Scaled restoration of the giant titanosaur Puertasaurus by Nima Sassani, from the Art Evolved Sauropod Gallery

Get on over to Art Evolved and scope out the sauroponderous Sauropod Gallery. It’s brobdingnaginormous. I don’t want to seem biased, but there’s a lot of hot brachiosaurian action on display. I’m happy to say that the other clades are not ignored–diplodocids, dicraeosaurids, titanosaurs, mamenchisaurids, basal eusauropods, and even a basal sauropodomorph are all in the mix.

Normally my brachiosaurcentricity would lead me to steal one of the numerous brachiosaur images–perhaps the awesome parade of brachiosaurs that includes both Sauroposeidon and the Archbishop (!!)–BUT my laziness led me to choose another piece by the same artist, Nima Sassani. That would be the Puertasaurus reconstruction shown at top, which includes vertebrae and thus fulfills our titular mandate. That means I can stop writing now and get back to gawking. Go do likewise.

…oh, and don’t forget to stop by Dracovenator and congratulate Adam Yates on his new critter, Aardonyx. You’ll be hearing more about Aardonyx here at SV-POW! in the hopefully not-too-distant future. I can say no more for now…

Lovers of fine sauropods will be well aware that, along with the inadequately described Indian titanosaur Bruhathkayosarus, the other of the truly super-giant sauropods is Amphicoelias fragillimus.  Known only from a single neural arch of a dorsal vertebra, which was figured and briefly described by Cope (1878) and almost immediately either lost or destroyed, it’s the classic “one that got away”, the animal that sauropod aficionados cry into their beer about late at night.

Amphicoelias fragillimus, holotype dorsal vertebral neural arch in posterior view. From Osborn and Mook (1921:fig. 21), which in turn was gently tweaked from Cope (1878:unnumbered and only figure).

I’m not going to write about A. fragillimus in detail here, because Darren’s so recently covered it in detail over at Tetrapod Zoology — read Part 1 and Part 2 right now if you’ve not already done so.  The bottom line is that it was a diplodocoid roughly twice as big as Diplodocus in linear dimension (so about eight times as heavy).  That makes it very very roughly 50 m long and 100 tonnes in mass.

But Mike!, you say, Isn’t it terribly naive to go calculating masses and all from a single figure of part of a single bone?

Why, yes!  Yes, it is!  And that is what this post is about.

As I write, the go-to paper on A. fragillimus is Ken Carpenter’s (2006) re-evaluation, which carefully and tentatively estimated a length of 58 m, and a mass of around 122,400 kg.

As it happens, Matt and a colleague submitted a conference abstract a few days ago, and he ran it past me for comments before finalising.  In passing, he’d written “there is no evidence for sauropods larger than 150 metric tons and it is possible that the largest sauropods did not exceed 100 tons”.  I replied:

I think that is VERY unlikely. [...] the evidence for Amphicoelias fragillimus looks very convincing, Carpenter’s (2006) mass estimate of 122.4 tonnes is conservative, being extrapolated from Greg Paul’s ultra-light 11.5 tonne Diplodocus.

Carpenter’s estimate is based on a reconstruction of the illustrated vertebra, which when complete he calculated would have been 2.7 m tall.  That is 2.2 times the height of the corresponding vertebra in Diplodocus, and the whole animal was considered as it might be if it were like Diplo scaled up by that factor.  Here is his reconstruction of the vertebra, based on Cope’s figure of the smaller but better represented species Amphicoelias altus:

One possible reconstruction of the Alphicoelias fragillimus vertebra, from Carpenter (2006:fig. 1). Part A is Cope's original figure annotated with lamina designations; part B is Cope's illustration of an Amphocoelias altus dorsal; part C is Carpenter's reconstruction of the former after the latter.

