Orthoceratoid theoretical morphologies

Supplementary materials for: Exploring the influence of cameral deposits on the stability, maneuverability, and orientation of orthocone cephalopods David J. Peterman1*, Neil H. Landman2, Charles Ciampaglio3 1Department of Geology and Environmental Earth Science, Miami University, Oxford, OH 45056, USA 2Division of Paleontology, American Museum of Natural History, NY 10024, USA 3Department of Science, Mathematics, and Engineering, Wright State University Lake Campus, Celina, OH 45822 USA *Corresponding author email: [email protected] This PDF file includes Supplementary text for Equation S1 Figures S1 to S5 Tables S1 to S6 Legend for Dataset S1 Supplementary text for Equation S1: Body chambers with the terminal septum preserved can be used for minimum estimates of the body chamber proportions. Assuming isometric proportions, the total conch length (𝐿𝑡𝑜𝑡𝑎𝑙), based on the preserved body chamber, can be computed with the following equation: 𝐿𝑡𝑜𝑡𝑎𝑙=(ℎ𝑎𝑛𝑡 2) ((ℎ𝑎𝑛𝑡 2− ℎ𝑏𝑎𝑠𝑒 2) 𝑙𝐵𝐶 ) = (𝐷1−𝐷2) 𝐷1 (S1) where ℎ𝑎𝑛𝑡 and ℎ𝑏𝑎𝑠𝑒 are the heights measured at the anterior portion and base of the preserved body chamber, respectively, and 𝑙𝐵𝐶 is the body chamber length. The body chamber length divided by this estimate of total conch length can be used to estimate body chamber ratio (BCR). Note that this assumption of isometry underestimates BCR for ectocochleate cephalopods, which can have comparatively larger expansion rates at their juvenile, apical portions. Furthermore, reductions in aperture height in mature body chambers would produce negative values. Therefore, this approach only provides rough estimates of conch length and BCR. Figured and measured material: This SI document contains figured specimens that were used to build theoretical morphologies of orthocone (straight shelled) and cyrtocone (slightly curved) cephalopods. Relevant measurements from these specimens are also listed in accompanying supplementary tables. Figure S1. Pseudorthoceratid specimen (Smithorthoceras unicamera (Smith, 1938); AMNH-FI145916) used to model asymmetric distributions of cameral deposits in theoretical hydrostatic models. A) Unstained specimen. B) Specimen stained with Feigl’s solution to distinguish between aragonite and calcite mineralogy. Note that aragonitic components have been stained black. This specimen was also used to quantify geometric properties of the conch (see Table S1). Figure S2. Pseudorthoceratid specimen (Smithorthoceras unicamera (Smith, 1938); AMNH-FI138966) used to quantify conch taper for the high-taper orthocone model. This specimen was also used to quantify geometric properties of the conch (see Table S1). Figure S3. Pseudorthoceratid specimen (Smithorthoceras unicamera (Smith, 1938); AMNHFI-138970) used to quantify geometric properties of the conch (see Table S1). Figure S4. Cyrtocone (slightly curved) specimen (AMNH-FI-145902) used to model two theoretical morphologies, 1) a cyrtocone, and 2) a high-taper orthocone. A) Photo of the exterior before grinding. Note this specimen was exposed by splitting a bulk sample. B) Specimen ground down just before the medial plane. C) Specimen ground down to