Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2024 Mar 6;19(3):e0298957.
doi: 10.1371/journal.pone.0298957. eCollection 2024.

Diving dinosaurs? Caveats on the use of bone compactness and pFDA for inferring lifestyle

Nathan P Myhrvold  1 , Stephanie L Baumgart  2   3 , Daniel Vidal  2   4 , Frank E Fish  5 , Donald M Henderson  6 , Evan T Saitta  2 , Paul C Sereno  2   7
Affiliations

Diving dinosaurs? Caveats on the use of bone compactness and pFDA for inferring lifestyle

Nathan P Myhrvold et al. PLoS One. .

Abstract

The lifestyle of spinosaurid dinosaurs has been a topic of lively debate ever since the unveiling of important new skeletal parts for Spinosaurus aegyptiacus in 2014 and 2020. Disparate lifestyles for this taxon have been proposed in the literature; some have argued that it was semiaquatic to varying degrees, hunting fish from the margins of water bodies, or perhaps while wading or swimming on the surface; others suggest that it was a fully aquatic underwater pursuit predator. The various proposals are based on equally disparate lines of evidence. A recent study by Fabbri and coworkers sought to resolve this matter by applying the statistical method of phylogenetic flexible discriminant analysis to femur and rib bone diameters and a bone microanatomy metric called global bone compactness. From their statistical analyses of datasets based on a wide range of extant and extinct taxa, they concluded that two spinosaurid dinosaurs (S. aegyptiacus, Baryonyx walkeri) were fully submerged "subaqueous foragers," whereas a third spinosaurid (Suchomimus tenerensis) remained a terrestrial predator. We performed a thorough reexamination of the datasets, analyses, and methodological assumptions on which those conclusions were based, which reveals substantial problems in each of these areas. In the datasets of exemplar taxa, we found unsupported categorization of taxon lifestyle, inconsistent inclusion and exclusion of taxa, and inappropriate choice of taxa and independent variables. We also explored the effects of uncontrolled sources of variation in estimates of bone compactness that arise from biological factors and measurement error. We found that the ability to draw quantitative conclusions is limited when taxa are represented by single data points with potentially large intrinsic variability. The results of our analysis of the statistical method show that it has low accuracy when applied to these datasets and that the data distributions do not meet fundamental assumptions of the method. These findings not only invalidate the conclusions of the particular analysis of Fabbri et al. but also have important implications for future quantitative uses of bone compactness and discriminant analysis in paleontology.

