In a comment on the last post, on the mass of Dreadnoughtus, Asier Larramendi wrote:

The body mass should be considerably lower because the reconstructed column don’t match with published vertebrae centra lengths. 3D reconstruction also leaves too much space between vertebrae. The reconstruction body trunk is probably 15-20% longer than it really was. Check the supplementary material:

So I did. The table of measurements in the supplementary material is admirably complete. For all of the available dorsal vertebrae except D9, which I suppose must have been too poorly preserved to measure the difference, Lacovara et al. list both the total centrum length and the centrum length minus the anterior condyle. Centrum length minus the condyle is what in my disseration I referred to as “functional length”, since it’s the length that the vertebra actually contributes to the articulated series, assuming that the condyle of one vertebra sticks out about as far as the cotyle is recessed on the next vertebra. Here are total lengths/functional lengths/differences for the seven preserved dorsals, in mm:

  • D4 – 400/305/95
  • D5 – 470/320/150
  • D6 – 200/180/20
  • D7 – 300/260/40
  • D8 – 350/270/80
  • D9 – 410/ – / –
  • D10 – 330/225/105

The average difference between functional length and total length is 82 mm. If we apply that to D9 to estimate it’s functional length, we get 330mm. The summed functional lengths of the seven preserved vertebrae are then 1890 mm. What about the missing D1-D3? Since the charge is that Lacovara et al. (2014) restored Dreadnoughtus with a too-long torso, we should be as generous as possible in estimating the lengths of the missing dorsals. In Malawisaurus the centrum lengths of D1-D3 are all less than or equal to that of D4, which is the longest vertebra in the series (Gomani 2005: table 3), so it seems simplest here to assign D1-D3 functional lengths of 320 mm. That brings the total functional length of the dorsal vertebral column to 2850 mm, or 2.85 m.

At this point on my first pass, I was thinking that Lacovara et al. (2014) were in trouble. In the skeletal reconstruction that I used for the GDI work in the last post, I measured the length of the dorsal vertebral column as 149 pixels. Divided by 36 px/m gives a summed dorsal length of 4.1 m. That’s more than 40% longer than the summed functional lengths of the vertebrae calculated above (4.1/2.85 = 1.44). Had Lacovara et al. really blown it that badly?

Before we can rule on that, we have to estimate how much cartilage separated the dorsal vertebrae. This is a subject of more than passing interest here at SV-POW! Towers–the only applicable data I know of are the measurements of intervertebral spacing in two juvenile apatosaurs that Mike and I reported in our cartilage paper last year (Taylor and Wedel 2013: table 3, and see this post). We found that the invertebral cartilage thickness equaled 15-24% of the length of the centra.* For the estimated 2.85-meter dorsal column of Dreadnoughtus, that means 43-68 cm of cartilage (4.3-6.8 cm of cartilage per joint), for an in vivo dorsal column length of 3.28-3.53 meters. That’s still about 15-20% shorter than the 4.1 meters I measured from the skeletal recon–and, I must note, exactly what Asier stated in his comment. All my noodling has accomplished is to verify that his presumably off-the-cuff estimate was spot on. But is that a big deal?

Visually, a 20% shorter torso makes a small but noticeable difference. Check out the original reconstruction (top) with the 20%-shorter-torso version (bottom):

Dreadnoughtus shortened torso comparison - Lacovara et al 2014 fig 2

FWIW, the bottom version looks a lot more plausible to my eye–I hadn’t realized quite how weiner-dog-y the original recon is until I saw it next to the shortened version.

In terms of body mass, the difference is major. You’ll recall that I estimated the torso volume of Dreadnoughtus at 32 cubic meters. Lopping off 20% means losing 6.4 cubic meters–about the same volume as a big bull elephant, or all four of Dreadnoughtus‘s limbs put together. Even assuming a low whole-body density of 0.7 g/cm^3, that’s 4.5 metric tons off the estimated mass. So a ~30-ton Dreadnoughtus is looking more plausible by the minute.

