We’ve touched on this several times in various posts and comment threads, but it’s worth taking a moment to think in detail about the various published mass estimates for the single specimen BM.R.2181 (formerly known as HMN SII), the paralectotype of Giraffatitan brancai, which is the basis of the awesome mounted skeleton in Berlin.

Here is the table of published estimates from my 2010 sauropod-history paper, augmented with the two more recent estimates extrapolated from limb-bone measurements:

Author and date Method Volume (l) Density (kg/l) Mass (kg)
Janensch (1938) Not specified `40 t’
Colbert (1962) Displacement of sand 86,953 0.9 78,258
Russell et al. (1980) Limb-bone allometry 13,618
Anderson et al. (1985) Limb-bone allometry 29,000
Paul (1988) Displacement of water 36,585 0.861 31,500
Alexander (1989) Weighing in air and water 46,600 1.0 46,600
Gunga et al. (1995) Computer model 74,420 1.0 74,420
Christiansen (1997) Weighing in air and water 41,556 0.9 37,400
Henderson (2004) Computer model 32,398 0.796 25,789
Henderson (2006) Computer model 25,922
Gunga et al. (2008) Computer model 47,600 0.8 38,000
Taylor (2009) Graphic double integration 29,171 0.8 23,337
Campione and Evans (2012) Limb-bone allometry 35,780
Benson et al. (2014) Limb-bone allometry 34,000

(The estimate of Russell et al. (1980) is sometimes reported as 14900 kg. However, they report their estimate only as “14.9 t”; and since they also cite “the generally accepted figure of 85 tons”, which can only be a reference to Colbert (1962)”, we must assume that Russell et al. were using US tons throughout.)

The first thing to notice is that there is no very clear trend through time, either upwards or downwards. Here’s a plot of mass (y-axis) against year of estimate (x-axis):

giraffatitan-mass-by-year

I’ve not even tried to put a regression line through this: the outliers are so extreme they’d render it pretty much useless.

In fact, the lowest and highest estimates differ by a factor of 5.75, which is plainly absurd.

But we can go some way to fixing this by discarding the outliers. We can dump Colbert (1962) and Alexander (1989) as they used overweight toys as their references. We more or less have to dump Russell et al. (1980) simply because it’s impossible to take seriously. (Yes, this is the argument from personal incredulity, and I don’t feel good about it; but as Pual (1988) put it, “so little flesh simply cannot be stretched over the animal’s great frame”.) And we can ignore Gunga et al. (1995) because it used circular conic sections — a bug fixed by Gunga et al. (2008) by using elliptical sections.

With these four unpalatable outliers discarded, our highest and lowest estimates are those of Gunga et al. (2008) at 38,000 kg and Taylor (2009)at 23,337. The former should be taken seriously as it was done using photogrammetrical measurements of the actual skeletal mount. And so should the latter because Hurlburt (1999) showed that GDI is generally the least inaccurate of our mass-estimation techniques. That still gives us a factor of 1.63. That’s the difference between a lightweight 66 kg man and and overweight 108 kg.

Here’s another way of thinking about that 1.63 factor. Assuming two people are the same height, one of them weighing 1.62 times as much as the other means he has to be 1.28 times as wide and deep as the first (1.28^2 = 1.63). Here is a man next to his 1.28-times-as-wide equivalent:

two-men

 

I would call that a very noticeable difference. You wouldn’t expect someone estimating the mass of one of these men to come up with that of the other.

So what’s going on here? I truly don’t know. We are, let’s not forget, dealing with a complete skeletal mount here, one of the very best sauropod specimens in the world, which has been extensively studied for a century. Yet even within the last six years, we’re getting masses that vary by as much as the two dudes above.

 

As promised, some thoughts on the various new brachiosaur mass estimates in recent papers and blog-posts.

