The humerus of Brachiosaurus altithorax, part 1: the fossil
May 20, 2014
In the comments on Matt’s post about the giant new Argentine titanosaur specimens, Ian Corfe wondered why Benson et al. (2014) estimated the circumference of the humerus of Brachiosaurus altithorax instead of just measuring it. (Aside: I can’t find that data in their paper. Where is it?)
I replied:
Yes, the humerus is half-encased in a jacket, face down (we should post photos some time), which would make the circumference impossible to measure directly. But the mounted Brachiosaurus skeleton right outside the Field Museum (and the identical one at O’Hare Airport) have casts of that humerus, so measuring the circumference shouldn’t require any equipment more exotic than a stepladder. Maybe the anterior aspect was sculpted — but I doubt it, as there certainly was a time when the humerus was out of its jacket and mounted vertically.
Here is the evidence that the humerus wasn’t always in that jacket (from Getty Images):
Femur of Apatosaurus and right humerus Brachiosaurus altithorax holotype on wooden pedestal (exhibit) with labels and 6 foot ruler for scale, Geology specimen, Field Columbian Museum, 1905. (Photo by Charles Carpenter/Field Museum Library/Getty Images)
I have no idea why it was put back in a plaster jacket: does anyone?
Back in 2005, when Matt and I visited the Field Museum, the staff were amazingly, almost embarrassingly, helpful. They mounted a whole elaborate project to remove the humerus jacket from the cabinet that held it, so we could get a better look:
Unfortunately, Matt and I were doofuses back in the day: terrible photographers who knew embarrassingly little about appendicular material. So nearly all of our photos are worthless. Here is a rare nice one, showing the humerus in posterodistal aspect. You can see how layers have flaked away towards this end:
Here is the humerus in proximal view — something that’s relevant to my interests, as at tells us about the area of articular cartilage where it connected to the shoulder:
And finally — because it would be rude not to — here is Matt, going the Full Jensen with the humerus:
Next time: what we can learn about the humerus from the mounted skeleton outside the museum!
Sauropod Vertebra Picture of the Week 
May 20, 2014 at 12:13 pm
Awesome! The data for Benson et al 2014 is on the web page for the paper under ‘Supporting Information’ then ‘Dataset S1’ as a .xls file. Looking forwards to part 2!
May 20, 2014 at 12:16 pm
Thanks, Ian. I’d looked in vain is Table S1, little suspecting that PLOS’s idea of brilliant object identifiers was to have Figure S1, Table S1, Appendix S1 and Dataset S1, all separate objects.
I do love PLOS, but sometimes they can induce some pretty epic facepalm.
May 20, 2014 at 12:26 pm
Very comprehensive data reporting there by the Benson et al. team (which is what I’d expect from them). So they estimate Brachiosaurus at 56000 (based only on the femur) and Giraffatitan at 34000 (based on femur and humerus) — as in your original long comment on the previous post.
Leaving aside the absolute values, the difference seems much too high — 65% more for Brachiosaurus! — for animals that are pretty much the same size. My best guess is that this is because its estimate is based on an estimated humeral circumference, and this is done by a regression line across other animals, which of course fails to take into account the unique slenderness of brachiosaur humeri. I bet that if they did their Brachiosaurus calculation with an actual measurement of the humerus from the mounted cast, they’d get a much lower mass — maybe about 23% more than Giraffatitan, the ratio that I got by GDIing skeletal reconstructions and waving my hands. That would give them 41800 kg for Brachiosaurus, which is high but doesn’t seem completely unreasonable.
Mind you, I’d love to believe their 56-tonne estimate :-)
May 20, 2014 at 3:04 pm
i fixed the caption on that archival photo, which was copied from Getty Images–the femur is clearly that of Brachiosaurus alithorax, not Apatosaurus.
May 20, 2014 at 8:20 pm
Mike – yep, great data in and accompanying the Benson et al 2014 paper but somewhat tricky to find the specific bits you’re after!
