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'''''Tyrannosaurus''''', '''the Lean Killing Machine - Gregory S. Paul'''

Posted by gspauldinodotcom on 22 Oct 2011 at 19:52 GMT

This researcher had previously carefully prepared skeletal restorations with muscle profiles of the Tyrannosaurus labeled Sue and Stan using photographs and measurements of the remains, and following consistent anatomical criteria that maximize the cross comparability of individual specimens (see figure link below). The dorsal ribs are swept caudally because this posture is preserved in numerous articulated dinosaur skeletons including tyrannosaurs, a posture that minimized the volume of the trunk [1, 2]. Plasticine volumetric models measured by water immersion produced mass estimates of 6100 kg for Sue and 5700 kg for Stan assuming a specific gravity of 0.85 [2]. The modest difference in mass between the two specimens is logical since the two skeletons are very similar in dimensions; the femur of the larger skeleton is only about 2% longer than that of Stan, and total skeleton lengths are about the same (it is not possible to precisely restore total length, all the more so since neither specimens’ tails are complete). If the two skeletons were mounted in an identical manner and placed next to one another it would be difficult for a viewer to distinguish them in form and size. An attempt to achieve a maximum plausible mass by applying as much plasticine as appeared anatomically plausible (considering that predators bear minimal soft tissue mass not dedicated to improving hunting success) to a second model of a previously modeled Tyrannosaurus specimen boosted the tonnage by only about a tenth. My skeletal restorations affirm that Tyrannosaurus is notable for the enormous size of its head both absolutely and relative to its body, while tyrannosaurid tails are reduced compared to other large theropods especially distally. In Sue the mandibles are 6-8% longer than the femur [Append. 2 in ref. 3 and my photographs].
Hutchinson estimated the mass of a number of Tyrannosaurus skeletons that were mounted by varying teams using differing anatomical criteria of sometimes dubious validity, reducing the opportunity to obtain maximally reliable and comparable results. The extreme discrepancy in body forms of the adult specimens in their Figs. 2, 4 and especially 3 greatly exceeds the variation seen within a given species or even genus. There are multiple reasons for these discrepancies. To ease removal for study the dorsal ribs of the original mounted skeleton of Sue utilized by Hutchinson et al. as they note were set too far laterally, and worse are swept strongly cranially, greatly inflating the volume of the trunk. Making matters worse are proportional problems with their scanned skeleton of Sue. The side view digital image of the Sue skeleton in the Hutchinson et al. Fig. 3 appears proportionally off kilter, with an untyrannosaurid small skull and inflated tail. More precisely the mandible is about 6% shorter the femur which cannot be correct (I use the mandible because both ends or easily determined in their Fig 3, the caudal ends of the skull are more obscure amidst the first cervicals). The tail is significantly larger than those of the other specimens with their more modest distal caudal series in their Fig. 3, this too cannot be correct. The Sue scan somehow became skewed in a manner that inflated the caudal section at the expense of the cranial end of the great avepod (perhaps the track of the scanner approached closer to the midline of the skeleton as it moved caudally). The other scanned skeletons appear to be more in accord with the actual dimensions of the fossils.
The minimum mass estimate for Stan of 5900 kg by Hutchinson et al. is not statistically distinct from my result. Also plausible is their 5800 kg minimum for the MOR specimen (which I have not restored) since its dimensions are broadly similar to those of Stan and Sue. That these specimens were more correctly mounted and accurately scanned is probably responsible for this accord in results. The far higher 9500 kg minimum for Sue is highly anomalous. It is at best very unusual for mass to vary by 50% in wild individuals whose dimensions differ by just a few percent. A comparison of their computer generated minimum volumetric model profile to my skeletal/muscle profile of Sue (see figure link below) shows that the volume of the trunk in their version is far greater than that of mine at least in part because of the incorrectly mounted ribs, and their tail is multiple times larger partly because of the enlarged caudal series. The overall impression is much too bloated for a predator that should be lithe compared to its prey. The Carnegie skeleton is too incomplete to warrant a volumetric restoration, but its dimensions are similar to those to Sue and Stan so its mass should have also been in the 6 tonne range, rather than at least 7400 kg. Their minimal mass of 640 kg for the juvenile Jane is very close to mine of 610.
The methodology employed by Hutchinson et al. produces inconsistent results among adult Tyrannosaurus whose similar skeletal dimensions strongly suggest they weighed about the same. It must be concluded that the exceptionally high Hutchinson et al. mass estimate for Sue is excessive by about 50% both in absolute tonnage and relative to other large adults, partly due to errors in the Chicago mount and their scan of the same. I am not aware of a Tyrannosaurus specimen that is markedly larger than those discussed herein. In that case a number of large adult Tyrannosaurus specimens share similar adult mass of around 6 tonnes, about the same as typically large bull African elephants, including the famed Jumbo [2]. There is no fossil evidence that any tyrannosaurid approached the 10 tonnes that may be reached by the occasional world record African elephant. This does not exclude the possibility that some avepod species did so. The over minimum mass estimates up to 18 tonnes are not viable for Tyrannosaurus or any predaceous dinosaur that is likely to have lived.
The tail-heavy restoration of Sue will bias attempts to use it restore its center of mass. But whether it is possible to accurately restore this factor in extinct organisms, whose actual distribution of volume and mass is long lost and probably unrecoverable when slight shifts in these factors can result in major differences in results, is an inherently dubious proposition. Mass restoration of fossils is always a ball park project.
So no method can ensure precise results for extinct creatures whose individual weights fluctuated substantially over the normal course of their adult lives. But lower tech physical volumetric models continue to remain competitive with digital techniques for restoring the masses of extinct organisms, and it should not be presumed that digitally scanned imagery is dimensionally accurate unless it has been checked against direct measurements and/or conventional photographs.

