Research Article

A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth

  • John R. Hutchinson mail,

    Affiliation: Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom

  • Karl T. Bates,

    Affiliation: Department of Musculoskeletal Biology, Institute of Aging and Chronic Disease, University of Liverpool, Liverpool, United Kingdom

  • Julia Molnar,

    Affiliation: Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom

  • Vivian Allen,

    Affiliation: Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom

  • Peter J. Makovicky

    Affiliation: Department of Geology, Field Museum of Natural History, Chicago, Illinois, United States of America

  • Published: October 12, 2011
  • DOI: 10.1371/journal.pone.0026037
  • Published in PLOS ONE

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Reply to reply by Hutchinson (11-15-11) and comment to Celestist

Posted by gspauldinodotcom on 19 Jan 2012 at 23:38 GMT

Hutchinson claims that I have not documented my methods for deriving mass estimates from nondigital, illustrative multi-view skeletal restorations, or even the scale of the volumetric models. The methodology has been described in a number of locations in greater detail than for any other similar efforts [1-5], including that the models are constructed at a femur length of 52.5 mm. For Tyrannosaurus that is close to the 1/24 scale that for similar sized World War II fighters results in large models. There is no reason to presume that at this large a scale that modeling accidents will result in substantial errors in the volume within the context of the particular skeletal restoration or volumetric model if the latter is carefully measured and assembled. For example, possible parallax in lateral view photographs can be searched for and if necessary corrected by use of direct measurements of the specimen. My lateral photograph of the front half of the Sue mount used to help restore the specimen records the same length ratio between the mandible and femur as the published measurements [6], as does the resulting skeletal restoration (see right column in figure link below), so it is not possible for substantial errors in the dimensions of the restoration to exist. Unless grave error has occurred in the skeletal restoration there is no cause to presume that the resulting model will be grossly deflated or inflated in proportional terms relative to the size of the actual individual – an error of 5% in the model will remain 5% for the specimen at full size.

Hutchinson seems to be under the misimpression that I assumed that the skeletal scans in Hutchinson et al. were presented at the same scale. What I did use was the length of the femur to determine the scale of each skeleton separately. The statements by Hutchinson concerning the accuracy of the skeletal scans as figured in the paper are rather odd and confusing. He indicates that the views are 'not perfectly orthographic' due to software issues, but claims that the 3D volumetric models are not likewise distorted. Even assuming this is correct, this means that viewers of the paper are left without proper documentation of the skeletal scans vis-à-vis the volumetric models. Such a failing cannot be charged concerning skeletal restorations such as mine that directly surround the skeleton with the restored soft tissue profile, leaving no ambiguity about the relationship between the two. In the future those presenting scanned skeletons and volumetric models based on the former would be well advised to publish accurate scans, and to imbed the skeleton within the volumetric model/s so that the skeleton-profile correspondence problem is eliminated. In any case, the Sue volumetric model in their figure 3 appears to retain the same under sizing of the skull relative to the femur that mars the skeleton in which the mandible is shorter than the femur rather than being longer as it should be. It is not possible to clarify the matter with the information on hand.

Other researchers restore the caudofemoralis as substantially larger than in my restorations, but even presuming this is correct the larger muscles add only a few percent of total mass, and the difference is well within the inherent margin of error. The very deep tail profiles utilized by Hutchinson et al. appear to offer a greater source of potential error, and negates their claim to have modeled the minimal plausible mass that requires that the soft tissues of the tail do not extend far above the neural spines or below the chevrons.

Hutchinson addresses the issue of how the gastralia series impacts body volume. The preserved arc of the series is not necessarily reliable because of the high possibility that the abdomen was inflated by bloating of the carcass. My restorations feature a hollow belly because of the near certainty that large predators – unlike herbivores whose bellies normally contain substantial amounts of forage – are gorge and fast animals whose bellies are slim when they are on the hunt and engaging in the locomotary activities that put the most load on their limbs. However, if the lateral thoracic air-sacs that line the sides of the trunk extended well caudal to the ribcage as some [7] but not all [8-9] researchers indicate, then it is possible that the belly never hollowed out. The latter possibility does not increase the mass of the animal since the larger volume consisted of air. At any rate the mass of the model will be dramatically affected only if the belly is restored as extremely bloated as if the subject had just gorged itself on a large carcass, doing that adds the prey to the mass of the predator.