the medial plane. This specimen was also used to quantify geometric properties of the conch (see Table S1). Figure S5. Various pseudorthocerid (Spyroceratinae) specimens used to quantify geometric properties of the conch (listed in Table S1). A) AMNH-FI-138968; Smithorthoceras unicamera (Smith, 1938), B) AMNH-FI-145912; Arbuckleoceras tricamerae (Smith, 1938), C) AMNH-FI145913; Arbuckleoceras tricamerae (Smith, 1938), D) AMNH-FI-145908; c.f. Arbuckleoceras tricamerae (Smith, 1938), E) AMNH-FI-145922; Arbuckleoceras tricamerae (Smith, 1938), F) AMNH-FI-145921; Spyroceratinae, G) AMNH-FI-145906; Smithorthoceras unicamera (Smith, 1938), H) AMNH-FI-145923; c.f. Sulphurnites taffi (Niko et al., 2018), I) AMNH-FI-145903; Smithorthoceras unicamera (Smith, 1938), J) AMNH-FI-145904; c.f. Smithorthoceras unicamera (Smith, 1938). Table S1. Raw conch measurements used to build digital hydrostatic models. Note that whorl height was measured from the internal interface of the shell. Specimen In matrix? Chamber Whorl height (px) Siphuncle thickness (px) Shell thickness (px) Septal thickness (px) Septal spacing (px) AMNH-FI-138966 Yes 1 585.8 95.1 23.3 467.9 2 589.5 19.4 2 601.4 83.8 23.6 530.3 3 607.3 24.6 3 621.3 101.5 23.0 504.2 4 620.7 20.4 4 638.1 99.6 19.9 553.1 5 637.5 26.6 627.1 AMNH-FI-138968 Yes 1 1208.7 179.6 37.9 1099.7 2 1216.4 179.9 38.8 24.8 AMNH-FI-145912 No 1 1865.3 237.8 60.5 1037.4 2 1928.1 245.2 61.5 32.4 1145.1 3 2012.1 278.7 56.5 31.6 1084.6 AMNH-FI-145913 No 1 2105.5 55.2 1198.7 2 2169.4 68.2 37.1 1323.3 3 2248.5 72.0 37.5 1353.9 AMNH-FI-145906 No 1 2875.8 521.8 2840.1 AMNH-FI-145916 No 1 1649.5 270.5 1663.0 2 1788.8 233.1 62.0 47.8 1786.4 3 1803.6 241.2 63.4 52.5 1808.5 AMNH-FI-145908 No 1 1465.3 45.2 961.9 2 1530.4 50.2 27.2 1069.7 3 1572.9 54.0 26.0 1106.5 4 1671.2 47.2 AMNH-FI-145922 No 1 1344.7 28.2 28.5 754.1 2 1398.9 37.8 29.5 783.0 3 1443.5 32.4 28.2 AMNH-FI-145921 No 1 2 1146.2 135.3 33.4 18.4 913.9 3 1236.7 196.1 33.8 19.8 922.7 AMNH-FI-145923 No 1 1886.7 290.2 94.4 43.7 AMNH-FI-145902 Yes 1 729.3 166.2 17.7 13.6 706.8 2 758.6 125.8 15.4 18.5 705.6 3 814.7 152.4 20.6 710.3 4 878.3 31.5 5 6 AMNH-FI-138970 Yes 1 1105.0 134.1 28.3 960.5 2 1174.0 164.0 32.7 32.9 974.0 3 1194.0 43.5 34.1 1009.0 4 1184.1 31.5 36.3 1144.1 5 1209.4 39.0 39.6 1281.0 6 1256.0 49.7 54.5 AMNH-FI-145904 Yes 1 657.0 26.0 20.4 710.7 2 677.4 29.0 21.8 698.8 3 697.6 28.7 23.5 703.3 4 712.6 29.3 21.9 745.2 5 AMNH-FI-145903 Yes 1 1138.5 30.8 32.8 Table S5. Centroids for each component used to compute hydrostatics, and centers of buoyancy and mass computed for each model. Each model corresponds to figure numbers in the main paper. Note that all measurements are with respect to an arbitrary datum (placed at the center of the aperture). Model Conch, taper BCR (%) Deposits Soft body Shell Cameral liquid Cameral deposits Center of buoyancy Center of mass x (mm) z (mm) x (mm) z (mm) x (mm) z (mm) x (mm) z (mm) x (mm) z (mm) x (mm) z (mm) Fig. 2A ortho, low 30 Asymmetric -0.032 59.294 -0.001 135.471 NA NA -0.423 355.542 -0.019 118.806 -0.053 108.223 Fig. 2B ortho, low 25 Asymmetric -0.036 51.259 -0.001 135.177 NA NA -0.503 330.060 -0.019 118.806 -0.087 117.183 