TABLE 1. Summary of morphometric and morphogenetic models proposed to study ectochocleate cephalopods in chronological order. The selection criteria were the description of new parameters, indices, or rates. Here we do not include models used to study the conch functional morphology (see text).
| Name | References |
| Linear Dimensions | Moseley, 1838; Sandberger, 1851, 1853, 1857; Trueman, 1940 |
| Raupian Model | Raup, 1961, 1966, 1967; Raup and Michaelson, 1965 |
| Logarithmic Model | Burnaby, 1966 |
| Modified Raupian Model for Carboniferous ammonoids | Saunders and Andrew, 1984 |
| Wire-cage Models | Savazzi, 1985 |
| Ammonoid Descriptors Model | Smith, 1986 |
| Growing Tube Model for Heteromorphs | Okamoto, 1988 |
| Sectorial Spacing Model | Checa, 1991 |
| Korn's Modified Raupian Model or 'Standard Model' | Korn, 1991, 1997, 1999, 2010; Klug et al., 2015 |
| Weighted Standardization Model | Hohenegger and Tatzreiter, 1992 |
| Reaction-Diffusion Model | Hammer and Bucher, 1999 |
| Morphometric Models for Ancyloceratidae | Kakabadze and Hoedemaeker, 2004; Bersac and Bert, 2020 |
| Piggyback Whorls Model | Ubukata et al., 2008 |
| Modified Raupian Model for nautiloids | Wani and Ayyasami, 2009; Wani and Mapes, 2010 |
| Free-Form Vector Model | Urdy et al., 2010 |
| ADA Model | Parent et al., 2012 |
| Modified Raupian Model for early ammonoids | De Baets et al., 2013 |
| Morphomechanical Model | Moulton et al., 2015; Erlich et al., 2016 |
TABLE 2. Information of the 50 specimens used in this work in alphabetical order.
| No. | ID | Age max | Age min | Specimen # | Locality | Country | Reference |
| 1 | Achguigites tafilaltensis Klug, 2002 |
402.50 | 391.90 | MB.C.15691.1 | Tafilalt | Morocco | Ebbighausen et al., 2011 |
| 2 | Acrocanites disparilis Korn et al., 2010 |
360.70 | 345.30 | MB.C.19025.1 | Mouydir | Algeria | Korn et al., 2010 |
| 3 | Acutimitoceras depressum Vöhringer, 1960 |
358.90 | 346.70 | MB.C.10152.2 | Aguelmous | Morocco | Ebbighausen and Bockwinkel, 2007 |
| 4 | Allothalassoceras bogoslovskayae Leonova, 1989 |
303.40 | 272.50 | PIN 3591/411 | Pamir | Tajikistan | Leonova and Boiko, 2011 |
| 5 | Almites invariabilis Ruzhencev, 1933 |
290.10 | 279.50 | PIN 317/12337 | Aktobe | Kazakhstan | Leonova, 2011 |
| 6 | Ammonellipsites pareyni Ebbighausen et al., 2010 |
348.50 | 345.30 | MB.C.18604.5 | Gourara | Algeria | Ebbighausen et al., 2010 |
| 7 | Aristoceras appressum Ruzhencev, 1950 |
305.00 | 294.60 | PIN 318/1500 | Aktobe | Kazakhstan | Leonova, 2011 |
| 8 | Artinskia artiensis Grünewaldt, 1860 |
295.00 | 279.50 | 203595 | Aktobe | Kazakhstan | Leonova, 2011 |
| 9 | Baculites cazadorianus Paulcke, 1907 |
85.80 | 84.90 | DJ.1507.120 | Brandy Bay | Antarctica | Kennedy et al., 2007 |
| 10 | Beloceras sp. Hyatt, 1886 |
383.70 | 376.10 | PM−29053 | Erfoud | Morocco | Ubukata et al., 2008 |
| 11 | Brahmaites (Brahmaites) mikobokensis Collignon, 1971 |
70.60 | 66.04 | SAM-PCZ22196 | Zululand | South Africa | Kennedy and Klinger, 2012 |
| 12 | Colchidites pseudovulanensis Kakabadze and Hoedemaeker, 2004 |
