Tyrannosaurus rex "Goliath"

[Vladimír Socha]

Good day to everyone! I was wondering, how big could this T. rex specimen be, based on femur that is 137 cm long (141 cm if complete) and has a circumference of almost 65 cm. Some lay estimates go as high as 13.1 meters and 12.4 tonnes. Is anything new and will it be published? Thank you, in advance. VS.

[Mickey Mortimer]

First step- someone has to buy it from BHI (probably).

Mickey Mortimer

[Isaac Wilson]

Oh, if I had $500,000... (I have no idea how much it's selling for)

That being said, Brian Curtice measured the femur at my request, so we at least have the measurements verified. If you want to use circumference allometry, Campione and Evans' bipedal equation would predict a mass in excess of 11,000 kilograms, but it's worth noting that this equation typically results in lower masses for theropods than more precise volumetric methods.

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[Gregory Paul]

As my nifty Table 2 in the Supplementary accompanying Mesozoic paper shows, the longest femora to date have been -- Stan 1350 mm, Scotty 1333, Sue 1321. My trusty volumetric models are about the same for all three of them at ~7.5 tonnes  (see the mass table at the Princeton U Press website for my Predatory Dinosaurs Field Guide) in the hungry lean-healthy condition expected in predators on the hunt, significantly higher values for these specimens are excessive. A 1410 mm femur implies a mass 15-20% higher, maybe 8.5-9 tonnes. But there is a lot of slop in these figures so don't take that too literally. 

Robust Scotty (T. rex) and Sue (T. imperator) femur circ is 590 and 580, for gracile Stan (T. regina) it is just 505. The 650 mm circ for a 1410 mm long femur puts it in the robust category. Never use femur circ to estimate mass when sufficient material is on hand to do a rigorously executed profile-skeletal, circ/mass ratios are very variable. 

GSPaul

On Wednesday, July 2, 2025 at 10:02:37 AM EDT, Vladimír Socha <vladimir....@gmail.com> wrote:

Good day to everyone! I was wondering, how big could this T. rex specimen be, based on femur that is 137 cm long (141 cm if complete) and has a circumference of almost 65 cm. Some lay estimates go as high as 13.1 meters and 12.4 tonnes. Is anything new and will it be published? Thank you, in advance. VS.

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[Isaac Wilson]

Thanks for the response, Greg. I'm curious as to your specific methodology for restoring Tyrannosaurus specimens as so thin compared to the majority of other expertly-constructed volumetric models, especially those in the literature (Bates et al 2009; Hutchinson et al. 2011; Snively et al. 2019; Hartman 2020; Dempsey et al. 2025) in addition to independent volumetric reconstructions (Paes, Folkes). I certainly agree that volumetry is a superior method when sufficient material is available, but clearly there's subjectivity in how much soft tissue is added, given how your reconstructions for Tyrannosaurus place the biggest specimens as 2-3 tonnes lighter than the expert consensus. I'd point to Dempsey's AMNH 5027 as a particularly poignant illustration of this: in terms of skeletal dimensions, AMNH 5027 is notably smaller than either Sue or Scotty, but Dempsey's painstakingly reconstructed model that takes individual musculature and skeletal proportions into account arrives at well over 7,000 kilograms. I'd love to hear your thoughts and rationale.

Isaac

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[Franco Sancarlo]

I'm not gregory s paul, but Bates et al 2009 makes bellies look like they're full of air, Hutcinson et al 2011's models are mostly unnatural. I haven't read Snively et al 2019 so I can't tell you. I don't know what density Hartman used and the models used but in 2021 Larramendi et al changed a lot of things. Dempsey et al 2025 has already received a response from Paul. Dan Folkes and Paes's models are great but they have a pot-belly belly which is when the animal is full of air so the volume changes a lot. The belly went from a pot-belly to a classic position with breathing (CLAESSEN 2004 Dinosaur gastralia: Origin, morphology, and function). Plus, it seems to me that Paul had already done studies in the past on how to best reconstruct a dinosaur. But honestly, he has to confirm this for you

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[Gregory Paul]

For some reason folks these days seem to have gotten into restoring theropods with big bellies. As per the Zallinger Tyrannosaurus (which when I look at it the postorbital boss best fits into the T. imperator style sort of, but I digress). That is accurate actually - when the animals had gorged on a carcass and were stuffed like after TG dinner. This is something I have been warning against since Dinosaurs Past and Present and PDW but do folks care? 

Of course predators have small digestive tracts, and the bigger fast and gorge have tight bellies when hungry and on the hunt. 

https://kids.nationalgeographic.com/animals/mammals/facts/lion (see 2nd pic in series)

https://www.krugerpark.co.za/africa_lion.html

https://www.gettyimages.com/detail/photo/siberian-huskie-portrait-royalty-free-image/1220257340

And note that the lower edge of the thin latissimus dorsi humerus retractor can be seen on the flanks of the lions. They is lean mean fighting machines. As were predaceous theropods. 