Hutchinson contends that a caudal sweep of the ribs in tyrannosaurs is an assumption based on a presumption of minimal mass rather than anatomical fact. This posture has been well documented as standard for archosaurs and most other diapsids (2,3,5,10), being essentially universal in living crocodilians and birds, and the same in countless articulated fossil skeletons (as per Fig. 19 in [11], figs. 1,2,5 in [12]; fig. 1 in [13], Pls. 2-4,8,14B,15B,17-19 in [8], Pl. 24 in [14], figs. 14-1, 14-2 in [1]; occasional lack of caudal sweep is probably due to bloating of the carcass inflating its volume). So restoring Tyrannosaurus with the vertical or especially cranially swept ribs that will inflate the volume of the trunk is a markedly inferior hypothesis that lacks substantiation.

Hutchinson acknowledges that the inconsistencies in the skeletal mounts utilized in Hutchinson et al. reduces their cross comparability, reinforcing the argument that the much higher mass obtained for Sue over Stan is not demonstrated by their study. The contention that scans of skeletal mounts provide a better measure of the volume of fossil vertebrates than technical restorations is problematic because it is rare for fossils to be preserved without some degree of plastic distortion created by the pressure of overlying sediments. Correcting the distortions always involves some subjectivity whether it be digital or otherwise. The comment by Brochu concerning the distortion of the ribcage of Sue is particularly pertinent in this regard. Many fossil vertebrate specimens are literally flattened, precluding their being mounted. For these reasons nondigital technical restorations remain competitive with digital scans, neither of which can produce precise volumetric estimates for animals whose mass normally fluctuated in any case (up to a third in healthy adults over the course of a year [15,16]). To be blunt, there is so much slop in estimating masses that resorting to computers is not going to significantly improve the results, it is getting the proportions and anatomy consistently correct that is the most important whether doing so digitally or not, and there is little to choose between them.

Henderson [17] and Henderson and Snively [18] used my skeletal restoration of AMNH 5027 to generate computer mass estimates of 7200 to 10,200 kg, far above my sculpted model estimate of 5700 kg for the specimen. To test this issue I measured out enough modeling clay to represent the mass in ref. 18 and tried to apply it to my skeletal restoration. The effort was hopeless, I was only able to apply an additional 10% without bloating the 3-D model beyond reasonable bounds. That is not surprising because the problem lay elsewhere. A same scale comparison of my skeletal restoration with the models presented in refs. 17 & 18 solves the paradox, it is simply because the dimensions of 5027 somehow become increasingly inflated in the two papers (see left column in figure link below). I suspect that part of the initial inflation may have been due to a misunderstanding that my length measurement of 10.6 meters was along the curve of the vertebral series that was assumed to be between perpendiculars in ref. 17. How the length further expanded to 10% in ref 18 is a mystery. The differences in dimensions accounts for most but not all the difference in the mass estimates between refs. 3, 17 and 18, and the residual differences are minor and within plausible variation. The correspondence between the computer volume estimates and my plasticine models of my skeletal restorations in fact supports that the old fashioned analog method is not inferior to the digital.

Concerning the mass estimate of 12 tonnes for Tyrannosaurus in ref. 3, this was based on the assessment at the time that maxilla UCMP 118742 was exceptionally gigantic. Because it later proved to be no larger than those of other specimens such as Sue the claim of extra colossal Tyrannosaurus was withdrawn [4]. The implication by Celestist that I lowered the mass estimate for the taxon by being subjectively influenced by the femur circumference method is entirely errant I having long strongly criticized the unreliability of the equation [4]. Using the robustness of individual elements to estimate total mass is notoriously capricious because mass/ circumference-diameter values vary enormously between and within taxon. The citation by Celestist of the greater robustness of the elements of some Tyrannosaurus specimens as indicating greater total mass assumes that greater robustness of elements corresponds to a correspondingly greater total animal volume and therefore mass, but it is also possible and indeed probable that the differences record differing skeletal strength factors relative to mass (which could be the result of either sexual morphs or multiple gigantic species whose predatory behaviors were divergent). The only way to test the mass/strength alternatives is to restore the volume of the differing skeletons.

The figure link is at –

All images to same scale, bar equals 2 m. Upper left GSP skeletals of AMNH 5027, immediately below Henderson 1999 volumetric model, further below Henderson & Snively (2004) volumetric model. Upper right GSP skeletals of Stan and Sue, immediately below solid extract profile of Sue with head and limbs removed to compare to same of the minimum Hutchinson et al. (2011) version of Sue (right column is from the figure in the initial comment).

