothesis, these are beyond the scope of this work and will be the focus of future research.

Ammonoids have been argued to possess a relatively large chamber surface area due to shell morphology—such as whorl overlap—and, more commonly, septal morphology (Olóriz and Palmqvist 1995; Kröger 2002; Perez-Claros 2005; Klug et al. 2008). The increased folding of the septa is thought to increase the surface area of the chambers (Mutvei and Dunca 2007) leading to a range of physiological hypotheses for septa such as those of Kröger (Kröger 2002) who argued septal complexity increases the relative surface area and volume of the pellicle

(Denton and Gilpin-Brown 1966, 1973; Mutvei 1967; Ward 1986), which allows a greater degree of buoyancy compensation due to retention of a greater volume of liquid. Increasing the relative surface area of a membrane, in our case this is the pellicle and siphuncular epithelium, is a common adaptation in biology that allows a maximization of fluid transport (West et al. 1999).

Increased rates of buoyancy change and enhanced respiration are further hypotheses implementing physiological functions to explain septal complexity (Newell 1949; Bayer 1978;

Saunders 1995; Daniel et al. 1997; Perez-Claros 2005). These hypotheses tend to depend on a relatively high functional surface area, here defined as the ratio between surface area and volume. The previous studies (Newell 1949; Denton and Gilpin-Brown 1966; Saunders 1995;

Daniel et al. 1997; Kröger 2002; Perez-Claros 2005) lead to the first hypothesis tested herein: the surface area to volume ratio of the phragmocone chambers will be higher in ammonoids than in either S. spirula or the nautilids. Growth is partially dependent on emptying rates as the chamber formation cycle is connected to the emptying of the prior chamber and the buoyancy of the animal depends on fluid being removed from the chambers as shell material is added

(Chamberlain 1978; Ward 1982). A second hypothesis focuses on the siphuncle, because some

88 authors (Hewitt and Westermann 2003) argue that it is the siphuncle, not the pellicle that is the major constraint of diffusion into and out of the chambers. If ammonites increased the functional area of the siphuncle relative to chamber volume compared to nautilids, as suggested by Ward

(Ward 1987), then the surface area of the siphuncle vs. chamber volume should be higher in ammonoids than in nautilids and S. spirula.

Volume and surface area are notoriously difficult to measure directly in fossil shells hence the classical dependence on volumetric reconstructions based on simple geometric shapes

(Trueman 1940; Raup and Chamberlain 1967; De Baets et al. 2012; Klug et al. 2015). These reconstructions are ultimately incapable of fully describing biological structures and accounting for changes in growth through ontogeny. This has led to the application of tomographic techniques, computed tomography (Hoffmann et al. 2014; Lemanis et al. 2015; Tajika et al.

2015a) and grinding tomography (Naglik et al. 2015b; Tajika et al. 2015b), in order to directly quantify shell and chamber volume. Tomographic data are available for chamber volumes but not for surface area. Therefore, we reconstruct the surface area and volume trajectories of: A. scrobiculatus, N. pompilius, Cadoceras sp., Kosmoceras sp., Amauroceras sp., Arnsbergites sp., and S. spirula.

Surface area scales with the square of length while volume scales with the cube of length; maintenance of a constant surface area to volume ratio through ontogeny requires changes in shape to compensate for the disproportionate scaling between surface area and volume (Gould

1966). As an object increases in size alone, the ratio of surface area to volume will decrease regularly. We therefore expect an overall decreasing trend in the surface area to volume ratios as the chambers increase in all specimens. The comparisons we will focus on in this paper are twofold: firstly, the surface area to volume ratios between specimens at equivalent sizes and,

89 secondly, the Vogel number. The Vogel number is the ratio of the linearized surface area and volume which eliminates the effects of scaling differences between surface area and volume. i.e., if a shape increases its dimensions in constant proportion the Vogel Number will be a constant value even through the SA:V will decrease. If the ratios of interest are only influenced by size then all specimens should show the same ratio at a specific size.

We present the first study of the ontogenetic and evolutionary change in the surface area and volume ratios of cephalopod shell chambers (SAC:VC) and ratios of siphuncular surface area and chamber volume (SAS:VC).

Specifically, we test the following hypotheses derived earlier:

1. Ammonoids will have a consistently higher SAC:VC ratio than, nautilids, and S. spirula.

2. Ammonoids will also possess a higher SAS:VC than the nautilids.

2. Material and Methods

All fossil specimens used in this study are stored in the Ruhr-Universität Bochum (RUB),

Universitätsstrasse 150, Bochum 44801, Germany and are accessible to interested parties.

Specimen designations: Cadoceras sp.: RUB-Pal 11245, Kosmoceras sp.: RUB-Pal 11246,

Allonautilus scrobiculatus: RUB-Pal 11247, Nautilus pompilius: RUB-Pal 11248, Spirula spirula: RUB-Pal 11249, Spirula spirula (pathological): RUB-Pal 11250, Amauroceras sp.:

RUB-Pal 11251, Arnsbergites sp.: MB.C.25122. No permits were required for the described study, which thus complied with all relevant regulations.

2.1 Specimens

A total of eight shells were used in this study (Table 1). Computed tomographic scans were produced for all specimens and the data were processed with ZIBAmira (Zuse Institute,

Berlin-ZIB). Processing tomographic data is very time intensive and computed tomography (CT)

requires hollow fossil preservation in order to have the highest precision. Due to this the number

of specimens available for this study is limited due to the extreme rarity of this type of

material; however, we used specimens from several geological periods from the Palaeozoic and

Mesozoic and specimens with a variety of morphologies. The genera Allonautilus, Nautilus, and

Spirula represent the only extant forms that possess a fully formed, spiral phragmocone. Fossil

cephalopods with four different morphologies, reflected by differences in chamber geometry, are

presented in this study. Three of them are represented by Jurassic ammonites: Amauroceras sp.

(Pliensbachian), Cadoceras sp. (Callovian) and Kosmoceras sp. (Callovian). The fourth

morphology is represented by the Carboniferous goniatite Arnsbergites sp. (Viséan).

Specimen Age Diameter Tube:voltage Data set Voxel size Average (mm) (kV)/current dimensions (mm) percent (µA) error of volume (+/-) Nautilus Recent 170 180/150 962x1008x560 0.17500 7.06746 pompilius Allonautilus Recent 177.13 100/350 2383x1746x3046 0.06000 2.31144 scrobiculatus S. spirula Recent 16.51 75/200 1880x1880x2200 0.00875 1.86725 S. spirula (path.) Recent 19.09 150/150 894x774x338 0.02523 5.56178 Cadoceras sp. Middle Jurassic 0.98 27.2 2048x2048x1948 0.00074 1.59767 Amauroceras sp. Lower Jurassic 2.99 80/200 1432x2314x1829 0.00315 4.08041 Arnsbergites sp. Mississippian 1.64 50/190 1880x1880x1700 0.00250 5.00604 Carboniferous Kosmoceras sp. Middle Jurassic 13.06 120/350 2489x1677x2266 0.00815 1.73740 Table 1. Specimen Data and Tomographic Scan Meta-Data.

2.2 CT Scanning

Micro-computed tomographic scans of Nautilus pompilius and the pathological specimen

of Spirula spirula were performed at the Steinmann Institute at the University Bonn using a

phoenix|x-ray|v|tome|x s (General Electric). Nanofocus-computed tomographic (nano-CT) scans

of Spirula spirula and Arnsbergites sp. were done at the GeoForschungsZentrum (GFZ,

Potsdam) using a phoenix nanotom-s (General Electric). Allonautilus scrobiculatus, Kosmoceras sp. and Amauroceras sp. were scanned using nano-CT at the TPW Prüfzentrum (Neuss,

Germany) with a phoenix nanotom m (General Electric). Cadoceras sp. was scanned at the

Advanced Photon Source at Argonne National Laboratory using phase contrast synchrotron radiation based micro-computed tomography. All data are deposited at the Ruhr Universität-

Bochum. All recent specimens are adults as indicated by the presence of their terminal countdown morphology (Seilacher and Gunji 1993); Cadoceras sp. is a juvenile while the other ammonoids are juvenile-sub-adult.

CT data were imported into ZIBAmira where the relevant volumes were segmented using the threshold function and manual selection function. All recent shells were completely segmented (i.e., shell and chamber volumes) while the ammonoid shell chambers were segmented where available as some chambers were damaged or not preserved (Fig. 1C). The chambers of Kosmoceras sp. were segmented two per whorl for the final two and a half whorls

(Fig. 1G). The shells of S. spirula, A. scrobiculatus and Amauroceras sp. were segmented with the preserved siphuncular tube. Three chambers of the Amauroceras sp. specimen and the rest of the specimens did not preserve the siphuncle; however, the volume and surface area of the siphuncle was reconstructed from linear measurements, as described for Cadoceras sp. in [38], and subtracted from the volumes and surface areas for their respective chambers in each specimen. Comparisons between siphuncular area and chamber volume were performed on the three specimens that preserved the siphuncular tube in the species A. scrobiculatus, S. spirula, and Amauroceras sp.

Figure 1. Three-dimensional surface renderings of the segmented chambers of all specimens used in this study. A) Spirula spirula, B) pathological S. spirula (pathological chamber indicated by black arrow), C)

Nautilus pompilius D) Allonautilus scrobiculatus E) Arnsbergites sp. F) Amauroceras sp. G) Cadoceras sp. H) Kosmoceras sp. Segmented chambers appear in sequentially different colors; only six chambers of

Kosmoceras were segmented. The largest segmented chamber is shown in dorsal/ventral view (top) and lateral view (bottom). The boundaries of the chamber volumes trace the shape of the septa. Images are not to scale. 93

All volume data was converted into surface files from which surface area and volume values were taken. Partial volume effects (PVE) are the primary source of error in the reconstruction of volumes (Hoffmann et al. 2014). In order to estimate the susceptibility of our data to such errors we transformed volume data for each specimen by expanding/shrinking it by one voxel layer relative to the total 3D volume. Percent error was calculated for each transform and the average error is presented in Table 1. This value is a representation of the variability of the data due to resolution and the segmentation process.