The figure link is at -

All images to same scale, bar equals 2 m. From top to bottom, my skeletal restorations with muscle profile of Stan and then Sue, solid extract profile of Sue with head and limbs removed to compare to same of the minimum but much bulkier Hutchinson et al. version of Sue (from their Fig. 3).

1. Paul, GS (2010) The Princeton field Guide to dinosaurs. Princeton: Princeton University Press.
2. 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.
3. Brochu, CA (2003) Osteology of Tyrannosaurus rex. Journal of Vertebrate Paleontology 22 (4 suppl): 1-138.

No competing interests declared.

RE: Tyrannosaurus, the Lean Killing Machine - Gregory S. Paul

JohnRHutchinson replied to gspauldinodotcom on 15 Nov 2011 at 10:37 GMT

We thank Paul for his thoughts on our paper on growth in "Tyrannosaurus rex". Many of his points such as the uncertainty in estimates of body shape, mass and centre of mass were already pointed out and quantified in our paper, so we will not reiterate those here except to note that those uncertainties apply just as fully if not more to all other methods, including the scale model approach that Paul favours.

Paul’s point about caudally swept ribs in theropods being the “correct” articulation is presented as fact rather than assumption. Paul assumes that animals must minimize their trunk volume and thereby chooses rib angular orientations that do this. While we agree that this can be accommodated to some degree by the arrangement of costal articulations in the trunk vertebrae of "Tyrannosaurus", there still remains a range of interpretation feasible for what articulation will obtain the “correct” level of caudal inclination of the ribs, as refined by a recent study [1]. As stated in our paper, the current mount of Sue is overly barrel-chested, but this is not the result of design for the ease of bone removal as Paul assumes. Rather, it is a result of both the preservational distortion that is inevitable even in a specimen as well preserved as Sue, the wide latitude that exists in re-articulating skeletons of extinct taxa, and the truly massive volumetric dimensions of the bones, which are easy to overlook when modelling from linear dimensions alone. Digital articulation of the skeleton using scans of individual bones indicates that even with trunk ribs backswept to the same caudal angle as the respective transverse processes they articulate with, relatively minor changes in maximum rib cage width are achieved. The very reason that use of scan data is superior to scale models is that real skeletons are constrained by the physical dimensions of the bones and their articulations. They are not victim to the countless implicit assumptions, adjustments, and accommodations of skeletal anatomy that any scale model involves, which may cumulatively have a huge potential effects. Indeed the high, near vertical position of the scapular blade reaching the vertebral column in Paul’s reconstructions is incompatible with the curvature of the ribs and scapulae, and serves to illustrate how easily inaccuracies can make their way into 2D reconstructions based largely on linear measurements. We explicitly noted in our paper that the mounted skeletons of the Carnegie and Sue specimens had articulations that were implausibly laterally extended, and took this into account in our estimates.