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3. Paul GS (1988) Predatory Dinosaurs of the World. New York: Simon & Schuster.
4. Paul GS (1997) Dinosaur models: The good, the bad, and using them to estimate the mass of dinosaurs. In: Wolberg DL, Stump E, eds. Dinofest international proceedings. Philadelphia: The Academy of Natural Sciences. Pp 471-496.
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6. Brochu C (2003) Osteology of Tyrannosaurus rex: insights from a nearly complete skeleton and high-resolution computed tomographic analysis of the skull. Society of Vertebrate Paleontology Memoir 7: 1-138.
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14. Osborn HF (1916) Skeletal adaptations of Ornitholestes, Struthiomimus, Tyrannosaurus. Bulletin American Museum of Natural History 35: 733-771.
15. McEwen LC, et al. (1957) Nutrient requirements of the white-tailed deer. Transactions of the Twenty-Second North American Wildlife Conference:119-132.
16. Tarr M (2006) Winter feeding is not the key to deer survival.
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No competing interests declared.

RE: Reply to reply by Hutchinson (11-15-11) and comment to Celestist

jrhutch replied to gspauldinodotcom on 31 Jan 2012 at 10:51 GMT

We (Hutchinson et al. have been writing all replies; not just Hutchinson as Paul’s reply states) completely disagree that Paul has tested and documented his methodology as thoroughly as other studies have. He has described the general approach but not to a degree that it is easily reproducible by other authors without severe subjective errors that can be demonstrably absent in 3D scanned data. For example, how angles between articulating bones are measured from 2D photographs, and how accurately such angles can be measured, has never been explained in detail. Any error in those angles will influence body contours and hence mass, but that error has not been addressed. In contrast, 3D scanners generally use a linear ray-measurement technique, assembling a point cloud of linear absolute distances (within ~0.1-1mm accuracy) to the surface of the object being scanned. With properly calibrated software and hardware, scaling and parallax errors (whose effects have not been explicitly, quantitatively investigated by Paul and others) are not an issue, and thus high angular and linear fidelity are achieved without need for manual investigator correction.

While Paul cites two single linear measurements of the largest bones as possibly reflecting the accuracy of his models (and the strangely circular assertion that a skeletal reconstruction retaining the proportions of the model it was based on is evidence for the accuracy of the model), there is ample opportunity for small human errors in models to accumulate and cause large errors in the overall reconstruction. As we noted in our previous reply, Mallison has documented such errors for Plateosaurus, as the best (and still uncontested) skeptical investigation of illustration/scale model-based methods for reconstructing dinosaurs.

There is little or no sensitivity analysis of error in any of Paul’s reconstructions; single body mass values are generally reported (this may be due to the extremely labour-intensive process of iterating a physical model). In contrast, recent studies by Hutchinson, Bates, Allen and others have emphasized that single mass estimates are implausible (due to the massive ambiguities in any reconstructions) and reporting a range of values is the more scientific approach. While Paul rightly cites ample body mass variation within organisms’ lives as confounding single mass estimates (but nonetheless presents and uses such single estimates as data in his studies), it is unscientific to dismiss methodological inaccuracies as leaving “little to choose between” various methods. Furthermore, for scale model methods used by Paul and others there is little direct validation of body mass estimates for extant animals of known mass, or analysis of repeatability or investigator bias, which computational methods have performed. Comparison of, for example, the methods and evidence used by our study or Allen et al’s. (2009) with any or all of Paul’s studies provides ample demonstration. However, we encourage Paul to take the opportunity to produce a peer-reviewed study that quantitatively analyzes the accuracy of his methods; if the method is as accurate as he claims there is little to lose and much to gain.

Even in Paul’s latest reply, his reconstructions are not adjusted in light of the latest research showing that the entire tail (not just the caudofemoralis muscle) was much larger than he and others have restored it, nor does he acknowledge that this deviation of soft tissues from the surrounding skeleton is nearly universal among tetrapods, especially in well-muscled archosaur tails. The influence of this extra soft tissue on overall body mass, centre of mass, and locomotor mechanics have thoroughly analyzed (see references in our original paper). His reply does not demonstrate an understanding of the anatomical realities underlying this phenomenon; “minimal mass” reconstructions are only as viable as their adherence to such realities. It would be less scientific to adhere to such skeleton-hugging reconstructions when such deviations of soft tissues from the underlying skeleton are very plausibly expected from documented quantitative evidence (see in particular Allen et al. 2009 cited in our study).

We find it implausible that gastralia orientations in preserved carcasses were “inflated by bloating of the carcass”; otherwise rib orientations that Paul accepts as realistic in the next paragraph would plausible likewise be distorted. Subsequent pressures during diagenesis, especially in large heavy animals, would have prevented such air pockets from persisting throughout fossilization. More likely these poses, when undisturbed by disarticulation, approximate a resting or slightly deflated (i.e. exhalation) orientation.