I do not see a finely crafted Tyrannosaurus model in Dempsey et al. What is there is another crude convex hull thingy. And I cannot assess it because there is no lateral view with a scale bar -- is there one somewhere with the publication? Now if you want the most proportionally accurate 5027 profile-skeletal see Fig. 1E in my new Mesozoic paper (which is same as in the 2022 paper). It's dimensions have always been a bit squirrely, so I asked Carl M. at the AMNH to have someone stand directly beneath the dorsal series with a meter bar to pin those down. With that and the rise in SGs in the paper I coauthored with Asier L I am getting just shy of 7 tonnes (see the mass list with the PUP website for the Princeton Field Guide). Which is not statistically different from Dempsey et al. Using the same method with Sue, Stan, Scotty I get the 7.5 tonnes. 

What is known of this Goliath? Enough to do a profile-skeletal as per those in my Fig. 1?

GSPaul

 

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[Isaac Wilson]

I'm not certain that I'd consider modern reconstructions as "air-bellied," given how the skeletal recons I linked portray the bellies as having the ribs and gastralia as close as possible as seen in the largest living archosaurs, alligators and crocodiles. That seems a far more natural form than folding the gastralia to curve down towards the pubis like breaking the spine of a book. 

As for Dempsey's model, I failed to provide a link to the detailed version. Included are his skeletal and muscular models. The detailed recon also favors a natural, smooth ventral surface instead of jutting the pubis out from the rest of the soft tissue and warping the gastralia towards it. I'm just curious what the objective difference is between your recons and the majority of other paleontologists, apart from ecological presuppositions and anatomical comparisons to modern mammalian predators that seem more adapted for speed-based predation.

If it's not mathematical, that's perfectly fine. I just want to understand the logic behind the assumption that dimensionally elephantine reptiles were lean, mean, lion-like machines with levels of soft tissue that didn't resemble their closest non-flight-adapted relatives.

In terms of Goliath, there isn't enough material for a skeletal. It's an extraordinarily large femur collected in September 2024 that's longer and much wider than any other theropod femur collected. It's not enough material to get more than a wide range of estimates. 

Cheers, 

Isaac



Matt Dempsey - Tyrannosaurus skeletal reconstruction https://share.google/UzCpOmI4shI9znD0k 

Matt Dempsey - Tyrannosaurus muscle anatomy study https://share.google/9QFGbXrPSUtcL6hyv

BIO370-Alligator Skeleton https://share.google/4RGnVfnX1RVjhKaDD 

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[Jura]

I think the discussion thus far really encapsulates the inherent problem with volumetric mass estimates. There is a core level of arbitrary decision making taking place that has huge consequences for final mass estimates as exemplified by the now infamous, photogrammetry-based graphic-double integration from Hanns-Christian Gunga and colleagues (Gunga et al. 1995, 2008) for Brachiosaurus brancai (38–74 tonnes). Volumetric-based estimates have a history of not showing their error margins (in large part because they are hard to quantify) and I would say that even now only a few modern volumetric-density studies offer min–max values (e.g., Bates et al. 2009; Hutchinson et al. 2011).  

In contrast, extant-scaling from the minimal circumference of the proximal limb bones has the strongest statistical support (Campione and Evans 2020) coupled with a functional underpinning (thinnest region of the long bone is going to be the weakest link in that bone). Further, thanks to Nic Campione's statistical work in the original papers (Campione and Evans 2012; Campione et al. 2014), this method offers a built-in error range to it (+/- 25%). This is still a high range for mass, but it's a marked improvement over previous methods. 

Lastly, I would make note that Dempsey et al. (2025) agree with the extant-scaling equations for figuring out mass. What they were pointing out was that this method only gives you the gross mass estimate for the animal, not how that mass was distributed. Their study attempted to address this limitation by providing a means of determining regional mass in dinosaurs, which can in turn tell us something about body shape evolution.

Jason

Refs

Bates, K.T., Manning, P.L., Hodgetts, D. and Sellers, W.I., 2009. Estimating mass properties of dinosaurs using laser imaging and 3D computer modelling. PloS one, 4(2):e4532.

Campione, N.E. and Evans, D.C., 2020. The accuracy and precision of body mass estimation in non‐avian dinosaurs. Biological Reviews, 95(6):1759-1797.

Campione, N.E. and Evans, D.C., 2012. A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods. BMC biology, 10:1-22.

Campione, N.E., Evans, D.C., Brown, C.M. and Carrano, M.T., 2014. Body mass estimation in non‐avian bipeds using a theoretical conversion to quadruped stylopodial proportions. Methods in Ecology and Evolution, 5(9):913-923.

Dempsey, M., Cross, S.R., Maidment, S.C., Hutchinson, J.R. and Bates, K.T., 2025. New perspectives on body size and shape evolution in dinosaurs. Biological Reviews.

Gunga, H.C., Kirsch, K.A., Baartz, F., Röcker, L., Heinrich, W.D., Lisowski, W., Wiedemann, A. and Albertz, J., 1995. New data on the dimensions of Brachiosaurus brancai and their physiological implications. Naturwissenschaften, 82:190-192.

Gunga, H.C., Suthau, T., Bellmann, A., Stoinski, S., Friedrich, A., Trippel, T., Kirsch, K. and Hellwich, O., 2008. A new body mass estimation of Brachiosaurus brancai Janensch, 1914 mounted and exhibited at the Museum of Natural History (Berlin, Germany). Fossil Record, 11(1):33-38.