Fig. 2C ortho, low 24.3 Asymmetric -0.036 50.020 -0.001 135.075 NA NA -0.799 322.171 -0.019 118.806 -0.134 117.946 Fig. 2D ortho, low 20 Asymmetric -0.041 42.814 -0.001 134.318 NA NA -0.566 307.082 -0.019 118.806 -0.131 126.748 Fig. 3A ortho, low 40 None -0.027 74.493 0.000 134.738 NA NA NA NA -0.019 118.806 -0.019 93.429 Fig. 3B ortho, low 30 Symmetric -0.032 59.294 -0.001 135.471 NA NA -0.003 356.207 -0.019 118.806 -0.020 108.277 Fig. 3C ortho, low 25 Symmetric -0.036 51.259 -0.001 135.177 NA NA -0.004 330.853 -0.019 118.806 -0.020 117.290 Fig. 3D ortho, low 24.3 Symmetric -0.036 50.020 -0.001 135.075 NA NA -0.003 326.284 -0.019 118.806 -0.020 118.538 Fig. 3E ortho, low 20 Symmetric -0.041 42.814 -0.001 134.318 NA NA -0.003 308.160 -0.019 118.806 -0.020 126.962 Fig. 4A ortho, low 30 None; 27.6% Liquid -0.032 59.294 -0.001 135.471 -0.001 229.259 NA NA -0.019 118.806 -0.019 98.041 Fig. 4B ortho, low 30 Apical -0.032 59.294 -0.001 135.471 NA NA -0.003 367.528 -0.019 118.806 -0.020 109.187 Fig. 4C ortho, low 30 Ventral -0.032 59.294 -0.001 135.471 NA NA -1.343 334.337 -0.019 118.806 -0.127 106.519 Fig. 4D ortho, low 30 Oblique -0.032 59.294 -0.001 135.471 NA NA -1.925 332.782 -0.019 118.806 -0.174 106.394 Fig. 4E ortho, low 25 None; 38.6% Liquid -0.036 51.259 -0.001 135.177 -0.001 212.588 NA NA -0.019 118.806 -0.019 101.286 Fig. 4F ortho, low 25 Apical -0.036 51.259 -0.001 135.177 NA NA -0.002 343.415 -0.019 118.806 -0.019 118.987 Fig. 4G ortho, low 25 Ventral -0.036 51.259 -0.001 135.177 NA NA -1.592 303.957 -0.019 118.806 -0.234 113.657 Fig. 4H ortho, low 25 Oblique -0.036 51.259 -0.001 135.177 NA NA -1.848 315.412 -0.019 118.806 -0.269 115.205 Fig. 5A ortho, high 40 None -0.054 31.925 -0.001 60.001 NA NA NA NA -0.039 49.631 -0.038 40.038 Fig. 5B ortho, high 30 Symmetric -0.061 25.093 -0.001 60.457 NA NA -0.002 172.440 -0.039 49.631 -0.040 43.023 Fig. 5C ortho, high 25 Symmetric -0.068 21.303 -0.001 60.343 NA NA -0.002 158.190 -0.039 49.631 -0.040 47.382 Fig. 5D ortho, high 22.365 Symmetric -0.072 19.379 -0.001 60.179 NA NA -0.003 152.132 -0.039 49.631 -0.040 49.551 Fig. 5E ortho, high 20 Symmetric -0.076 17.654 -0.001 59.976 NA NA -0.002 148.144 -0.039 49.631 -0.040 51.661 Fig. 6A ortho, high 30 None; 18.8% Liquid -0.061 25.093 -0.001 60.457 -0.001 106.270 NA NA -0.039 49.631 -0.040 39.906 Fig. 6B ortho, high 30 Apical -0.061 25.093 -0.001 60.457 NA NA -0.001 172.952 -0.039 49.631 -0.040 43.047 Fig. 6C ortho, high 30 Ventral -0.061 25.093 -0.001 60.457 NA NA -1.132 160.221 -0.039 49.631 -0.093 42.450 Fig. 6D ortho, high 30 Oblique -0.061 25.093 -0.001 60.457 NA NA -1.876 156.001 -0.039 49.631 -0.128 42.252 Fig. 6E ortho, high 25 None; 32.7% Liquid -0.068 21.303 -0.001 60.343 -0.001 98.154 NA NA -0.039 49.631 -0.040 41.396 Fig. 6F ortho, high 25 Apical -0.068 21.303 -0.001 60.343 NA NA -0.001 158.889 -0.039 49.631 -0.040 47.451 Fig. 6G ortho, high 25 Ventral -0.068 21.303 -0.001 60.343 NA NA -1.454 142.538 -0.039 49.631 -0.184 45.825 Fig. 6H ortho, high 25 Oblique -0.068 21.303 -0.001 60.343 NA NA -1.737 146.928 -0.039 49.631 -0.213 46.261 Fig. 7A cyrto, high 40 None 4.678 31.305 15.766 55.564 NA NA NA NA 12.440 46.254 7.881 38.314 