What would the world look like if, as proposed by the Max Planck Institute, the scholarly world flipped from being dominated by subscriptions to Gold open access? I think there are three things to say.

First, incentives. A concern is sometimes expressed that when publishers are paid per paper published, they will have an incentive to want more papers to be published. Would this exacerbate the existing publish-or-perish culture where we are flooded by quantity of publications, sometimes at the expense of quality?

It’s certainly true that in a Gold OA world, the publishers would like to see more papers (and monographs) published. But whether we the academic community respond to that desire by publishing more is not a decision that the publishers get to make. This — like so many issues — comes back to the problem of what incentives apply in academia. While scholars gains rewards like promotion and tenure by publishing many papers (for example because committees evaluate people based on their H-index), it is inevitable that those scholars will seek to publish many papers — and this would be true whether in a subscription-based or Gold OA-based system. Thus I think the problem of publishing quantity rather than quality is quite independent from the problem of how we pay for publications.

Second, costs. I sometimes hear a concern is that a flip to Gold OA would create an environment where funds are tied up, and resources are not sufficient of fund new and innovative journals.

I’m sure these numbers are not new to regular readers, but it seems pretty clear that a flipped world would have much lower total costs than the present system. Here are the numbers:

The STM Report for 2015, page 6, reports total publisher income in the STM field as $10 billion for 2013, and says that about 2.5 million papers were published that year. That gives an average income per paper of $4000. (We can probably assume a broadly similar figure for non-STM papers, too.) By contrast, the Wellcome Trust’s recent report on its APC spending in 2013-14 shows an average APC of £1837, currently about $2634. This is slightly less than 2/3 what the world at large is paying per paper.

In other words, even using the relatively high APCs paid by the Wellcome Trust, the world’s 2.5 million papers per year could be published for $6.6 billion — saving $3.4 billion to spent elsewhere.

Third, markets. This one is a question, and I think it’s crucial for the prospects of a Gold-OA ecosystem: will we get an efficient market in APCs? If we do, then prices will be forced down until they are very close to costs — which publishers like Hindawi, Ubiquity Press and PeerJ have shown can be in the $400-500 range, almost literally an order of magnitude less than the world presently pays for publication. But if no true market emerges, prices will not fall — indeed publishers may have the leverage to raise APCs at rates greater than inflation, as they have been doing for subscriptions.

That is why I believe that, however tempting “APC Big Deals” are to individual libraries or consortia, they should be strenuously resisted. As with subscription Big Deals, the short-term savings (while real) would be absolutely dwarfed by the long-term losses.

If I’m right about this, then we face a tragedy of the commons during this phase of transition from subscriptions to Gold OA: it will be in the short-term interests of each library to accept a Big Deal on APCs; but again the interests of the community. We will need to communicate well, and function as a global community, to avoid falling into this trap.

[I first wrote this post as an email to a list for delegates of the OSI2016 conference. Then I realised that it’s of broader interest, and edited it into the form seen here.]

I was a bit disappointed to hear David Attenborough on BBC Radio 4 this morning, while trailing a forthcoming documentary, telling the interviewing that you can determine the mass of an extinct animal by measuring the circumference of its femur.

We all know what he was alluding to, of course: the idea first published by Anderson et al. (1985) that if you measure the life masses of lots of animals, then measuring their long-bone circumferences when they’ve died, you can plot the two measurements against each other, find a best-fit line, and extrapolate it to estimate the masses of dinosaurs based on their limb-bone measurements.


This approach has been extensively refined since 1985, most recently by Benson et al. (2014). but the principle is the same.

But the thing is, as Anderson et al. and other authors have made clear, the error-bars on this method are substantial. It’s not super-clear in the image above (Fig 1. from the Anderson et al. paper) because log-10 scales are used, but the 95% confidence interval is about 42 pixels tall, compared with 220 pixels for an order of magnitude (i.e. an increment of 1.0 on the log-10 scale). That means the interval is 42/220 = 0.2 of an order of magnitude. That’s a factor 10 ^ 0.2 = 1.58. In other words you could have two animals with equally robust femora, one of them nearly 60% heavier than the other, and they would both fall within the 95% confidence interval.