Back in 2008, when I did the GDI of Giraffatitan and Brachiosaurus for my 2009 paper on those genera, I came out with estimates of 28688 and 23337 kg respectively. At the time I said to Matt that I was suspicious of those numbers because they seemed too low. He rightly told me to shut up and put my actual results in the paper.

More recently, Benson et al. (2014) used limb-bone measurements to estimate the masses of the same individuals as 56000 and 34000 kg. When Ian Corfe mentioned this in a comment, my immediate reaction was to be sceptical: “I’m amazed that the two more recent papers have got such high estimates for brachiosaurs, which have the most gracile humeri of all sauropods“.

So evidently I have a pretty strong intuition that Brachiosaurus massed somewhere in the region of 35000 kg and Giraffatitan around 30000 kg. But why? Where does that intuition come from?

I can only assume that my strongly held ideas are based only on what I’d heard before. Back when I did my 2008 estimate, I probably had in mind things like Paul’s (1998) estimate of 35000 kg for Brachiosaurus, and Christiansen’s (1997:67) estimate of 37400 for Giraffatitan. Whereas by the time the Benson et al. paper came out I’d managed to persuade myself that my own much lower estimates were right. In other words, I think my sauropod-mass intuition is based mostly on sheer mental inertia, and so should be ignored.

I’m guessing I should ignore your intuitions about sauropod masses, too.

References

Way back in November 2011, I got this inquiry from Keiron Pim:
I’m currently writing a popular guide to dinosaurs, to be published by Random House next autumn [Ed.: available now at amazon.com and at amazon.co.uk]. I’ve been writing about [Brachiosaurus and Giraffatitan], and have read your 2009 study vindicating the proposal to separate them into two genera.
[...]
I know you consider Brachiosaurus likely to have been bigger (and note that the specimen was not fully grown), with a longer trunk and tail – but most of the sources I can find give both animals the same body length, generally around 26m. Presumably this doesn’t reflect your work, and your calculations are different.

I replied at the time, and said that I’d post that response here on SV-POW!. But one thing and another prevented me from getting around to it, and I forgot all about it until recently. Since we’re currently in a sequence of Brachiosaurus-themed posts [part 1, part 2, part 3, part 4, part 5, part 6], this seems like a good time to fix that. So here is my response, fresh from November 2011, lightly edited.

dscn1253

Well, Giraffatitan has only been recognised as a separate animal at all in the last couple of years, and nearly everything that has been written about “Brachiosaurus“, at least in the technical literature, is actually about Giraffatitan. So existing sources that give the same length for both are probably not making a meaningful distinction between the two animals.

First, on Giraffatitan: Janensch (1950b:102) did a great job of measuring his composite mounted skeleton. His figure for the total length of Giraffatitan along the neural canal is 22.46 m, and is certainly the best estimate in the literature for an actual brachiosaur specimen (and quite possibly the best for any sauropod).

I don’t know where the figure of 26 m comes from, but as Janensch (1961:213) notes, the isolated fibula XV2 of Giraffatitan in the Berlin collection is 134 cm long, compared with 119 cm for that of the mounted skeleton. This is 1.126 times as long, which if scaled isometrically would yield a total length of 25.29 m.  So that is defensible, but 26 m is not, really.

I would advise sticking with Janensch’s published figure of 22.46 m, as it’s based on good material, and also because it forms the basis of my comparative estimate for a Brachiosaurus of similar limb length.

Now in my 2009 paper I estimated with reasonable rigour that the torso of Brachiosaurus was probably about 23% longer than that of Giraffatitan, yielding 4.82 m rather than 3.92 that Janensch gave for Giraffatitan. On much less solid evidence, I tentatively estimated that the tail of Brachiosaurus might have been 20-25% longer than that of Giraffatitan. Given the paucity of evidence I would play safer by going with the lower end of that estimate, which would give a tail length of 9.14 m compared with Janensch’s 7.62 for Giraffatitan. Riggs (1904) tells us that the sacrum of Brachiosaurus is 0.95 m long, which is slightly less than 1.07 m for Giraffatitan. Finally, since we know nothing of the head and neck of Brachiosaurus, the null hypothesis has to be that they were similar in proportion to those of Giraffatitan.

