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Wavelet analysis of ammonoid sutures

Takao Ubukata, Kazushige Tanabe, Yasunari Shigeta, Haruyoshi Maeda, and Royal H. Mapes

Plain Language Abstract

Ammonite suture is one of the most sophisticated structures of past creatures. The suture is the curved line of intersection between the shell wall and a series of partitions that divides the interior of the conch into several chambers. There is a wide variation in suture form from species to species and there has been much interest in how to represent its geometric properties. However, measures of suture complexity hitherto been proposed poorly describe various features of intricate suture shape. Here, we introduce a new method for the comparison of suture forms by use of wavelet analysis, which is originally designed for analyzing a time series. The results of a pilot analysis are successful in characterizing a localized change in morphological features along a suture curve of each ammonite.

Resumen en Español

Análisis de ondícula de suturas de ammonoideos

Se presenta un método morfométrico basado en la transformada de ondícula continua (=transformada wavelet continua) para describir la forma de las líneas de sutura de los ammonoideos. Se usó una serie de datos de coordenadas a lo largo de la línea de sutura, en un sistema de referencia común, como la función de descriptor de la longitud cordal acumulada a lo largo de la línea de sutura. La transformada de ondícula se define como un producto interno entre la función de descriptor y una forma de onda localizada de longitud finita, denominado "óndula hija." Los valores absolutos de las transformadas de ondícula, o amplitudes, se calcularon para las óndulas hija individuales con diferentes longitudes de onda y posiciones, y se utilizó una serie de amplitudes para diferentes frecuencias como una función de la forma en la caracterización de la forma de la sutura que se simplificó a unos pocos componentes principales.

Palabras clave: análisis de ondícula; morfometría; línea de sutura; ammonoideos

Traducción: Enrique Peñalver

Résumé en Français

Analyse d'ondelettes de sutures d'ammonoïdes

Une méthode morphométrique basée sur une transformée d'ondelettes continues est introduite pour décrire
la forme de lignes de suture d'ammonoïdes. Une série de données de coordonnée y, le long de la ligne de suture, placée dans un système de référence courant, est utilisée en tant que fonction descriptive de la longueur de corde cumulée, le long de la ligne de suture. La transformée d'ondelettes est définie comme un produit interne entre la fonction descriptive et une forme d'onde localisée de longueur finie, appelée une "ondelettes fille." Les valeurs absolues des transformées d'ondelettes, ou amplitudes, sont calculées pour chaque ondelettes fille à partir de différentes longueurs d'onde et de positions, et une série d'amplitudes pour les différentes fréquences est utilisée comme une fonction de forme caractérisant la forme des sutures, et est résumée dans quelques composantes principales.

Mots­clés: analyse d'ondelettes; morphométriques; ligne de suture; ammonoïdes

Translator: Kenny J. Travouillon

Deutsche Zusammenfassung

Wavelet-Analyse von Ammonitenstrukturen

Es wird eine morphometrische Methode, die auf einer kontinuierlichen Wavelet-Transformation basiert, vorgestellt, um die Form von ammonitischen Suturenlinien zu beschreiben.
Eine Serie von y-Koordinaten-Daten entlang der Suturenlinien, die in einem allgemeinen Referenzsystem platziert waren, wurden als Deskriptor-Funktion der kummulativen chordalen Länge entlang der Suturenlinie verwendet. Die Wavelet-Transformation ist definiert als ein inneres Produkt zwischen Deskriptor-Funktion und einer begrenzten Wellenform mit endlicher Länge, die als „Tochter-Wavelet" bezeichnet wird. Die absoluten Werte der Wavelet-Transformation oder Amplituden wurden für individuelle Tochter-Wavelets mit variierenden Wellenlängen und Positionen berechnet. Ebenso wurde eine Serie von Amplituden für verschiedene Frequenzen als Form-Funktion zur Charakterisierung der Suturenform genutzt und in wenige Hauptbestandteile zusammengefasst.