Paul seems to misunderstand the nature of 3D scan data and 2D renderings from those data. As we noted in our previous reply, we neglected to render an orthographic projection from our 3D software, and instead used a perspective projection render (the default setting). This is entirely an optical effect common to many types of 3D modelling software, meant to mimic a lens of various amounts of 'fish-eye' for the purposes of animation. The use of orthographic vs. perspective render views for displaying our 3D models in 2D has no effect whatsoever on the geometry of the 3D model. Numerous books and webpages explain the technology further—e.g. We encourage Paul and any other skeptics of the accuracy of digital vs. manual measurement techniques to study these modern techniques first, so they can present more informed criticisms. Regardless, we have taken the opportunity to present 2D orthographic views of all 5 skeleton scans (and 2 minimal models) from our study on our website:

There is an issue here of adequacy vs. improvement of technique. Scale modelling can produce scientifically valid results, and as Paul points out, has historically been used in demanding fields such as aeronautical engineering. Scale modelling thus can be an adequate technique. However, as engineers have recognised for decades now, the clear improvements in fidelity (1/1 modelling with absolute dimensional control) that CAD represents, so Paul’s example of engineering usage is actually evidence for the ascendance and modern superiority of digital techniques. Given the ease and economy with which 3D digitisations can be obtained and processed (it is now possible to do so entirely for free, as a recent paper points out [http://palaeo-electronica...], and the commonality of 3D image processing packages such as Blender []), there is little point in persisting to champion what are at best adequate techniques (with a greater possibility for human error) at the expense of improvement in clearly superior methods. Digital modelling techniques, like any method, can and should be improved, and in the 13 years since Henderson’s 1999 classic study in this field they have continued to do so. Scale modelling techniques, in contrast, have achieved little but greater obsolescence.

No competing interests declared.

RE: Reply to reply by Hutchinson (11-15-11) and comment to Celestist

Celestist replied to gspauldinodotcom on 09 Feb 2012 at 23:05 GMT

I now see that discrepancy between yours and Hutchinson's estimate
1) your hindlimb mucle is probably 60-75% the value of Hutchinson's estimate. appears to be emaciated.

The SUE skeleton is 12.29 meter long measure by Hutchinson but only 10 meter "linear between two point" in your drawing, which seems much too short.
if your 10 meter model is 6100kg, than it is reasonable to say that Henderson's 12.29 meter model will 10000kg.

I know your drawing of gigantosauurs MUCPv-CH1 is slightly over 12.2 meter, how did that came about? there is no reason to propose MUCPv-CH1 any longer than FMNH PR 2081. MUCPv-CH1's femur is only 3-5cm longer only because carcharodontosauridae has their femur head rasie in angle above the greater trochanter. while T-rex is head and greater trochanter is in parallell.

2) There is no spacing between bones or Cartilage which will increase the Osteological length by significent amount, which can be seem in some modern panthera cats[1], although T-rex length definitely will not increase to the extent of panthera.

3) it is difficult to compare the femur of MOR 555 and BHI 3033, since one is longer, the other is shorter but robust, but when came to FMNH PR 2081 and BHI 3033, the former is 2% longer than the latter, but 10~20% more robust, doesn't take

I strongly felt that although the illium and femur in your drawing sees to be in right dimension, you underestimated the overall length of FMNH PR 2081, later today, I will direct use photoshop to cut out the drawing from Brochu's 2003 Osteology paper and make recosntruction the skeleton my self and see what happens.

[1]Osteology and ecology of Megantereon cultridens SE311 (Mammalia; Felidae; Machairodontinae), a sabrecat from the Late Pliocene – Early Pleistocene of Senéze, France

No competing interests declared.

RE: Reply to reply by Hutchinson (11-15-11) and comment to Celestist

Celestist replied to gspauldinodotcom on 10 Feb 2012 at 01:53 GMT

The smaller abdomenal cavity in your reconstruction ( personel I felt yours is more accurate) will also affect body mass

I made a drawing from photoshoped picture from 2003 paper on FMNH PR 2081, my reconstruction is actually quite close to yours, only 3-4% longer, the torso is much smaller than Hutinchson's, probably becasue of the inflated ribs cage in the original skeleton. the tail is little bigger than his, but the torso is a lot smaller,

Torso 3500kg + Head neck 1000kg + 2800kg Hindlimb + 1500kg tail = 8800kg.....?

Thank you for your comment

No competing interests declared.