Re their humeral estimate for Brachiosaurus – I haven’t yet figured out the method or the value for this, were you able to find these in the paper/various data files, or was the above your thoughts on how they’d probably made the estimate? Again the equation i gave in my first comment on the previous post could be solved, though not easily on my phone, to give the value they estimated for Brachiosauru. This could be checked against the reality of the casts, which I’m looking forwards to in part 2! All we need is for you or Matt to have ‘hugged’ a mounted Brachiosaurus humerus on camera, then we can measure your arm length and overlap and we have our missing number. Please say you photographed this event, as I’m sure it happened!
You mentioned your uncertainty about the methods in the previous blog entry comments, with the order of magnitude greater masses of sauropods potentially skewing things. The method does seem to hold over a range from 53grams to 6435000 grams, so 6 different orders of magnitude; I’d be inclined to think that adding a seventh order of magnitude on the top would be less of a difference than going from first to sixth.
May 20, 2014 at 8:49 pm
The method does seem to hold over a range from 53grams to 6435000 grams, so 6 different orders of magnitude; I’d be inclined to think that adding a seventh order of magnitude on the top would be less of a difference than going from first to sixth.
The problem is that the confidence intervals bow outward, away from the regression line, and they bow out rapidly as you get outside of the data that the regression line is based on. See this and this for graphical examples, or just do an image search for ‘regression line’. And that’s fine, that’s just how the math works. There’s no problem as long as people report the confidence intervals, which often get left out, especially from press releases.
May 20, 2014 at 9:05 pm
The humeri of mounted brachiosaurs are far too high to hug, sadly.
My problem with mass estimates from limb allometry is not so much the fear that extrapolation is misleading (though it easily could be) is that it assumes up front that all these critters were equally athletic — which we know is not true for closely-related extant animals. If you want to figure out the athletic indicator of Alexander, and you’re using a mass estimate based on limb bones, you’ll get a tautological answer.
May 20, 2014 at 10:56 pm
Matt, re CI’s in allometric relationships, the Campione paper gives both the 95% CI and 95% prediction error of their limb allometric best fit, which was extraordinarily tight over 6 orders of magnitude of body mass (here: http://www.biomedcentral.com/1741-7007/10/60/figure/F4).
So the CI would bow out beyond the measured dataset but nothing like as dramatically as your two examples (The linear measurements are over 3 orders of magnitude, and going from elephant to sauropod roughly doubles the linear measurement so just a nudge on the log scale).
Mike, that dataset includes animals with sprawling as well as graviportal gait and seems to hold true for most tetrapods excepting hopping mammals and burrowers, so athleticism may not be too big an issue.
Using the allometric equation employed by Pol & friends I make the new Argentinian beast out to have a femoral circumference CF of about 107.5 cm (reported humeral circumference CH of 79cm and reported mass estimate of 77t). Which is not only significantly smaller than the Argentinosaurus femur, but also works out as a CF/CH ratio of 1.36 – which seems extremely high. Something ain’t right there, since they seemed very confident their find would beat Argentinosaurus; you wouldn’t do that unless you had a thicker femur would you? So do they also have a bigger humerus somewhere…? questions questions…
By the way I have it on good authority that dozens of vertebrae were recovered from the dig. Read it and weep.
May 21, 2014 at 4:55 am
Kattato, I agree with all of that. My point is that there is still a 95% confidence interval, and because it’s a log scale even if the CI is pretty tight, it’s going to span a lot of potential masses. So far for the new animal we’ve got one number. I’d just like to know how far the uncertainty goes. Your points about the oddness of the humeral and femoral numbers are well taken. As for the vertebrae–bring ’em on! I want to see how they stack up against Argentinosaurus, Puertasaurus, Futalognkosaurus, Alamosaurus, etc.
May 21, 2014 at 6:32 am
Matt – agreed, an unlogged version of that graph would give a better ‘realworld’ feel for how high that uncertainty is and what that means in absolute numbers. I do agree with Kattato that the 95%CI and PE on the graph do look very tight even for logged data.