3. Results

3.1 Surface Area/Volume Ratios

Comparisons of chamber surface area/ chamber volume (SAC:VC) against chamber number are shown in Fig. 2A. In general, closely related taxa show similar SAC:VC ratios for each equivalent chamber; nautilids plot together as do the S. spirula and ammonoid shells. All tested shells show a decreasing SAC:VC through ontogeny as expected from simple scaling rules.

Interspecific comparisons are done on the basis of shell diameter (Fig. 2B). Nautilids show the

nd lowest SAC:VC relative to diameter, with a maximum ratio of 8.75 in the 2 chamber of A. scrobiculatus and a minimum ratio of 0.35 in the 32nd chamber of A. scrobiculatus. Ammonoids possess the largest ratios for diameters under 3 mm (Fig. 2B) with a maximum ratio of 70.38 in the second chamber of Arnsbergites sp. and a minimum ratio of 2.14 in the 59th chamber of

Kosmoceras sp. All ammonoids, regardless of stratigraphic age, show similar SAC:VC ratios throughout ontogeny. The SAC:VC ratios of ammonoids attain the highest overall values, however they reach the same values as S. spirula in later ontogeny.

Figure 2. Comparison between the surface area to volume ratio (SAC:VC) of each segmented chamber against chamber number for all specimens. B) SAC:VC against shell diameter at each chamber for A. scrobiculatus, S. spirula, Arnsbergites sp., Amauroceras sp., and Kosmoceras sp. SAC:VC is a parameter that reflects the capacity of the shell to compensate for potential buoyancy changes due to the water storing, organic lining in each chamber (Kroger, 2002). Chamber volume (C) and chamber surface area

(D) comparisons between S. spirula and selected ammonoids. A. scrobiculatus and N. pompilius have an overall larger volume and surface area due to the much larger size of the animal, maximum diameter is an order of magnitude larger than S. spirula or Kosmoceras. Comparison between S. spirula and the ammonoids is a comparison between extreme morphologies as S. spirula has a whorl interspace, conservative shell cross-section through ontogeny and simple sutures and ammonoids have overlapping whorls, more complex septa (complexity changes through ontogeny), and variable conch morphology and ornamentation. Hm is the potential hatching point, Pa is the pathological chamber, TC is the terminal countdown.

Nautilids and S. spirula shells show slight upturns in the SAC:VC ratios in the last

95 chambers reflecting their terminal countdown with septal crowding (Seilacher and Gunji 1993).

The pathological S. spirula shell shows a sudden increase in its SAC:VC corresponding to a non- lethal injury of its phragmocone (reported for the first time)—visible as the dorso-ventral compaction of one chamber—that results in a permanent offset from the non-pathological shell that lasts through ontogeny. SAC:VC in chamber 15 in the non-pathological shell is 4.79 while the same chamber in the pathological shell has a ratio of 9.52. The initial chamber of ammonoids and S. spirula show similar values, both have a spherical to ellipsoidal shape and similar diameters. Ammonoids show a much higher increase in SAC:VC between the initial chamber and the subsequent chamber (303.98% in Arnsbergites sp. and 293.89% in Amauroceras sp.) than S. spirula (17.83% in the non-pathological shell and 5.97% in the pathological shell) due to the large decrease in size in the second chamber compared to the initial chamber. Comparison of chamber volume (Fig. 2C) and chamber surface area (Fig. 2D) between S. spirula and the ammonoid specimens shows that S. spirula possess a persistently higher relative chamber volume through most of ontogeny, corresponding to a higher surface area as well, though

Kosmoceras sp. attains a slightly higher surface area and volume by the last segmented chamber despite Kosmoceras sp. and S. spirula having similar final shell diameters (Table 1).

3.2 Siphuncular Surface vs. Chamber Volume

SAS:VC trends are unsurprisingly similar to SAC:VC trends in that both show a general decrease through ontogeny and similar differentiation between taxa (Fig. 3A). Amauroceras sp. shows the highest values (maximum of 3.30), while the specimen of A. scrobiculatus shows the lowest values (minimum of 0.005) and that of S. spirula lying between them with an overlap with Amauroceras sp. being the initial chamber (Fig. 3B). SAS:VC values show a lower rate of decrease through ontogeny, slight increases in the trend are seen in the terminal chambers of S.

96 spirula and A. scrobiculatus (Fig. 3).

Comparison between a hypothetical, reconstructed siphuncle volume and surface area and true volume and surface area were made with the data from Amauroceras sp. The siphuncle was reconstructed as a series of connected cylinders spanning the length of each chamber.

Measurements for the cylinder were taken along the siphuncular foramen—the region of the septum through which the siphuncle passes through—see (Lemanis et al. 2015). Maximum percent error for siphuncle volume was 60%, average percent error was 25%. Maximum error for siphuncle surface area was 25%, average error was 10%. Hypothetical siphuncle measurements were used in specimens that did not preserved the siphuncle to correct the chamber volume and surface area, despite the significant error this was done because the relative contribution of the siphuncle to the total volume/surface area is minor even in small chambers. However, due to the potentially high error, SAS:VC were confined to specimens that preserved the siphuncle and no comparisons were made between the preserved siphuncles and the reconstructed siphuncles.

4. Discussion

4.1 Scaling

A short discussion of scaling is necessary in order to properly contextualize our data. It is well known that surface area to volume ratios inversely scale with size, the larger the object the lower the SA:V compared to a smaller, equivalent shape (Gould 1966). The clear differentiation of groups when ratios and values are plotted against chamber number (Fig. 2A, 2C, 2D, 3A) is an effect of scaling. These graphs are not a reliable basis for interspecific comparisons but do illustrate the trends for each group. In order to account for size scaling, comparisons are done against shell diameter, Fig. 2B and Fig. 3B. If size was the only factor affecting SA:V values then we would expect to see the same SA:V in each taxon for a given shell diameter.

Figure 3. Siphuncular

surface area to chamber

volume ratio (SAS:VC) for

the three specimens that

preserve the siphuncular

tube, A. scrobiculatus, S.

spirula, and Amauroceras,

plotted against chamber

number (A) and shell

diameter (B). The

siphuncle transfer liquid

and gas into and out of the

shell, therefore the surface

area of the siphuncle

limits the diffusion rates of liquid/gas. The higher the SAS:VC the higher the potential rate of diffusion.

There is a complication in this regard since S. spirula possesses a whorl interspace that artificially inflates the shell diameter. In order to correct for this, the SA:V ratios are plotted against cumulative chamber volume (Fig. 4). Comparison between shell diameter and cumulative chamber volumes shows the same trends and further illustrates the difference between SAC:VC and SAS:VC in early ammonoid ontogeny. While the difference in ratios between S. spirula and the nautilids decreases when compared to cumulative volume, it does not disappear completely demonstrating the influence of shape on these ratios.

Additionally, surface area and volume can be linearized by taking the square root of surface area and the cube root of volume to calculate the Vogel number. The Vogel number is a

98 shape parameter that is independent of size yet still shows the same trends in early ontogeny between ammonoids and S. spirula (Fig. 5). Kosmoceras sp. shows a very different trend in

Vogel number compared to all other specimens, namely it demonstrates a strong dependence of shape on size. As Vogel number is, in a way, an index of flatness it might be expected to be

Figure 4. Chamber surface area to chamber volume ratio (A) and siphuncular surface area to chamber volume ratio (B) plotted against cumulative chamber volume. 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 Spirula, 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.

99 strongly dependent on septal angle; however, this seems not to be the case (Fig. 6). Indeed the septal angle of the Jurassic ammonites and Carboniferous Arnsbergites sp. are quite different but all show similar SAC:VC and Vogel numbers. Septal angles of the tested ammonoids and S. spirula converge in early ontogeny but this does not correlate to a convergence of SAC:VC or

Vogel number. The shape of the chamber is dependent on three morphological parameters: conch and septal morphology and septal angle. Disentangling the contribution of each of these parameters on overall conch shape is a complex topic and may be an invigorating avenue of future research. However, we anticipate that no one single parameter will completely describe shape differences.

Figure 5. Calculated Vogel number for each specimen used in this study. Vogel number is calculated as the square root of the surface area of the chamber divided by the cube root of the volume of the chamber.

Linearizing these values allow direct comparisons between the two while removing scaling effects due to size. It is important to note that the difference between ammonites and S. spirula in early ontogeny exists even when corrected for size. The high values shown by the early chambers of A. scrobiculatus may be an artifact due to resolution and should be interpreted with care.

100

4.2 Siphuncle and SAS:VC

The expected recovery of a higher SAS:VC in ammonoids is supported by our data (Fig.

3B). The increase in the functional surface area of the siphuncle would increase the hypothetical limit of liquid and gas diffusion rate into and out of the chambers as the siphuncular soft tissue of ammonoids is not known to be very different than extant forms (Tanabe et al. 2000). It has been observed that the connecting rings of ammonoids shows morphological features that suggest higher diffusion rates of liquid through the siphuncular epithelium (Mutvei and Dunca 2007,

2011; Mutvei et al. 2010). Unfortunately it is impossible to take these morphological differences into consideration because there are no quantitative studies measuring fluid flow within the siphuncle and pellicle of Nautilus and Spirula. However, if ammonoids did indeed have a faster transmission of fluid into the siphuncle this would serve to further amplify the effect of the higher SAS:VC we observe.

There are several ways to increase the functional siphuncle surface area: a) increasing the length of the siphuncle, b) increasing the cross-sectional diameter, and c) increase the folding of the siphuncular epithelium (Gottobrio and Saunders 2005; Tanabe et al. 2015). Increasing the linear length of the siphuncle would necessitate increasing septal spacing, thereby increasing the chamber volume at a faster rate than the siphuncle length per unit increase in septal spacing; a counter-productive result. Increasing the cross-sectional diameter of the siphuncular tube should decrease the mechanical strength of the tube making it more susceptible to breakage

(Westermann 1982). Ammonoids do however show a migration of the siphuncle to the ventral edge of the chamber. This migration maximizes the arc length of the siphuncle relative to a median position, such as that in the nautilids or a dorsal position such as that in S. spirula.