PubMed Disclaimer

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Lifestyle overlap in femoral and rib data from Fabbri et al. [15].
Femoral (A, C) and rib (B, D) plots of maximum bone diameter (MD) versus bone compactness (Cg). (A, B) Convex hull polygons colored by functional group, as defined by Fabbri et al. Groups with four or fewer datapoints not shown. (C, D) Points and corresponding convex hull polygons for terrestrial groups (F0D0) and groups that include nonflying divers (F0D2). Abbreviations: 0, absent; 1, rarer; 2, habitual; Ba, Baryonyx; D, diving; F, flying; Sp, Spinosaurus; Su, Suchomimus; u, unknown.
Fig 2
Fig 2. Simulated data plots for LDA methods.
(A) 1000 pseudorandom points drawn from each of two multivariate normal distributions given by Eqs (1) and (2) and σ = 0.55, with points from each distribution colored according to the legend. The decision boundary for LDA is given by the red line; points above the line are classified as group 1, points below the line are classified as group 2. Note that one point from group 1 lies on the other side of the decision boundary and is incorrectly classified as group 2. One point from group 2 is similarly misclassified. The centroid of each distribution is denoted by a black cross, the distance d from the centroid to the decision boundary is denoted by a dashed blue line. The confusion matrix c (Eq (5) in S1 Appendix) is shown. (B) 59 points from distributions with the same centroids as (A) but with σ = 1.414. The higher value of σ leads to a larger number of points being misclassified. (C) The underlying probability density functions for the same distributions as in (B). The distributions of blue and gold points are equal at the red decision boundary line y = −x. Abbreviations: G1, group 1; G2, group 2.
Fig 3
Fig 3. Pneumatic features in the dorsosacral column in spinosaurids.
(A) Suchomimus tenerensis (MNBH GAD500) precaudal column and pelvic girdle showing pneumatic features in (B) D2 in lateral view with coronal (B1) and axial (B2) CT cross sections, (C) D13 in lateral view with axial (C1) and sagittal (C2, 3) CT cross sections, and (D) S2 in ventral view with axial (D1) and coronal (D2) CT cross sections. (E) Spinosaurus aegyptiacus precaudal column and pelvic girdle showing pneumatic features in (F) ~D2 in lateral, anterior, and dorsal views with coronal (F1, 2) and axial (F3) CT cross sections, (G) ~D6 in dorsal and lateral views showing coronal (G1) and axial (G,2, 3) CT cross sections, (H) ~D8 in dorsal and lateral views with axial (H1) and coronal (H) CT cross sections, and (I) S3 centrum in ventral and lateral views with coronal (I1) and axial (I2) CT scan sections. Neotypes FSAC-KK-11888 (panels G, H, I) and BSPG-2006-I-54 (panel F). CT section lines are color-coded by orientation (magenta, coronal; blue, axial-horizontal; black, sagittal/parasagittal). Scale bars are 10 cm. Abbreviations: bs, bony septum; c, cervical vertebra; cmr, camera; d, dorsal vertebra; for, foramen; fos, fossa; nc, neural canal.
Fig 4
Fig 4. Femora and a manual phalanx of cf. Spinosaurus aegyptiacus from the Kem Kem Group in Morocco.
(A, B) proximal one-half of an isolated right femur in anterior view and distal midshaft cross-sectional views (CMN 41869); (C) CT scan of the left femur of the neotype with eight cross sections (FSAC-KK 11888); (D) CT scan of an isolated right phalanx I-1 in sagittal cross section (UCRC PV8). Abbreviations: at, anterior trochanter; h, head; mc, medullary cavity. CMN 41869 images provided by Jordan Mallon.
Fig 5
Fig 5. Variation of Cg at different points along a single Nothosaurus dorsal rib.
Images from Klein et al. [147: Fig 3, panels B1–B8] were used to measure variation in Cg (~35%) along the rib shaft. Images supplied by Nicole Klein.
Fig 6
Fig 6. Reevaluation of Cg in a two-part thin section from the left femur of the neotype specimen of Spinosaurus aegyptiacus (FSAC-KK 11888).
(A) Transmitted light image of a two-part thin slice from the mid shaft. (B) Thin slice image modified to close gaps created by natural breaks. (C) Binary image and associated Cg value without filling the cracks and the gap between section halves. (D) Binary image and associated Cg after filling the cracks and the gap between section halves.
Fig 7
Fig 7. Impact of threshold choice on Cg in a cross section of the femoral shaft in a second subadult specimen of cf. Spinosaurus aegyptiacus (CMN 41869).
(A) CT section from the proximal end of the shaft. (B–D) Section images and corresponding Cg values after processing with gray-value (GV) lower thresholds ranging from 26 to 36 GV on a 256 GV gradient. Threshold values determine which pixels are regarded as bone versus nonbone; higher thresholds yield lower Cg values.
Fig 8
Fig 8. Transverse CT cross sections of the femoral shaft in two spinosaurids adjusted to the same side (left) and length.
(A) Suchomimus tenerensis, adult (holotype), length 107.5 cm (MNBH GAD500). (B) Suchomimus tenerensis, juvenile, length 54.6 cm (MNBH GAD72, reversed). (C) Spinosaurus aegyptiacus, subadult (holotype), length 61.0 cm (FSAC KK-11888). (D) Spinosaurus aegyptiacus, subadult, estimated length 61.0 cm (CMN 41869, reversed), (E) Spinosaurus aegyptiacus, juvenile, length 11.8 cm (CMN 50382, reversed).
Fig 9
Fig 9. Bone compactness derived from CT scan of a juvenile femur of cf. Spinosaurus aegyptiacus (CMN 50382).
(A) 3-D rendering and midshaft cross section generated from a CT scan, with binarized images (green) differing in their lower threshold gray-value setting. (B) Plot showing linear change of about 10% in Cg over the threshold range.
Fig 10
Fig 10. Cg measured in three adjacent CT cross sections through the distal shaft of the right femur of the spinosaurid Baryonyx walkeri (NHMUK 9951).
