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FIGURE 9 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 9. Menabites (Delawarella) tequesquitense (Young, 1963) from bed TPY36 of the Tepeyac section. CPC- 2383, right lateral view. Scale: 50 mm.
FIGURE 8 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 8. Menabites (Delawarella) tequesquitense (Young, 1963) from bed TPY36 of the Tepeyac section. CPC- 2383, left lateral view. Scale: 50 mm.
FIGURE 7 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 7. Menabites (Delawarella) tequesquitense (Young, 1963) from the middle Tepeyac section. A: CPC–2381, TPY33, B–C: CPC-2383, TPY36. Scale: 50 mm.
FIGURE 6 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 6. Menabites (Delawarella) tequesquitense (Young, 1963) from bed TPY33 of the Tepeyac section. A–B: CPC–2381. Scale: 50 mm.
FIGURE 22 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 22. Menabites (Bererella) walnutensis (Young, 1963) from bed TPY77. A–C: CPC–2580. Scale: 50 mm.
FIGURE 24 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 24. Pseudoschloenbachia (P.) mexicana (Renz, 1936) from the lower and middle Tepeyac section. A–C: CPC–2339, TPY13. D–F: CPC–2334, TPY48-50. Scale: 50 mm.
FIGURE 32. Pachydiscids from the Tepeyac section. A–B in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 32. Pachydiscids from the Tepeyac section. A–B: Pachydiscus (Pachydiscus) duelmensis (Schlüter, 1972), CPC–2193 from bed TPY40; C–F: Menuites stephensoni Young, 1963, CPC–2194 from bed TPY50. Scale: 50 mm.
FIGURE 27 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 27. Pachydiscus (Pachydiscus) duelmensis (Schlüter, 1972) from bed TPY40. A–B: CPC–2561. Scale: 50 mm.
FIGURE 2 in Ammonoids and their biozonation across the Santonian-Campanian boundary in north-eastern Coahuila, Mexico
FIGURE 2. The Tepeyac section, the stable carbon isotope curve and events, ammonoid species occurrences and ranges, and biozonation by ammonoids. Dashed lines mark species occurrences elsewhere.
FIGURE 10 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 10. Morphologic variation in the diameter (dm) and the mean stratigraphic age range (MAR) illustrated through linear plots, showing the direct or inverse relationships of the variates. A) PC1 against the diameter (R² = 0.25, p = <0.05). B) PC1 against MAR (R² = 0.20, p = <0.05). C) PC2 against the diameter (R² = 0, p = 0.88). D) PC2, against MAR (R² = 0.22, p = <0.05).
FIGURE 11 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 11. Morphological variation of the virtual whorl cross-section at different diameters in Proleymeriella schrammeni. Three ontogenetic stages can be distinguished. The first consists of a rapid morphological change at the beginning of the ontogeny with a predominance of PC1 transformations, this ontogenetic stage is followed by a short interval of morphological stasis. The third ontogenetic stage is likely related to maturity with a predominance of PC2 and PC3 transformations.
FIGURE 5 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 5. Transformations from negative to positive values in PC1. A) Semilandmark configuration at PC1=-0.4 showing the x (red) and y (blue) vectorial components towards PC1 positive values. B) Semilandmark configuration at PC1=0.4 obtained from the transformation of A. C). Graph bar illustrating the translations for each semilandmark in the x-axis for PC1. Empty bars illustrate the closest covariation pattern from Figure 4; in this case, transformations adjusted to an overall expansion of the whorl cross-section. D) Graph bar indicating the translations for each semilandmark in the y-axis for PC1. Empty bars illustrate the closest covariation pattern from Figure 4; in this case, a contraction with an increase in the involution degree. Note that the highest variation is observed on semilandmarks related to the imprint zone (5 to 9 and 14 to 18).