For more on how torso length can affect the visual appearance and estimated mass of an animal, see this post and Taylor (2009).

* I asked Mike to do a review pass on this post before I published, and regarding the intervertebral spacing derived from the juvenile apatosaurs, he wrote:

That 15-24% is for juveniles. For the cervicals of adult Sauroposeidon we got about 5%. Why the differences? Three reasons might be relevant: 1, taxonomic difference between Sauroposeidon and Apatosaurus; 2, serial difference between neck and torso; 3, ontogenetic difference between juvenile and adult. By applying the juvenile Apatosaurus dorsal measurement directly to the adult Dreadnoughtus dorsals, you’re implicitly assuming that the adult/juvenile axis is irrelevant (which seems unlikely to me), that the taxonomic axis is (I guess) unknowable, and that the cervical/dorsal distinction is the only one that matter.

That’s a solid point, and it deserves a post of its own, which I’m already working on. For now, it seems intuitively obvious to me that we got a low percentage on Sauroposeidon simply because the vertebrae are so long. If the length-to-diameter ratio was 2.5 instead of 5, we’d have gotten 10%, unless cartilage thickness scales with centrum length, which seems unlikely. For a dorsal with EI of 1.5, cartilage thickness would then be 20%, which is about what I figured above.

Now, admittedly that is arm-waving, not science (and really just a wordy restatement of his point #2). The obvious thing to do is take all of our data and see if intervertebral spacing is more closely correlated with centrum length or centrum diameter. Now that it’s occurred to me, it seems very silly not to have done that in the actual paper. And I will do that very thing in an upcoming post. For now I’ll just note three things:

  1. As you can see from figure 15 in our cartilage paper, in the opisthocoelous anterior dorsals of CM 3390, the condyle of the posterior vertebra is firmly engaged in the cotyle of the anterior one, and if anything the two vertebrae look jammed together, not drifted apart. But the intervertebral spacing as a fraction of centrum length is still huge (20+4%) because the centra are so short.
  2. Transferring these numbers to Dreadnoughtus only results in 4.3-6.8 cm of cartilage between adjacent vertebrae, which does not seem unreasonable for a 30- or 40-ton animal with dorsal centra averaging 35 cm in diameter. If you asked me off the cuff what I thought a reasonable intervertebral spacing was for such a large animal, I would have said 3 or 4 inches (7.5 to 10 cm), so the numbers I got through cross-scaling are actually lower than what I would have guessed.
  3. Finally, if I’ve overestimated the intervertebral spacing, then the actual torso length of Dreadnoughtus was even shorter than that illustrated above, and the volumetric mass estimate would be smaller still. So in going with relatively thick cartilage, I’m being as generous as possible to the Lacovara et al. (2014) skeletal reconstruction (and indirectly to their super-high allometry-derived mass estimate), which I think is only fair.



How massive was Dreadnoughtus?

September 11, 2014

Dreadnoughtus published body outline - Lacovara et al 2014 fig 2

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.

Dreadnoughtus decomposed for GDI - Lacovara et al 2014 fig 2

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:

Dreadnoughtus 3D skeleton 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.

Opisthocoelicaudia torso x-s - Borsuk-Bialynicka 1977 fig 5

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:

Dreadnoughtus Table 1 three volumes


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.

Dreadnoughtus Table 2 twelve masses

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

Dreadnoughtus Table 3 body region comparison

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.


Yay, vertebrae! Lacovara et al. (2014: fig. 1)

Yay, vertebrae! Lacovara et al. (2014: fig. 1)

Mike and I are in York for SVPCA — more on that soonish — and I just wanted to get out some quick thoughts about the world’s newest giant sauropod.

First off, the paper (Lacovara et al. 2014) is open access, which is great. And, hey, 3D PDFs of the whole skeleton and selected elements — I’m going to be having some fun with those.

