Sauropod Vertebra Picture of the Week

In the paper describing the new giant titanosaur Dreadnoughtus, Lacovara et al. (2014) use the limb bone allometry equation of Campione and Evans (2012) to derive a mass estimate for the holotype individual of 59.3 metric tons. This is presumably the “middle of the road” value spat out by the equation; the 95% confidence interval on either side probably goes from 40 to 80 metric tons or maybe even wider.

I decided to see if 59 metric tons was plausible for Dreadnoughtus by doing Graphic Double Integration (GDI) on the published skeletal reconstruction and body outline (Lacovara et al. 2014: fig. 2). The image above is the one I used, so if you like, you can check my numbers or try your hand at GDI and see what you get.

First up, I have to congratulate Lacovara et al. for the rare feat of having everything pretty much to scale, and a properly-sized scale bar. This is not always the case. Presumably having a 3D digital model of the reconstructed skeleton helped — and BTW, if you haven’t downloaded the 3D PDFs and played with them, you are missing out bigtime.

Here are my measurements of various bits in the picture and the scale factors they give:

Meter scale bar: 37 pixels – 1.0 meters – 37 px/m
Human figure: 66 pixels – 1.8 meters – 37 px/m
Scapula: 62 pixels – 1.7 meters – 36 px/m
Humerus: 58 pixels – 1.6 meters – 36 px/m
Femur: 70 pixels – 1.9 meters – 37 px/m
Cervical: 45 pixels – 1.1 meters – 41 px/m (not included in average*)
Neck: 407 pixels – 11.3 meters – 36 px/m
Post-cervical vertebral column: 512 pixels – 13.8 meters – 37 px/m
Total length: 922 pixels – 26.0 meters – 35 px/m
AVERAGE 36 px/m

* I didn’t include the cervical because when I measured it I sorta guessed about where the condyle was supposed to be. That was the odd measurement out, and I didn’t want to tar Lacovara et al. for what might well be my own observer error.

Here’s the chopped-up Dreadnoughtus I used for my estimate. Just for the heck of it, for the first time out I assigned all of the body regions circular cross-sections. We’ll come back to how realistic this is later. Here’s what I got for the volumes of the various bits:

Head: 0.2 m^3
Neck: 13.9
Body: 32.1
Tail: 4.0
Limbs: 6.8
TOTAL: 57.0 m^3

Okay, this is looking pretty good, right? Lacovara et al. (2014) got 59.3 metric tons using limb allometry, I got a volume of 57 cubic meters using GDI. If Dreadnoughtus was the same density as water — 1 metric ton per cubic meter — then my estimated mass would be 57 tons, which is crazy close given all of the uncertainties involved.

BUT there are a couple of big buts involved. The first is that a lot of sauropods had distinctly non-round body cross-sections (Diplodocus, Camarasaurus). So assuming circular cross-sections might inflate the body well beyond its likely volume. Second is that sauropods were probably much less dense than water (discussed here, here, and here, and see Wedel 2005 for the full scoop). What are the implications for Dreadnoughtus?

Round and Round

It turns out that circular cross-sections are probably defensible for some parts of Dreadnoughtus. By playing around with the 3D PDF of the assembled skeleton I was able to get these orthogonal views:

I don’t remember what the pixel counts were for the max height and max width of the torso, but they were pretty close. I measured at several points, too: front of the pelvis, max extent of ribcage, mid-scap. This is probably not super-surprising as the fatness of titanosaurs has been widely noted before this. Here’s a cross-section through the torso of Opisthocoelicaudia at D4 (Borsuk-Bialynicka 1977: fig. 5) — compare to the more taconic forms of Diplodocus and Camarasaurus linked above.

Okay, a round torso on Dreadnoughtus I can buy. A round neck and tail, not so much. Look at the skeletal recon and you can see that even with a generous allowance for caudofemoralis muscles on the tail, and diapophyses on the cervical vertebrae, no way were those extremities circular in cross-section. Just off the cuff I think a width:height ratio of 2:3 is probably about right.

But there are some body regions that probably were round, or close enough as to have made no difference, like the head and limbs. So I actually toted up the volume three times: once with circular cross-sections throughout (probably too fat), once with a 2:3 width:height ratio in the neck, trunk, and tail (probably too thin, at least in the torso), and once with the 2:3 ratio only in the neck and tail (my Goldilocks version). Here are the numbers I got:

Air Apparent?

Now, for density. Birds are usually much less dense than water — lotsa cited data in this hummingbird post, the punchline of which is that the average whole-body density of a bunch of birds is 0.73 g/cm^3. Why so light? In part because the lungs and air sacs are huge, and account for 15-20% of the whole-body volume, and in part because many of the bones are pneumatic (= air-filled). For a really visceral look at how much air there can be in the bones of birds, see this post, and this one and this one for sauropods.