Schlüsselwörter: Wavelet-Analyse; morphometrisch; Suturenlinie; Ammonoidea

Translator: Eva Gebauer

Arabic

381 arab

Translator: Ashraf M.T. Elewa

 

 

author1Takao Ubukata
Institute of Geosciences
Shizuoka University
Oya 836
Surugaku
Shizuoka 422-8529
Japan
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Takao Ubukata is a paleontologist working at Shizuoka University. He has focused on the morphological aspects of fossil organisms since he got a PhD from the University of Tokyo in 1996 based on a research on theoretical morphology of bivalve mollusks. His current research interest covers methodology in morphometrics, dynamics of morphological disparity, functional and constructional morphologies of mollusks, analysis of microevolution through stratophenetic series, and biomineralization of molluscan shell, as well as theoretical morphologic modeling of shell morphogenesis.

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author2Kazushige Tanabe
University Museum
University of Tokyo
Hongo 7-3-1
Bunkyouku
Tokyo 113-0033
Japan
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Kazushige Tanabe, Ph.D., an Emeritus Professor of the University of Tokyo, is now working as a project researcher at the University Museum, the University of Tokyo. His research interests include comparative morphology, anatomy, embryology and (paleo)ecology of modern and fossil cephalopod mollusks, and marine biology and ecology of bivalve mollusks. For more details of his academic records, see the following site: https://www.researchgate.net/profile/Kazushige_Tanabe/?ev=hdr_xprf.

 

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author3Yasunari Shigeta
Department of Geology
National Museum of Nature and Science
Amakubo 4-1-1
Tsukuba 305-0005
Japan
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Yasunari Shigeta mainly works on ammonoid biostratigraphy, taxonomy, and paleobiology. He got a PhD from the University of Tokyo in 1992. As senior curator, he is working in the National Museum of Nature and Science in Tsukuba. He is currently studying the Early Triassic biotic recovery on the basis of detailed field works in Vietnam and Russian Far East. Other research interests include paleobiogeography and evolution of the Cretaceous ammonoids in the Pacific area.

 

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author4Haruyoshi Maeda
Kyushu University Museum
Hakozaki 6-10-1
Higashi-ku
Fukuoka 812-8581
Japan
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Haruyoshi Maeda is a paleontologist working at the Kyushu University Museum. He has focused on the paleoecological and taphonomic aspects of ammonoids since he got a PhD from the University of Tokyo in 1989 based on a research on dimorphism of Cretaceous ammonite species. His current research interest covers systematics, paleoecology and taphonomy of ammonoids, as well as preservational histories of fossil-Lagerstätten of various organisms.

 

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author5Royal H. Mapes
Department of Geological Science
Ohio University
Athens, Ohio 45701
USA
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Royal H. Mapes is now an Emeritus professor and former chairman at the Department of Geological Sciences, Ohio University at Athens, OH 45701. he has taught basic geology courses and Paleontology at that university for about 30+ years before his full retirement in December 2012. To date, he has published more than 300 research papers and abstracts. Most of his research has been on fossil cephalopods of the Upper Paleozoic, although with other researchers he has contributed reports on other fossil phyla and their occurrences. His current research focus is on phylogeny, taphonomy and paleobiology of modern (specifically Nautilus) and Upper Paleozoic cephalopods.

 

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APPENDIX. Specimens examined and measured values of parameters.

 

Order

Suborder

Species

PC scores for each harmonic of suture function

Specimens

Age

Locality

     

1st

2nd

     

Agoniatitida

 

Latanarcestes sp.

0.962

-0.836

UMUT-PM-29049

Devonian

Taouz, Morocco

   

Fidelites sp.

0.978

-1.195

UMUT-PM-29050

Devonian

Erfoud, Morocco

   

Achguigites sp.

1.191

-0.583

UMUT-PM-29051

Devonian

Erfoud, Morocco

   

Psedoprobeloceras costulatum

0.893

-1.801

UMUT-PM-30079

Devonian

Taouz, Morocco

   

Beloceras sp.

0.555

1.567

UMUT-PM-29053

Devonian

Erfoud, Morocco

   

Anarcestes mateviai

1.159

-0.227

UMUT-PM-30080

Devonian

Erfoud, Morocco

   

Anarcestes sp.