Hutchinson, J.R., Bates, K.T., Molnar, J., Allen, V. and Makovicky, P.J., 2011. A computational analysis of limb and body dimensions in Tyrannosaurus rex with implications for locomotion, ontogeny, and growth. PloS one, 6(10):e26037.

[Mike Taylor]

The Gunga et al. volumetric estimate of Giraffatitan was in a whole other category of Wrong, since it built its 3d models out of circular rather than eliptical sections. Hence (for example) a ludicrously over-wide neck.

-- Mike.

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[Adrian Boeye]

I will toss in something to consider with femoral circ. as well, with the margin of 25%, some of the newer convex hull models aren't that far off from femoral circ. estimates. Animal body mass can range pretty significantly, especially with overall body condition (things like lifestyle, nutrition, activity level etc). It is far from an ideal comparison, but some of the photos in "The Serengeti Lion" show just how widely body condition can vary, and by implication an animal's mass. As such, some mass estimates being in the upper margins as predicted by newer convex hull models may not be as dramatic a shift as it may initially appear. It's briefly touched on in the 2020 Scotty description and further fleshed out in the Dempsey et al. (2025), but these higher masses would also definitely have some serious functional implications. 

Schaller, G. B. (2009). The Serengeti lion: a study of predator-prey relations. University of Chicago press.

Persons IV, W. S., Currie, P. J., & Erickson, G. M. (2020). An older and exceptionally large adult specimen of Tyrannosaurus rex. The Anatomical Record, 303(4), 656-672.

Dempsey, M., Cross, S. R., Maidment, S. C., Hutchinson, J. R., & Bates, K. T. (2025). New perspectives on body size and shape evolution in dinosaurs. Biological Reviews.

[Russell Engelman]

> I think the discussion thus far really encapsulates the inherent problem with volumetric mass estimates

There's really been this push in recent years to treat volumetric mass reconstructions as the be all and end all, and allometric regression estimates as essentially useless (I've seen comments to that effect), but it really does seem like these methods have their own potential set of pitfalls that need to be taken into account to use effectively, just like any other method.

> In contrast, extant-scaling from the minimal circumference of the proximal limb bones has the strongest statistical support (Campione and Evans 2020) coupled with a functional underpinning (thinnest region of the long bone is going to be the weakest link in that bone). Further, thanks to Nic Campione's statistical work in the original papers (Campione and Evans 2012; Campione et al. 2014), this method offers a built-in error range to it (+/- 25%).

Something else to consider is there is systematic, non-random, non-negligable error in femoral-based body masses that's largely correlated to body construction (see cited study). Robust species have far more robust stylopodia than expected , whereas very gracile or lanky species have proportionally more gracile stylopodia than expected if the circumference of the humerus or femur was only driven by body mass. This seems to be driven by biological factors like in vivo safety factors and loading rather than a species maintaining a Platonic correlation between stylopodial circumference and body size. We estimated that proportional differences in stylopodial circumference independent of their correlation with size could be causing stylopodial-based mass estimates to be off as much as 25%, and explained a significant amount of the residual error in the estimation models. Stylopodia may not be the silver bullet people often treat it as.

https://doi.org/10.1007/s10914-023-09669-1

> this method offers a built-in error range to it (+/- 25%).

Every allometric regression equation has a built-in error range. It is just that quite often margins of error and other relevant summary statistics aren't reported when this kind of work is done for paleontology. This goes double for volumetric methods given it's almost inherently based on vibes and personal interpretation of how much soft tissue/muscle is reasonable versus something quantifiable.

> This is still a high range for mass, but it's a marked improvement over previous methods. 

This is actually very low for mass. In general, anything with an error rate of below 33% +/- the actual value is considered "good" when using allometric regression equations. Rates below 10-15% may not even be possible without aggressive use of phylogenetic comparative methods (I want to say Ruff, 1990, talks about how there may be hard limits on just how accurate we can make these equations due to sample selection?) It's just error bars are usually so ridiculously bad we just look the other way. A lot of this is due to log-transforming all of our data (and hence our error bars are log-distributed as well) and also because the cubic nature of body mass versus the linear nature of, say, total length means that error values in body mass estimates seem to balloon quick.

On Thursday, July 3, 2025 at 1:03:32 AM UTC-4 Jura wrote:

[Gregory Paul]

The Dempsey skeletal is the wrong scale according to the scale bar. The dorso-sacral series is 3270 mm, when it is actually 2920 in the 5027 mount. I know that because Carl Mehling AMNH collections manager had a person stand directly beneath the dorsal series holding a meter bar flat onto the camera - see my Fig. 1F in the Mesozoic paper for correct proportions. That indicates the volume will be overestimated by 40%. 

For volumetric models to be accurate they have to have the scale correct. Basic item. 

Also, as I note in the PredDinoGuide, when predators gorge they can take in about a quarter of their mass, which is huge. A Tyranno after dining on a three horned victim it just killed would look like the Zallinger mural version. When hungry its small digestive tract would mean the belly would be somewhat hollow of course. The notion that the theropod gastralia basket was not super flexible is correspondingly silly. As for crocs, they are mainly fishers that usually have something digesting in their bellies. And they are semi-erect, short legged quadrupedal bradyenergetic armored aquatic forms. So why do people keep looking to them as croc analogs, they are thecodont analogs. Theropods have no comparable living relations so lets move on. 