Matt’s answer to me was:

First, Paul’s ultra-light 11.5 tonne Dippy is not far off from my 12 tonne version that you frequently cite, and mine should be lighter because it doesn’t include large air sacs (density of 0.8 instead of a more likely 0.7). If my Dippy had an SG of 0.7, it would have massed only 10.25 tonnes. Second, Carpenter skewed [...] in the direction of large size for Amphicoelias. I don’t necessarily think he’s wrong, but his favoured estimate is at the extreme of what the data will support. Let’s say that Amphicoelias was evenly twice as large as Dippy in linear terms; that could still give it a mass as low as 90 tonnes. And that’s not including the near-certainty that Amphicoelias had a much higher ASP than Diplodocus. If Amphicoelias was to Diplodocus as Sauroposeidon was to Brachiosaurus—pneumatic bones about half as dense—then 1/10 of its volume weighed ½ as much as it would if it were vanilla scaled up Dippy, and we might be able to knock off another 5 tonnes.

There’s lots of good stuff here, and there was more back and forth following, which I won’t trouble you with.  But what I came away with was the idea that maybe the scale factor was wrong.  And the thing to do, I thought, was to make my own sealed-room reconstruction and see how it compared.

So I extracted the A.f. figure from Osborn and Mook, and deleted their dotted reconstruction lines.  Then I went and did something else for a while, so that any memory of those lines might have been had a chance to fade.  I was careful not look at Carpenter’s reconstruction, so I could be confident mine would be indepedent.  Then I photoshopped the cleaned A. fragillimus figure it into a copy the A. altus figure, scaled it to fit the best as I saw it, and measured the results.  Here it is:

My scaling of a complete Amphicoelias fragillimus vertebra: on the left, Cope's figure of the only known vertebra; on the right, Cope's figure of an A. altus dorsal vertebra, scaled to match the preserved parts of the former. Height of the latter scaled according to the measured height of the former.

As you can see, when I measured my scaled-to-the-size-of-A.f. Amphicoelias vertebra, it was “only” 2293 mm tall, compared with 2700 mm in Ken’s reconstruction.  In other words, mine is only 85% as tall, which translates to 0.85^3 = 61% as massive.  So if this reconstruction is right, the big boy is “only” 1.87 times as long as Diplodocus in linear dimension — maybe 49 meters long — and would likely come in well below the 100-tonne threshhold.  Using Matt’s (2005) 12-tonne estimate for Diplodocus, we’d get a mere 78.5 tonnes for Amphicoelias fragillimus.  So maybe Matt called that right.

Amphicoelias altus dorsal vertebra, almost certainly the holotype, in left lateral view, lying on its back. Photograph by Matt Wedel, from the collections of the AMNH. I can't believe -- can't BELIEVE -- that I didn't take ten minutes to look at this vertebra when I was in that basement last February. What a doofus.

The Punchline

Folks — please remember, the punchline is not “Amphicoelias fragillimus only weighed 78.5 tonnes rather than 122.4 tonnes”.  The punchline is “when you extrapolate the mass of an extinct animal of uncertain affinities from a 132-year-old figure of a partial bone which has not been seen in more than a century, you need to recognise that the error-bars are massive and anything resembling certainty is way misplaced.”

Caveat estimator!

References

For reasons that will soon become apparent (yes, that’s a teaser), Matt and I wanted to figure out how heavy Camarasaurus was.  This is the story of how I almost completely badgered up part of that problem.  I am publishing it as a cautionary tale because I am very secure and don’t mind everyone knowing that I’m an idiot.

Those who paid close attention to my recent paper on Brachiosaurus and Giraffatitan will remember that when I estimated their mass using Graphic Double Integration (Taylor 2009: 802-804) I listed separately the volumes of the head, neck, forelimbs, hindlimbs, torso and tail of each taxon.  In Giraffatitan, the torso accounted for 71% of the total volume (20588 of 29171 litres), and in Brachiosaurus, 74% (26469 of 35860 litres), so it’s apparent that torso volume hugely dominates that of the whole animal.  In the giant balloon-model Giraffatitan of Gunga et al.’s (1995, 1999) estimates, the torso accounted for 74% of volume (55120 of 74420 litres) so even though their fleshing out of the skeleton was morbidly obese, the relative importance of the torso came out roughly the same.  Finally, Gunga et al’.s (2008) revised, less bloated, model of the same Giraffatitan had the torso contributing 68% of volume (32400 of 47600 litres).  So far as I know, these are all of the published accounts that give the volumes of separate parts of a sauropod body, but if there are any more, please tell me in the comments!   (Odd that they should all be for brachiosaurids.)

