Lower rotational inertia and larger leg muscles indicate more rapid turns in tyrannosaurids than in other large theropods

Abstract

Synopsis: Tyrannosaurid dinosaurs had large preserved leg muscle attachments and low rotational inertia relative to their body mass, indicating that they could turn more quickly than other large theropods.

Methods: To compare turning capability in theropods, we regressed agility estimates against body mass, incorporating superellipse-based modeled mass, centers of mass, and rotational inertia (mass moment of inertia). Muscle force relative to body mass is a direct correlate of agility in humans, and torque gives potential angular acceleration. Agility scores therefore include rotational inertia values divided by proxies for (1) muscle force (ilium area and estimates of m. caudofemoralis longus cross-section), and (2) musculoskeletal torque. Phylogenetic ANCOVA (phylANCOVA) allow assessment of differences in agility between tyrannosaurids and non-tyrannosaurid theropods (accounting for both ontogeny and phylogeny). We applied conditional error probabilities a(p) to stringently test the null hypothesis of equal agility.

Results: Tyrannosaurids consistently have agility index magnitudes twice those of allosauroids and some other theropods of equivalent mass, turning the body with both legs planted or pivoting over a stance leg. PhylANCOVA demonstrates definitively greater agilities in tyrannosaurids, and phylogeny explains nearly all covariance. Mass property results are consistent with those of other studies based on skeletal mounts, and between different figure-based methods (our main mathematical slicing procedures, lofted 3D computer models, and simplified graphical double integration).

Implications: The capacity for relatively rapid turns in tyrannosaurids is ecologically intriguing in light of their monopolization of large (>400 kg), toothed dinosaurian predator niches in their habitats.

Keywords: Agility; Biomechanics; Phylogenetic ANCOVA; Predation; Theropoda; Tyrannosauridae.

Figure 1. Methods for digitizing body outlines and calculating mass properties, for “maximum tail width” estimate for Tyrannosaurus rex.

Reconstructions of Tyrannosaurus rex (Field Museum FMNH PR 2081) in lateral view (A) and dorsal view (B) enable digitizing of dorsal, ventral, and lateral extrema where they cross the vertical red lines. The lateral view (A) is modified with the dorsal margin of the neck conservatively raised based on recent muscle reconstructions (Snively & Russell, 2007a, 2007b). The hind leg (A and C) is outlined in green, and straightened (C) for digitizing. A red dot (A and B) specifies the center of mass of the axial body (minus the limbs) using this reconstruction. An equation for the volume of a given frustum of the body (D), between positions 1 and 2, assumes elliptical cross-sections.

Figure 2. Methods for approximating attachment cross-sectional area of hind limb muscles, on lateral view (A) of a Tyrannosaurus rex skeleton (FMNH PR 2081; modified from Hartman, 2011).

The blue line shows the position of the greatest depth from the caudal ribs to the ventral tips of the chevrons, and greatest inferred width of the m. caudofemoralis longus. (B) The inferred region of muscle attachment on the ilium (modified from Brochu, 2003) is outlined in red, for scaled area measurement in ImageJ. (C) The initial reconstructed radius (blue) of m. caufofemoralis longus (CFL) is 0.5 times the hypaxial depth of the tail (blue line in A), seen in anterior view of free caudal vertebra 3 and chevron 3. The maximum lateral extent of CFL is here based on cross-sections of adult Alligator mississippiensis (Mallison, Pittman & Schwarz, 2015). Note that the chevron in c is modified to be 0.93 of its full length, because it slopes posteroventrally when properly articulated (Brochu, 2003). Bone images in (A) and (C) are “cartoonized” in Adobe Photoshop to enhance edges.

Figure 3. Log-linear plot of body mass (x-axis) vs. an agility index (y-axis) based on muscles originating from the ilium, with tyrannosauruids in blue and non-tyrannosaurids in red.

95% confidence intervals do not overlap. Larger circles show positions of depicted specimens. (A) Allosaurus fragilis. (B) Tarbosaurus bataar. (C) Giganotosaurus carolinii (a shorter-headed reconstruction was used for regressions). (D) Tyrannosaurus rex. (E) Gorgosaurus libratus (juvenile). The Tyrannosaurus rex silhouette is modified after Hartman (2011); others are modified after Paul (1988, 2010). The inset enlarges results for theropods larger than three tones in mass. Note that the tyrannosaurids have two to five times the agility index magnitudes of other theropods of similar mass. Discrepancies between tyrannosaurids and non-tyrannosaurids are greater at smaller body sizes. Abbreviations: A.a., Acrocanthosaurus; A.f., Allosaurus; C.n., Ceratosaurus; D.t., Daspletosaurus; D.w., Dilophosaurus; E.o., Eustreptospondylus oxoniensis; G.c., Giganotosaurus; G.l., Gorgosaurus; S.h., Sinraptor; T.b., Tarbosaurus; T.r., Tyrannosaurus; Y.s., Yangchuanosaurus.

Figure 4. Phylogenetically generalized least squares regressions of (A) Agility_force and (B) Agility_moment for non-tyrannosaurid theropods (red), adult tyrannosaurids (dark blue), and putative juvenile tyrannosaurids (light blue), turning the body with both legs planted.

Tyrannosaurids lie above or on the upper 95% confidence limit of the regression, indicating definitively greater agility than expected for theropods overall when pivoting the body alone. See Figure, and Supplementary Information Figure and R script, for data point labels.

Figure 5. Phylogenetically generalized least squares regression of (A) Agility_force and (B) Agility_moment for non-tyrannosaurid theropods (red), adult tyrannosaurids (dark blue), and putative juvenile tyrannosaurids (light blue), when pivoting on one leg (en pointe).

Tyrannosaurids lie above or on the upper 95% confidence limit of the regression, indicating definitively greater agility than expected for theropods when pursuing prey. See Fig. 1, and the Supplementary Information Figure and R script, for data point labels.

Figure 6. Axial body models (constructed in FreeCAD) of (A) Yangchuanosaurus shangyouensis (CV 00215), (B) Sinraptor hepingensis (ZDM 0024), and (C) Tarbosaurus bataar (ZPAL MgD-I/4) are within 0.5% of the volumes calculated by summing frusta volumes from Eq. (2).

Three workers built different respective models, and congruence of results suggests low operator variation and high precision between the methods. The Tarbosaurus is lofted from fewer elliptical cross-sections than the others, giving it a smoother appearance that nevertheless converges on the frustum results from many more cross-sections. Note that this is an exercise in cross-validation of volume estimates using uniform densities. Our mass property comparisons use frustum-based calculations that incorporate different densities for different regions of the body.