1.159

-0.227

UMUT-PM-30081

Devonian

Erfoud, Morocco

   

Praewerneroceras hollardi

1.084

-0.203

OUZC-5600

Devonian

Taouz, Morocco

   

Stenopharciceras viseireuge

0.265

1.166

UMUT-PM-29058

Devonian

Taouz, Morocco

   

Stenopharciceras lunulicosta

0.633

-0.925

UMUT-PM-30082

Devonian

Taouz, Morocco

   

Synpharciceras clavilobum

0.460

2.096

UMUT-PM-30083

Devonian

Taouz, Morocco

Goniatitida

Tornoceratina

Epitornoceras mithracoides

0.269

-1.412

UMUT-PM-29060

Devonian

Taouz, Morocco

   

Phoenixites aff. frechi

1.031

-0.632

UMUT-PM-30085

Devonian

Taouz, Morocco

   

Cheiloceras unclulosum

1.333

0.566

UMUT-PM-30086

Devonian

Taouz, Morocco

   

Sporadoceras sp.

0.331

-1.597

UMUT-PM-29064

Devonian

Taouz, Morocco

   

Sporadoceras muensteri

0.762

0.221

UMUT-PM-30087

Devonian

Erfoud, Morocco

   

Imitoceras rotatorium

0.633

-0.605

OUZC-5601

Carboniferous

Rockford, Indiana

 

Goniatitina

Girtyoceras meslerianum

0.353

-1.349

OUZC-5602

Carboniferous

Jackforth Creek, Oklahoma

   

Eumorphoceras bisulcatum

0.361

-0.980

OUZC-5603

Carboniferous

Leslie, Searcy Co., Arkansas

   

Hudsonoceras proteum

0.580

-1.764

UMUT-PM-30088

Carboniferous

Knockauns Mts., Clare Co., Ireland

   

Goniatites aff. crenestria

0.269

-1.122

UMUT-PM-29069

Carboniferous

Jackforth Creek, Oklahoma

   

Goniatites muliliratum

0.448

-0.776

UMUT-PM-29070

Carboniferous

Jackforth Creek, Oklahoma

   

Perrinites hilli

-0.480

2.024

UMUT-PM-30089

Permian

Las Pelicias, Coahuita, Mexico

   

Cravenoceras hesperium

0.632

-0.353

OUZC-5604

Carboniferous

Death Valley, California

   

Neodimorphoceras sp.

0.322

-1.171

OUZC-5605

Carboniferous

Texas

   

Cymoceras sp.

0.530

-1.138

OUZC-5606

Carboniferous

Searcy Co., Arkansas

   

Glaphyrites clinei

0.644

-0.756

UMUT-PM-30090

Carboniferous

Collinsville, Oklahoma

   

Syngastrioceras oblatum

0.227

-0.280

OUZC-5607

Carboniferous

Searcy Co., Arkansas

   

Homoceras smithi

0.647

-0.924

OUZC-5608

Carboniferous

Knockauns Mts., Clare Co., Ireland

   

Bisatoceras sp.

0.399

-0.748

UMUT-PM-30091

Carboniferous

Oklahoma

   

Bisatoceras primum

0.435

-0.834

OUZC-5609

Carboniferous

Oklahoma

   

Thalassoceras gemmellaroi

-0.170

-0.531

UMUT-PM-29078

Permian

Actasty R., S. Ural, Kazakhstan

   

Pseudoparalegoceras kesslerense

0.410

-0.126

OUZC-5610

Carboniferous

Winslow, Washington Co., Arkansas

   

Wellerites mohri

0.382

1.171

OUZC-5611

Carboniferous

Carroll, Ohio

   

Gonioloboceras sp.

0.379

-1.354

OUZC-5612

Carboniferous

South Bend, Texas

   

Mescalites sp.

0.670

-2.696

OUZC-5613

Permian

Tularosa, New Mexico

   

Wewokites sp.

0.706

0.013

UMUT-PM-30092

Carboniferous

Oklahoma

   

Crimites subkrotowi

0.473

1.980

UMUT-PM-30093

Permian

Actasty R., S. Ural, Kazakhstan

   

Peritrochia typicus

0.240

1.251

UMUT-PM-29080

Permian

Actasty R., S. Ural, Kazakhstan

   

Peritrochia invaribilis

0.289

1.765

UMUT-PM-30095

Permian

Actasty R., S. Ural, Kazakhstan

   

Uraloceras involutum

0.214

-0.545

UMUT-PM-30096

Permian

Actasty R., S. Ural, Kazakhstan

   

Popanoceras annae

0.758

1.595

UMUT-PM-30097

Permian

Actasty R., S. Ural, Kazakhstan

Clymeniida

 

Cymaclymenia sp.1

1.151

-0.620

UMUT-PM-29089

Devonian

Morocco

   

Cymaclymenia sp.2

1.255

-0.262

UMUT-PM-29090

Devonian

Morocco

   

Platyclymenia sp.1

1.059

-0.958

UMUT-PM-29091

Devonian

Morocco

   

Platyclymenia sp.2

1.317

0.117

UMUT-PM-29092

Devonian

Morocco

   

Oxyclymenia sp.