Putting it all together, Brachiosaurus may have been longer in the torso by 0.9 m, and in the tail by 1.52 m, but shorter in the sacrum by 0.12 m — for a total additional length of 2.3 m. That would make Brachiosaurus 24.76 m long, which is 10% longer than Giraffatitan.

Note that all the Brachiosaurus figures are given with much greater precision than the sparse data we have really allows.  I think you could round Janensch’s 22.46 m for Giraffatitan to 22.5 and be pretty confident in that number, but you shouldn’t really say anything more precise than “maybe about 25 m” for Brachiosaurus.

Finally, you correctly note that the Brachiosaurus specimen was not fully grown — we can tell because its coracoid was not fused to the scapula. But the same is true of the mounted Giraffatitan, so these two very similarly sized animals were both subadult. How much bigger did they get?  We know from the fibula that Giraffatitan got at least 12-13% bigger than the well-known specimen, and I’d be pretty happy guessing the same about Brachiosaurus.  And I wouldn’t rule out much bigger specimens, either.

References

Continuing with what seems to have turned out to be Brachiosaur Humerus Week here on SV-POW! (part 1, part 2, part 3), let’s consider the oft-stated idea that brachiosaurs have the most slender humeri of any sauropod. For example, Taylor (2009:796) wrote that:

Discarding a single outlier, the ratio of proximodistal length to minimum transverse width (Gracility Index or GI) in humeri of B. brancai [i.e. Giraffatitan] varies between 7.86 for the right humerus HMN F2 and 9.19 for the left humerus HMN J12, with the type specimen’s right humerus scoring 8.69, slightly more gracile than the middle of the range [...] For the B. altithorax type specimen, the GI is 8.50, based on the length of 204 cm and the minimum transverse width of 24 cm reported by Riggs (1904:241). However, the B. altithorax humerus looks rather less gracile to the naked eye than that of B. brancai, and careful measurement from Riggs’s plate LXXIV yields a GI of 7.12, indicating that the true value of the minimum transverse width is closer to 28.5 cm. As noted by Riggs (1903:300-301), the surface of the distal end of this humerus has flaked away in the process of weathering. Careful comparison of the humeral proportions with those of other sauropods (Taylor and Wedel, in prep.) indicates that the missing portion of this bone would have extended approximately a further 12 cm, extending the total length to 216 cm and so increasing the GI to 7.53 – still less gracile than any B. brancai humerus except the outlier, but more gracile than any other sauropod species except Lusotitan atalaiensis (8.91), and much more gracile than the humerus of any non-brachiosaurid sauropod (e.g., Diplodocus Marsh, 1878 sp., 6.76; Malawisaurus dixeyi Jacobs, Winkler, Downs and Gomani, 1993, 6.20; Mamenchisaurus constructus Young, 1958, 5.54; Camarasaurus supremus Cope, 1877, 5.12; Opisthocoelicaudia skarzynskii Borsuk-Bialynicka, 1977, 5.00 – see Taylor and Wedel, in prep.)

Implicit in this (though not spelled out, I admit) is that the humeri of brachiosaurs are slender proportional to their femora. So let’s take a look at the humerus and femur of Giraffatitan, as illustrated in Janensch’s beautiful 1961 monograph of the limbs and girdles of Tendaguru sauropods:

Janensch1961-tendaguru-limbs--plates-AJ--giraffatitan-limb-bones

The first thing you’ll notice is that the humerus is way longer than the femur. That’s because Janensch’s Beilage A illustrates the right humerus of SII (now properly known as MB R.2181) while his Beilage J illustrates the right femur of the rather smaller referred individual St 291. He did this because the right femur of SII was never recovered and the left femur was broken, missing a section in the middle that had to be reconstructed in plaster.

