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.

References
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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.
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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.