3D "slim" version of reconstruction of the "Brachiosaurus" brancai mounted and exhibited at the Museum of Natural History in Berlin (Germany). A. Side view, upper panel; B. top view, lower panel. The cross in the figure of upper panel indicates the calculated center of gravity. (Gunga et al. 2008: figure 2)

So it’s evident that, in brachiosaurs at least, the torso accounts for about 70% total body volume, and therefore for about that much of the total mass.  (The distribution of penumaticity means that it’s denser than the neck and less dense than the limbs, so that its density is probably reasonably close to the average of the whole animal.)

Now here’s the problem.  How fat is the sauropod?  Look at the top-view of Giraffatitan in the Gunga et al. figure above: it’s easy to imagine that the torso could be say 20% narrower from side to side, or 20% broader.  Those changes to breadth would affect volume in direct proportion, which would mean (if the torso is 70% of the whole animal) a change in total body volume of 14% either way.  Significant stuff.

So what do we know about the torso breadth in sauropods?  It obviously dependant primarily on the orientation of the ribs and their articulation to the dorsal vertebrae.  And what do we know about that?

Nothing.

Well, OK, I am over-simplifying a little.  It’s been mentioned in passing in a few papers, but it’s never been discussed in any detail in a published paper that I know of.  (There’s a Masters thesis out there that starts to grapple with the subject, but I don’t know whether I should talk about that while it’s still being prepared for publication, so I won’t say anything more.)  The most important published contribution is more than a century old — Holland’s (1910) smackdown of Tornier’s and Hay’s comical Diplodocus postures, which included the following cross-sections of the torsos of several animals at the seventh dorsal vertebra:

(This figure previously appeared on SV-POW! in Matt’s post, Sauropods were tacos, not corn dogs, which as far as I am aware is the only existing non-technical treatment of sauropod torso-shape.)

Holland unfortunately did not discuss the torso shape that he illustrated, merely asserting it.  Presumably it is based on the mounted skeleton of the Diplodocus carnegii holotype CM 84, which is at the Carnegie Museum in Pittsburgh, where Holland was based.  I have no reason to doubt it; just noting that it wasn’t discussed.

All right then — what about Camarasaurus?  I think it’s fair to say that it’s generally considered to be fairly rotund among sauropods, as for example this skeletal reconstruction by Greg Paul shows:

Camarasaurus lentus skeletal reconstruction, in dorsal and right lateral views. (Paul 2010:197)

Measuring off the height and width of the torso at the seventh dorsal vertebra, using GIMP, I find that they are 341 and 292 pixels respectively, so that the eccentricity is 341/292 = 1.17.  This compares with 1760/916 = 1.92 for Holland’s Diplodocus above, so if both figures are accurate, then Camarasaurus is much fatter than Diplodocus.

But is Paul’s Camarasaurus ribcage right?  To answer that, I went back to my all-time favourite sauropod paper, Osborn and Mook’s (1921) epic descriptive monograph of Camarasaurus (and Cope’s other sauropods).  I knew that this awesomely comprehensive piece of work would include plates illustrating the ribs; and in fact there are four plates that each illustrate a complete set of dorsal ribs (although the associations are doubtful).  Here they all are:

Left dorsal ribs of Camarasaurus (Osborn and Mook 1921:pl. LXXVIII)

Left dorsal ribs of Camarasaurus (Osborn and Mook 1921:pl. LXXIX)

Left dorsal ribs of Camarasaurus (Osborn and Mook 1921:pl. LXXX)

Left dorsal ribs of Camarasaurus (Osborn and Mook 1921:pl. LXXXI)

But hang on a minute — what do you get if you articulate these ribs with the dorsal vertebrae?  Osborn and Mook also provided four plates of sequences of dorsal vertebrae, and the best D7 of the four they illustrate is probably the one from plate  LXX.  And of the four 7th ribs illustrated above, the best preserved is from plate LXXIX.  So I GIMPed them together, rotated the ribs to fit as best I could and …

What on earth?!

I spent a bit of time last night feeling everything from revulsion to excitement about this bizarre vertebra-and-rib combination.  Until I happened to look again Osborn and Mook — earlier on, in the body of the paper, in the section about the ribs.  And here’s what I saw:

(Note that this is the vertebra and ribs at D4, not D7; but that’s close enough that there’s no way there could be a transition across three vertebrae like the change between this and the horrible sight that I presented above.)