(What’s a Beilage? It’s a German word that seems to literally mean something like “supplement”, but in Janensch’s paper it means a plate (full-page illustration) that occurs in the main body of the text, as opposed to the more traditional plates that come at the end, and which are numbered from XV to XXIII.)

How long would the intact SII femur have been? Janensch (1950b:99) wrote “Since the shaft of the right femur is missing for the most part, it was restored to a length of 196 cm, calculated from other finds” (translation by Gerhard Maier). Janensch confused the left and right femora here, but assuming his length estimate is good, we can upscale his illustration of St 291 so that it’s to SII scale, and matches the humerus. Here’s how that looks:

Janensch1961-tendaguru-limbs--plates-AJ--giraffatitan-limb-bones-scaled

Much more reasonable! The humerus is still a little longer, as we’d expect, but not disturbingly so.

Measuring from this image, the midshaft widths of the femur and humerus are 315 and 207 pixels respectively, corresponding to absolute transverse widths of 353 and 232 mm — so the femur is broader by a factor of 1.52. That’s why I expressed surprise on learning that Benson et al (2014) gave Giraffatitan a CF:CH ratio (circumference of femur to circumference of humerus) of only 1.12.

Anyone who would like to see every published view of the humeri and femora of these beasts is referred to Taylor (2009:fig. 5). In fact, here it is — go crazy.

Taylor (2009: figure 5). Right limb bones of Brachiosaurus altithorax and Brachiosaurus brancai, equally scaled. A-C, humerus of B. altithorax holotype FMNH P 25107; D-F, femur of same; G-K, humerus of B. brancai lectotype HMN SII; L-P, femur of B. brancai referred specimen HMN St 291, scaled to size of restored femur of HMN SII as estimated by Janensch (1950b:99). A, D, G, L, proximal; B, E, H, M, anterior; C, K, P, posterior; J, O, medial; F, I, N, distal. A, B, D, E modified from Riggs (1904:pl. LXXIV); C modified from Riggs (1904:fig. 1); F modified from Riggs (1903:fig. 7); G-K modified from Janensch (1961:Beilage A); L-P modified from Janensch (1961:Beilage J). Scale bar equals 50 cm.

Taylor (2009: figure 5). Right limb bones of Brachiosaurus altithorax and Brachiosaurus brancai, equally scaled. A-C, humerus of B. altithorax holotype FMNH P 25107; D-F, femur of same; G-K, humerus of B. brancai paralectotype HMN SII; L-P, femur of B. brancai referred specimen HMN St 291, scaled to size of restored femur of HMN SII as estimated by Janensch (1950b:99). A, D, G, L, proximal; B, E, H, M, anterior; C, K, P, posterior; J, O, medial; F, I, N, distal. A, B, D, E modified from Riggs (1904:pl. LXXIV); C modified from Riggs (1904:fig. 1); F modified from Riggs (1903:fig. 7); G-K modified from Janensch (1961:Beilage A); L-P modified from Janensch (1961:Beilage J). Scale bar equals 50 cm.

Notice that the femur of Giraffatitan, while transversely pretty broad, is freakishly narrow anteroposteriorly. The same is true of the femur of Brachiosaurus, although it’s never been shown in a published paper — I observed it in the mounted casts in Chicago.

Weird.

Calculations

So let’s take a wild stab at recalculating the mass of Giraffatitan using the Benson et al. formula. First, measuring the midshaft transverse:anteroposterior widths of the long bones gives eccentricity ratios of 2.39 for the femur and 1.54 for the humerus (I am not including the anterior prejection of the deltopectoral crest in the anteroposterior width of the humerus) . Dividing the absolute transverse widths above by these ratios gives us anteroposterior widths of 148 for the femur and 150 mm for the humerus. So they are almost exactly the same in this dimension.

