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FIGURE 17 in Identifying tooth position of isolated teeth of sparassodonts (Mammalia: Metatheria) using geometric morphometrics

FIGURE 17. Comparison of the TPS deformation grids for the M3 of Procladosictis anomala (A) and the mean M3 shape for the entire sample exaggerated by a factor of 3 (B), both contrasted against the mean tooth shape for the entire sample.

FIGURE 5 in Identifying tooth position of isolated teeth of sparassodonts (Mammalia: Metatheria) using geometric morphometrics

FIGURE 5. Plot of the first two principal components (PCs) of variation of the Procrustes-transformed landmark dataset for the all-taxon, trigon-only analysis along with deformation grids representing the extreme changes in shape on each axis relative to the mean shape of the entire sample. Upper molar loci are plotted by color, with unknown specimens (M?) in black.

FIGURE 1 in Identifying tooth position of isolated teeth of sparassodonts (Mammalia: Metatheria) using geometric morphometrics

FIGURE 1. Right upper molar rows (M1-3) of three representative sparassodonts in occlusal view: (A) Patene coluapiensis (AMNH 28448); (B) Sipalocyon gracilis (AMNH 9254, left reversed), and (C) Cladosictis patagonica (MACN-A 5950), showing how the teeth at a certain position in the tooth row (tooth locus) in one taxon can resemble a different tooth position in another taxon (e.g., the M3 of C. patagonica resembles both the M2 of Sipalocyon gracilis and the M1 of Patene coluapiensis). Anterior is to the right in all images. Scales equal 5 mm.

FIGURE 4 in Identifying tooth position of isolated teeth of sparassodonts (Mammalia: Metatheria) using geometric morphometrics

FIGURE 4. Plot of the first two principal components (PCs) of variation of the Procrustes-transformed landmark dataset for the all-taxon, trigon + talon dataset along with deformation grids representing the extreme changes in shape on each axis relative to the mean shape of the entire sample. Upper molar loci are plotted by color, with unknown specimens (M?) in black. Circled region in the upper right corner of the graph represents specimens of the Tiupampa taxa Allqokirus and Mayulestes.

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.

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Fig. 5 in Geometric morphometric analysis of cyclical body shape changes in color pattern variants of Cichla temensis Humboldt, 1821 (Perciformes: Cichlidae) demonstrates reproductive energy allocation

Fig. 5. Relative mean GSI vs. relative mean HSI of color pattern variants of Cichla temensis. Points for GSI represent the mean value for each CPV grade as compared to the range encountered. Points for HSI represent the mean value for each CPV grade compared to the range encountered.

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Fig. 3 in Geometric morphometric analysis of cyclical body shape changes in color pattern variants of Cichla temensis Humboldt, 1821 (Perciformes: Cichlidae) demonstrates reproductive energy allocation

Fig. 3. Biplot of the uniform components in each direction (UniX and UniY) of morphometrical differences in 80 specimens of Cichla temensis in 4 color variation patterns (CPV) as measured by 9 Thin Plate Spline (TPS) distortion variables (V1-V9). Colored numbers indicate the CPV grade of individuals. The total spread of scores among individuals of each CPV are indicated by an envelope (solid line polygon) calculated as the minimum convex hull for that group. Position in the plot relative to other individuals indicates the degree of similarity in morph. Vectors point in the direction of gradient change for that TPS variable and the magnitude indicates the strength of the gradient. Angles between vectors indicate the TPS interset correlations.

Figure 6 in A geometric morphometric approach to the analysis of the shape variability of the haptoral attachment structures of Ligophorus species (Platyhelminthes: Monogenea)

Figure 6. Combination of the outlines of all dorsal anchors of each analyzed Ligophorus species (other haptoral structures outlines see http://marineparasites.org/morphometry/

Figure 5 in A geometric morphometric approach to the analysis of the shape variability of the haptoral attachment structures of Ligophorus species (Platyhelminthes: Monogenea)

Figure 5. Cluster (A, C) and PC analysis (B, D) of the combinations of four harmonics for each dorsal and ventral anchors, and ventral bar obtained for each Ligophorus specimens. Upper graphs (A, B) are based on the size-invariant EFDs; lower graphs (C, D) – on the size-considered EFDs.

Figure 4 in A geometric morphometric approach to the analysis of the shape variability of the haptoral attachment structures of Ligophorus species (Platyhelminthes: Monogenea)

Figure 4. PCA of the size-invariant (A, C, E) and size-considered (B, D, F) harmonics of the dorsal (А, B) and ventral (C, D) anchors, and the ventral bars (E, F) of Ligophorus species. All graphs are based on fifty harmonics. Keys: dots – dorsal anchors; triangles – ventral anchors; rhombus – ventral bars.

Figure 2. A in A geometric morphometric approach to the analysis of the shape variability of the haptoral attachment structures of Ligophorus species (Platyhelminthes: Monogenea)

Figure 2. A After the automatic normalization, the outlines of anchors still have different orientation of the blades, different positions of the digitization starting point and directions of digitization; this affects the signs of the first harmonic components, which are shown in pink rectangle, and the signs of identical components differ. B, C After manual correction of the orientation of anchors (B) and bars (C), the outlines and signs of first harmonic components are identical.

Figure 3 in A geometric morphometric approach to the analysis of the shape variability of the haptoral attachment structures of Ligophorus species (Platyhelminthes: Monogenea)

Figure 3. PCA of the size-invariant (A, B) and the size-considered (C, D) harmonics of all dorsal and ventral anchors of analyzed Ligophorus species. Left graphs (A, C) are based on fifty harmonics; right graphs (B, D) – on four ones. Keys: dots – dorsal anchors; triangles – ventral anchors.

Figure 1. A in A geometric morphometric approach to the analysis of the shape variability of the haptoral attachment structures of Ligophorus species (Platyhelminthes: Monogenea)

Figure 1. A Ligophorus szidati dorsal (top) and ventral (bottom) anchors were outlined by cubic Bezier polylines and stored in SVG files. B ElFourier computer program converted digitized outlines into 50 EFDs. Only first four harmonics are visible at the screenshot's bottom; the negative components of harmonics are colored in light gray. The restored outline perfectly satisfies the shape of anchor (red line around gray anchor). At the left side used anchors are shown; they differ by orientation of blades and direction of digitization; outlines oriented counterclockwise are filled.