In my 2005 paper (almost a decade old already — gosh!), I found that for Diplodocus, even a fairly conservative estimate suggested that air inside the bones accounted for about 10% of the volume of the whole animal in life. That may be higher than in a lot of birds, because sauropods were corn-on-the-cob, not shish-kebabs. And that’s just the air in the bones — we also have several lines of evidence suggesting that sauropods had air-sacs like those of birds (Wedel 2009). If the lungs and air sacs occupied 15% of the volume of the whole animal, and the air in the bones occupied another 10%, that would give a whole-body density pretty close to the 0.73 g/cm^3 found for birds. Sauropods might have been lighter still — I didn’t include visceral, intermuscular, or subcutaneous diverticula in my calculations, because I couldn’t think of any way to constrain their volumes.

What about Dreadnoughtus? As Lacovara et al. (2014) describe, the cervical, dorsal, and sacral vertebrae and sacral ribs are honeycombed with pneumatic camellae (small, thin-walled chambers). And the dorsal ribs have pneumatic foramina and were probably at least partly hollowed-out as well. The caudal vertebrae do not appear to have been pneumatic, at least internally (but diverticula going into the tail can be cryptic — see Wedel and Taylor 2013b). Diplodocus has a big, long, highly pneumatic tail, but Dreadnoughtus has a much longer neck, both proportionally and absolutely, and pneumatic dorsal ribs. So this one may be too close to call. But I also ran the numbers for T. rex way back when and found that air in its vertebrae accounted for 7% of its body volume (this abstract). Pessimistically, if we assume Dreadnoughtus had small lungs and air sacs (maybe 10% of whole-body volume) and not much air in the bones (7%), it’s whole-body density was probably still closer to 0.8 g/cm^3 than to 0.9. Optimistically, a lot of titanosaurs were radically pneumatic and they have may have had big air sac systems and extensive diverticula to match, so a bird-like 0.7-0.75 g/cm^3 is certainly not beyond the bounds of possibility.

This table shows a spectrum of masses, based on the three body volumes from GDI (columns) and some possible whole-body densities (rows). Note that the columns are not in the same order as in the first table — I lined them up from most t0 least voluminous here. The 57-ton estimate is the max, and that assumes that the neck and tail were both perfectly round, and that despite the lungs, air sacs, and air reservoirs inside the bones, the whole-body density of Dreadnoughtus was still 1.0 g/cm^3, neither of which are likely (or, I guess, that a real Dreadnoughtus was significantly fatter than the one shown, and that all of that extra bulk was muscle or some other heavy tissue). The 28t mass in the lower left corner is also unrealistic, because it assumes a tall, narrow torso. My pick is the 36t estimate at the bottom of the middle column, derived from what I think are the most defensible volume and density. Your thoughts may differ — the comment thread is open.

Roll Your Own

This last table is just a quick-and-dirty comparison of how the volume of the body breaks down among its constituent parts in Plateosaurus (from this post), Giraffatitan (from Taylor 2009), and Dreadnoughtus (based on my “tall neck and tail” GDI). Dreadnoughtus seems to have a more voluminous neck and a less voluminous trunk, proportionally, than Giraffatitan, but I think a lot of that is down to the very fat fleshy envelope drawn around the cervicals of Dreadnoughtus. We are fortunate to count some fearsomely talented paleoartists among our readers — I’ll look forward to seeing what you all come up with in your independent skeletal recons.

So, what’s the take-home? Based on the data available, I don’t think the holotype individual of Dreadnoughtus massed anything like 59 metric tons. I think 35-40 metric tons is much more defensible. But I’m happy to have my errors pointed out and new data and arguments brought to the fore. Your thoughts are most welcome.

References

• Borsuk-Bialynicka, M. 1977. A new camarasaurid sauropod Opisthocoelicaudia skarzynskii, gen. n., sp. n. from the Upper Cretaceous of Mongolia. Palaeontologia Polonica 37: 5-64.
• Lacovara, Kenneth J.; Ibiricu, L.M.; Lamanna, M.C.; Poole, J.C.; Schroeter, E.R.; Ullmann, P.V.; Voegele, K.K.; Boles, Z.M.; Egerton, V.M.; Harris, J.D.; Martínez, R.D.; Novas, F.E. (September 4, 2014). A Gigantic, Exceptionally Complete Titanosaurian Sauropod Dinosaur from Southern Patagonia, Argentina. Scientific Reports. doi:10.1038/srep06196.
• Taylor, Michael P.  2009.  A re-evaluation of Brachiosaurus altithorax Riggs 1903 (Dinosauria, Sauropoda) and its generic separation from Giraffatitan brancai (Janensch 1914).  Journal of Vertebrate Paleontology 29(3):787-806.
• Wedel, M.J.  2005.  Postcranial skeletal pneumaticity in sauropods and its implications for mass estimates.  pp. 201-228 in Wilson, J. A., and Curry-Rogers, K. (eds.), The Sauropods: Evolution and Paleobiology.  University of California Press, Berkeley.
• Wedel, M.J. 2009. Evidence for bird-like air sacs in saurischian dinosaurs. Journal of Experimental Zoology 311A:611-628.
• Wedel, Mathew J., and Michael P. Taylor. 2013. Caudal pneumaticity and pneumatic hiatuses in the sauropod dinosaurs Giraffatitan andApatosaurus.PLOS ONE 8(10):e78213. 14 pages. doi:10.1371/journal.pone.0078213