Also, although the scapcoracoids are placed OK fore and aft, it is too ventrally positioned. It is sort of floating down there with out much support on the ribs, and overlong sternal ribs. And the upper end of the blade too low relative to the dorsals. In lizards the shoulder girdle is tighter up on the chest for maximal axial skeleton support. Shallowing the chest will drop some more volume. 

Aside from the femoral retractors why is the tail so massively muscled? That is not a croc-style sculling organ, Tyranno had to be as light as possible to be a fast and agile land predator that engaged in head to head combat (as Happ showed in his spiffy paper in the Tyrannosaurs book most ignore). 

GSPaul

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[Isaac Wilson]

I wonder what Dempsey would say to that analysis of his model. That might shed some light on methodological differences, at least for that particular model, but not the numerous others cited.

If crocodiles aren't appropriate analogs as you've decided, and theropods "have no comparable living relations," why would the more distantly related lizards or lions be any better?

The argument that T. rex "had to be as light as possible" is again entirely subjective, and somewhat circular reasoning, but I do appreciate the clarification on your position. As several others mentioned there's a great deal of subjectivity involved in any reconstruction, and I now have a better understanding of your position on the topic.

Isaac

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[Gregory Paul]

I seriously doubt Dempsey had access to an accurate measurement of 5027. Osborn only had scale ratios with the figures of the elements which was common practice back then, and they are not always exact. No scale bars, no measurements. I used to scale the specimen from the classic old photograph of the mount, using the cast of the holotype femur that was put on it for scaling. Which used to be stated to by 1300 mm which is not correct. So I am the first to get a good measurement with the recent photo of a scale bar.  

Lions are long and erect limbed, tachyenergetic, fast and gorge arch land predators like Tyrannosaurus. Crocs are highy specialized aquatic fish and other small game predators. 

My argument is not circular. It is based on the sound premise that land predators don't lug around unneeded weight that would limit their attack performance. 

GSPaul

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[Vladimír Socha]

Good day, you mean the 1995 study (using laser scan, resulted in 74.42 m3 and 63 tonnes) or 2008 study with volume estimate revised down to 47.9 m3? I suppose the most precise estimates of Giraffatitan's weight are Henderson (2004), which is 25.8 tonnes, and yours from 2009, which is quite similar (23.3 tonnes). OK, you completely ruined my childhood "Brachiosaurus brancai perception" - firstly, by renaming it (albeit "Giraffe Titan" is a pretty cool generic name) and also by reducing its mass from good old Burian times estimates of 80 to 100 tonnes (e. g. Colbert) to a mere mass of four grown African elephant bulls :-) VS.

Dne čtvrtek 3. července 2025 v 12:29:34 UTC+2 uživatel Mike Taylor napsal:

[Mike Taylor]

On Fri, 4 Jul 2025 at 15:56, Vladimír Socha <vladimir....@gmail.com> wrote:

Good day, you mean the 1995 study (using laser scan, resulted in 74.42 m3 and 63 tonnes) or 2008 study with volume estimate revised down to 47.9 m3?

Yes, the first one  — IIRC they used elliptical sections in the second paper, which is why they got a much more realistic number.

I suppose the most precise estimates of Giraffatitan's weight are Henderson (2004), which is 25.8 tonnes, and yours from 2009, which is quite similar (23.3 tonnes).

Well, that is indeed the mass that I got from the GDI, but for what it's worth my gut says that's too low. Make of that what you will. At any rate, you should CERTAINLY not consider my estimate in any way definitive.

 

OK, you completely ruined my childhood "Brachiosaurus brancai perception" - firstly, by renaming it (albeit "Giraffe Titan" is a pretty cool generic name) [...]

Hey, don't blame for that name — That's Greg's doing :-)

 

[...] and also by reducing its mass from good old Burian times estimates of 80 to 100 tonnes (e. g. Colbert) to a mere mass of four grown African elephant bulls :-) VS.

Yes, it feels off. But I trust Don Henderson's work in this area more than my own, and as you point out his estimate is pretty similar, so /shrug/. I don't remember what Greg's most recent estimate is.

-- Mike.

P.S. *See*, everyone? It *is* possible to have a DMG thread that's not about that vulgar overstudied theropod.

[Gregory Paul]

In  1980 I  did a dope slap and realized I was doing dinosaur life restorations all wrong. I  was doing them as sketch art like Knight, Burian, Zallinger, Bakker (remember his erect necked terrestrial Barosaurus pair). When to do them  scientifically meant first producing a rigorous  (i.e. meticulous) profile-skeletal produced to consistent standards. It started with either Daspletosaurus or Tyrannosaurus 5027, then Centrosaurus, Corythosaurus, Stegosaurus USNM,  and when  I had some experience I took on my fav dinosaur, the trickier B. brancai. I realized I could also use the P-Ss to rigorously estimate masses. I was already skeptical of the Colbert 80 tonnes for G. brancai. One issue is that the old Janensch skeletal is  schematic, with the dorsals longer than they actually are in the 1988 Hunteria paper. My mass was between 30-35 tonnes (it is now just below the latter largely because of the increased SG values out of the recent paper on the subject (for which I tortured poor little bugs by plopping them into water to see how they floated, mostI then saved by pouring out the glass outdoors, the pest species did not survive). I also did the Carnegie Brontosaurus (it is not Apatosaurus) and it was a little over half the tonnage of G. brancai, which makes sense it not being nearly as large. This was intended to set the standards for the future that all would use, and I have published at lot on this subject since. 