I’m surprised that someone as experienced and knowledgeable as Attenborough would perpetuate the idea that you can measure mass with any precision in this way (even more so when using only a femur, rather than the femur+humerus combo of Anderson et al.)

More: when the presenter told him that not all scientists buy the idea that the new titanosaur is the biggest known, he said that came as a surprise. Again, it’s disappointing that the documentary researchers didn’t make Attenborough aware of, for example, Paul Barrett’s cautionary comments or Matt Wedel’s carefully argued dissent. Ten minutes of simple research would have found this post — for example, it’s Google’s fourth hit for “how big is the new argentinian titanosaur”. I can only hope that the actual documentary, which screens on Sunday 24 January, doesn’t present the new titanosaur’s mass as a known and agreed number.

(To be clear, I am not blaming Attenborough for any of this. He is a presenter, not a palaeontologist, and should have been properly prepped by the researchers for the programme he’s fronting. He is also what can only be described as 89, so should be forgiven if he’s not quite as quick on his feel when confronted with an interviewer as he used to be.)

Update 1 (the next day)

Thanks to Victoria Arbour for pointing out an important reference that I missed: it was Campione and Evans (2012) who expanding Anderson et al.’s dataset and came up with the revised equation which Benson et al. used.

Update 2 (same day as #1)

It seems most commenters are inclined to go with Attenborough on this. That’s a surprise to me — I wonder whether he’s getting a free pass because of who he is. All I can say is that as I listened to the segment it struck me as really misleading. You can listen to it for yourself here if you’re in the UK; otherwise you’ll have to make do with this transcript:

“It’s surprising how much information you can get from just one bone. I mean for example that thigh bone, eight feet or so long, if you measure the circumference of that, you will be able to say how much weight that could have carried, because you know what the strength of bone is. So the estimate of weight is really pretty accurate and the thought is that this is something around over seventy tonnes in weight.”

(Note also that the Anderson et al./Campione and Evans method has absolutely nothing to do with the strength of bone.)

Also if interest was this segment that followed immediately:

How long it was depends on whether you think it held its neck out horizontaly or vertically. If it held it out horizontally, well then it would be about half as big again as the Diplodocus, which is the dinosaur that’s in the hall of the Natural History Museum. It would be absolutely huge.

Interviewer: And how tall, if we do all the dimensions?

Ah well that is again the question of how it holds its neck, and it could have certainly reached up about to the size of a four or five storey building.

Needless to say, the matter of neck posture is very relevant to our interests. I don’t want to read too much into a couple of throwaway comments, but the implication does seem to be that this is an issue that the documentary might spend some time on. We’ll see what happens.


I imagine that by now, everyone who reads this blog is familiar with Mark Witton’s painting of a giant azhdarchid pterosaur alongside a big giraffe. Here it is, for those who haven’t seen it:

Arambourgiania vs giraffe vs the Disacknowledgement redux Witton ver 2 low res

(This is the fifth and most recent version that Mark has created, taken from 9 things you may not know about giant azhdarchid pterosaurs.)

It’s one of those images that really kicks you in the brain the first time you see it. The idea that an animal the size of a giraffe could fly under its own power seems ludicrous — yet that’s what the evidence tells us.

But wait — what do we mean by “an animal the size of a giraffe”? Yes, the pterosaur in this image is the same height as the giraffe, but how does its weight compare?

Mark says “The giraffe is a big bull Masai individual, standing a healthy 5.6 m tall, close to the maximum known Masai giraffe height.” He doesn’t give a mass, but Wikipedia, citing Owen-Smith (1988), says “Fully grown giraffes stand 5–6 m (16–20 ft) tall, with males taller than females. The average weight is 1,192 kg (2,628 lb) for an adult male and 828 kg (1,825 lb) for an adult female with maximum weights of 1,930 kg (4,250 lb) and 1,180 kg (2,600 lb) having been recorded for males and females, respectively.” So it seems reasonable to use a mass intermediate between those of an average and maximum-sized male, (1192+1930)/2 = 1561 kg.

So much for the giraffe. What does the azhdarchid weigh? The literature is studded with figures that vary wildly, from the 544 kg that Henderson (2010) found for Quetzalcoatlus, right down to the widely cited 70 kg that Chatterjee and Templin (2004) found for the same individual — and even the astonishing 50 kg that seems to be favoured by Unwin (2005:192). In the middle is the 259 kg of Witton (2008).