FIGURE 4. Covariation patterns derived from the standard model studied using a in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 4. Covariation patterns derived from the standard model studied using a theoretical subrectangular whorl cross-section with the following parameters: aperture height (ah) = ¾, whorl width (ww) = 1, whorl height (wh) = 1. A) Semilandmark configuration showing the expected transformations from an arbitrary variation (± 0.1 units) in the whorl width, causing an expansion (red) or compression (blue). B) Graph bars showing the change in locations for each semilandmark in the horizontal x-axis from A. C) Semilandmark configuration showing the expected transformations from an arbitrary variation (± 0.1 units) in the aperture height and whorl height, causing an elongation (orange) or contraction (purple), and an increase (yellow) or decrease (green) in involution. D) Graph bars showing the change in locations for each semilandmark in the vertical y-axis from C. Note that a covariation pattern will be a combination of the x and y vectorial components (e.g., an expansion, elongation, and a decrease in involution).
FIGURE 12 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 12. Examples of additional applications for the virtual modelling technique described in this study. A) Basic segment ready to generate a 3D virtual model for hydrodynamic and hydrostatic analyses based on the whorl crosssection of Deshayesites grandis (Bersac and Bert, 2012, figure 2). B–C) Semilandmark configuration and virtual whorl cross-section for the galeate ammonoid Paratornoceras lentiforme (Korn et al., 2020, figure 5A). B) Simplified virtual whorl cross-section based on the 18 semilandmarks model used in this study. C) Modified virtual whorl cross-section based on a 24 semilandmarks model adjusted to emphasize the sharp ventral region.
FIGURE 3 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 3. Virtual whorl cross-sections (grey surfaces) showing the 18 semilandmark configurations (black wireframes) used for this study (four subdivisions leves employed). A) Basic virtual model showing the zones defining the shape of a theoretical whorl cross-section in ammonoids. The horizontal length of the contact zone determines an acute or blunt transition between the dorsolateral zone and the imprint zone. B) Semilandmark model and virtual whorl cross-section for the ammonoid illustrated in Figure 1 at maximum diameter. C) Semilandmark model adapted to the heteromorph ammonoid Pedioceras multicostatum. In evolute ammonoids the contact and imprint zones are reduced, consequently, some of the semilandmarks share the same coordinates (the vertices are merged). D) Semilandmark model adapted to Nautilus pompilius. In nautilids the contact zone is trapezoidal following a rounded umbilical wall.
FIGURE 1 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 1. Summary of linear dimensions measured for the calculation of the Raupian parameters, and the shell diameter in a cross-section of an ammonoid. Some of these linear dimensions were adopted and modified by Korn (2010): whorl height (a = wh), whorl width (b = ww), maximum diameter (dm = d + e). Korn (2010) added some parameters to ammonoids such as the aperture height (f), the imprint zone (g), the umbilical width (h + c), and indices and rates related (see Korn 2010; Klug et al. 2015). (Modified from Raup, 1967)
FIGURE 2 in Geometric morphometrics in ammonoids based on virtual modelling
FIGURE 2. Catmull and Clark´s subdivision surface applied to a two-dimensional rectangular plane. A) Original plane. B) Result of one subdivision. C) Result of two subdivisions.
FIGURE 12 in Computational fluid dynamics modeling of fossil ammonoid shells
FIGURE 12. Simulated Nautilus data plotted alongside live Nautilus behavior data from Niel and Askew (2018).
FIGURE 8 in Computational fluid dynamics modeling of fossil ammonoid shells
FIGURE 8. Plot of the coefficient of drag versus Reynolds number for each of the 10 morphotypes in this study. Drag coefficient and Reynolds number were calculated following the equations of Jacobs (1992). Only shells that had a uniform diameter of approx. 5 cm from aperture to venter are shown.
FIGURE 7 in Computational fluid dynamics modeling of fossil ammonoid shells
FIGURE 7. Plot of drag force versus velocity for each of the 10 different morphotypes used in this study. Only shells that had a uniform diameter of approx. 5 cm from aperture to venter are shown.
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