Then the first paper using humerus-femur circs to calculate mass with Dale Russell as a co-author came out. I was aghast to see G. brancai at 15  tonnes and less than Bronto which was crazy. How could that be? Because the conceit of these papers is that you can take a whole bunch of mass/circ values from modern animals, mix them all up in a statistical blender, and then use the average result to apply to anything extinct that has legs. The premise being that all animals are adapted to meet the same strength factors. Which is nonsense. In those data sets the +/- errors are over two fold so that obviously have wildly differing strength factors.  

Brachiosaurs were lightly built sauropods, apatosaurs were much more massively boned and athletic brutes -- compare their tall dorsoscacrals with the much smaller ones of brachiosaurs -- with larger diameter linb bones even when the overall volume of the body was much less than that of the brachiosaurs. Thus you cannot estimate their masses with bone strength factors, have to model their volumes. Same as I showed with Tyrannosaurus with the robusts have stronger femora than the size sized graciles. A number of papers agree as are cited in my iAnnals of the Carnegie Museum and Journal of Anatomy papers.  

But the models have to be rigorously proportioned and articulated to common standards. So I was appalled by the Gunga et al. Giraffatitan because it was based on the old Janensch schematic skeletal, ignoring by way better 1988 P-S. 

When masses from bone dimensions match those from a P-S, that is nice, but it is really a coincidence. The volumetric takes precedence if the remains are sufficiently complete, and the skeletal is properly proportioned and articulated, and the SG is appropriate. 

GSPaul

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[Jura]

The original work by Anderson, Hall-Martin, and Russell (1985) was pretty good despite the limited sample set and the presence of potentially confounding outliers. 

However, we have come a long way since then and Campione and Evans (2012) tested the three major criticisms of the extant scaling method by using a much larger sample size of 200 mammal species, 47 reptile species, and eventually 161 bird species (Campione et al. 2014). In comparison, the original model by Anderson et al. (1985) covered 33 mammal species and 75 bird species. The updated model from Campione and Evans covers a larger size range, more species, and is more statistically robust, allowing the authors to empirically test criticisms of ungulate bias, postural differences, and large outliers on this scaling relationship. In all cases, they found that the combined minimal stylopodial circumference has a strong relationship to mass and is robust to differences in posture and muscle attachment (Campione and Evans 2012). Outlier taxa tended to disappear under log transformation and even removing them from the dataset had little affect on the final equation. Similarly, ungulates do not appear to drive the direction of the equation and mix into the data pool pretty easily. 

All of these results are unaffected by the higher safety factors of reptiles compared to birds and eutherian mammals (marsupials and monotremes have safety factors on par with reptiles and amphibians; Blob et al. 2014). Regardless of stance or movement, if the limbs are supporting body mass then the smallest region of the stylopodia will adjust with it in a predictable manner. This predictable manner still has slop (as does all biology), but we are far and away from the 2x error range of the past (if that's true. I've not been able to validate this). Again, a +/- of 25% is still not great, but as Russell Engelman mentioned earlier on, this is pretty damned good for a mass estimate.

Refs

Anderson, J.F., Hall‐Martin, A. and Russell, D.A., 1985. Long‐bone circumference and weight in mammals, birds and dinosaurs. Journal of Zoology, 207(1), pp.53-61.

Blob, R.W., Espinoza, N.R., Butcher, M.T., Lee, A.H., D’Amico, A.R., Baig, F. and Sheffield, K.M., 2014. Diversity of limb-bone safety factors for locomotion in terrestrial vertebrates: evolution and mixed chains.

Campione, N.E. and Evans, D.C., 2012. A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods. BMC biology, 10, pp.1-22.

Campione, N.E., Evans, D.C., Brown, C.M. and Carrano, M.T., 2014. Body mass estimation in non‐avian bipeds using a theoretical conversion to quadruped stylopodial proportions. Methods in Ecology and Evolution, 5(9), pp.913-923.

[Milo Gaillard]

To Jura:

Eh, I’m not so sure that allometry is the gold standard for body mass estimates in extinct taxa. I’m not an advanced math wiz and I’m not saying that volumetric analysis is a perfect measurement method (no mass estimate method is). However, I heard from many people who tried estimating size (including paleontologists) that allometry has tremendous error bars. Apparently it historically has a tendency to underestimate quadrupeds & overestimate bipeds.

If this is the gold standard of body mass estimation in extinct taxa, why do many people who try using it keep getting wrong and nonsensical size estimates?

Personally, I think that the method in Matt Dempsey’s paper is the best one. It’s seems to combine the best aspects of femur/stylopodial allometry & volumetric measurements, and work its way around the issues with both. Although it’s not without its limitations, obviously.