Maximizing the surface area of the siphuncle would permit higher potential growth rates and the

101 faster growth of the chamber volume (i.e., cameral fluid) compared to siphuncular area would lead to decreasing growth rates through ontogeny.

Figure 6. Comparison of various expansion rates against septal angle and septal angle expansion rate for the ammonite Amauroceras sp. The expansion rate of a parameter is defined as the value of that parameter in one chamber divided by the value of the same parameter in the preceding chamber; e.g. Vc expansion rate = Vn/Vn-1 where Vn is the volume of chamber n. Interestingly while changes septal angle have the highest correlation with changes in volume (correlation coefficient of 0.60), the correlation with our functional parameter (SC/VC) and our shape parameter (Vogel number) is lower, -0.58 and -0.29 respectively.

102

4.3 Curvature

The curvature across the face of the folded septa of Kosmoceras sp. is greater than an equivalently sized chamber of A. scrobiculatus (Fig. 7). It can be seen that the suture line traces an area of highest curvature in both Kosmoceras sp. and A. scrobiculatus (Fig. 7); extreme frilling of the septal margin may increase the relative length of this area of high curvature.

Contrary to (Daniel et al. 1997), Kosmoceras sp. does not show dramatically higher curvature than A. scrobiculatus; however, the consistently higher curvature over a larger percentage of the chamber surface and a potentially longer relative suture line could contribute to a quicker chamber reflooding system (Daniel et al. 1997).

4.4 Evolution of high SAC:VC

We anticipated that the Mesozoic ammonites were going to possess the highest SAC:VC, however, the Paleozoic goniatite Arnsbergites sp. shows similar values compared with the

Jurassic ammonites (Fig. 2B). Above three millimeters the SAC:VC of ammonoids seems to converge with the chamber ratios seen in S. spirula which themselves would converge with the value of A. scrobiculatus at an estimated shell size of 20-30 mm (Fig. 2B). This convergence is an unexpected trend (Mutvei and Dunca 2007) as S. spirula has the simplest septal morphology: a semi-hemispherical dome-shaped structure, compared to the multi-lobed septa of Kosmoceras sp. (Fig. 1A, 1H). S. spirula also possesses a nearly circular whorl cross-section throughout most of its ontogeny as well as a whorl interspace and smooth inner conch surface whereas

Kosmoceras sp. shows strong shell ornamentation that affects the inner conch surface and constant whorl overlap which is expected to increase the relative surface area of the chambers

(Klug et al. 2008; Hoffmann et al. 2015). At sizes above 3 mm, ammonoids do not seem to possess a higher functional surface area (Fig. 2B), or indeed higher absolute surface area (Fig.

103

2D), in the phragmocone chambers.

Figure 7. Comparison of the curvature between one chamber of A. scrobiculatus and Kosmoceras sp.

Both chambers have similar volume and the chamber of Kosmoceras sp. was resampled to the same voxel size to make the datasets comparable. Curvature is measured at the vertices of the surface mesh. Overall,

Kosmoceras sp. shows a consistently higher curvature over a greater percentage of its available surface area. Both chambers show highest curvature along the suture line.

Although ammonoids seem to have a relatively “normal” SAC:VC compared to S. spirula

104 in later ontogeny, they possess a high SAC:VC in earliest ontogeny. What then, if anything, does this seemingly characteristic high SAC:VC in ammonoids reflect? A suite of morphological changes during the origination of ammonoids from their bactritid ancestors as well as the early evolution of ammonoids towards tightly coiled planispiral shells has been connected to the evolution of a rapid, high fecundity reproductive style similar to that of modern coleoids (De

Baets et al. 2012; Laptikhovsky et al. 2013; Ritterbush et al. 2014). In contrast, the reproductive strategy of nautilids is characterized by slow growth, multiple reproductive events over the life of the animal, and relatively large hatchlings which closely resemble the adult animal (Ward

1987; Arnold 2010; Ritterbush et al. 2014). The high SAC:VC shown in the studied ammonoids may be another expression of a general evolutionary trend towards a high fecundity reproductive strategy as high SAC:VC would increase potential fluid exchange rates that could permit quicker growth.

Ward et al. (1981) found that chamber formation in Nautilus macromphalus occurs when the previous chamber is nearly half emptied of cameral fluid, the coupled-decoupled transition point. This observation allowed a very precise prediction on the timing of new chamber formation although it was observed that new chambers can be formed under certain conditions without the previous chamber being emptied at all (Ward 1987). It stands to reason, however, that because the shell’s primary function is a buoyancy device, if the animal continued to grow without emptying the chamber, then it would accrue too much weight to remain buoyant; speed of chamber emptying is therefore one necessary factor limiting potential growth rate. The relatively high SAC:VC and SAS:VC seen in ammonoids therefore fits well with an evolutionary trend towards rapid early growth as both would increase the potential speed of chamber emptying.

105

Growth rates in some coleoids are known to be very sensitive to water temperature

(Boyle and Boletzky 1996; Leporati et al. 2006); however, juveniles tend to show a consistently higher, exponential, growth rate which decreases in later ontogenetic stages (Bigelow 1992;

Laptikhovsky et al. 1993; Wells and Clarke 1996; Semmens et al. 2004; Ramos et al. 2014).

Squids invest more energy in growth than do other iteroparous mollusks resulting in relatively higher overall growth rates through life (Rodhouse 1998). As ammonoids develop a more coleoid-like reproductive strategy (De Baets et al. 2012) we might expect changes towards a more coleoid-like growth patterns.

If this idea is true we would expect to see a trend towards increasing SAC:VC and SAS:VC between the bactritids and ammonoids and during the evolution of the relatively tightly coiled, planispiral shell of early ammonoids. As noted before the high SAC:VC and SAS:VC seen in the early ontogeny of the ammonoid shell decreases through ontogeny eventually equaling that of S. spirula and, presumably given a large enough specimen, A. scrobiculatus (Fig. 4A). This means that the potentially rapid emptying rates seen in early shell chambers decreases significantly when the animal grows, losing this function when the animal enters later ontogenetic stages as this enhanced function seems to only exist in the hatchling and early juvenile shell. This fits with the general decrease in growth rates of coleoids through ontogeny (Ward 1987; Wells and Clarke

1996). It must be noted that rapid early growth does not demand that the animal had a shorter total life-span or even that the high growth rate was selected for in order to reach sexual maturity faster since the high functional surface area operates only in small sizes and disappears before the animal actually reaches maturity.

Rapid early growth could also be a protective mechanism, evolved to compensate for decreasing hatchling size (De Baets et al. 2012) and to protect from predators. (Watson 1949;

106

O’Dor and Webber 1986) hypothesized that the evolution of rapid early growth in coleoids, along with their particular reproductive strategy, was a response to predation as larger animals are less likely to be eaten (Calow 1987; Aronson 1991). The hatchling size of nautilids is an order of magnitude greater than the hatchling size of ammonoids and S. spirula. The hatchling size of N. pompilius is between 2-3 cm (De Baets et al. 2015) while the hatchling size of our Arnsbergites sp. is 0.71 mm, Amauroceras sp. is 1.09 mm, Cadoceras sp. is 0.9 mm, and Kosmoceras sp. is

0.86 mm. This small size confines ammonoid hatchlings to low Reynolds numbers where jet propulsion is known to be much less effective relative to the adult because of the low relevance of inertial effects at these low Reynolds numbers (Staaf et al. 2014; Lemanis et al. 2015; Naglik et al. 2015a). Smaller forms also have higher energetic costs for locomotion (Jacobs 1992) and decreased metabolic efficiency compared to larger forms (Hill 1950). This suggests a selective advantage towards rapid early growth when the hatchling size is small. S. spirula would also hatch with a small shell, diameter of approximately 1.5 mm for our S. spirula, however as this is an internal shell it does not necessarily directly reflect hatchling size.

To test if ammonoids possessed a persistently high growth rate, studies focusing on the ontogenetic change in the SAS:VC are necessary as SAS:VC in this study was confined to a single ammonite specimen, which was unfortunately not the largest ammonite studied, due to preservation.

4.5 Septal Complexity

The evolution of septal complexity is, perhaps, the most debated trend in ammonoid evolution encompassing decades of research; ideas of the function of complex septal are summarized in (Klug and Hoffmann 2015). While we do not directly address septal complexity in this paper, septal complexity is one of three morphological features that control chamber

107 volume and surface area. The other parameters, shell wall shape and septal spacing, show a complex relationship to both SA:V and Vogel Number (Fig. 6) and we propose septal complexity contributes a non-negligible amount to both of these values though we cannot say to what degree it contributes. However, as chambers increase rapidly in volume and as the septa only border the chamber on two sides, the influence of septal complexity on chamber morphology should decrease through ontogeny. The increase in septal complexity does increase the curvature of the septal face, however (Fig. 7), and may contribute to survivability by increasing the tolerance of the animal to shell loss (Daniel et al. 1997; Kröger 2002).

If septal complexity is biologically constrained by the morphology of the shell (Garcia-

Ruiz et al. 1990; Olóriz et al. 2002), then the evolutionary drive to enhance early physiological function in the shell that we propose can, at least partially, explain the origin of septal complexity as a consequence of high SAC:VC/SAS:VC. A correlation between conch shape and septal complexity has been observed and can be interpreted in favor of this idea (Olóriz et al.

1999; Ubukata et al. 2008; Monnet et al. 2011; De Baets et al. 2012). Covariation between morphological features, including septa, such as Buckman’s laws of covariation demonstrate the presence of developmental constraints in shell morphology (Olóriz et al. 1999; Monnet et al.

2015a, b).