What’s going on here?  In the plates above, the ribs do not curve inwards as in this cross-section: they are mostly straight, and in many case seem to curve negatively — away from the torso.  So why do O&M draw the ribs in this position that looks perfectly reasonable?

And figure 70, a few pages earlier, makes things even weirder: it clearly shows a pair of ribs curving medially, as you’d expect them to:

So why do these ribs look so totally different from those in the plates above?

I’ll give you a moment to think about that before I tell you the answer.

Seriously, think about it for yourself.  While you’re turning it over in your mind, here is a picture of the beautiful Lego kit #10198, the Blockade Runner from the original Star Wars movie.  (I deeply admire the photography here: clear as a bell.)

OK, welcome back.

Got it?  I bet most of you have.

The answer was right there in figure 71:

Left rib of Camarasaurus supremus Cope. Rib 4 (Amer. Mus. Cope Coll. No. 5761/R-A-24. (A) direct external view when placed as in position in the body; (B) direct anterior view, when placed as in position in the body. Capit. capitulum; Sh. shaft; Tub. tuberculum. Reconstructed portion in outline (Osborn and Mook 1921:fig. 71)

And, my word, isn’t it embarrassingly obvious once you see it?  I’d been blithely assuming that the ribs in O&M’s plates were illustrated in anterior view, with the capitula (which articulate with the parapophyses) located more medially, as well as more ventrally, than the tubercula (which articulate with the diapophyses).  But no: as in fact the captions of the plates state perfectly clearly — if I’d only had the wits to read them — the ribs are shown in “external” (i.e. lateral) view.  Although it’s true that the capitula in life would indeed have been more medially positioned than the tubercula, it’s also true that they were more anteriorly positioned, and that’s what the plates show at the rib heads.  And the curvature that I’d been stupidly interpreting as outward, away from the midline, is in fact posteriorly directed: the ribs are “swept back”.  The ventral portions of the ribs also curve medially, away from the viewer and into the page … but of course you can’t see that in the plates.

The important truth — and if you take away nothing else from this post, take this — is that I am dumb bones are complex three-dimensional objects, and it’s impossible to fully understand their shape from single-view illustrations.  It’s for this reason that I make an effort, when I can, to illustrate complex bones from all cardinal directions — in particular, with the Archbishop bones, as for example “Cervical S” in the Brachiosaurus coracoid post.

Because ribs, in particular, are such complex shapes — because their curvature is so unpredictable, and because their articulation with the dorsal vertebrae is via two points which are located differently on successive vertebrae, and because this articulation still allows a degree of freedom of movement — orthoganal views, even from all cardinal directions, are of limited value.  Compositing figures will give misleading results … as demonstrated above.  PhotoShop is no more use here.  Fly, you fools!

Paradoxically, our best source of information on the shapes of saurpod torsos is: mounted skeletons.  I say “paradoxically” because we’ve all grown used to the idea that mounts are not much use to us as scientists, and are really there only as objects of awe.  As Brian Curtice once said, “A mounted skeleton is not science.  It’s art.  Its purpose is to entertain the public, not to be a scientifically accurate specimen”.  In many respects, that’s true — especially in skeletons like that of the “Brontosaurus” holotype, YPM 1980, where the bones are restored with, and in some cases encased in, plaster so you can’t tell what’s what.  But until digital scanning and modelling make some big steps forward, actual mounted skeletons are the best reference we have for the complex articulations of ribs.

Giraffatitan brancai paralectotype HMN SII, composite mounted skeleton, torso in left posteroventrolateral view (photograph by Mike Taylor)

And I finish this very long (sorry!) post with yet another note of caution.  Ribs are long and thin and very prone to damage and distortion.  It’s rare to find complete sauropod ribs (look closely at the O&M plates above for evidence), but even when we do, we shouldn’t be quick to assume that the shape in which they are preserved is necessarily the same as the shape they had in life.  (If you doubt this, take another look at rib #6 in the third of the four O&M plates above.)  And as if that weren’t enough to discourage us, we should also remember that the vertebra-rib joints would have involved a lot of cartilage, and we don’t know its extent or shape.