Paul seems to have missed an implicit point of our analysis when he states that we had “varying teams using differing anatomical criteria of sometimes dubious validity, reducing the opportunity to obtain maximally reliable and comparable results.” We did not conduct an exhaustive re-articulation of our specimens’ skeletons, or correct errors in proportions due to lack of preservation, etc., because these errors illustrate important points. It might be tempting to rely on mounted skeleton morphology, even for complete skeletons, as reliable subjects for 3D scanning and reconstruction, but many sources of error can creep in, only some of which are due to specimen completeness/articulations/proportions. We found it interesting to try to tease apart what errors were introduced by those specimen-based errors vs. more methodological errors (e.g. investigator bias). We would hope that researchers would agree that maximizing the amount of objective anatomical criteria and minimizing speculation (i.e. subjective errors/investigator biases) should be a goal for the field, and we and others have done that for the tail (discussed below) and other structures noted in our other papers. But the goal of our analysis was not to produce the most perfect reconstructions of articulated dinosaurs ever. Indeed that goal may be less effective in maximizing reliability of reconstructions, because the subjective sources of error are so pervasive. No one knows how far the flesh extended beyond the skeletons of dinosaurs, and to a certain degree the detailed articulations of the bones will have little influence on body mass estimates because of this.

While Paul is correct that digital models could introduce errors due to distortion of 3D images by improper use of scanning equipment, on further investigation we find no evidence that this happened with our specimens. Our figures noted that the images were not to scale, but Paul has taken measurements from them anyway. We checked the lateral view images used in the figures and found that the views were not perfectly orthographic (the Blender software used to make the figures defaults to a simulated perspective view when rendering), but we had not intended them to be so as they were merely used to illustrate scan and specimen quality. This seems to be the source of the apparent distortion that Paul notes, but it is not present in the actual 3D models that we used to do any of our calculations. Indeed, by checking our 3D scan data we find that the ratio of left mandible/left femur length is 1.063, which compares very well with the hand-measured ratio of 1.066 from [2]. The problem lies in uncritically taking measurements from figures that are not intended for such usage, than in any skewing of the Sue scan.

In stark contrast to our paper, in which initial assumptions, sensitivity to degrees of ‘fleshiness’, and investigator biases are quantified and discussed, Paul provides scant details on his modelling approach. His studies fail to provide basic information such as the scale of the models he used for volumetric displacement measures, the accuracy of those measures, or how he modelled underlying skeletal architecture beyond figures that show only two of the three relevant dimensions for volumetric calculations. Moreover, as noted above some of the aspects of Paul’s reconstruction are disputable based on either fossil or anatomical evidence. He presents a thin tail reconstruction with muscle confined to the lateral faces of the neural spines and haemal arches, which is discounted by recent studies [3,4] documenting that non-avian sauropsid tails are more massive and muscular than their skeletons indicate. Hence his reconstructions conflict in at least one regard where subjectivity has been reduced by anatomical study; i.e. by the quantitative tail shape reconstruction method of Allen et al. [3].