0.707

-2.270

UMUT-PM-29094

Devonian

Morocco

   

Gonioclymenia sp.

0.390

-1.326

UMUT-PM-30098

Devonian

Erfoud, Morocco

Prolecanitida

 

Boesites sp.

0.347

0.273

UMUT-PM-30099

Carboniferous

Rochelle, Texas

   

Daraelites elegans

0.148

0.353

UMUT-PM-29097

Permian

Actasty R., S. Ural, Kazakhstan

   

Akmilleria electraensis

0.155

2.148

UMUT-PM-29098

Permian

White Pine Co., Nevada

   

Medlicottia intermedia

-0.338

1.087

UMUT-PM-29099

Permian

Actasty R., S. Ural, Kazakhstan

   

Neopronorites skvorzovi

0.290

1.853

UMUT-PM-29100

Permian

Actasty R., S. Ural, Kazakhstan

   

Pseudopronorites arkansiensis

-0.582

0.117

OUZC-5614

Carboniferous

Woolsey, Arkansas

Ceratitida

 

Xenoceltites subevolutus

0.433

-0.539

UMUT-MM-29103

Triassic

Spitsbergen, Norway

   

Paraceltites elegans

0.639

-1.055

UMUT-PM-29101

Permian

Gaudalupe Mts., Texas

   

Dinartes asiaticus

0.817

-0.255

UMUT-MM-30101

Triassic

Mangyshlak, Dolnapa, Kazakhstan

   

Pseudosageceras sp.

0.164

1.776

UMUT-MM-29104

Triassic

Spitsbergen, Norway

   

Amphipopanoceras cf. medium

0.287

1.940

UMUT-MM-30102

Triassic

Spitsbergen, Norway

   

Paranannites spathi

0.909

0.616

UMUT-MM-29106

Triassic

Criienden Spring, Nevada

   

Paranannites aspenensis

0.583

-1.039

UMUT-MM-30104

Triassic

Criienden Spring, Nevada

   

Prosphingites czekanowskii

0.487

0.435

UMUT-MM-30105

Triassic

Olenek River, Mengilach, Arctic Siberia

   

Meekoceras graciliatus

0.637

0.441

UMUT-MM-30106

Triassic

Criienden Spring, Nevada

   

Boreomeekoceras keyserlingi

0.925

1.093

UMUT-MM-30107

Triassic

Olenek River, Mengilach, Arctic Siberia

   

Arctoprionites nodosus

0.847

0.284

UMUT-MM-30108

Triassic

Stensiö-Fiellet, Spitsbergen, Norway

   

Dieneroceras spathi

0.706

0.672

UMUT-MM-30109

Triassic

Criienden Spring, Nevada

   

Arctoceras blomstrandi

0.683

0.326

UMUT-MM-30110

Triassic

Spitsbergen, Norway

   

Nordphiceras schmidti

0.794

-0.355

UMUT-MM-30111

Triassic

Olenek River, Mengilach, Arctic Siberia

   

Wasatchites tridentinus

0.650

0.373

UMUT-MM-30112

Triassic

Botheheia, Spitsbergen, Norway

   

Wasatchites tardus

0.732

-0.084

UMUT-MM-30113

Triassic

Spitsbergen, Norway

   

Ceratites nodosus

0.611

1.035

UMUT-MM-30114

Triassic

Würzburg, Germany

   

Anagymnotoceras varium

0.530

-0.342

UMUT-MM-30115

Triassic

Wallenbergfjellet, Spitsbergen, Norway

   

Favreticeras wallacei

0.618

0.471

UMUT-MM-29117

Triassic

McCoy Mine, Nevada

   

Stolleyites tenuis

0.693

1.033

UMUT-MM-29119

Triassic

Spitsbergen, Norway

   