So bearing in mind the complicated 3D shape of ribs and of dorsal vertebrae, the tendency for both to distort during and after fossilisation, and the complex and imperfectly known nature of the joints between them, I think that maybe I wasn’t too far wrong earlier when I said that what we know about sauropod torso shape is: nothing.

It’s a sobering thought.

References

• Gunga, H. C., K. A. Kirsch, F. Baartz, L. Rocker, W.-D. Heinrich, W. Lisowski, A. Wiedemann and J. Albertz.  1995.  New Data on the Dimensions of Brachiosaurus brancai and Their Physiological Implications.  Naturwissenschaften 82 (4): 190-192. doi:10.1007/s001140050167
• Gunga, H. C., K. A. Kirsch, J. Rittweger, A. Clarke, J. Albertz, A. Wiedemann, S. Mokry, T. Suthau, A. Wehr, W.-D. Heinrich and H.-P. Schulze.  1999.  Body Size and Body Volume Distribution in Two Sauropods from the Upper Jurasic of Tendaguru (Tanzania). Mitteilungen des Museums fur Naturkunde Berlin, Geowissenschaftliche Reihe 2: 91-102.
• Gunga, Hans-Christian, Tim Suthau, Anke Bellmann, Stefan Stoinski, Andreas Friedrich, Tobias Trippel, Karl Kirsch and Olaf Hellwich. 2008.  A new body mass estimation of Brachiosaurus brancai Janensch, 1914 mounted and exhibited at the Museum of Natural History (Berlin, Germany). Fossil Record 11: 28-33.
  
• Holland, W. J.  1910.  A review of some recent criticisms of the restorations of sauropod dinosaurs existing in the museums of the United States, with special reference to that of Diplodocus carnegiei [sic] in the Carnegie museum.  American Naturalist 44: 259-283.
• Osborn, Henry Fairfield, and Charles C. Mook.  1921. Camarasaurus, Amphicoelias and other sauropods of Cope. Memoirs of the American Museum of Natural History, n.s. 3:247-387, and plates LX-LXXXV.
• Paul, Gregory S.  2010.  The Princeton Field Guide to Dinosaurs. Princeton University Press, Princeton, New Jersey.  320 pages.
• Taylor, Michael P.  2009a.  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.

Why we do mass estimates

Mass estimates are a big deal in paleobiology. If you want to know how much an animal needed in terms of food, water, and oxygen, or how fast it could move, or how many offspring it could produce in a season, or something about its heat balance, or its population density, or the size of its brain relative to its body, then at some point you are going to need a mass estimate.

All that is true, but it’s also a bit bogus. The fact is, people like to know how big things are, and paleontologists are not immune to this desire. We have loads of ways to rationalize our basic curiosity about the bigness of extinct critters. And the figuring out part is both very cool and strangely satisfying. So let’s get on with it.

Two roads diverged

There are two basic modes for determining the mass of an extinct animal: allometric, and volumetric. Allometric methods rely on predictable mathematical relationships between body measurements and body mass. You measure a bunch of living critters, plot the results, find your regression line, and use that to estimate the masses of extinct things based on their measurements. Allometric methods have a couple of problems. One is that they are absolutely horrible for extrapolating to animals outside the size range of the modern sample, which ain’t so great for us sauropod workers. The other is that they’re pretty imprecise even within the size range of the modern sample, because real data are messy and there is often substantial scatter around the regression line, which if faithfully carried through the calculations produces large uncertainties in the output. The obvious conclusion is that anyone calculating extinct-animal masses by extrapolating an allometric regression ought to calculate the 95% confidence intervals (e.g. “Argentinosaurus massed 70000 kg, with a 95% confidence interval of 25000-140000 kg), but, oddly, no-one seems to do this.

Volumetric methods rely on creating a physical, digital, or mathematical model of an extinct animal, determining the volume of the model, multiplying by a scale factor to get the volume of the animal in life, and multiplying that by the presumed density of the living animal to get its mass. Volumetric methods have three problems: (1) many extinct vertebrates are known from insufficient material to make a good 3D model of the skeleton; (2) even if you have a complete skeleton, the method is very sensitive to how you articulate the bones–especially the ribcage–and the amount of flesh you decide to pack on, and there are few good guidelines for doing this correctly; and (3) relatively small changes in the scale factor of the model can produce big changes in the output, because mass goes with the cube of the linear measurement. If your scale factor is off by 10%, you mass will be off by 33% (1.1^3=1.33).