If we simplify by treating these bones as elliptical in cross section, we can  approximate their midshaft circumference. It turns out that the formula for the circumference is incredibly complicated and involves summing an infinite series:

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But since we’re hand-waving so much anyway, we can use the approximation C = 2π sqrt((a²+b²)/2). where a and b are the major and minor radii (not diameters). For the femur, these measurements are 176 and 74 mm, so C = 848 mm; and for the humerus, 116 and 75 mm yields 614 mm. (This compares with FC=730 and HC=654 in the data-set of Benson et al., so we have found the femur to be bigger and the humerus smaller than they did.)

So the CF:CH ratio is 1.38 — rather a lot more than the 1.12 reported by Benson et al.  (Of course, if they measured the actual bones rather than messing about with illustrations, then their numbers are better than mine!)

And so to the mass formula, which Campione and Evans (2012) gave as their equation 2:

log BM = 2.754 log (CH+CF) − 1.097

Which I understand to use base-10 logs, circumferences measured in millimeters, and yield a mass in grams, though Campione and Evans are shockingly cavalier about this. CH+CF is 1462; log(1462) = 3.165. That gives us a log BM of 7.619, so BM = 41,616,453 g = 41,616 kg.

Comparison with Benson et al. (2014)

Midshaft measurements and estimates for SII long bones (all measurements in mm)
SV-POW! Benson et al.
Femur Humerus Femur Humerus
Transverse diameter 353 232 240
Transverse radius 176 116 120
Anteroposterior diameter 148 150 146
Anteroposterior radius 74 75 73
Circumference 848 614 730 654
Total circumference 1462 1384
Mass estimate (kg) 41,616 34,000

My new mass estimate of 41,616 kg is is a lot more than the 34,000 kg found by Benson et al. This seems to be mostly attributable to the much broader femur in my measurement: by contrast, the humerus measurements are very similar (varying by about 3% for both diameters). That leaves me wondering whether Benson et al. just looked at a different femur — or perhaps used St 291 without scaling it to SII size. Hopefully one of the authors will pass by and comment.

More to come on this mass estimate real soon!

References

 

Illustration talk slide 58

Illustration talk slide 59

Illustration talk slide 60

The rest of the series.

References

Sauroposeidon and friends

February 24, 2014

Sauroposeidon and kin cervicals - DRAFTAs a break from photography posts, here are four pretty big vertebrae that swirl in the same thought-space in my head. All are shown to scale, in right lateral view. These are not the biggest sauropod cervical vertebrae–Supersaurus beats them all, and there are vertebrae of Puertasaurus, Alamosaurus, and Futalognkosaurus that rival the big Sauroposeidon vert, but those are either less well preserved or still awaiting detailed description.

Incidentally, I think BYU 12867 is a C10. The centrum proportions are about right, compared to Giraffatitan, and the neural spine looks good, too, like a geometric transformation of the big Giraffatitan C8. Also, the drawn-in prezyg outline for MIWG.7306 is a little short; the actual prezyg is a monster and would have overhung the condyle by another 10cm or so. I’m pretty sure that we had a composite photograph showing this at one point, but irritatingly none of us can find it at the moment. If it turns up, I’ll update the image.

For a long time I thought Sauroposeidon was a brachiosaurid. Now it seems to be a somphospondyl (D’Emic 2012) or possibly even a basal titanosaur (Mannion et al. 2013), even if we stick just to the holotype. But if it’s not a brachiosaurid, it’s cervical vertebrae are at least coarsely brachiosaur-y in outline.

You  may recall from Naish et al. (2004) that MIWG.7306 shares several derived characters with the holotype vertebrae of Sauroposeidon. Does that mean that Angloposeidon is a somphospondyl or titanosaur as well? I dunno–as always, we need more material–but it’s an interesting possibility.

References

Illustration talk slide 19

Illustration talk slide 20

Illustration talk slide 21

Illustration talk slide 22

This whole section, including the title, is mostly swiped from Mike’s Tutorial 17.

Other posts in this series are here.

Papers referenced in these slides:

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