Another questionable aspect of Paul’s reconstructions is the ‘tucked’ belly, in which the gastral cuirasse follows a ventrally concave curvature. This curvature is observed in a few theropod specimens; especially ornithomimids (e.g. American Museum of Natural History specimen PR 5017); found in the classic opisthotonic death pose, but presumably is an artifact of that pose. Many of other well preserved skeletons, including tyrannosaurids, show that the gastralia extended in a straight line from the pubic boot to the sternum or near the coracoids. Good examples of this include two specimens of "Gorgosaurus" ([5]; Royal Tyrrell Museum of Palaeontology 1999.033.0001) as well as ornithomimids [6], dromaeosaurids, and the Paris specimen of "Compsognathus".

Paul mentions a more massive whole body reconstruction that he produced by adding flesh limited by the assumption that 'predators bear minimal soft tissue mass not dedicated to improving hunting success' or that 'a predator... should be lithe compared to its prey'. While such assumptions may be attractive, we are aware of no documented quantitative scientific evidence supporting such anecdotes, but it certainly would factor into subjective investigator biases like the ones mentioned above. As our paper noted, some investigators implicitly favour more skinny dinosaurs, some do not. We presented a wide range of models covering both extreme ends of this continuum. That Paul finds our minimal mass estimates (from our skinniest models) to match his reasonably well in some cases is not necessarily a sign of accuracy or 'not statistically distinct' measurements for either method, but rather a clear example of that investigator bias, which in this case could be considered confirmation bias. Consistent mass estimates between investigators could either be accurate, all wrong, or coincidence –defining optimality criteria is very difficult for such parameters.

We agree that the differences between our Sue mass estimates and our other adult tyrannosaurs are interesting, but it seems Paul is reading them too literally. Like any approach should, our mass estimates have a range of uncertainty encapsulated by minimal mass models on one end of the spectrum, and (as an extreme that we admitted in the paper is excessive) maximal mass models on the other end. A goal of future research should be to objectively reduce that maximal mass extreme closer to the minimum. But until then, it is unclear how much heavier Sue was than other adult tyrannosaurs. We agree that we do not know how large tyrannosaurs or other theropods grew to be. Paul contradicts his earlier work [7] by asserting that no tyrannosaurs exceeded 10,000 kg. We are not so confident in that assertion; there is no clear evidence for or against this notion. Likewise there is no conclusive (i.e. statistical) evidence that other large theropods were necessarily heavier; sample sizes for most theropods are too small to make conclusions about population-level variation. Our paper stated that the ~18,000 kg estimates for our Sue specimen were not plausible, so we see no argument there with Paul. Our point was that it is unknown how wide the upper ends of the 'error bars' for specimen-based mass estimation are.

We agree with Paul that no method is perfect for estimating body masses or dimensions in extinct dinosaurs, and have explored that point in many of our prior studies. However, that does not mean that all methods have equivalent reliability, or that science cannot proceed to diminish the level of uncertainty in any methods. Indeed, users of scale models have contributed little or nothing to check the errors inherent in their models, apply them to extant taxa of known mass, assess individual variability or ontogenetic changes, contribute data on densities of extant taxa, or check investigator biases and errors caused by preservation, as we have done for digital volumetric estimates [3,8-12]. To become competitive, users of the scale model method need to explicitly outline its procedure and scrutinize its accuracy and repeatability. The scale model method Paul cites on his website, commentary, and other studies is far too vague in its methodology to meet these criteria.