Fig. 7B cyrto, high 30 Symmetric 2.932 24.749 15.696 56.118 NA NA 88.514 126.365 12.440 46.254 10.929 39.297 Fig. 7C cyrto, high 25 Symmetric 2.200 21.039 15.516 56.087 NA NA 74.833 124.392 12.440 46.254 13.682 42.515 Fig. 7D cyrto, high 22.365 Symmetric 1.890 19.143 15.393 55.972 NA NA 69.333 122.491 12.440 46.254 14.888 44.276 Fig. 7E cyrto, high 20 Symmetric 1.646 17.434 15.266 55.808 NA NA 65.903 121.054 12.440 46.254 16.037 46.006 Fig. 8A cyrto, high 30 None; 18.9% liquid 2.932 24.749 15.696 56.118 34.857 95.698 NA NA 12.440 46.254 8.403 37.843 Fig. 8B cyrto, high 30 Apical 2.932 24.749 15.696 56.118 NA NA 88.892 126.498 12.440 46.254 10.947 39.303 Fig. 8C cyrto, high 30 Convex side 2.932 24.749 15.696 56.118 NA NA 76.831 126.178 12.440 46.254 10.380 39.288 Fig. 8D cyrto, high 30 Concave side 2.932 24.749 15.696 56.118 NA NA 76.536 123.856 12.440 46.254 10.367 39.179 Fig. 8E cyrto, high 25 None; 32.8% liquid 2.200 21.039 15.516 56.087 30.313 89.315 NA NA 12.440 46.254 9.244 39.010 Fig. 8F cyrto, high 25 Apical 2.200 21.039 15.516 56.087 NA NA 75.591 124.775 12.440 46.254 13.757 42.553 Fig. 8G cyrto, high 25 Convex side 2.200 21.039 15.516 56.087 NA NA 60.656 120.186 12.440 46.254 12.270 42.096 Fig. 8H cyrto, high 25 Concave side 2.200 21.039 15.516 56.087 NA NA 61.140 117.240 12.440 46.254 12.319 41.803 Table S6. Volumes and masses computed for each modeled material and each cephalopod morphotype. Each model corresponds to figure numbers in the main paper. Sb = soft body, Sh = shell, Cl = cameral liquid, Cd = cameral deposits, All cam = all camerae, Wd = water displaced. Model Conch, taper BCR (%) Deposits Volumes (cm3) Masses (g) Sb Sh Cl Cd All cam Wd Sb Sh Cl Cd Wd Total Fig. 2A ortho, low 30 Asymmetric 31.575 7.289 NA 1.777 15.912 54.780 33.122 18.515 NA 4.513 56.150 56.150 Fig. 2B ortho, low 25 Asymmetric 28.270 7.445 NA 2.986 19.062 54.780 29.655 18.909 NA 7.585 56.150 56.150 Fig. 2C ortho, low 24.3 Asymmetric 27.734 7.469 NA 3.183 19.572 54.780 29.093 18.971 NA 8.085 56.150 56.150 Fig. 2D ortho, low 20 Asymmetric 24.457 7.625 NA 4.381 22.695 54.780 25.656 19.366 NA 11.128 56.150 56.150 Fig. 3A ortho, low 40 None 37.121 7.028 NA NA 10.629 54.780 38.940 17.851 NA NA 56.150 56.791 Fig. 3B ortho, low 30 Symmetric 31.575 7.289 NA 1.777 15.912 54.780 33.122 18.515 NA 4.513 56.150 56.150 Fig. 3C ortho, low 25 Symmetric 28.270 7.445 NA 2.986 19.062 54.780 29.655 18.909 NA 7.585 56.150 56.150 Fig. 3D ortho, low 24.3 Symmetric 27.734 7.469 NA 3.183 19.572 54.780 29.093 18.971 NA 8.085 56.150 56.150 Fig. 3E ortho, low 20 Symmetric 24.457 7.625 NA 4.381 22.695 54.780 25.656 19.366 NA 11.128 56.150 56.150 Fig. 4A ortho, low 30 None; 27.6% Liquid 31.575 7.289 4.389 NA 15.912 54.780 33.122 18.515 4.499 NA 56.150 56.136 Fig. 4B ortho, low 30 Apical 31.575 7.289 NA 1.777 15.912 54.780 33.122 18.515 NA 4.513 56.150 56.150 Fig. 4C ortho, low 30 Ventral 31.575 7.289 NA 1.777 15.912 54.780 33.122 18.515 NA 4.513 56.150 56.150 Fig. 4D ortho, low 30 Oblique 31.575 7.289 NA 1.777 15.912 54.780 33.122 18.515 NA 4.513 56.150 56.150 Fig. 4E ortho, low 25 None; 38.6% Liquid 28.270 7.445 7.387 NA 19.062 54.780 29.655 18.909 7.571 NA 56.150 56.136 