We suggest that the initial evolution of folded septa from a hemispherical septum contributed to a chamber morphology that allowed faster growth of the hatchling but we do not disregard other existing ideas of septal complexity. We postulate that conch morphology, septal complexity, and septal spacing would covary but any of these features can be shaped by variable selective pressure. Conch morphology may be shaped by hydrodynamics (Ritterbush and Bottjer

2012; Tendler et al. 2015; Klug et al. 2016) or further folding of the septa seen in later Mesozoic

108 forms may be driven by mechanical strength (Hewitt and Westermann 1987) or enhancement of curvature (Fig. 7) but evolutionary shaping of these parameters will induce changes in the other parameters that would not necessarily be functional but a consequence of growth. SAC:VC may reflect this constrained growth. The increasing complexity of septa and increase in the shell ornamentation of Kosmoceras sp. does not cause any shifts in the SAC:VC (Fig. 4A) and we expect all chambered shells to show stable trajectories through ontogeny, despite changes in conch or septal morphology, under normal growth (Fig. 2). This is not a controversial statement as it merely says that we do not expect rapid changes in size and morphology at any single growth stage (chamber). The SA:V ratio is a quantitative way of phrasing this idea that can be tested. Furthermore, Vogel number can be used to test for changes in the chamber morphology through ontogeny with a constant Vogel number indicating no morphological change of the chamber.

Interestingly, comparisons between the two S. spirula specimens used in this study defy this trend. One specimen shows an abrupt shift in both volume and surface area (Fig. 2C, 2D) and a sudden perturbation in the SAC:VC that persists for about 5 chambers (Fig. 4A). The shift and subsequent displacement is related to a sudden change in the morphology of one pathological chamber that has been crushed. While we suggest normal growth will always result in stable surface area, volume, and SAC:VC trends due to size scaling and growth limits, sudden displacements in these trends may indicate the presence of pathologies—indicating either predation or sudden, massive environmental perturbations (e.g., temperature, salinity, food supply). The shifts in these trends in Arnsbergites sp. may to be related with sudden changes in septal spacing and may be indicative of environmental stress. Kinks in these trends may indicate certain life events, the two kinks seen in A. scrobiculatus and N. pompilius may indicate the

109 hatching moment (Fig. 2A).

4.6 Mechanical resistance and shell internalization

One of the most common explanations for the evolution of septal complexity is that the increase in septal folding increased the mechanical resistance of the shell against hydrostatic stress (Hewitt and Westermann 1986, 1987, 1997; Westermann 1996; Polizzotto et al. 2015).

While addressing this idea is beyond the scope of this paper, it is interesting to note that the initial evolution of a complex septum from a simpler, dome-shaped septum decreases mechanical strength (Daniel et al. 1997; Hassan et al. 2002). The evolutionary increase in septal complexity may be due to mechanical resistance though a lack of correlation between habitat and septal complexity challenges this idea (Olóriz and Palmqvist 1995; Perez-Claros et al. 2007). Increased shell and septal thickness also influence mechanical resistance to hydrostatic pressure; however, comparing Kosmoceras sp. and S. spirula show that for equivalent diameters Kosmoceras sp. has a thicker shell wall but a slightly thinner median septal thickness. An extension of the mechanical explanation is that the septa increase resistance to point forces such as those from bites (Daniel et al. 1997; Hassan et al. 2002). This idea however has been challenged (Perez-

Claros et al. 2007) and recent attempts to find a correlation between septal complexity and rate of survival from shell breakage—which would be expected if increased septal foldings protected from predation—have failed to find a significant link (Kerr and Kelley in press). Mechanical hypotheses therefore are unlikely to explain the initial evolution of complexity; however, our comparisons between S. spirula and the derived ammonoids suggest that SAC:VC and SAS:VC enhancement may be an important factor in this event. Internal shells do not show the complex morphologies seen in either ammonoids or nautilids. If septal morphology is connected to hydrostatic pressure then cephalopods living in deep waters should have more complex septa

110 than shallow water forms regardless of possessing an internal or external shell. If however, septal complexity is viewed as an aspect of growth than this relationship need not exist; indeed S. spirula has the simplest septal morphology but can dive to a depth of ~1000 meters (Hoffmann and Warnke 2014), a depth deeper than most depth estimates for ammonoids (Denton and

Gilpin-Brown 1971; Westermann and Tsujita 1999). This view permits some speculation of the evolution on an internal shell.

The soft body of ammonoids and nautiloids is encased in the shell throughout ontogeny and therefore the size of the soft body is strongly limited by the size of the shell; therefore, growth of the animal is strongly connected to the growth of the shell as discussed before. The internalization of the shell may result in a partial decoupling of the growth of the shell and the growth of the animals soft body. The animal is no longer constrained in a rigid container allowing an increase in soft body growth without necessarily growing the shell. The internal shell still functions as a buoyancy device; however, as the soft body is no longer within the shell, the evolution of a mantle-pump propulsion system can compensate for the increase in weight without a proportional increase in phragmocone volume. The mantle-pump system of coleoids involves the inflation of the soft body and allows greater total velocity and is more energetically efficient than the nautilid propulsion system (Chamberlain 1976, 1993; O’dor et al. 1990; Wells

1990; Alexander 2003).

5. Conclusions

1. The chamber surface area to chamber volume ratio (SAC:VC) of ammonoid chambers

shows an initially high value compared to S. spirula and nautilids; however, at sizes

larger than about 3 mm, the ratio of ammonoids becomes nearly identical to the values of

S. spirula. Larger ammonoid shells are expected to show ratios similar to nautilids at

111

sizes around 20-30 mm.

2. The siphuncle surface area to chamber volume (SAS:VC) is higher in ammonoids than in

either S. spirula or the nautilids. This confirms the increase in functional area of the

siphuncle that can be explained by the migration of the siphuncle to the ventral edge of

the chamber.

We propose that the initial high SAC:VC and persistently high SAS:VC in ammonoids reflects a trend towards increased growth rates in early, post-hatching stages. Ammonoids have been found to have evolved a more coleoid like reproductive strategy relative to extant nautilids (De Baets et al. 2012; Ritterbush et al. 2014). Coleoids are known to have a higher growth rate in post-hatching juveniles which decreases through ontogeny (Wells and Clarke

1996). High early growth rates in ammonoids may therefore be supplementary to a high fecundity reproductive strategy.

Septal complexity is one of three morphological characters that influence SAC:VC and

SAS:VC, the other two being septal spacing and conch morphology. Therefore, septal complexity may have contributed to the enhancement of SAC:VC and SAS:VC in the early shell.

Scaling eliminates this benefit at moderate sizes, however, we further demonstrate that septal folding increases the curvature of the septal face and elongates the region of highest curvature, which is traced by the suture line.

This hypothesis is strengthened by the fact that a multi-lobed septum would be mechanically weaker compared to the ancestral, hemispherical dome-shaped septa (Daniel et al. 1997; Hassan et al. 2002). We further suggest that septal morphology, conch morphology, and septal spacing are covarying parameters which are reflected by stable surface area, volume, and SAC:VC trends through ontogeny. Displacements of this trend may indicate pathologies

112

and stressed environments while single, point deviations in this trend may indicate life events

such as hatching. The observation of high functional area being limited to the early shell also

presents potential problems for some physiological explanations for septal function.

Acknowledgments

This research is funded by the Deutsche Forschungsgemeinschaft, grant number HO

4674/2-1. We would like to thank H. Knappe and D. Weyer for the Arnsbergites sp. specimen and S. R. Gerden who segmented it. The specimen of Kosmoceras sp. was donated by S.

Schneider, Cadoceras sp. was donated by V. Mitta, and F. Rudolph donated the Amauroceras specimen. L. Wulff segmented the pathological S. spirula. H. Wesendonk at the TPW (Neuss,

Germany) provided several nano-CT scans. Julia Shultz scanned the N. pompilius and pathologic

S. spirula at the Steinmann Institute. K. Stevens for fruitful discussions. Additionally M. Ehlke provided continued support for ZIBAmira.

113

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Evolution. Princeton University Press, New Jersey.

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individual cephalopod. Philosophical Transactions of the Royal Society of London B:

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implications for ammonoid bathymetry. Lethaia 15:373–384.

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Davis, eds. Ammonoid Paleobiology. Springer US.

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the Invertebrate Skeleton. John Wiley & Sons.

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309.

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Chapter 5

Comparative Cephalopod Shell Strength and the Role of Septum Morphology on Stress

Distribution

Robert Lemanis, Stefan Zachow, René Hoffmann

Abstract

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 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

125 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.

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1. Introduction

The cephalopod shell is a complex structure that has multiple functions including buoyancy regulation and protection of the animal against predation, water pressure, and strong currents (Derham 1726; Hewitt and Westermann 1997; Hassan et al. 2002). These shells, whether they be the internal shells of Recent coleoids—such as Spirula and Sepia—or the external shells of Nautilus and the extinct ammonoids, must resist the hydrostatic pressure of the surrounding water that depends on the mechanical strength of the shell. This is due to the fact that the internal pressure of the chambers of cephalopod shells is only around one atmosphere

(Swammerdam 1758; Buckland 1836; Denton and Gilpin-Brown 1961, 1966). The maximum depth of some extant, shelled cephalopods ranges from several hundred meters to around 1000 m

(Bruun 1943; Dunstan et al. 2011; Hoffmann and Warnke 2014); depth estimates for ammonoids and extinct nautiloids cover a similar range and, in some cases, even deeper (Westermann 1996,

1999). Water pressure at 1000 m depth is around 100 times atmospheric pressure at sea level.

Accordingly, the shell must be able to resist this pressure while also resisting deformation that would impact the buoyancy ability of the shell. (Buckland 1836) hypothesized that the extreme folding of the septa—mineralized partitions that divide the shell into a series of chambers— famously displayed by ammonoids, was an adaptation to increase the resistance of the shell against implosion by hydrostatic pressure. This idea has become known as the Buckland model.