129.40 | 125.00 | RGM 353 680 | Galan | Colombia | Kakabadze and Hoedemaeker, 2004 |
| 13 | Deshayesites grandis Spath, 1930 |
122.46 | 99.7 | GSM Zm1917 | Atherfield | England | Bersac and Bert, 2012 |
| 14 | Dieneroceras tientungense Chao, 1959 |
251.30 | 247.20 | PIMUZ 25970 | Guangxi | China | Brayard and Bucher, 2008 |
| 15 | Discoclymenia cucullate Buch, 1839 |
364.70 | 360.70 | Ü164/10 | Fezzou | Morocco | Becker, 1995 |
| 16 | Agoniatites (Fidelites) fidelis Barrande, 1865 |
391.90 | 388.10 | L133 | Koneprusy | Czech Republic | Chlupáč and Turek, 1983 |
| 17 | Geyeroceras cylindricum Sowerby,1831 |
201.30 | 190.80 | No. 5798.Hm | Töpe Valley | Romania | Tomas and Pálfy, 2007 |
| 18 | Girtyoceras meslerianum Girty, 1909 |
336.00 | 326.40 | PM−29068 | Oklahoma | USA | Ubukata et al., 2008 |
| 19 | Grossouvrites joharae Salazar et al., 2010 |
70.60 | 66.04 | IAA-Pi265 | Marambio Island | Antarctica | Ubukata et al., 2008 |
| 20 | Gunnarites antarcticus Weller, 1903 |
70.60 | 66.04 | CPBA-8841 | Marambio Island | Antarctica | Coll. Paleontología Universidad de Buenos Aires (Argentina) |
| 21 | Hammatocyclus pollex Ebbighausen et al., 2010 |
360.70 | 345.30 | MB.C.18601.1 | Gourara | Algeria | Ebbighausen et al., 2010 |
| 22 | Hypacanthoplites sp. Spath, 1923 |
112.60 | 89.3 | RUB-Pal 11253B | Werner Beckert | Germany | Coll. Ruhr-Universität Bochum (Germany) |
| 23 | Imitoceras dimidium Korn et al., 2010 |
360.70 | 345.30 | MB.C.18859.3 | Mouydir | Algeria | Korn et al., 2010 |
| 24 | Juraphyllites gigas Fucini 1901 |
196.50 | 189.60 | No. 5810.H | Alsórákos. | Romania | Tomas and Pálfy, 2007 |
| 25 | Kitchinites darwini Steinmann, 1895 |
70.60 | 66.04 | CPBA-16823 | Marambio Island | Antarctica | Coll. Paleontología Universidad de Buenos Aires (Argentina) |
| 26 | Kossmaticeras (Natalites) erbeni Stinnesbeck, 1986 |
70.60 | 66.04 | CPUC/Q/TO/3644 | Cocholgüe | Chile | Salazar et al., 2010 |
| 27 | Kutatissites densecostatus Kakabadze, 1981 |
129.40 | 125.00 | RGM 353 840 | Galan | Colombia | Kakabadze and Hoedemaeker, 2004 |
| 28 | Lissoceras inflatum Wetzel, 1950 |
170.30 | 168.30 | MGUPT-PU 112706 | Sully | France | Pavia and Fernandéz-López, 2019 |
| 29 | Maorites densicostatus Kilian and Reboul 1909 |
68.30 | 66.04 | CPBA-17199a | Marambio Island | Antarctica | Coll. Paleontología Universidad de Buenos Aires (Argentina) |
| 30 | Maorites seymourianus Kilian and Reboul, 1909 |
71.00 | 68.30 | CPBA-16847 | Marambio Island | Antarctica | Coll. Paleontología Universidad de Buenos Aires (Argentina) |
| 31 | Meekoceras gracilitati White, 1879 |
251.30 | 247.20 | MM−29111 | Nevada | USA | Ubukata et al., 2008 |
| 32 | Neodeshayesites columbianus Riedel, 1938 |
112.00 | 108.00 | C12C-4 | Mesitas del Colegio | Colombia | Coll. Museo José Royo y Gómez (Colombia) |
| 33 | Neopericyclus arenosus Ebbighausen et al., 2010 |
348.50 | 345.30 | MB.C.18603.1 | Gourara | Algeria | Ebbighausen et al., 2010 |
| 34 | Normannites mitis Westermann, 1954 |
170.30 | 168.3 | emp. CT-data | Thurnen | Switzerland | Tajika et al., 2015 |
| 35 | Otoceras concavum Tozer, 1967 |