Olenekoceras middendorffi

0.689

0.834

UMUT-MM-30116

Triassic

Olenek River, Mengilach, Arctic Siberia

   

Olenikites spiniplicatus

0.463

-0.556

UMUT-MM-30117

Triassic

Olenek River, Mengilach, Arctic Siberia

   

Svalbardiceras spitsbergense

0.681

0.246

UMUT-MM-30118

Triassic

Wallenbergfjellet, Spitsbergen, Norway

   

Arctohungarites triformis

0.379

0.837

UMUT-MM-30119

Triassic

Olenek Bay, Laptev Sea, Russia

   

Lenotropites caurus

0.788

1.295

UMUT-MM-30120

Triassic

West Humboldt Range, Nevada

   

Pseudosvalbardiceras sibiricum

0.651

0.567

UMUT-MM-30121

Triassic

Olenek River, Mengilach, Arctic Siberia

Ammonitida

Phylloceratina

Phylloceras consanguineans

-1.354

0.755

UMUT-MM-29121

Jurassic

Sakaraha, Madagascar

   

Phylloceras sp.

-1.768

0.969

UMUT-MM-29122

Cretaceous

Mahajang, Madagascar

   

Holcophylloceras sp.

-0.534

1.006

UMUT-MM-29123

Jurassic

Sakaraha, Madagascar

   

Calliphylloceras sp.

-0.863

1.762

UMUT-MM-29124

Jurassic

Sakaraha, Madagascar

   

Ptychophylloceras sp.

-1.169

1.055

UMUT-MM-29125

Jurassic

Sakaraha, Madagascar

   

Phyllopachyceras ezoense

-1.398

0.105

UMUT-MM-29126

Cretaceous

Saku, Hokkaido, Japan

   

Hypophylloceras subramosum

-2.350

-0.503

UMUT-MM-30123

Cretaceous

Saku, Hokkaido, Japan

   

Tragophylloceras ibex

-0.141

0.693

UMUT-MM-29130

Jurassic

Osuabrük, Germany

 

Lytoceratina

Pterolytoceras sp.

-1.997

-1.398

UMUT-MM-29131

Jurassic

Sakaraha, Madagascar

   

Argonauticeras sp.

-1.559

0.184

UMUT-MM-29132

Cretaceous

Mahajang, Madagascar

   

Tetragonites glabrus

-1.955

-0.660

UMUT-MM-30125

Cretaceous

Saku, Hokkaido, Japan

   

Tetragonites popetensis

-2.426

-0.234

UMUT-MM-30126

Cretaceous

Saku, Hokkaido, Japan

   

Eotetragonites sp.

-1.201

-0.213

UMUT-MM-29136

Cretaceous

Mahajang, Madagascar

   

Gaudryceras striatum

-2.584

-0.746

SUM-RC-MM004

Cretaceous

Saku, Hokkaido, Japan

   

Gaudryceras tenuiliratum

-1.920

-0.802

UMUT-MM-30128

Cretaceous

Saku, Hokkaido, Japan

   

Gaudryceras sp.

-2.097

-0.488

UMUT-MM-30129

Cretaceous

Saku, Hokkaido, Japan

 

Ammonitina

Grammoceras doerntense

-0.011

-0.026

UMUT-MM-29147

Jurassic

Döruten, Germany

   

Hecticoceras sp.

0.082

0.485

SUM-RC-MM020

Jurassic

Saltwick Nab, Yorkshire, England

   

Taramelliceras sp.

-1.024

0.248

UMUT-MM-29149

Jurassic

Sakaraha, Madagascar

   

Lissoceras sp.

-1.265

-0.905

UMUT-MM-29150

Jurassic

Sakaraha, Madagascar

   

Grossouvia sp.

-0.174

-0.159

UMUT-MM-29152

Jurassic

Sakaraha, Madagascar

   

Aspidoceras sp.

-0.392

-0.080

UMUT-MM-29153

Jurassic

Sakaraha, Madagascar

   

Euaspidoceras sp.