Mike – how have people worked out athletic indicators for extinct taxa in the past, if not using mass estimates using limb bones? (I guess you could use skull or toothrow or tooth sizes for non-dinosaurian taxa i.e. mammals where these are fairly constant within large clades, or volumetric mass estimates though I think these are generally rare especially outside of dinosaurs).
Kattato – we had a figure in the comments of the previous post of 1040mm for femoral circumference of the new beast using the equations, so already there are errors creeping in :-) Did you use the equation 1 or 2 of Campione & Evans, the one I quoted and I think CoherentSheath used was equation 2. This was used by Campione & Evans 2012 but Benson et al 2014 used equation 1, so i.e. the weights of Giraffatitan are slightly different (35780 for C&E2012, 34000 (rounded) for B2014).
Something I wondered in comments on the previous post was whether we actually have any info on whether Pol et al are using the same method to give 70t for Argentinosaurus or some other animal. This is especially the case given the complete lack of humerus which would then have to be estimated from scratch unlike the Brachiosaur humerus which at least can be estimated from a half jacketed specimen or a possibly real, possibly partially sculpted cast… Could they have come up with a taxon for which femur and humerus can both be measured that is bigger in these dimensions (and thus heavier) than Brachiosaurus, but smaller than the Argentinosaurus, and so are not comparing at all with Argentinosaurus? Do they explicitly state that somewhere or is that us/media assuming this is the case? Diego did state explicitly in the BBC video that they were measuring the largest (at least longest!) humerus of the new animal…
Diplodocus longus gets a CF/CH ratio of 1.20 and Giraffatitan 1.12 which is perhaps the opposite of what we might expect from the seemingly gracile humeri of brachiosaurs Mike mentioned earlier. Does this not apply to Giraffatitan in the same way as it does for Brachiosaurus altithorax? Comparing the top photo in this post for B altithorax with https://svpow.files.wordpress.com/2013/11/fig1-giraffatitan-skeleton.jpeg fir Giraffatitan that may be the case, with the latter having more equal diameter proximal limb bones than Brachiosaurus. Alternatively it may be a visual illusion: is the Brachiosaurus femur in the top pic above relatively rectangular and flattened versus a circular humerus (at least for the midshaft, with the flared ends contributing further to the illusion), meaning we see a difference but the circumference numbers suggest less of one?
May 21, 2014 at 9:40 am
Ian, Alexander (1989:52-59) uses Z/Wx as an indicator of athletic ability for a specific bone, where Z is the section modulus of the bone (a quantity that captures its size and shape relative to the direction of force), W is the weight of the animal and x is proportional to the length of the bone.
For the femur, tibia and humerus of various animals, he gets values ranging from 7-11 in an African elephant, 21-22 in a buffalo, 3-5 in Diplodocus, 6-14 in Apatosaurus, 12-21 in Triceratops, 18-44 in the ostrich, 15 in humans and 9 in Tyrannosaurus. (All values in square meters per giganewton) This seems like an interesting value to calculate, and I wonder if his work has been superseded? I don’t recall seeing anything similar, but that would be surprising given that this work is a quarter of a century old.
To determine W, Alexander used volumetric methods. (Flawed, in this case, since the models were mostly rather poor, but still.) You could equally use GDI. What you can’t do, meaningfully, is use a mass estimate based on the dimensions of the limb bones whose measurements you’re about to compare with that mass estimate.
On the methods that Pol et al. are actually using — does anyone know Diego or another member of the team, and can invite them to come on here and comment? I worry that we’re in danger of building an edifice of speculation and supposition based on the few factoids reported in the press. Much better to get it from the horse’s mouth if we can.
I am very surprised at the idea that CF/CH in Giraffatitan could be as low as 1.12 when the femur is twice as wide as the humerus. I guess I’ll post images in a few days. You’re right that the photo is misleading: the femur and humerus have similar anteroposterior widths but very different transverse widths.