Fig. 4F ortho, low 25 Apical 28.270 7.445 NA 2.986 19.062 54.780 29.655 18.909 NA 7.585 56.150 56.150 Fig. 4G ortho, low 25 Ventral 28.270 7.445 NA 2.986 19.062 54.780 29.655 18.909 NA 7.585 56.150 56.150 Fig. 4H ortho, low 25 Oblique 28.270 7.445 NA 2.986 19.062 54.780 29.655 18.909 NA 7.585 56.150 56.150 Fig. 5A ortho, high 40 None 18.546 3.113 NA NA 4.075 25.733 19.455 7.906 NA NA 26.376 27.361 Fig. 5B ortho, high 30 Symmetric 16.128 3.237 NA 0.487 6.369 25.733 16.918 8.222 NA 1.236 26.376 26.376 Fig. 5C ortho, high 25 Symmetric 14.617 3.314 NA 1.033 7.802 25.733 15.333 8.419 NA 2.624 26.376 26.376 Fig. 5D ortho, high 22.365 Symmetric 13.800 3.356 NA 1.329 8.577 25.733 14.476 8.525 NA 3.375 26.376 26.376 Fig. 5E ortho, high 20 Symmetric 13.035 3.396 NA 1.605 9.303 25.733 13.674 8.626 NA 4.076 26.376 26.376 Fig. 6A ortho, high 30 None; 18.8% Liquid 16.128 3.237 1.200 NA 6.369 25.733 16.918 8.222 1.230 NA 26.376 26.370 Fig. 6B ortho, high 30 Apical 16.128 3.237 NA 0.487 6.369 25.733 16.918 8.222 NA 1.236 26.376 26.376 Fig. 6C ortho, high 30 Ventral 16.128 3.237 NA 0.487 6.369 25.733 16.918 8.222 NA 1.236 26.376 26.376 Fig. 6D ortho, high 30 Oblique 16.128 3.237 NA 0.487 6.369 25.733 16.918 8.222 NA 1.236 26.376 26.376 Fig. 6E ortho, high 25 None; 32.7% Liquid 14.617 3.314 2.554 NA 7.802 25.733 15.333 8.419 2.618 NA 26.376 26.370 Fig. 6F ortho, high 25 Apical 14.617 3.314 NA 1.033 7.802 25.733 15.333 8.419 NA 2.624 26.376 26.376 Fig. 6G ortho, high 25 Ventral 14.617 3.314 NA 1.033 7.802 25.733 15.333 8.419 NA 2.624 26.376 26.376 Fig. 6H ortho, high 25 Oblique 14.617 3.314 NA 1.033 7.802 25.733 15.333 8.419 NA 2.624 26.376 26.376 Fig. 7A cyrto, high 40 None 18.547 3.112 NA NA 4.075 25.735 19.456 7.905 NA NA 26.378 27.361 Fig. 7B cyrto, high 30 Symmetric 16.128 3.237 NA 0.488 6.369 25.735 16.919 8.221 NA 1.239 26.378 26.378 Fig. 7C cyrto, high 25 Symmetric 14.617 3.314 NA 1.034 7.802 25.735 15.334 8.418 NA 2.627 26.378 26.378 Fig. 7D cyrto, high 22.365 Symmetric 13.800 3.356 NA 1.330 8.577 25.735 14.476 8.525 NA 3.377 26.378 26.378 Fig. 7E cyrto, high 20 Symmetric 13.036 3.395 NA 1.606 9.526 25.735 13.674 8.625 NA 4.080 26.378 26.378 Fig. 8A cyrto, high 30 None; 18.9% liquid 16.128 3.237 1.202 NA 6.369 25.735 16.919 8.221 1.232 NA 26.378 26.372 Fig. 8B cyrto, high 30 Apical 16.128 3.237 NA 0.488 6.369 25.735 16.919 8.221 NA 1.239 26.378 26.378 Fig. 8C cyrto, high 30 Convex side 16.128 3.237 NA 0.488 6.369 25.735 16.919 8.221 NA 1.239 26.378 26.378 Fig. 8D cyrto, high 30 Concave side 16.128 3.237 NA 0.488 6.369 25.735 16.919 8.221 NA 1.239 26.378 26.378 Fig. 8E cyrto, high 25 None; 32.8% liquid 14.617 3.314 2.556 NA 7.802 25.735 15.334 8.418 2.620 NA 26.378 26.372 Fig. 8F cyrto, high 25 Apical 14.617 3.314 NA 1.034 7.802 25.735 15.334 8.418 NA 2.627 26.378 26.378 Fig. 8G cyrto, high 25 Convex side 14.617 3.314 NA 1.034 7.802 25.735 15.334 8.418 NA 2.627 26.378 26.378 Fig. 8H cyrto, high 25 Concave side 14.617 3.314 NA 1.034 7.802 25.735 15.334 8.418 NA 2.627 26.378 26.378 Legend for Dataset S1: This dataset contains 3D models of 43 theoretical morphologies used in hydrostatic analyses. 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