CT sections (A–C, posterior aspect of femur oriented toward bottom) were taken in successively in more distal positions across 1 cm of the distal shaft of the femur in the portion of the shaft used by Fabbri et al. [: S3E Fig] for their best estimate of Cg. The small inset view shows distal end of the femur in medial view with mm distance from the bottom of the radiograph provided by Fabbri et al. To the right are three gray-value (GV) thresholds (left to right: 40–243, 36–243, 36–235) capturing a reasonable range of values that might be selected by researchers to binarize the radiograph. For each threshold, masking of the matrix infilling of the medullary space is shown in transparent (left) and binarized (right) views. Option 1 (top row) attempts to replicate medullary masking as published by Fabbri et al. Option 2 (bottom row) eliminates additional medullary material that we confirmed from the CT scan as matrix infill rather than cancellous medullary bone. Fabbri et al. reported a Cg of 0.876. The Cg range for our three slices in the vicinity of their preferred CT section using their masking is 0.873–0.887 (mean 0.880); their Cg measure is near the low end of that range. The Cg range with our masking is 0.767–0.778 (mean 0.773), considerably lower than their Cg measure.
Fig 11
Fig 11. Cg derived from a thin section from the distal femoral shaft of an adult specimen of Suchomimus tenerensis (MNBH GAD99).
(A) Composite image of the four-part thin section with an enlargement showing the complex relation between cancellous bone and dark-stained mineral infilling. (B) Cancellous bone (red) adjacent to dark-stained matrix in the core of the femoral shaft. (C) Digital removal of matrix adjacent to cancellous bone. (D) Cg from binarized image shown in (C). (E) Comparison of our binarized image (orange) to the Cg and binarized image published by Fabbri et al. (black) [: S3D Fig]. (F) Final Cg after filling in matrix-filled cracks. (G) Distal femur showing position of thin section.
Fig 12
Fig 12. Sample-size effects in LDA/FDA.
(A) Decision boundaries and centroids of point groups for 500 trials of 59 points drawn from a multivariate normal distribution of Eqs (1) and (2) with specified values of σ and d. The centroids of the distributions are shown by the magenta crosses; empirical centroids of each group of 59 points are black dots. The decision boundaries are red lines. Groups of 59 points are insufficient to accurately estimate the distribution centroid. The estimation error leads to variations in both the empirical-group centroids and the decision boundaries across Monte Carlo runs. (B) A histogram of the training-dataset classification accuracy is shown for 10,000 trials with the same parameters as (A). See Materials and methods for definitions of standard error σ and distance d. The theoretical accuracy for the values of σ and d shown is 0.885, but the 95% confidence interval extends from 0.831 to 0.941, a width of 12%. (C) Monte Carlo simulations of classification accuracy for point groups with d = 1.7 and varying values of σ and n points per group. Lines show an empirically derived relationship for the width of the 95% confidence interval in classification accuracy: CI width = a/n1/2, where is a is a fitting constant determined for each value of σ. (D) Monte Carlo simulations of 10,000 trials of LDA plot the lower bound ALB of the 95% CI for accuracy A. Each curve has a different value of the ratio d/σ, from 0.5 to 2.5, and illustrates how the lower bound changes as a function of the number of points in each group, which range from 10 to 2500. Abbreviations: CI, confidence interval.
Fig 13
Fig 13. Sample-size effects for pFDA with F0D0 and F0D2 data from Fabbri et al. [15].
(A) Decision boundaries (red lines) and point-group centroids (black dots) for 100 trials created using a bootstrap method described in the text, operating on the F0D0 and F0D2 subsets of the Fabbri et al. femoral dataset ds1. Each bootstrap trial draws 100 trees at random, each with its own decision boundary. Even more than in Fig 12, considerable scatter is evident in both the centroid positions and decision boundaries. Data points for Spinosaurus, Baryonyx, and Suchomimus are plotted in blue. The downward slopes of most of the decision boundaries, as well as the leftward offset of the centroids of the F0D0 subset versus that for F0D2, show the effect of lower MD for F0D0. (B) A histogram of classification accuracy of the training dataset is shown for 2000 trials of a parametric bootstrap. The median training-set classification accuracy is 0.795, and the 95% confidence interval is 0.718 to 0.863, a width of 0.163. (C) Histograms of P2, the posterior probability of belonging to group D = 2, for spinosaurid taxa across 2000 trials of the same dataset as (A) and (B). (D) Histogram of training-set classification accuracy similar to (B), but for rib data. The median training-set classification accuracy is 0.821, and the 95% confidence interval is 0.696 to 0.884, a width of 0.188. Abbreviations: Sp, Spinosaurus; Ba, Baryonyx; Su, Suchomimus; CI, confidence interval; BCa, bias-corrected-and-accelerated method.
Fig 14
Fig 14
Smoothed kernel distributions for the pFDA discriminants vs. pFDA normal distributions from the (A) femur ds1 and (B) rib ds2 datasets of Fabbri et al. [15]. For both datasets, distributions of the discriminants from the F0D0 and F0D2 subsets (filled areas) differ from the normal distributions imposed by pFDA (dashed curves), which have different means but the same variance. The distributions from the F0D0 and F0D2 groups also overlap considerably in both datasets.
Fig 15
Fig 15. Histograms and fitted distributions for pFDA discriminants.
(A, B) Histograms (light blue) of the discriminants for the F0D0 and F0D2 subsets of ds1. The pFDA normal distributions (black dashed curves) were computed with a standard deviation parameter pooled across F0D0 and F0D2. The three best-fitting distributions (Table 10) are shown in red, dark blue, and green. (C, D) Comparable plots for ds2.
Fig 16
Fig 16. Comparison of data from Fabbri et al. [15] to uniform random points.
(A) Data points for the terrestrial (F0D0) group (black dots) in the femoral dataset of Fabbri et al. are plotted along with (B) uniform random points (red dots), both clipped to the convex hull enclosing the F0D0 data. The apparent absence of any nonrandom concentration or clustering of the F0D0 data is confirmed by statistical tests (Table 13).
See this image and copyright information in PMC