-Milo Gaillard

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[Gregory Paul]

Robust boned, short and slab sides trunked brontosaurs have higher humerus and femur circumferences than lightly built brachosaurs that have much longer, broader trunks and weighted much much more. So the limb strength factors will not give results at all in accord with reality. Scotty, Sue and Stan have very similar skeletal dimensions and models indicate they were all about 7.5 tonnes. But the femur circumferance of gracile Stan is 15% less than the two more robust species. When doing dinosaurs, as long as they are reasonably complete, volumetric is the way to go. This is also an issue when using bone ring circumferances to estimates masses for growth curves in growing dinosaurs that underwent extreme allometry with maturity. That kind of drove me nuts doing the calculations in the Mesozoic paper -- the relationship between mass and femur circumferance in Jane is wlldly different than in Stan -- you have to do a series of volumetric models to get the basic parameters, a general formula with produce extremely inaccurate results. Circumferences may work great for adult fossil ungulates, but they are not dinosaurs without ready modern analogs.  

GSPaul

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[Jura]

Your modeling approach produces surprisingly little variation in body mass even for specimens that have fairly large differences in skeletal size. Nonetheless, your proposed values of 7.5–7.8 tonnes for these three Tyrannosaurus fall in or just outside of the range of values given via Campione et al's bipedal equation using minimal femoral circumference (FC):

Scotty (FC= 590 mm). Estimated body mass = 8,870 kg (6,653–11,088)

Sue (FC = 579 mm). Estimated body mass = 8,422 kg (6,317–10,528)

Stan (FC = 505 mm). Estimated body mass = 5,779 kg (4,334–7,224)

I'm not really seeing any evidence that these stylopodial equations are being misled by bone safety factors. 

As for sauropods, the quadruped equation for Campione and Evans (2012) has Graffatitan brancai and Apatosaurus louisae hovering around the same masses (G. brancai =  29,8640–49,734 kg; A. louisae = 35,910–59,850 kg). G. brancai does appear to be a slightly lighter animal based on this and it's overall build. 

Note that these extant scaling equations align well with volumetric approaches by both Bates et al. 2016 (G. brancai = 19,717–34,830 kg; A. louisae = 21,473–38,078 kg) and Dempsey et al. 2025 (G. brancai = 40,124–54,736 kg; A. louisae = 39,112–54,432 kg). 

Regardless of the approach used it does appear that the robust diplodocid had a mass on par with the brachiosaurid. I don't see any support for G. brancai being "much, much" heavier. 

Brachiosaurus alithorax, on the other hand does appear to have been a giant (quadruped equation= 57,606 kg with a range of 42,842–72,371 kg).

[Russell Engelman]

> I'm not really seeing any evidence that these stylopodial equations are being misled by bone safety factors. 

Did you read Nelson et al. 2023? Or Romano and Manucci (2021) on Lisowicia? Or Romano and Rubidge (2021) on Tapinocanis? Or Bates et al. (2015) on Dreadnoughtus? Or Brassey et al. (2015) on Stegosaurus?

Nelson et al. (2023) pretty clearly demonstrate there is systematic error in stylopodial-based regression equations correlated with body construction. The error in femoral-based mass estimation equations is pretty strongly correlated with relative limb robustness with an r2 of like 0.7. Figure 6 explicitly shows it. This correlation might be even stronger if all variables were drawn from the same individuals and thus measurement noise was reduced, but the existing correlation is strong enough to suggest the pattern is real. It's worth noting that some of the mammalian data that produced this conclusion came from Campione and Evans 2012.

The other studies are all case studies that find little to no overlap between estimates based on stylopodial circumferences and volumetric models, despite the very large error bars in some of these cases. In the case of Lisowicia I believe the authors explicitly attribute it to the stylopodia being overly thick for the animal's size. This difference in size isn't minor but makes the difference between Lisowicia being elephant-sized versus rhino-sized in terms of mass.

Fariña et al. (1998) find stylopodial circumferences to be one of the worst performing metrics they used when estimating body masses of xenarthrans, to the point they just said the estimates could not be used.

There are also concerns limb bones circumferences may not scale log-linearly, but log-quadratically or with otherwise non-linear allometry (Campione 2017, Bertram and Biewener 1990, Biewener 1990), which would further distort methods.

I think both allometric and volumetric models can be useful, but treating any given method as flawless and not having some kind of problem is probably not a good idea.

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[Gregory Paul]

You are not looking at key data. 

As shown in Fig. 8 in the Mesozoic paper, the meticulously produced and scaled profile-skeletals of Stan (C, femur 1350 mm), Scotty (1333) & Sue (1321). They are all the same size in all major measures, and therefore share similar masses of close to 7.5. Stan is well known to be huge, with the longest femur associated with a skeleton. To propose that it's mass was a mere two thirds of the other two is laughable, helps show the highly unreliability of the FC method. It has long been know that unlike all other tyrannosaurids even when combined, Tyrannosaurus comes in very different boned robusts and graciles, with the later being more lightly built when their bones are the same length as the robusts (Stan femur 85% less than the similar length Scotty and Sue bones). That means they are more weakly constructed, even when the overall dimensions, volume and mass is the same as a robust. That pattern is common in tetrapods in which safety factors vary widely, which is why the FC method is inherently unreliable. In many cases even when applied within a species, including where sexual dimorphism is present. It is well understood that bone dimensions including FC are is not a reliable means of estimating the mass of a given adult human, it only gives a wide ballpark estimate.