It occurred to me that I could visualise these mass estimates by shrinking the giraffe in Mark’s image down to the various proposed masses, and seeing how credible it looks to imagine these reduced-sized giraffes weighting the same as the azhdarchid. The maths is simple. For each proposed azhdarchid mass, we figure out what it is as a proportion of the giraffe’s 1561 kg; then the cube root of that mass proportion gives us the linear proportion.

  • 544 kg = 0.389 giraffe masses = 0.704 giraffe lengths
  • 259 kg = 0.166 giraffe masses = 0.549 giraffe lengths
  • 70 kg =0.0448 giraffe masses = 0.355 giraffe lengths

Let’s see how that looks.

Arambourgiania vs giraffe vs the Disacknowledgement redux Witton ver 2 low res

On the left, we have Mark’s artwork, with the giraffe massing 1561 kg. On the right, we have three smaller (isometrically scaled) giraffes of masses corresponding to giant azhdarchid mass estimates in the literature. If Don Henderson (2010) is right, then the pterosaur weighs the same as the 544 kg giraffe, which to me looks pretty feasible if it’s very pneumatic. If Witton (2008) is right, then it weighs the same as the 259 kg giraffe, which I find hard to swallow. And if Chatterjee and Templin (2004) are right, then the giant pterosaur weighs the same as the teeny tiny 70 kg giraffe, which I find frankly ludicrous. (For that matter, 70 kg is in the same size-class as Georgia, the human scale-bar: the idea that she and the pterosaur weigh the same is just silly.)

What is the value of such eyeball comparisons? I’m not sure, beyond a basic reality check. Running this exercise has certainly made me sceptical about even the 250 kg mass range which now seems to be fairly widely accepted among pterosaur workers. Remember, if that mass is correct then the pterosaur and the 259 kg giraffe in the picture above weight the same. Can you buy that?

Or can we find extant analogues? Are there birds and mammals with the same mass that are in the same size relation as these images show?


  • Chatterjee, Sankar, and R. J. Templin. 2004. Posture, locomotion, and paleoecology of pterosaurs. Geological Society of America, Special Paper 376. 68 pages.
  • Henderson, Donald M. 2010. Pterosaur body mass estimates from three-dimensional mathematical slicing. Journal of Vertebrate Paleontology 30(3):768-785.
  • Witton, Mark P. 2008. A new approach to determining pterosaur body mass and its implications for pterosaur flight. Zitteliana 28:143-159.

Last night, I submitted a paper for publication — for the first time since April 2013. I’d almost forgotten what it felt like. But, because we’re living in the Shiny Digital Future, you don’t have to wait till it’s been through review and formal publication to read it. I submitted to PeerJ, and at the same time, made it available as a preprint (Taylor 2014).

It’s called “Quantifying the effect of intervertebral cartilage on neutral posture in the necks of sauropod dinosaurs”, and frankly the results are weird. Here’s a taste:

Taylor (2014:figure 3). Effect of adding cartilage to the neutral pose of the neck of Apatosaurus louisae CM 3018. Images of vertebra from Gilmore (1936:plate XXIV). At the bottom, the vertebrae are composed in a horizontal posture. Superimposed, the same vertebrae are shown inclined by the additional extension angles indicated in Table 1. If the slightly sub-horizontal osteological neutral pose of Stevens and Parrish (1999) is correct, then the cartilaginous neutral pose would be correspondingly slightly lower than depicted here, but still much closer to the elevated posture than to horizontal. (Note that the posture shown here would not have been the habitual posture in life: see discussion.)

Taylor (2014:figure 3). Effect of adding cartilage to the neutral pose of the neck of Apatosaurus louisae CM 3018. Images of vertebra from Gilmore (1936:plate XXIV). At the bottom, the vertebrae are composed in a horizontal posture. Superimposed, the same vertebrae are shown inclined by the additional extension angles indicated in Table 1. If the slightly sub-horizontal osteological neutral pose of Stevens and Parrish (1999) is correct, then the cartilaginous neutral pose would be correspondingly slightly lower than depicted here, but still much closer to the elevated posture than to horizontal. (Note that the posture shown here would not have been the habitual posture in life: see discussion.)