References

    1. Stromer E. Ergebnisse der Forschungreisen Prof. E. Stromers in den Wüsten Ägyptens II. Wirbeltierreste der Baharîje-Stufe (unterstes Cenoman) 3. Das Original de Theropoden Spinosaurus aegyptiacus nov. gen., nov. spec. Abh Konglich Bayer Akad Wiss Math-Phys Cl. 1915;28: 1–32.
    1. Charig AJ, Milner AC. Baryonyx, a remarkable new theropod dinosaur. Nature. 1986;324: 359–361. doi: 10.1038/324359a0 - DOI - PubMed
    1. Sereno PC, Beck AL, Dutheil DB, Gado B, Larsson HCE, Lyon GH, et al. A long-snouted predatory dinosaur from Africa and the evolution of spinosaurids. Science. 1998;282: 1298–1302. doi: 10.1126/science.282.5392.1298 - DOI - PubMed
    1. Charig AJ, Milner AC. Baryonyx walkeri, a fish-eating dinosaur from the Wealden of Surrey. Bull-Nat Hist Mus Geol Ser. 1997;53: 11–70.
    1. Ibrahim N, Sereno PC, Dal Sasso C, Maganuco S, Fabbri M, Martill DM, et al. Semiaquatic adaptations in a giant predatory dinosaur. Science. 2014;345: 1613–1616. doi: 10.1126/science.1258750 - DOI - PubMed

Publication types

LinkOut - more resources