On the plus side, volumetric mass estimates are cheap and easy. You don’t need hundreds or thousands of measurements and body masses taken from living animals; you can do the whole thing in your kitchen or on your laptop in the space of an afternoon, or even less. In the old days you’d build a physical model, or buy a toy dinosaur, and use a sandbox or a dunk tank to measure the volume of sand or water that the model displaced, and go from there. Then in the 90s people started building digital 3D models of extinct animals and measuring the volumes of those.

But you don’t need a physical model or a dunk tank or even a laptop to do volumetric modeling. Thanks to a method called graphic double integration or GDI, which is explained in detail in the next section, you can go through the whole process with nothing more than pen and paper, although a computer helps.

Volumetric methods in general, and GDI in particular, have one more huge advantage over allometric methods: they’re more precise and more accurate. In the only published study that compares the accuracy of various methods on extant animals of known mass, Hurlburt (1999) found that GDI estimates were sometimes off by as much as 20%, but that allometric estimates were much worse, with several off by 90-100% and one off by more than 800%. GDI estimates were not only closer to the right answers, they also varied much less than allometric methods. On one hand, this is good news for GDI afficionados, since it is the cheapest and easiest of all the mass estimation methods out there. On the other hand, it should give us pause that on samples of known mass, the best available method can still be off by as much as a fifth even when working with complete bodies, including the flesh. We should account for every source of error that we can, and still treat our results with appropriate skepticism.

Graphic Double Integration

GDI was invented by Jerison (1973) to estimate the volumes of cranial endocasts. Hurlburt (1999) was the first to apply it to whole animals, and since then it has been used by Murray and Vickers-Rich (2004) for mihirungs and other extinct flightless birds, yours truly for small basal saurischians (Wedel 2007), Mike for Brachiosaurus and Giraffatitan (Taylor 2009), and probably many others that I’ve missed.

GDI is conceptually simple, and easy to do. Using orthogonal views of a life restoration of an extinct animal, you divide the body into slices, treat each slice as an ellipse whose dimensions are determined from two perspectives, compute the average cross-sectional area of each body part, multiply that by the length of the body part in question, and add up the results. Here’s a figure from Murray and Vickers-Rich (2004) that should clarify things:

One of the cool things about GDI is that it is not just easy to separate out the relative contributions of each body region (i.e., head, neck, torso, limbs) to the total body volume, it’s usually unavoidable. This not only lets you compare body volume distributions among animals, it also lets you tinker with assigning different densities to different body parts.

An Example: Plateosaurus

Naturally I’m not going to introduce GDI without taking it for a test drive, and given my proclivities, that test drive is naturally going to be on a sauropodomorph. All we need is an accurate reconstruction of the test subject from at least two directions, and preferably three. You could get these images in several ways. You could take photographs of physical models (or toy dinosaurs) from the front, side, and top–that could be a cool science fair project for the dino-obsessed youngster in your life. You could use the white-bones-on-black-silhouette skeletal reconstructions that have become the unofficial industry standard. You could also use orthogonal photographs of mounted skeletons, although you’d have to make sure that they were taken from far enough away to avoid introducing perspective effects.

For this example, I’m going to use the digital skeletal reconstruction of the GPIT1 individual of Plateosaurus published by virtual dino-wrangler and frequent SV-POW! commenter Heinrich Mallison (Mallison et al 2009, fig. 14). I’m using this skeleton for several reasons: it’s almost complete, very little distorted, and I trust that Heinrich has all the bits in the right places. I don’t know if the ribcage articulation is perfect but it looks reasonable, and as we saw last time that is a major consideration. Since Heinrich built the digital skeleton in digital space, he knows precisely how big each piece actually is, so for once we have scale bars we can trust. Finally, this skeleton is well known and has been used in other mass estimate studies, so when I’m done we’ll have some other values to compare with and some grist for discussion. (To avoid accidental bias, I’m not looking at those other estimates until I’ve done mine.)