Alternatively, Pfaff (1911) postulated that the increase in septal complexity buttressed the final septum against the hydrostatic pressure acting against its face as pressure would be transmitted through the soft-tissue (Hewitt and Westermann 1986). This idea is now known as the Pfaff model. Both models were later complemented by the Westermann model that argued septa support previous whorls through management of bending moments (Westermann 1958;

127

Hewitt and Westermann 1986). In this view the septa are compared to springs, and septal complexity helped buttress the inner whorls against indirect hydrostatic pressure transmitted through the outermost whorl (Hewitt and Westermann 1987a, 1997).

The mechanical explanation of septal complexity has been heavily debated (e.g.,

Chamberlain and Chamberlain 1985; Westermann 1985; Saunders 1995; Hewitt and

Westermann 1997). Alternative hypotheses for the function of ammonitic septa focus on their potential physiological functions (e.g., Daniel et al. 1997; Perez-Claros 2005; Perez-Claros et al.

2007; Lemanis et al. 2016). For a comprehensive review of potential functions of complex septa see Klug and Hoffmann (2015)

One difficulty of testing mechanical hypotheses is accurately modelling the complex geometry of the shells and septa in order to test them. Generally, research in this field focuses on a small sub-sample of the domain of interest in order to model the complexity of the morphology or simplifying a larger domain of interest (Westermann 1973; Jacobs 1990; Hewitt 1996; Daniel et al. 1997; Hassan et al. 2002; De Blasio 2008). Finite element analysis (FEA) is one of the most promising, and powerful techniques to test the mechanical properties of the shell and septa.

FEA has become a popular method in palaeontology to address biomechanical questions

(Witzel and Preuschoft 2005; Rayfield 2006, 2007, 2009; Falkingham et al. 2010; Tseng 2013;

Button et al. 2014; Lautenschlager 2014; Cox et al. 2015; Ledogar et al. 2016). This technique converts a continuous structure into a set of discrete elements, in 3D these are typically tetrahedra or cubes, over which a set of solutions to a given problem are solved and then compiled to a representative continuum solution (Turner et al. 1956; Cook et al. 2001). One of the first applications of FEA in zoology was Guillet et al. (1985) who studied the beak of the

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African shoebill Balaeniceps rex; studies using FEA on ammonites quickly followed (Hewitt and

Westermann 1987b).

Hewitt published several FEA studies focusing on nautiloids (Hewitt and Westermann

1987b; Hewitt et al. 1989, 1993). Hewitt et al. (1989) modeled the final septum and surrounding shell region of the Carboniferous nautiloid Michelinoceras unicamera and subjected it to a simulated, external pressure load to estimate implosion depth (1125 m). The septal neck region of M. unicamera was modeled by Hewitt et al. (1993) who analyzed the relative strength of the nacreous/chitinous complex of the septal neck and connecting ring. The two most recent applications of FEA (Daniel et al. 1997; Hassan et al. 2002) on cephalopods focused on the previously discussed mechanical hypothesis of septal complexity and came to contradictory conclusions.

Both Daniel et al. (1997) and Hassan et al. (2002) recreated approximate septal morphologies using sequential Fourier equations and place the simulated structures in a cylindrical shell model. Both the shell and the septa have uniform thickness. Daniel et al. (1997) concluded that as septal complexity increases, stress on the septum also increases; furthermore as folding increases, stress is focused towards the center of the septum. The FEA of Hassan et al.

(2002) modeled three hypothetical morphologies of increasing complexity going from their

Goniatite model to Ammonite “A” and Ammonite “B”. Their analysis showed a decrease of maximum principal stress and shear stress in the septum as complexity increased, challenging the results of (Daniel et al. 1997), though both agreed that a simple, semi-hemispherical septum would be more resistant to stress than folded septa. Both studies used simplified, theoretical septal morphologies that focused on a single septum with uniform thickness exposed to a

129 pressure force of 0.1 MPa. These simplifications likely limit the comparability of these models to true septa.

Here we present the first FEA of empirical models of cephalopod shells. The whole shells of Nautilus pompilius, Spirula spirula, and Cadoceras sp. are modeled here to test the pattern of stress development and distribution across the shell and compare stress development and distribution in the septa due to pressure and point loading. The use of empirical models of shells allows us to bypass the geometric problems of Daniel et al. (1997) and Hassan et al. (2002) and gives a more accurate representation of stress due to realistic loading conditions.

2. Material & Methods

2.1 Specimens and Segmentation

A total of three specimens and four models were used in this study (Table 1). One shell of

Nautilus pompilius, collected from the Philippines, was scanned at the Steinmann Institute at the

University of Bonn with a phoenix|x-ray|v|tome|x s (General Electric) and an isotropic voxel size of 175 µm (the same specimen used in (Hoffmann et al. 2014)). One shell of Spirula spirula from Thailand was scanned using a phoenix nanotom m (General Electric) at the TPW

Prüfzentrum (Neuss, Germany) with an isotropic voxel size of 9 µm. Cadoceras sp. was scanned at the Advanced Photon Source at Argonne National Labs using phase contrast synchrotron tomography with an isotropic voxel size of 0.74 µm. According to the observed terminal changes in shell morphology N. pompilius and S. spirula are adult specimens (Seilacher and Gunji 1993).

Only the ammonitella, indicated by the nepionic constriction, of Cadoceras sp. is preserved and segmented.

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Table 1. General information of specimens, finite element models, and boundary conditions

Model Age Locality Total Elements Nodes Force Scaled Surface Applied Point Area by 8 MPa Force (N) (mm2) Pressure (N) Cadoceras Callovian Russia 6.70 1780464 428535 32.22 10 sp. (5 septa) Cadoceras “ “ 8.36 2373913 517318 21.41 12.48 sp. (10 septa) Spirula Recent Thailand 2720.99 2058092 583565 7262.31 4063.45 spirula Nautilus Recent Phillipines 152400.35 2434318 723832 693270.16 227590.56 pompilius

Segmentation of all specimens began with the application of an initial threshold that was manually refined using ZIBAmira (Zuse Institute, Berlin). For further details on the reconstruction of the Cadoceras sp. see Lemanis et al. (2015). Two Cadoceras sp. models were generated for this study. The first being the ammonitella with ten septa (the maximum number of septa present in the specimen) and a separate model with five septa. These two models offer a comparative demonstration of how the amplitude of septal folds affects stress distribution. The septa of S. spirula and N. pompilius only show minor changes through ontogeny and none of these changes are used to reconstruct the animal’s ecology.

2.2 Meshing and Finite Element Modelling

The final labelfields were used as the basis for the construction of a series of stereolithographic surface meshes (stl). Due to the high resolution of the original scans, the resulting stl files were oversampled, a single stl was composed of over 15 million faces. In order to produce workable sized meshes, all data sets were down-sampled to twice the original voxel size. Testing was performed to measure the effects of the down-sampling on the resulting finite

131 element analysis. Similar to the work of McCurry et al. (2015), the original data sets of N. pompilius and S. spirula were down-sampled to 2x, 4x, and 6x of their original voxel size. The resulting FE-models were then compared against an edited stl from the original data set. In both cases the results of the edited stl and the 2x down-sampled mesh showed nearly identical results.

Therefore, 2x down-sampled datasets were used as they were easier to work with compared to the original data.

Surface mesh editing and volumetric meshing were performed in ZIBAmira. All stl files were re-meshed using the implementation of the algorithm of Zilske et al. (2008). Surface meshes were edited to correct for triangle aspect ratio, dihedral angles, and tetrahedra quality.

Volumetric meshes composed of first-order tetrahedral elements were generated via the advancing front method (e.g. (Löhner and Parikh 1988)).

Convergence testing is a vital step in FEA that is necessary to determine the resolution of the meshes necessary for the analysis to solve completely and show an accurate stress distribution across the structure of interest (Bright and Rayfield 2011; Walmsley et al. 2013).

The convergence models were formed by altering the mesh size during surface generation and models were considered converged both upon visual inspections, when no further development of stress in the structure could be detected, and when the maximum values of stress in the models were within 10%. Final volumetric mesh sizes are in Table 1. Both four-node tetrahedral elements (TET4) and 10 node elements (TET10) were tested although the TET10 models proved to be too large to solve using the available computation resources (Windows PC with an Intel

Xeon E5-1620 CPU @3.6 GHz, 65 GB of RAM, Nvidia Quadro 6000 with 4 GB of video

RAM).

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2.3 Finite Element Analysis

All FEA were performed with Mecway v4.0 (Mecway Limited, New Zealand). For all specimens, models were run as a static 3D, linear analysis with the isotropic material properties of mollusk nacre: a Young's modulus of 50 GPa and a poisson's ratio of 0.29 (Hewitt 1996;

Daniel et al. 1997; Hassan et al. 2002). It should be noted that nacre tablets have orthotropic properties; however these properties are poorly studied for cephalopods as most studies focus on gastropods and bivalves (Jackson et al. 1988; Barthelat et al. 2006; Bertoldi et al. 2008). Loading cases are divided between pressure loads and point force loads.

2.4 Pressure Loading

Simulation of hydrostatic pressure is done by applying a pressure load, i.e. a load normal to the face of an element, to every external face of the model. This includes faces of the exterior shell wall, the interior surface of the body chamber and the external face of the final septum. All specimens are subjected to an 8 MPa pressure, roughly equivalent to 785 m depth. N. pompilius is further testing at 2 MPa, 4 MPa, and 6 MPa to model the development of stress in the final septum. No single constraint is present in any pressure load case. It is worth noting that this is a simplified hydrostatic load as pressure is modeled here as a uniform field while true hydrostatic pressure would increase along the length of the shell with depth; pressure would be higher on the bottom of the shell than the top. Furthermore, the minor pressure exerted by the gas within the chambers (<1 atm/0.1 MPa) is ignored (Denton and Gilpin-Brown 1966).

2.5 Point Loading

Additional point forces are modeled to test the resistance of the shell to simulated bite forces. For all specimens, two situations are modeled. The first situation has a point load on the chamber wall, mid-way between the two septa. The second situation is a point load applied along

133 the suture line, the attachment of the septa to the shell wall. In both cases the point force is applied along the side of the shell while the opposite side is constrained against translation and rotation in three dimensions. Point forces are applied to a single node with a resultant force of 10

N for Cadoceras sp. with five septa. Point forces are scaled (Table 1) to the total surface area of each specimen (Dumont et al. 2009).