In Fig. 1 in Paul & Larramendi 2023 (https://www.researchgate.net/publication/371417820_Body_mass_estimate_of_Bruhathkayosaurus_and_other_fragmentary_sauropod_remains_suggest_the_largest_land_animals_were_about_as_big_as_the_greatest_whales) are the high fidelity skeletals of Giraffatitan (femus 2090 mm) and Brontosaurus (1785) to same scale. In all regards the brachiosaur is the largest, except for the tail. In my dinosaur guides the top views of the skeletons are provided, the titanosauriform has a broader belly and pelvis. Contending that the apatosaurine was at all close to the brachiosaur in mass is ridiculous. 

As is thinking that simplostic scaling formulas can deal with the complexities of actual biology. 

GSPaul 

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[Mike Taylor]

On Sun, 6 Jul 2025 at 07:21, Jura <arch...@gmail.com> wrote:

As for sauropods, the quadruped equation for Campione and Evans (2012) has Graffatitan brancai and Apatosaurus louisae hovering around the same masses (G. brancai =  29,8640–49,734 kg; A. louisae = 35,910–59,850 kg). G. brancai does appear to be a slightly lighter animal based on this and it's overall build. 

Note that these extant scaling equations align well with volumetric approaches by both Bates et al. 2016 (G. brancai = 19,717–34,830 kg; A. louisae = 21,473–38,078 kg) and Dempsey et al. 2025 (G. brancai = 40,124–54,736 kg; A. louisae = 39,112–54,432 kg). 

I just want to say, having spent significant time with both these skeletons, that I just don't buy it. The Berlin Giraffatitan is a lot bigger than the Carnegie Apatosaurus.

-- Mike.

[Mike Habib]

As someone that has worked and published extensively on long bone biomechanics, a few notes here that may be relevant to the debate (take or leave at your discretion):

First, it’s important to note that bone circumference has a good, but by no means perfect, relationship with whole bone strength. What really matters is the distribution of compact bone, and so the cortical thickness and density are also important. The outer diameter alone does fairly well because strength is proportional to the cube of diameter. Still, cortical thickness does matter. If all the animals being compared have very thick cortices then modeling them all as solid has a low error margin for strength in bending (see for example Habib 2010). 

But note that I specified bending. For things like sauropods, especially, much of the loading is axial compression. The failure stress for bone in pure axial compression is enormous - much higher than bending (and even larger gap with torsion). So a bone in pure axial compression can be more gracile than one that experiences some bending and maintain the same safety factor. Even small differences in posture can have a substantial effect.

Then we have to consider that bone tracks in-life loading through remodeling. Safety factors in tetrapod long bones are actually remarkably consistent (with some exceptions - weird things happen with obesity, for example). Reptiles trend greater than mammals, and so forth, but they’re pretty consistent across large clades. The trick is that the safety factor isn’t relative to raw mass - it’s relative to maximum stress. So the strength is tracking maximum loading, not average loading (see Habib and Ruff 2008 for using this on birds). If you use FC of a raptorial bird to estimate mass it comes out heavy. Why? Because they’re hitting things with their feet. Hard. If you use the humeral circumference of a peregrine falcon to estimate mass you’d think its organs are made of stainless steel.

So the problem isn’t that safety factors are wildly variable, it’s that the safety factor isn’t relative to straight mass - it’s relative to maximum stress, which includes posture and behavior. And bone tracks that loading during the life of an individual. To the degree that rock climbers have measurably wider metacarpals (cool paper on this from Sylvester et al. Around 2006 I think?).

For what it’s worth, it wouldn’t surprise me if the quadruped long bone size regressions, which are based on data from mostly typical rear-loaded animals, give some weird results for more front-loaded brachiosaurids. Yes, the regression hypothetically takes that into account, but I’m not entirely convinced. It’s also quite probable that apatosaurines experienced more limb bone bending or torsion than brachiosaurids. Maybe because of posture (seems likely to me, but I’m not a specialist), or perhaps behavior (which Greg suggested earlier in the thread).

Cheers,

—Mike H.

Michael B. Habib, MS PhD
Research Associate, Dinosaur Institute
LA County Museum of Natural History
900 W Exposition Blvd. Los Angeles, 90007

Adjunct Professor, Biology

College of the Canyons

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On Jul 6, 2025, at 12:43 PM, Mike Taylor <saur...@gmail.com> wrote:



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[Jura]

On Sunday, July 6, 2025 at 8:01:42 AM UTC-5 Russell Engelman wrote:

Did you read Nelson et al. 2023? Or Romano and Manucci (2021) on Lisowicia? Or Romano and Rubidge (2021) on Tapinocanis? Or Bates et al. (2015) on Dreadnoughtus? Or Brassey et al. (2015) on Stegosaurus?

Nelson et al. (2023) pretty clearly demonstrate there is systematic error in stylopodial-based regression equations correlated with body construction. The error in femoral-based mass estimation equations is pretty strongly correlated with relative limb robustness with an r2 of like 0.7. Figure 6 explicitly shows it. This correlation might be even stronger if all variables were drawn from the same individuals and thus measurement noise was reduced, but the existing correlation is strong enough to suggest the pattern is real. It's worth noting that some of the mammalian data that produced this conclusion came from Campione and Evans 2012.