Of course, this is just a skeleton, and for GDI I need the body outline with the flesh on. So I opened the image in GIMP (still free, still awesome) and drew on some flesh. Here we necessarily enter the realm of speculation and opinion. I stuck pretty close to the skeletal outline, with the only major departures being for the soft tissues ventral to the vertebrae in the neck and for the bulk of the hip muscles. As movie Boromir said, there are other paths we might take, and we’ll get to a couple of alternatives at the end of the post.

This third image is the one I used for actually taking measurements. You need to lop off the arms and legs and tote them up separately from the body axis. I also filled in the body outlines and got rid of the background so I wouldn’t have any distracting visual clutter when I was taking measurements. I took the measurements using the measuring tool in GIMP (compass icon in the toolbar), in orthogonal directions (i.e., straight up/down and left/right), at regular intervals–every 20 pixels in this case.

One thing you’ll have to decide is how many slices to make. Ideally you’d do one slice per pixel, and then your mathematical model would be fairly smooth. There are programs out there that will do this for you; if you have a 3D digital model you can just measure the voxels (= pixels cubed) directly, and even if all you have is 2D images there are programs that will crank the GDI math for you and measure every pixel-width slice (Motani 2001). But if you’re just rolling with GIMP and OpenOffice Calc (or Photoshop and Excel, or calipers and a calculator), you need to have enough slices to capture most of the information in the model without becoming unwieldy to measure and calculate. I usually go with 40-50 slices through the body axis and 9 or 10 per limb.

The area of a circle is pi*r^2, and the area of an ellipse is pi*r*R, where r and R are the radii of the minor and major axes. So enter the widths and heights of the body segments in pixels in two columns (we’ll call them A and B) in your spreadsheet, and create a third column with the function 3.14*A1*B1/4. Divide by four because the pixel counts you measured on the image are diameters and the formula requires radii. If you forget to do that, you are going to get some wacky numbers.

One obvious departure from reality is that the method assumes that all of the body segments of an animal have elliptical cross-sections, when that is often not exactly true. But it’s usually close enough for the coarse level of detail that any mass estimation method is going to provide, and if it’s really eating you, there are ways to deal with it without assuming elliptical cross-sections (Motani 2001).

For each body region, average the resulting areas of the individual slices and multiply the resulting average areas by the lengths of the body regions to get volumes. Remember to measure the lengths at right angles to your diameter measurements, even when the body part in question is curved, as is the tail of Heinrich’s Plateosaurus.

For sauropods you can usually treat the limbs as cylinders and just enter the lateral view diameter twice, unless you are fortunate enough to have fore and aft views. It’s not a perfect solution but it’s probably better than agonizing over the exact cross sectional shape of each limb segment, since that will be highly dependent on how much flesh you (or some other artist) put on the model, and the limbs contribute so little to the final result. For Plateosaurus I made the arm circular, the forearm and hand half as wide as tall, the thigh twice as long as wide, and the leg and foot round. Don’t forget to double the volumes of the limbs since they’re paired!

We’re not done, because so far all our measurements are in pixels (and pixels cubed). But already we know something cool, which is what proportion each part of the body contributes to the total volume. In my model based on Heinrich’s digital skeleton, segmented as shown above, the relative contributions are as follows:

• Head: 1%
• Neck: 3%
• Trunk: 70%
• Tail: 11%
• Forelimbs (pair): 3%
• Hindlimbs (pair): 12%

Already one of the great truths of volumetric mass estimates is revealed: we tend to notice the extremities first, but really it is the dimensions of the trunk that drive everything. You could double the size of any given extremity and the impact on the result would be noticeable, but small. Consequently, modeling the torso accurately is crucial, which is why we get worried about the preservation of ribs and the slop inherent in complex joints.

Scale factor

The 170 cm scale bar in Heinrich’s figure measures 292 pixels, or 0.582 cm per pixel. The volume of each body segment must be multiplied by 0.582 cubed to convert to cubic cm, and then divided by 1000 to convert to liters, which are the lingua franca of volumetric measurement. If you’re a math n00b, your function should look like this: volume in liters = volume in pixels*SF*SF*SF/1000, where SF is the scale factor in units of cm/pixel. Don’t screw up and use pixels/cm, or if you do, remember to divide by the scale factor instead of multiplying. Just keep track of your units and everything will come out right.