May 21, 2014 at 10:31 am
Mike – I suspect Diego will say wait for the paper for the methods and data, even though he is a friendly guy by all accounts! This I think has mostly been us messing around to figure out what we can while we, er, wait for the paper. We may well be constructing a rather shakey sauropod mass estimate based edifice. But that’s part of the fun isn’t it…
Not having read Alexander 1989, his Z is maybe a better proxy even than the minimum circumferences used here, though more difficult to calculate (lots and lots of laser/CT scans perhaps needed?). Campione & Evans note that minimum circumference itself is a proxy for cross sectional area as it’s easier to measure, and a value that adds the shape and orientation might be a even better proxy but again harder to collect the data for.
More generally, some more on the CF:CH ratios Kattato bought up:
The actual values for Giraffatitan are femur minimum circumference = 730mm, humerus minimum circumference = 654mm – does that look anywhere near correct? I guess these are 3D measurements we are trying to extrapolate from 2D images, and what looks like a 2x wider femur in a photo may not relate well to the minimum circumference when you’re sliding a tape around it. Didn’t someone (Heinrich?) scan HMN SII; you could get the minimum cross sectional areas nicely from those!
Diplodocus longus is a different specimen in Benson et al 2014 to that used in Campione & Evans 2012, the ratios in my last post are for the latter. For Benson, we get:
– Diplodocus longus = 1.22 (larger individual than Campione & Evans but very similar ratio)
– Diplodocus hayi = 1.26
– Diplodocus carnegiei = 1.46
Similarly, for Apatosaurus:
– Apatosaurus excelsus = 1.25
– Apatosaurus louisae = 1.32
Apatosaurus ajax = 1.23
Barosaurus = 1.23
Amargasarus = 1.39
Dicraeosaurus = 1.65
Europasaurus (small brachiosaurid) = 1.05
Giraffatitan = 1.12
Brachiosaurus = ?
Cedarosaurus = 1.33
Given Europasaurus & Giraffatitan form successive outgroups to (Brachiosaurus + Cedarosaurus) in the D’Emic 2012 phylogeny (see https://svpow.com/2013/01/23/and-that-ladies-and-gentlemen-is-why-you-code-brachiosaurus-and-giraffatitan-separately/), it looks like perhaps a directional evolution trend within Brachiosauridae (very small sample size!). (By the way, you can’t use the phylogeny to say Brachiosaurus should be intermediate between Giraffatitan & Cedarosaurus, since Cedarosaurus clade and Brachiosaurus can be switched in position and there is no data for the other Cedasaurus clade taxa.)
Some more:
Saltasarus, a derived titanosaur = 1.13
Alamosaurus, a titanosaur = 1.12
Opisthocoelicaudia, a titanosaur = 1.20
Rapetosaurus, a titanosaur = 1.14
Lourinhasaurus, a macronarian = 1.44
Jobaria, a macronarian = 1.41
Turiasaurus, a non-neosauropodan eusauropod = 1.12
Mamenchisaurus constructus, a non-neosauropodan eusauropod = 1.14
Mamenchisaurus youngi, a non-neosauropodan eusauropod = 1.28
Plotting these onto a sauropod phylogeny in my head gives a confusing distribution! I don’t think it is related too well to body mass either.
The 1.36 for the new beastie then is within the range (1.20-1.46) of a single genus, Diplodocus, and well below the maximum of Dicraeosaurus. That’s a moderately wide range, but assuming the error of the measurements is reasonable, and they should all be actual measurements not estimates, then the 1.36 for the new animal also seems reasonable.
Finally, some of the data above suggests that the gracility index of Taylor 2009 (max length divided by minimum transverse width) is related to the length, and shape, of the humerus, and doesn’t capture the relative circumferences of the femur vs humerus (i.e. the relative gracility of femur vs humerus, and so possibly the relative load bearing proportions of fore- and hind-limbs). This is probably self evident though I was thinking about it in terms of fore- vs hind-limbs. E.g. Giraffatitan has the highest gracility index of all known sauropods for the humerus (9.19), but relatively low femur:humerus minimum circumference ratio (1.12, though as Mike points out, this perhaps doesn’t look right).
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