 

The other studies are all case studies that find little to no overlap between estimates based on stylopodial circumferences and volumetric models, despite the very large error bars in some of these cases. In the case of Lisowicia I believe the authors explicitly attribute it to the stylopodia being overly thick for the animal's size. This difference in size isn't minor but makes the difference between Lisowicia being elephant-sized versus rhino-sized in terms of mass.

 

Both Nelson et al. 2023 and Romano and Manucci 2019 (not 2021) discuss taxa that would fall out as outliers anyway in the original study by Campione and Evans from 2012. Burrowers and arboreal animals that use suspension locomotion (e.g., sloths) change their humeri in a manner outside the range of geometric, static, or elastic similarity. They are a known problem. 

Campione and Evans (2020) discuss the other outliers including Dreadnoughtus (Bates et al. 2015) and Stegosaurus (Brassey et al. 2015). Some of the discrepancies between volume-based reconstructions and extant scaling can be explained by the use of immature specimens for estimates of adult animals (an implicit requirement of extant scaling that has since been made explicit). The "sauropod problem" can be partially alleviated by using the quadratic form of the extant scaling equation, which seems to produce more congruent results for taxa in excess of 10 tonnes. In short, all the criticisms you raised have been addressed by that review paper. In relation to this thread, the most important part from that review paper is this:

"Comparisons underscore that (a) overall, there is prevalent consistency between VD [volume-density] and ES [extant scaling] approaches, and (b) the comparative framework presented herein is a powerful tool to      illuminate, and corroborate, the unavoidable subjectivity inherent to VD reconstructions...

VD and ES approaches are fundamentally different and should not be viewed in opposition. ES approaches provide accuracy, whereas VD approaches should provide precision. As a result, differences between these  approaches should be regarded as an opportunity to reassess assumptions – such as body envelopes, density, etc. – or identify anatomical novelties – such as apomorphically robust/gracile limbs possibly associated with particular ecologies... 

Emphatically, the results of mass estimation should never be presented as a point estimate. Errors, whether methodological or statistical need to be quantified, presented, and their knock-on effects considered."

 

I think both allometric and volumetric models can be useful, but treating any given method as flawless and not having some kind of problem is probably not a good idea.

At no point in this thread did I ever say or even imply that extant-scaling is a flawless panacea for figuring out dinosaur body mass. This ties in well with Milo Gaillard's reply as well in which it was implied that I was calling ES the "gold standard". I don't know if this is a side effect of our currently hyperpolarized society, but one need only look back at the start of this thread to see that my response was in opposition to the proposal that volume-based reconstructions were superior to extant scaling methods (see: Isaac Wilson's or Greg Paul's posts). Just because I think volume-based reconstructions have problems and that extant scaling is more versatile doesn't mean that I think that this is the only way to go, or even the preferred way to go when assessing dinosaur body masses.

So, to make things clear for future responses: Volume-based reconstructions are not superior to extant-scaling methods. They require near complete skeletons, thus limiting most volume estimates to only a handful of taxa, and many are rife with underlying problems of subjectivity in soft-tissue placement and material properties. Too often they are presented as a black box that only produces point estimates devoid of error margins, leading to an overconfidence in the resulting values. When Volume-based reconstructions are done rigorously (good documentation, validation against extant taxa, error ranges shown) they produce results that largely overlap with extant-scaling methods. When possible, both methods should be used as a crosscheck against the other. The strengths of volume-based methods are their precision and better description of mass distribution across an entire animal. Extant-scaling excels with producing masses for taxa with limited material (i.e., one or two good long bones), and have been shown to be robust against most changes in long bone shape with ecology (outliers noted above).

Finally, none  of these methods produce accurate estimates for extinct animal body masses. They only give us realistic bounds that likely contain the real value. We are unlikely to ever known the real body mass of a given extinct animal. As with electron clouds in chemistry, paleontology needs to get comfortable with this area of dinosaur biology always being fuzzy. 

Or, to quote George Box: "All models are wrong, but some are useful."

[Milo Gaillard]

To Jura:

I didn’t mean to imply that you were treating Extant Scaling as the gold standard. If anything, extant scaling seems to be divisive from what I’ve seen among both palaeontologists and paleo enthusiasts. I have seen some people treat is as the gold standard of estimating body masses (e.g., the Skeleton Crew (a YouTube channel made by actual palaeontologists) outright called it the gold standard), and I’ve seen others treat it like it’s unreliable (e.g., on an SV-POW blog post, Matt Wedel tried estimating Dreadnoughtus’ mass with extant scaling, and got implausible results; it also resulted in the mass of Acrocanthosaurus being horribly underestimated).

Without being an advanced math wiz myself, I just see it as some methods working better for certain people than others. I agree that there is no prefect size estimation method. ES & VD both seem to have their advantages and disadvantages.

That’s what I’ll say.

Thank you for reading,

-Milo Gaillard

Sent from my iPhone

On Jul 6, 2025, at 16:42, Jura <arch...@gmail.com> wrote:



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