A year back, as I was composing a blog-post about our neck-cartilage paper in PLOS ONE (Taylor and Wedel 2013c), I found myself writing down the rather trivial formula for the additional angle of extension at an intervertebral joint once the cartilage is taken into account. In that post, I finished with the promise “I guess that will have to go in a followup now”. Amazingly it’s taken me a year to get that one-pager written and submitted. (Although in the usual way of things, the manuscript ended up being 13 pages long.)

To summarise the main point of the paper: when you insert cartilage of thickness t between two vertebrae whose zygapophyses articulate at height h above the centra, the more anterior vertebra is forced upwards by t/h radians. Our best guess for how much cartilage is between the adjacent vertebrae in an Apatosaurus neck is about 10% of centrum length: the image above shows the effect of inserting that much cartilage at each joint.

And yes, it’s weird. But it’s where the data leads me, so I think it would be dishonest not to publish it.

I’ll be interested to see what the reviewers make of this. You are all of course welcome to leave comments on the preprint itself; but because this is going through conventional peer-review straight away (unlike our Barosaurus preprint), there’s no need to offer the kind of detailed and comprehensive comment that several people did with the previous one. Of course feel free if you wish, but I’m not depending on it.


Gilmore Charles W. 1936. Osteology of Apatosaurus, with special reference to specimens in the Carnegie Museum. Memoirs of the Carnegie Museum 11:175–300 and plates XXI–XXXIV.

Stevens, Kent A., and J. Michael Parrish. 1999. Neck posture and feeding habits of two Jurassic sauropod dinosaurs. Science 284(5415):798–800. doi:10.1126/science.284.5415.798

Taylor, Michael P. 2014. Quantifying the effect of intervertebral cartilage on neutral posture in the necks of sauropod dinosaurs. PeerJ PrePrints 2:e588v1 doi:10.7287/peerj.preprints.588v1

Taylor, Michael P., and Mathew J. Wedel. 2013c. The effect of intervertebral cartilage on neutral posture and range of motion in the necks of sauropod dinosaurs. PLOS ONE 8(10):e78214. 17 pages. doi:10.1371/journal.pone.0078214

Gender balance at SVPCA

September 17, 2014

I’ve always thought of SVPCA as a pretty well gender-balanced conference: if not 50-50 men and women, then no more than 60-40 slanted towards men. So imagine my surprise when I ran the actual numbers.

1. Delegates. I went through the delegate list at the back of the abstracts book, counting the men and women. Those I knew, or whose name made it obvious, I noted down; the half-dozen that I couldn’t easily categorise, I have successfully stalked on the Internet. So I now know that there were 39 women and 79 men — so that women made up 33% of the delegates, almost exactly one third.

Official conference photo, SVPCA 2014, York, UK.

Official conference photo, SVPCA 2014, York, UK.

2. Presentations. There were a total of 50 presentations in the three days of SVPCA: 18 on days 1 and 3, and 14 on day 2, which had a poster session in place of the final session of four talks. I counted the presenters (which were usually, but not always, the lead authors). Here’s how the number of talks by women broke down:

Day one: 2 of 18
Day two: 8 of 14
Day three: 3 of 18

In total, this gives us 13 of 50 talks by women, or 26%.

3. Presenter:delegate ratios. Since 37 of the 79 attending men gave talks, that’s 47% of them; but only 13 of the 39 attending women gave talks, which is 33%. On other words, a man attending SVPCA was 40% more likely to give a talk than a woman.

I’m not sure what to make of all this. I was shocked when I found that only one ninth of the first day’s talks were by women. It’s a statistical oddity that women actually dominated day two, but day three was nearly as unbalanced as day one.

Since SVPCA accepts pretty much every submitted talk, the conference itself can’t be blamed for the imbalance. (At least, not unless you think the organisers should turn down talks by men just because they’re men, leaving blank spots in the program.) It seems that the imbalance more likely reflects that of the field in general. Maybe more disturbing is that the proportion of women giving talks was rather less than the proportion attending (26% vs. 33%) which suggests that perhaps women feel more confident about attending than about presenting.

It would be interesting to know how these numbers compare with SVP’s.

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: http://www.nature.com/srep/2014/140904/srep06196/extref/srep06196-s1.pdf

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.