And given that this is a short initial descriptive paper, I was really happy to see a reasonably detailed table of measurements. The materials and methods section at the end spells out explicitly how the team arrived at their estimates of the animal’s length and mass. All of that looks very solid, and it’s more information that we often get in these short initial descriptions. So although I will look forward to seeing a complete osteological description of Dreadnoughtus in the future, this first paper is better than a lot of similar papers in that it includes a lot of actually useful information.

As for whether Dreadnoughtus was the world’s heaviest sauropod — how could anyone possibly tell? The femur of Dreadnoughtus is 1.9 meters, which is only three-quarters of the estimated length of the largest partial femur of Argentinosaurus. Now, there is plenty of evidence from both histology and macro-level indicators of skeletal age that the holotype individual was still growing, but how much bigger was it going to get, 10%, 25%? I think that given its size, completeness, and immature state it is fair to discuss Dreadnoughtus in the same breath as Argentinosaurus, Puertasaurus, the largest specimens of Alamosaurus, and other giant sauropods. But I think any claim that it is ‘the’ heaviest is premature until we know how big a fully adult Dreadnoughtus was.

Dreadnoughtus and kin. Lacovara et al. (2014: fig. 3)

Dreadnoughtus and kin. Lacovara et al. (2014: fig. 3)

Here’s a weird thing: according to Table 1, the 113-cm cervical vertebra of Dreadnoughtus is the longest known among titanosauriforms. But the longest cervical of Sauroposeidon has a 125-cm centrum, and Sauroposeidon always comes out as a titanosauriform in phylogenetic analyses, including the one in the Dreadnoughtus paper. The estimated 2.5-meter femur of Argentinosaurus reported by Mazzetta et al. (2004) is also not listed in that table, although some estimated lengths for other incomplete elements are given. I don’t think there’s any conspiracy here — it is actually quite a challenge to keep up with all of the relevant numbers — but I would like to have seen a bit more thoroughness in reporting measurements of other sauropods where at least some individual elements are larger than in Dreadnoughtus.

Anyway, as we found for the next-most-recent “world’s largest dinosaur” earlier this year, Dreadnoughtus does not extend the known size range of the largest sauropods. Period. Anyone who says definitively otherwise is actually making assumptions about ontogeny and mass estimation that just aren’t justified.

Does that mean that Dreadnoughtus isn’t interesting? Of course not! For one thing, now we can start talking intelligently about the body proportions of these giant titanosaurs. Up until now we’ve had a good idea of what other, smaller sauropods looked like, things like Mamenchisaurus, Diplodocus, and Giraffatitan, and we’ve had reasonably complete skeletons of small titanosaurs such as Malawisaurus and Rapetosaurus, but we haven’t had a very clear idea of the proportions of the largest titanosaurs (sometimes because of conflicting measurements). So now we can start investigating questions involving the biomechanics and hopefully the growth trajectories of giant titanosaurs, which were more in the realm of speculation until now. There are some tantalizing hints toward this in the current paper — for example, the authors mention that a lot of the bones preserve muscle attachments. That would be a fascinating study in its own right, just knowing what the muscle attachments can tell us about the soft-tissue anatomy of Dreadnoughtus, and in turn what soft tissue can tell us about how the muscles and joints worked.

Big and getting bigger: the limb bones of Dreadnoughtus. Lacovara et al. (2014: fig. 2)

Big and getting bigger: the limb bones of Dreadnoughtus. Lacovara et al. (2014: fig. 2)

There are myriad interesting questions dealing with the ability of the limb bones and vertebrae to support the mass of the body and how that skeletal support changed, both over the lifespan of an animal and over evolutionary time. Now, there is a limit to how much Dreadnoughtus can add here, since it’s only known by two individuals that weren’t radically different in size, but given how bleak the data landscape is for giant titanosaurs, it’s an important addition to our knowledge.

In conclusion, although I have some reservations about overlooked measurements of some other giant sauropods, and although the media-driven Dreadnoughtus-vs-Argentinosaurus pissing contest is pointless, I’m excited about this first paper. And I’m looking forward to more, both more complete descriptive work, and functional and biomechanical analyses building on that. Happy days.