252.30 | 247.20 | YIG 921/165 | Arctic Siberia | Russia | Monnet et al., 2015a |
| 36 | Pachydiscus ultimus Macellari, 1986 |
61.50 | 68.30 | CPBA-8854 | Marambio Island | Antarctica | Coll. Paleontología Universidad de Buenos Aires (Argentina) |
| 37 | Paragastrioceras modulatum Ruzhencev, 1956 |
290.10 | 279.50 | PIN 317/4710 | Zhil-Tau Hill | Kazakhstan | Korn and Klug, 2012 |
| 38 | Paratumaroceras ruzhencevi Kutygin, 2003 |
279.50 | 272.50 | GM IGABM 55-563 | Verkhoyansk | Rusia | Kutygin, 2003 |
| 39 | Pedioceras multicostatum Kakabadze and Hoedemaeker, 2004 |
125.00 | 113.00 | RGM 353 635. | Villa de Leyva | Colombia | Kakabadze and Hoedemaeker, 2004 |
| 40 | Phylloceras consanguineum Gemmellaro, 1876 |
155.70 | 145.50 | MM−29121 | Sakaraha | Madagascar | Ubukata et al., 2008 |
| 41 | Phyllopachyceras forbesianum D’Orbigny, 1850 |
84.90 | 66.04 | CPUC/Q/ LT/248 | Concepción Bay | Chile | Salazar et al., 2010 |
| 42 | Pictetia astieriana Kennedy and Klinger, 1978 |
112.60 | 109.00 | MAo-519 | Mangyshlak | Kazakhstan | Hoffmann, 2010 |
| 43 | Polonoceras subundulatum Frech, 1887 |
376.10 | 364.70 | Bockwinkel coll. | Montaigne Noire | France | Korn and Klug, 2002 |
| 44 | Posttornoceras sapiens Korn, 1999 |
369.60 | 367.60 | GPIT 1850-31 | Rich Sidi Ali | Morocco | Korn, 1999 |
| 45 | Proarceste bramantei Mojsisovics 1869 |
247.20 | 242.00 | PIMUZ 25356 | Oliver Gulch | USA | Monnet and Bucher, 2005 |
| 46 | Proleymeriella schrammeni Jacob, 1907 (adult) |
112.6 | 109.00 | RUB-Pal 11285 | Wolgast-Hohendorf | Germany | Coll. Ruhr-Universität Bochum (Germany) |
| 47 | Proleymeriella schrammeni Jacob, 1907 (juvenile) |
112.6 | 109.00 | RUB-Pal 11285 | Wolgast-Hohendorf | Germany | Coll. Ruhr-Universität Bochum (Germany) |
| 48 | Pseudophyllites indra Forbes, 1846 |
84.90 | 66.04 | AQ203 | Koppeh Dagh | Iran | Niebuhr et al., 2016 |
| 49 | Roinghites aktubensis Bogoslovskii 1971 |
370.00 | 367.60 | Ebbighaussen coll. | Aktobe | Kazakhstan | Korn and Klug, 2002 |
| 50 | Staffites complanatus Matern, 1931 |
376.10 | 370.60 | Korn coll. | Rhenish Massif | German-Belgium | Korn and Klug, 2002 |
TABLE 3. Eigenvalue, percentage of variance, and cumulative percentage, for the first 10 principal components.
| Eigenvalues | % Variance | Cumulative % | |
| PC1 | 0.06 | 56.92 | 56.92 |
| PC2 | 0.02 | 21.16 | 78.08 |
| PC3 | 0.01 | 10.82 | 88.90 |
| PC4 | 0.01 | 4.78 | 93.68 |
| PC5 | 0.00 | 2.23 | 95.91 |
| PC6 | 0.00 | 1.52 | 97.43 |
| PC7 | 0.00 | 0.91 | 98.34 |
| PC8 | 0.00 | 0.60 | 98.95 |
| PC9 | 0.00 | 0.48 | 99.43 |
| PC10 | 0.00 | 0.24 | 99.67 |
TABLE 4. Summary of MANOVA results for a multivariate linear regression (MLR) with the diameter and the mean stratigraphic age range as independent variates, and the 29 PCs as dependent variates. Abbreviations: MSE, mean squared error; Λ, Wilk’s lambda.
| Diameter | MAR | |||
| R2: | 0.14 | R2: | 0.1447 | |
| MSE: | 0 | MSE: | 0.00326 | |
| Λ: | 0.27 | Λ: | 0.1839 | |
| F: | 1.89 | F: | 3.076 | |
| df1: | 29 | df1: | 29 | |
| df1: | 20 | df1: | 20 | |
| p: | 0.07 | p: | <0.05 | |