2.6 Septal Strength Index

Septal strength index (eq. 1) calculations were done on median sections of the final septa of N. pompilius and S. spirula following the work of Westermann (1973), and transverse sections of the final septa of N. pompilius (Westermann 1985).

훿 ∗ 1000 eq. 1 푅

δ is thickness and R is the radius of curvature. Minimum septal thickness and radii of curvature are measured in ImageJ (Schneider et al. 2012). Radius of curvature is computed using the

“ThreePointCircularROI” plugin (G. Landini, http://www.mecourse.com/landinig/software/software.html). Approximate depth limits are calculated using a conversion factor derived from Westermann (1973).

3. Results

3.1 Pressure

All tested shells show the same general pattern of stress distribution: overall the shell shows mostly compression or very minor tension while the final septum is under the highest tension as illustrated by elevated max. principal stress (Fig. 1). All septa show high tension along the area where the septa are attached to the shell wall, while the final septum of N. pompilius shows the most widespread distribution of high max. principal stress along the septal face compared to all other specimens (Fig. 2A). Only N. pompilius and Cadoceras sp. show notable

134 stress on the external shell wall, generally corresponding to the area of the suture. Cadoceras sp. with five septa is the only model to show a global average compression while N. pompilius shows the highest global average values (Table 2). All tested shells also show a development of high tension around the siphuncular foramen (the only discontinuity in the septal surface).

The ontogenetic development of the septa in Cadoceras sp. demonstrates an increase both in peak max. principal stress and the development of high max. principal stress as the sutural amplitude increases. There are no new lobes or saddles developed within the ontogenetic window between the 5th and 10th septa, though there is a slight dorso-ventral elongation of the septal surface. The adoral most edge of the saddles are the weakest points of the shell of

Cadoceras sp., compare this with the development of high tension along most of the suture of S. spirula and N. pompilius though there is an asymmetry of stress development in these models.

Progressive loading of N. pompilius under increasing pressure shows the development of high tension along the suture and the lateral edges of the siphuncular foramen (Fig. 2B, 3).

Furthermore, max. principal stress is diverted from the lateral regions of the septal surface corresponding to the area where the septum curves into the shell wall. Assuming the values of tension from the FEA are accurate (an incorrect assumption but one used here for illustrative purposes), the depth of implosion of this shell is between 4 and 6 MPa (roughly equivalent to

390 to 590 m below sea level). The calculated SSI (Westermann 1973) estimates depth ranges from 406 m to 1304 m (Table 3).

3.2 Point Force

Point forces oriented along the suture show lower maximum stress values compared to point forces on the chamber wall for all specimens (Table 2). Cadoceras sp. with 10 septa shows the largest decrease in max. principal stress between the chamber point force and the suture point

135

Figure 1. Results of the finite element analyses of N. pompilius, S. spirula, Cadoceras sp. Each model is loaded with a pressure load of 8 MPa. Forces are directed normal to the exterior surface of the model, comprising the external shell wall, internal faces of the body chamber, and the external (adapertural) faces of the final septum. Nautilus nacre has a theoretical tensile strength of about 130 MPa (Westermann and

Ward 1980) which is used here. Areas outside the range of the scale are rendered in black. Black areas on the septum are above the 130 MPa maximum.

136 force with a 59% decrease while N. pompilius shows the lowest decrease at 8%. Both Cadoceras sp. and S. spirula show similar decreases at 42% and 40% respectively.

The point force along the suture line of both Cadoceras sp. models are the only results that do not exceed the applied universal threshold (Fig 4).

Cadoceras sp. shows a marked decrease in global average max. principal stress with increasing numbers of septa (Table 2). The 10 septa model shows a 15% decrease in global average max. principal stress under the chamber point force load while the point force suture load shows a 25% decrease in global average max. principal stress.

4. Discussion

4.1 Pressure and Comparisons with Previous Results

Both Daniel et al. (1997) and Hassan et al (2002) agree that spherical shaped septa would show less stress due to hydrostatic pressure when compared to more complexly folded septa. Our results corroborate this as S. spirula shows the lowest max. principal stress over the septum face as well as the lowest peak max. principal stress on the final septum (Fig. 1, Table 2). The range of septal complexity explored here is limited, the morphology of the Cadoceras sp. septum can be compared to the “Goniatitic” model of Hassan et al. (2002) and the six-wave model of Daniel et al. (1997) as all three models possess only primary flutes, i.e. lobes and saddles (Klug and

Hoffmann 2015).

The fluted septum model of Daniel et al. (1997), with six primary waves, shows elevated tension along the fold axis of the lobes and saddles with compressive stress along the flanks.

Hassan et al. (2002) showed elevated tension along the flanks of the flutes in their goniatitic model with compressive stress concentrated along the fold axis of the lobes and saddles and

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Table 2. Selected values of maximum principal stress under all loading conditions

Cadoceras sp. Cadoceras sp. 5 Spirula spirula Nautilus 10 Septa Septa pompilius 8 MPa Pressure Average Max 1.4 -1.09 2.45 4.25 Principal Stress (Mpa) Peak Max. 332.18 293.14 154 272.2 Principal Stress on Final Septum (MPa) Max/Min Stress 21.92/10.81 22.10/-4.02 88.54/71.45 150.21/97.10 in the Center of the Final Septum (MPa) Max/Min Stress 119.10/46.97 183.75/77.57 110.27/0.36 170.10/32.62 in the Ventral Margin of the Final Septum (MPa) Point Force on Chamber Wall Average 687 584.30 474.03 254.58 Maximum Principal Stress (MPa) Peak Max. 18920.21 17983.78 47071 79987.09 Principal Stress on Internal Shell Surface (MPa) Point Force on Suture Average 735.44 552.22 416.89 457.55 Maximum Principal Stress (MPa) Max. Maximum 7750.25 10468.20 28136 73318.09 Principal Stress on Internal Shell Surface (MPa)

138

Figure 2. A) Measurements of max. principal stress taken along a horizontal transect through the middle of the final septum. Note the asymmetric distribution of tension in the septum, likely due to the asymmetry of the shell itself. B) Plot of the max. principal stress taken from the nodes of N. pompilius under four different (2, 4, 6, and 8 MPa) pressure loads. minor, periodic compressive stress along the periphery of the septum. Our model of Cadoceras sp. shows a very different pattern of tension and compression (Fig. 1). Tension forms along the attachment of the saddles to the shell wall, compression forms in two limited, concave zones between the siphuncular foramen and the suture. The high tension extends along the saddle with increasing amplitude. However we see no notable development of either tension or compression

139 along the flanks nor such a dramatic, clean shift from tension to compression as seen in the models of Hassan et al. (2002) and Daniel et al. (1997). The increase of max. principal stress with increasing amplitude directly contradicts the sutural amplitude index of Batt (1991) who argued that increasing amplitude would improve resistance to hydrostatic pressure by buttressing more of the shell wall following the Buckland model.

All shells demonstrate the concentration of stress along the final septum with, generally, minimal stress developing along the shell wall. This observation is antithetical to the statements of Hewitt and Westermann (1997) and Hassan et al. (2002), that the strength of the septa and the shell wall are very similar if not the same. This result does agree with the explosion experiments and analyses of Kanie et al. (1980) and Kanie and Hattori (1983) where the final septum seems to be the place of initial fracture during implosion and also shows the greatest deformation in stress tests. Progressive loading of N. pompilius (Fig. 3) further demonstrates the accelerated development of stress in the final septum. This being said, the redistribution of stress as parts of the shell break cannot be predicted here; therefore, we cannot comment on the predicted pattern of total failure of the entire shell during implosion.

Figure 3. Development of max. principal stress on the final septum of N. pompilius under increasing (2, 4,

6, and 8 MPa) hydrostatic pressure. The results of these models are graphically illustrated in Fig. 2B.

4.2 Septal Strength Index

We attempted to predict the critical depth for N. pompilius using the septal strength index

(Westermann 1973). There have been other attempts to create a formula to calculate maximum

140 habitat depth, such as the siphuncle strength index (Westermann 1971) and the index of wall strength (Hewitt and Westermann 1997). Due to fossil limitations, we do not deal with the siphuncle here and the SSI is a common and simple attempt to estimate habitat depth (Hewitt and

Westermann 1990). The SSI failed to produce consistent results and varied greatly with the choice of region being used to calculate the radius of curvature. Tomographic data allows easy access to a, essentially, infinite number of oblique slices through the septa that can be used to calculate curvature. While one can find a curvature that happens to give a reasonable depth estimate, there is no good criterion with which such a curvature can be chosen reliably between different specimens and morphologies.

The unreliability of the SSI might have motivated the alternative estimates of wall strength mentioned prior. However, the simplistic morphological characterization of the septum, dividing thickness by a radius of curvature, also formed the basis for the current calculation of tensile strength of cephalopod nacre (Westermann and Ward 1980; Hassan et al. 2002). These calculations also use estimates of the critical hydrostatic pressure which is taken from implosion data. Unfortunately, implosion data for Nautilus has a history of sub-optimal depth control

(Ward et al. 1980; Westermann and Ward 1980). Direct measurements of tensile strength were performed but were limited to dry specimens whose organic matter, though they were hydrated, had likely decayed (Currey 1976).