-1.390

-1.570

UMUT-MM-29154

Jurassic

Sakaraha, Madagascar

   

Craspedites subditus

0.196

1.255

UMUT-MM-30131

Jurassic

Iwanowa, Russia

   

Desmoceras latidorsatum

-1.578

0.153

UMUT-MM-29156

Cretaceous

Mahajang, Madagascar

   

Tragodesmoceroides subcostatus

-1.255

0.553

UMUT-MM-29157

Cretaceous

Tappu, Hokkaido, Japan

   

Damesites semicostatus

-1.831

-0.275

UMUT-MM-30132

Cretaceous

Kotanbetsu, Hokkaido, Japan

   

Damesites sp.

-1.225

0.162

UMUT-MM-29158

Cretaceous

Saku, Hokkaido, Japan

   

Hauericeras angustum

-1.303

0.133

SUM-RC-MM006

Cretaceous

Saku, Hokkaido, Japan

   

Puzosia sp.

-1.368

-0.514

UMUT-MM-29162

Cretaceous

Mahajang, Madagascar

   

Yokoyamaoceras ishikawai

-1.800

-0.578

UMUT-MM-29164

Cretaceous

Saku, Hokkaido, Japan

   

Cleoniceras besairiei

-1.008

0.210

UMUT-MM-29167

Cretaceous

Mahajang, Madagascar

   

Anapachydiscus naumanni

-1.797

-0.028

UMUT-MM-29168

Cretaceous

Saku, Hokkaido, Japan

   

Teshioites ryugasensis

-1.526

0.476

UMUT-MM-29169

Cretaceous

Saku, Hokkaido, Japan

   

Canadoceras kosmatti

-1.969

-0.033

UMUT-MM-30133

Cretaceous

Saku, Hokkaido, Japan

   

Neogastroplites meulleri

0.240

0.727

UMUT-MM-29171

Cretaceous

Teigen, Petroleum Co., Montana

 

FIGURE 1. Signal waveform (1) and wavelets with various frequencies placed in various locations along the waveform (2). The frequency and magnitude of the signal plotted in (1) changes with location in a constant manner.

figure1

FIGURE 2. The Morlet wavelet used in the present study as a mother wavelet. The Morlet wavelet is a complex wavelet in which a pair of wavelets with different phases constitutes the real and imaginary components. The horizontal axis represents the relative position with respect to the center of the wavelet, and the vertical axis measures the magnitude of the wavelet.

figure2

FIGURE 3. Contour plots of scalograms in the frequency (h = 2j)–location (b) domain.

figure3

FIGURE 4. Measurements of coordinate data along a suture line. A synthetic image of an external hemi-suture was formed by combining multiple photographs (1), and a traced suture line was placed in a reference system so that its ventral and umbilical extremes were located on the x-axis separated by a distance of 10,000 pixels (2). Next, a series of y coordinates was measured along the suture line as a function of its cumulative chordal length (l) (3).

figure4

FIGURE 5. Series of y coordinates (red) and x' functions (blue). Series of x' function were detrended by subtracting the expected linear increase in x to introduce periodic boundary condition to the x-coordinate data. 1, Goniatites multiliratum. 2, Medlicottia intermedia. 3, Amphipopanoceras cf. medium. 4, Phylloceras sp.

figure5

FIGURE 6. Three-dimensional contour diagrams showing the amplitudes of wavelet transforms against location (b) and frequency (h = 2j). 1, Goniatites multiliratum. 2, Medlicottia intermedia. 3, Amphipopanoceras cf. medium. 4, Phylloceras sp. 5, Gaudryceras striatum. 6, Hauericeras angustum.

figure6

FIGURE 7. Series of shape functions obtained from repeated measurements for the identical suture of a single specimen of Gaudryceras striatum (dotted lines in red) showing that the measurement error is smaller than variation among its closely related species, i.e., G. tenuiliratum (orange), G. sp. (green), Tetragonites popetensis (blue) and T. glabrus (purple). The original digitized suture shape was illustrated for each species in the same color as the corresponding shape function.

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FIGURE 8. Synthetic models of suture lines represented by inverse wavelet transform with increasing number of frequencies (j). 1, Goniatites multiliratum. 2, Medlicottia intermedia. 3, Amphipopanoceras cf. medium. 4, Phylloceras sp. 5, Gaudryceras striatum. 6, Hauericeras angustum.

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FIGURE 9. Plots of the first two principal component scores, showing examples of selected original suture shapes.

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FIGURE 10. Mean of the first (1) and second (2) principal component loadings over all locations b.

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