We thus find it curious that Paul concludes that scale model methods 'remain competitive' with digital methods, implying equivalent overall accuracy or effort invested in critically evaluating their reliability. Scale models involve the same level of subjectivity in estimating body outlines from skeletal dimensions, and as we have noted in our previous papers [3,8-12], this subjectivity is probably the major source of error in these estimates. But we find it extremely implausible that scale model and digital mass estimate methods have the same accuracy. Extra steps involving human hand-measurements are involved in building scale models: the skeleton must be measured by hand (including from photographs; involving errors in parallax or camera angles) with a series of 2D measurements to represent the 3D shape (e.g. digital callipers of perhaps 1 cm accuracy at best when used to measure long bones; vs. digital methods that can approach 0.1 mm accuracy for fully 3D representations), then those skeletal measurements must be represented in drawings or sculptures to represent scale models (involving an unknown level of inaccuracy in scaling hand measurements to artwork reconstructions), then those scale models must be scaled up mathematically to represent the real specimen (multiplying up any earlier errors by the scaling factor; e.g. 1/20 scale models will have 20x amplification of human hand/eye measurements, which for linear measurement would then be cubed when making volumetric estimates—e.g. 20% errors could become a 1.23=173% volumetric error). Mallison [13-15] has shown how Paul’s reconstruction technique can result in considerable errors, in which dorsal and lateral view reconstructions do not match up when the same specimens are articulated in 3D digital models—errors in bone angles, dimensions and articulations are easily introduced. This is a technical problem of accuracy that is separate from investigator anatomical expertise; it is an obvious limitation of the manual reconstruction method.

Estimates of dinosaur body dimensions still have plenty of room for improvement. Manual measurements of dinosaur skeletons will always be important for basic data collection and analysis, but the digital era permits far more accurate 3D representations of 3D specimens to be made. We contend that the scale model method is far behind 3D computational methods because of this greater accuracy of digital approaches and the cautious application of computational analyses to date. While it may always be salutary to compare the results of scale model, 3D computational, bone scaling, and other methods of mass and body dimension estimation, scale model users have a lot of catch up work to do before they are on equal scientific footing with more explicit quantitative methods that leave less, though still considerable, room for human error and subjectivity.

1. Hirasawa T (2009) The ligamental scar on the costovertebral articulation of the tyrannosaurid dinosaurs. Acta Palaeontologica Polonica 54:49-59.
2. Brochu CA (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.
3. Allen V, Paxton H, Hutchinson JR (2009) Variation in center of mass estimates for extant sauropsids, and its importance for reconstructing inertial properties of extinct archosaurs. The Anatomical Record 292: 1442–1461.
4. Persons WS, Currie PJ (2011) The tail of "Tyrannosaurus": reassessing the size and locomotive importance of the M. caudofemoralis in non-avian theropods. The Anatomical Record 294: 119–131.
5. Lambe L (1917) The Cretaceous theropodous dinosaur "Gorgosaurus". Memoir of the Geological Survey of Canada 100: 1-84.
6. Sternberg CM (1933) A new "Ornithomimus" with a complete gastral cuirasse. Canadian Field Naturalist 47: 79-83.
7. Paul GS (1988) Predatory Dinosaurs of the World. Simon & Schuster, New York.
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13. Mallison H (2007) Virtual dinosaurs- developing Computer Aided Design and Computer Aided Engineering modeling methods for vertebrate paleontology. 102 pp. Unpublished Ph.D. thesis. Eberhard-Karls-Universität Tübingen, Tübingen. http://tobias-lib.ub.uni-...
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No competing interests declared.

Sue's ribs

cabrochu replied to gspauldinodotcom on 15 Nov 2011 at 12:34 GMT

Paul made the following comment: "To ease removal for study the dorsal ribs of the original mounted skeleton of Sue utilized by Hutchinson et al. as they note were set too far laterally, and worse are swept strongly cranially, greatly inflating the volume of the trunk."

Although he is correct in stating that the ribs on this specimen are not mounted in a completely accurate anatomical position, ease of removal was not the only reason. An even larger concern was distortion to both the ribs and the vertebrae. Articulation surfaces on the vertebrae were displaced dorsoventrally, and the rib shafts were no longer aligned as they would have been in life. Correcting all of these problems would have involved far more destructive manipulation than was deemed appropriate.

A choice was encountered when assembling the specimen - mounting the ribs accurately, or mounting them so that they actually looked like a rib cage.

No competing interests declared.