4.3 Point Force

The peak max. principal stress measured along the wall decreased when the force was directed along the suture line for all models compared to when the force was directed on the chamber wall (Table 2). However, not all models showed the same magnitude of decrease. Peak

141 tension decreased in N. pompilius by 8%, in S. spirula by 40%, Cadoceras sp. by 41 % on the 5th septum, and by 59% on the 10th septum. This result suggests a positive correlation between flute

Table 3. Septal strength index and depth approximations

Radius of Curvature Septal Strength Index Depth Approximation (m) Nautilus pompilius Median section 18.39 43.50 1304.92 23.87 33.51 1005.27 25.05 31.93 957.97 34.01 23.52 705.61 25.76 31.06 931.66 23.40 34.18 1025.53 28.53 28.04 841.19 22.52 35.53 1065.80 21.87 36.58 1097.40 28.65 27.92 837.73 Transverse Section 26.88 29.76 892.91 59.11 13.53 406 Spirula spirula Median Section 3.14 52.83 1584.94 3.36 49.34 1480.13 3.78 43.88 1316.55 3.55 46.72 1401.49 3.26 50.97 1529.16

amplitude and max. principal stress due to hydrostatic pressure as max. principal stress increases in the 10th septa compared to the 5th. Conversely, max. principal stress along the suture decreases with increasing flute amplitude. This corresponds with the results of Daniel et al. (1997) who also suggested sutural complexity increases resistance to point loads. Recently, Kerr and Kelley

(2015) found no correlation between septal complexity and repair scar frequency and doubted the connection between septal complexity and mechanical resistance to predators. However, it is important to note that shell repair can only occur when damage is done along, or near, the body chamber. Damage to the phragmocone cannot be repaired unless in very rare circumstances and 142 damage to the phragmocone is usually fatal due to drowning (Kröger and Keupp 2004; Keupp

2012; Tsujino and Shigeta 2012). The resistance to point loads supplied by the folded septa would not directly contribute to the strength of the body chamber. Therefore, no correlation between repair scars and septal complexity are to be expected.

4.4 Septal Complexity and Palaeoenvironment

The previously mentioned sutural amplitude index was used by Batt (1991) to assess habitat depth of ammonites of the Cretaceous Western Interior Seaway. Batt (1989, 1991) studied the change in morphology of ammonite groups during the Western Interior Greenhorn

Cyclothem, a transgression-regression cycle, and concluded that increases in sutural amplitude in similar shell morphotypes indicated a deeper habitat. Connections between sutural morphology and environmental changes during transgressions/regressions have been well noted and indicate some connection between morphology and water depth (Bayer and McGhee 1984; Batt 1991;

Lukeneder 2015). However, in light of our results, it seems unlikely that this connection with water depth is caused by water depth itself. The maximum depth of the Western Interior Seaway basin is between 250-300 m (Batt 1989, 1991). Not only does sutural amplitude weaken the shell to hydrostatic pressure (Fig. 1), even the weakest shell used in this study shows low stress due to hydrostatic pressure at this depth (Fig. 3) and differences in depth on the order of 50 m might not be enough to result in systematic changes in morphology. It seems more likely that changes in water depth results in palaeoecologic changes that cause changes of shell and septal morphology.

5. Conclusion

This is the first application of FEA to empirical models of cephalopods shell. The limited number of specimens and morphologies explored here mean this is an area ripe for future research. Furthermore, as the final septum seems to be the weakest point of the shell in our

143

Figure 4. Point force loads were directed along the suture (left column) and the unsupported chamber wall

(right column). Black regions are areas where the max. principal stress exceeds the limits of the scale

(130 MPa). The magnitude of stress due to the point load decreases when the load in directed along the suture line rather than the chamber wall. Cadoceras sp. shows the greatest decrease in max. principal stress when the point load is moved to the suture line. models, subsequent FEA of cephalopod shells may not need the entire shell in order to study comparative strength and potential implosion depths.

The shell of S. spirula, with a nearly circular whorl cross section and semi-hemispherical septa, shows the highest resistance to hydrostatic pressure while the shell of N. pompilius, which has a more elliptical whorl cross section and dorsoventrally elongated septa, shows the lowest resistance. Due to this, we cannot make a simple connection of septal complexity to hydrostatic 144 pressure Furthermore, the influence of the overall septal shape—which is limited by the cross- sectional morphology of the aperture—may play a more important role in minimizing the observed max. principal stress when comparing Cadoceras sp. with N. pompilius. Our results suggest a positive correlation of sutural amplitude with max. principal stress due to hydrostatic pressure. However, the septal morphology explored here is limited to primary flutes and higher order flutes may diminish or migrate the principal stress that develops along the saddles.

Cadoceras sp. shows the greatest ability to resist point loads, especially when the load is directed along the suture line. Greater sutural amplitude seems to decrease the max. principal stress developed by a point load along the suture. This suggests that sutural complexity may have helped strengthen the phragmocone against predation.

Acknowledgements

We would like to thank Julia A. Schultz (University of Chicago) for micro-CT scans of

Nautilus pompilius. Alexander Lukeneder (Naturhistorisches Museum Wien) for the Spirula spirula specimen from Thailand.

145

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Chapter 6

Conclusions

The main goals of this study were: 1) test the applicability of computed tomography (CT) to reconstruct ammonoid palaeobiology; 2) test the buoyant properties of the cephalopod shell;

3) test potential functions of folded septa. These goals were met through the application of high resolution computed tomography, namely micro-CT, nano-CT, and synchrotron radiation based micro-CT (Fig. 1). The application of these methods is the main novelty of this work as it has never been done prior. Prior to this work, investigations into the field of ammonoid palaeobiology have relied on simplified geometric models, with few exceptions (e.g., Kruta et al.

2011). This chapter will summarize the main conclusions and interpretations of this thesis as well as discuss future work suggested by our findings.

1. Tomographic methods and ammonoid data

Multiple methods of computed tomography were tested including medical CT, micro-CT,

nano-CT and synchrotron based CT. Synchrotron CT possessed the highest overall resolution

and the ability to perform phase contrast tomography, used in chapter three, to differentiate

the shell from calcite crystals. This method will continue to be important in future work on

ammonoids; however, many synchrotron datasets possessed heavy artefacting that wasn’t as

noticeable or was entirely absent in datasets gathered with other CT methods. Medical CT

was deemed inappropriate for serious, quantitative work due to poor resolution and contrast

even in specimens as large as Nautilus (around 18 cm in diameter). Micro-CT was a clear

improvement over medical CT but was outperformed by nano-CT. Nano-CT possessed better

resolution and less artefacts than micro-CT though these devices are less common as they are

relatively new compared to micro-CT devices. Two nano-CT devices were used over the

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course of this project, a nanotom s and a nanotom m. Both devices were capable of

comparable resolution but the nanotom m showed less noise and improved contrast.

Compared to synchrotron CT, nano-CT is more accessible, less stringent in terms of size of

specimens that can be scanned, and doesn’t require a successful proposal to be allowed to

scan specimens.

All fossil specimens used throughout this thesis are preserved in hollow condition.

Several filled specimens, including pyritic internal molds, were scanned and we achieved

some success in visualizing their internal structures (Lamas-Rodríguez et al. 2015). Nano-CT

seems to be able to visualize internal structures of filled ammonoids sufficiently to allow

segmentation when coupled with image processing and a sufficiently large amount of time.

Significant error in the reconstruction of the volume of a Nautilus shell was identified

prior to the beginning of this project and was subsequently identified as being caused by

partial volume effects (PVEs). During this project, a method to estimate the quantitative

effects of PVE and subjectivity involved in the creation of a segmented specimen was

developed. This simple procedure involves growing and shrinking a final segmentation by one

voxel layer and calculating the percent error. This error does not represent the actual

difference between true volume and reconstructed volume but does show the impact of PVE

on volume in that data set. It is advised that this calculation is presented for any CT based

volumetric reconstructions when no other error estimate is possible.

1.1 Tomographic data and geometric models

We have employed these high resolution tomographic methods to scan eight cephalopod

shells ranging from extant specimens (Nautilus, Allonautilus, Spirula) to Paleozoic forms

(Arnsbergites). One persistent observation noted in this thesis is the failure of simplified

155

geometric models to produce highly accurate results. The equations of Trueman (1940) and

Raup and Chamberlain (1967) both underestimated shell volume by up to 60% (Chapter 3).

The equations used to calculate the center of gravity of the animal often ignored the shell as

the soft body would have the greatest influence on the position of the center of gravity and

calculating the volume of the shell and septa were extremely difficult (Trueman 1940). This

method creates a bias that artificially increases the stability of forms with short body

chambers (Chapter 3, Fig. 5). The Fourier based models of Hassan et al. (2002) and Daniel et

al. (1997) showed highly divergent stress values between themselves and compared to our

empirical models. Finite element analysis is known to be sensitive to boundary conditions and

material properties (Rayfield 2007; Bright and Rayfield 2011; Tseng and Flynn 2015). This

coupled with the only approximated geometry of real ammonoids and unrealistic thickness

used by Hassan et al. (2002) and Daniel et al. (1997) can explain the differences in our results

(Chapter 5) and prior studies. Overall mathematical models can be good first approximations

but results gained from such models should be viewed with the appropriate skepticism.

2. Shell buoyancy and hatchling mode of life

Calculations of the buoyancy of Cadoceras show a hatchling achieves neutral buoyancy

when the ammonitella (the hatchling shell) had at least three chambers. Furthermore, analysis

of theoretical swimming ability shows the hatchling was capable of entering the water column

with only the protoconch. Ammonoid hatchlings might have had a similar movement pattern

as modern squid paralarvae, a hop and sink motion (Haury and Weihs 1976). The majority of

tested scenarios recover a nearly neutral buoyancy supporting the idea that ammonoid

hatchlings were planktonic, which is further supported by the recovery of ammonoid shells

from black shales (Mapes and Nützel 2009). A planktonic mode of life for a high fecundity

156

group would aid in dispersal of hatchlings due to ocean currents and may explain the recovery

of ammonoids after mass extinctions (Ward and Bandel 1987; Harries et al. 1996; De Baets et

al. 2012; Ritterbush et al. 2014).

3. Function of complex septa

The hypothesis that septal complexity reflects increased resistance to hydrostatic pressure

is a dominant idea in the field (Hewitt and Westermann 1986, 1997; Hewitt 1996;

Westermann 1996; Hassan et al. 2002; Klug and Hoffmann 2015). This idea has been

countered by arguments advancing physiological functions being the driving force behind the

development of complex septa, such as increasing the relative size of the pellicle to aid in

fluid transfer or increasing surface curvature (Daniel et al. 1997; Kröger 2002; Perez-Claros

2005; Mutvei and Dunca 2007). We report an early increase in the functional area of the

chambers (greater pellicle area) of ammonoids but this effect does not extend through

ontogeny (Chapter 4). This result argues against the idea that highly complex septa increased

the efficiency of fluid transport (Kröger 2002; Mutvei and Dunca 2007) as septal complexity

for early ontogeny is simpler than the corresponding adult forms and this complexity seems to

have no effect on the overall scaling of surface area to volume ratios in the shell. Furthermore,

we challenge the general interpretation that septal complexity can be used as a simple proxy

for shell strength as increasing septal amplitude weakens the shell as do deviations from the

simple semi-hemispherical septa and circular whorl shape (Chapter 5).

Of the functional hypothesis tested, two were unambiguously supported. Firstly, septal

complexity directly increases the overall curvature of the septal surface and attached pellicle

thereby helping chamber reflooding (Chapter 4; Daniel et al. 1997). Secondly, folded septa

increased resistance to point loads, and an increase in septal amplitude decreased stress due to

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applied point loads along the suture (Chapter 5). Interestingly, the findings from chapter four

and five both support functions that would aid in increasing survivability against predation.

This is very important for the animal as they lack the anti-predator adaptations of extant

coleoids: including fast swimming, ink sacs, and mimetic color change. Nautilus possesses a

tough hood that can be closed when attacked but has no proper defenses beyond that and there

is no evidence ammonoids possess hoods. Furthermore, injuries of the phragmocone can’t be

healed and are usually fatal (Kröger and Keupp 2004; Keupp 2012; Tsujino and Shigeta

2012). These observations highlight the importance of developing defenses against predation

and mechanisms to compensate for shell loss due to injury.

Predation has been suggested to play a role in the early evolutionary trends of ammonoids

to help the animals adjust during the radiation of jawed fishes (Monnet et al. 2015). During

the Mesozoic the most complex septal shapes evolved (Klug and Hoffmann 2015); during this

time there was a proliferation of multiple marine reptiles including mosasaurs, ichthyosaurs

and thalattosuchians that may have preyed on cephalopods (along with other prey) (Vermeij

1977; Massare 1987; Hewitt and Westermann 1990; Sato and Tanabe 1998; Motani 2009).

Whether predation was a significant driver of the evolution in septal complexity requires

more work; however, it is interesting to note that the most complicated septal morphologies

evolved with the Mesozoic ammonoids and studies report an increase in the frequency of

repair scars in ammonoids during the Jurassic and Cretaceous (Kerr and Kelley 2015).

4. Outlook

The application of high resolution computed tomography to ammonoids represents an important step forward, these 3D models can be used for everything from traditional morphometrics to more complex biomechanical modeling (e.g. finite element analysis and

158 computational fluid dynamics). However since we are the first group to apply this method, and as a single specimen can take up to nine months to fully segment, the number of specimens currently available is very small. Future work can focus on constructing a larger database of specimens that will encompass a greater diversity of morphologies. This will permit more thorough comparative analyses and allow more definitive conclusions on septal function.

Phylogenetic control is necessary in order to assess evolutionary trends and attempt to tie them to the development of specific functions; this requires a database of segmented specimens spanning the entire lineage of Ammonoidea and their immediate predecessors. There are several questions that are raised as an immediate consequence of the work presented here:

1. Buoyancy of ammonoid hatchlings might reflect the environment in which they hatched.

Slight negative buoyancy can counteract wave mediated dispersal (Martins et al. 2010).

Staying in certain environments for extended periods after hatching, such as upwelling

zones, may be beneficial prior to being moved out into the open ocean and therefore

hatchlings from such regions might show relatively thicker shells than the same taxon from

a different region.

2. The higher surface area to volume ratio in ammonoid chambers should increase the rate of

fluid flow and permit faster growth. This is dependent on quicker chamber emptying. The

actual rates of fluid flow in the pellicle and siphuncle per unit volume are unknown,

therefore we cannot quantify how much the increase in surface area to volume ratio would

increase chamber emptying. Measurements of fluid flow in Nautilus and Spirula would

permit some quantification of flow rates to test if this increase in surface area to volume

ratio makes a large difference in the time it takes to empty chambers.

159

3. If the initial evolution of septal complexity was driven by increasing chamber emptying,

we would expect to see an increase in the surface area to volume ratio during the initial

evolution of the spiral shell. Specimens from this time can be used to test if this was indeed

the case.

4. The septal complexity tested in the finite element analysis was limited to primary folds in

the ammonitella of Cadoceras. Future work should look at more complex septal

geometries and compare the effects of increasing numbers of primary and secondary folds

on stress magnitude and distribution. Additionally more ontogenetically advanced

specimens are needed to test the effects of septal complexity on the stress of internal

whorls due to indirect hydrostatic pressure (Hewitt and Westermann 1997; Hassan et al.

2002).

5. FEA on Cadoceras indicated a connection between septal amplitude and stress. Further

work can test this more thoroughly and investigate correlation between relative sutural

length and observed stress due to pressure and point loads.

6. Validation studies on extant cephalopod shells can test the quantitative results of FEA.

With proper material properties, the use of FEA in estimating shell implosion depth can be

investigated with the goal of setting a maximum boundary for bathymetric reconstructions

using shells.

160

Figure 1. Summary figure providing an overview of the research undertaken during this PhD. This process includes the digitization of physical shells into digital models using computed tomography and using these models to investigate the functional morphology and the paleobiology. Specifically we have used the CT models to calculate buoyancy and swimming dynamics to help us interpret animal ecology in terms of the position of the animal in the water column. Physiology was explored by calculating the size of the pellicle relative to the volume of fluid in the chambers and chamber shape to qualitatively assess the rates of fluid flow into and out of the chambers. Mechanics was studied through finite element analysis, which calculates the stress in the shell due to pre-specified loading conditions. In this study, we concluded that the ammonite shell is best able to resist predation compared to Nautilus and Spirula, while Spirula is best able to resist hydrostatic pressure.

161

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Robert Lemanis Curriculum Vitae Oberstraße 113 Date of Birth: June 22, 1989 44892 Bochum, Germany Nationality: American Phone: +49 (0) 176 729 123 26 E-mail: [email protected]

Education Expected 2016 Ph.D. Earth Sciences, Ruhr-University Bochum, DE Title: Complexity of septal surfaces and suture lines in ammonoids- implications for the hydrostatic apparatus and paleoecology using modern CT techniques 2012 M.Sc. Palaeobiology, University of Bristol, UK Title: Cranial functional morphology of the phytosaur Ebrachosuchus: implications for phytosaur ecology from comparative finite element analysis 2011 B.S. Geology, Rensselaer Polytechnic Institute, USA Title: Experimental Uranium diffusion in fossil teeth

Research Profile Biomechanics Functional morphology and the evolution of function Finite element analysis Ammonoid palaeobiology Computed tomography and volumetric analyses

Other Skills Scientific software: Amira, Avizo, PAST, ImageJ, Mecway, Hypermesh, Gmsh Office automation: Microsoft Office Suite, Libre Office Suite Drawing: GIMP

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Journal Publications Hoffmann, R., Richter, D., Neuser, R., Jöns, N., Linzmeier, B., Lemanis, R., Fusseis, F., Xiao, X., Immenhauser, A. 2016. Evidence for a composite organic-inorganic fabric of belemnite rostra: Implications for palaeoceanography and palaeoecology. Sedimentary Geology 341: 203-215.

Lemanis, R., Zachow, S., Hoffmann, R. Comparative cephalopod shell strength and the role of septum morphology on stress distribution. Under Review, PeerJ.

Lemanis, R., Korn, D., Zachow, S., Rybacki, R., Hoffman, R. 2016. The evolution and development of cephalopod chambers and their shape. PLoS ONE 11(3): e0151404.

Hoffmann, R., Reinhoff, D., Lemanis, R. 2015. Non-invasive imaging techniques combined with morphometry: a case study from Spirula. Swiss Journal of Palaeontology 134(2): 207-216.

Lemanis, R., Zachow, S., Fusseis, F., Hoffmann, R. 2015. A new approach using high- resolution computed tomography to test the buoyant properties of chambered cephalopod shells. Paleobiology 41(2): 313-329.

Hoffmann, R., Schultz, J.A., Schellhorn, R., Rybacki, E., Keupp, H., Gerden, S.R., Lemanis, R., Zachow, S. 2014. Non-invasive imaging methods applied to neo- and paleo- ontological cephalopod research. Biogeosciences 11: 2721-2739.

Book Publications Hoffmann, R., Lemanis, R., Naglik, C., & Klug, C. 2015. Ammonoid buoyancy. In C. Klug, D. Korn, K. De Baets, I. Kruta, & R. H. Mapes (Eds.), Ammonoid paleobiology: from Anatomy to Ecology. Topics in Geobiology, Volume 43.

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Oral Presentations Lemanis, R., Hoffmann, R., Zachow, S. 2013. Reconstructing ammonite life-habits: a modern perspective on a centuries old question. Progressive Palaeontology. Leeds.

Lemanis, R., Hoffmann, R., Zachow, S. 2014. Sink or swim: the function of the ammonoid shell. Progressive Palaeontology. South Hampton.

Lemanis, R., Hoffmann, R., Zachow, S. 2014. The swimming ammonite: how computed tomography can address questions of functional morphology. European Geosciences Union General Assembly. Vienna.

Lemanis, R., Hoffmann, R., Zachow, S. 2014. New insights into ammonite palaeobiology from tomographic data. 9th International symposium: Cephalopods- Present and Past. Zurich.

Poster Presentations Lemanis, R., Hoffmann, R., Zachow, S. 2013. A volumetric approach to reconstructing ammonite life-habits. Paläontologische Gesellschaft. Göttingen.

Lemanis, R., Hoffmann, R., Zachow, S. 2014. Testing the life-habits of hatchling ammonites using CT data. Palaeontological Association. Leeds.

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