If you’re not working from an example as perfect as Heinrich’s digital (and digitally measured) skeleton, you’ll have to find something else to use for a scale bar. Something big and reasonably impervious to error is good. I like the femur, if nothing else is available. Any sort of multi-segment dimension like shoulder height or trunk length is going to be very sensitive to how much gloop someone thought should go between the bones. Total length is especially bad because it depends not only on the intervertebral spacing but also on the number of vertebrae, and even most well-known dinos do not have complete vertebral series.

Density

Finally, multiply the volume in liters by the assumed density to get the mass of each body segment. Lots of people just go with the density of water, 1.0 kg/L, which is the same as saying a specific gravity (SG) of 1. Depending on what kind of animal you’re talking about, that may be a little bit off or it may be fairly calamitous. Colbert (1962) found SGs of 0.81 and 0.89 for an extant lizard and croc, which means an SG of 1.0 is off by between 11% and 19%. Nineteen percent–almost a fifth! For birds, it’s even worse; Hazlehurst and Rayner (1992) found an SG of 0.73.

Now, scroll back up to the diagram of the giant moa, which had a mass of 257.5 kg “assuming a specific gravity of 1″. If the moa was as light as an extant bird–and its skeleton is highly pneumatic–then it might have had a mass of only 188 kg (257.5*0.73). Or perhaps its density was higher, like that of a lizard or a croc. Without a living moa to play with, we may never know. Two points here: first, the common assumption of whole-body densities of 1.0 is demonstrably incorrect* for many animals, and second, since it’s hard to be certain about the densities of extinct animals, maybe the best thing is to try the calculation with several densities and see what results we get. (My thoughts on the plausible densities of sauropods are here.)

* Does anyone know of actual published data indicating a density of 1.0 for a terrestrial vertebrate? Or is the oft-quoted “bodies have the same density as water” basically bunk? (Note: I’m not disputing that flesh has a density close to that of water, but bones are denser and lungs and air spaces are lighter, and I want to know the mean density of the whole organism.)

Back to Plateosaurus. Using the measurements and calculations presented above, the total volume of the restored animal is 636 liters. Here are the whole body masses (in kg) we get using several different densities:

• SG=1.0 (water), 636 kg
• SG=0.89 (reptile high), 566 kg
• SG=0.81 (reptile low), 515 kg
• SG=0.73 (bird), 464 kg

I got numbers. Now what?

I’m going to describe three possible things you could do with the results once you have them. In my opinion, two of them are the wrong the thing to do and one is the right thing to do.

DON’T mistake the result of your calculation for The Right Answer. You haven’t stumbled on any universal truth. Assuming you measured enough slices and didn’t screw up the math, you know the volume of a mathematical model of an organism. If you crank all the way through the method you will always get a result, but that result is only an estimate of the volume of the real animal the model was based on. There are numerous sources of error that could plague your results, including: incomplete skeletal material, poorly articulated bones, wrong scale factor, wrong density, wrong amount of soft tissue on the skeleton. I saved density and gloop for last because you can’t do much about them; here the strength of your estimate relies on educated guesses that could themselves be wrong. In short, you don’t even know how wrong your estimate might be.

Pretty dismal, eh?

DON’T assume that the results are meaningless because you don’t know the actual fatness or the density of the animal, or because your results don’t match what you expected or what someone else got. I see this a LOT in people that have just run their first phylogenetic analysis. “Why, I could get any result I wanted just by tinkering with the input!” Well, duh! Like I said, the method will always give you an answer, and it won’t tell you whether the answer is right or not. The greatest advantage of explicit methods like cladistics and GDI is that you know what the input is, and so does everyone else if you are honest about reporting it. So if someone disagrees with your character coding or with how much the belly sags on your model sauropod, you can have a constructive discussion and hopefully science as a whole gets closer to the right answer (even if we have no way of knowing if or when we arrive, and even if your pet hypothesis gets trampled along the way).

DO be appropriately skeptical of your own results without either accepting them as gospel or throwing them out as worthless. The fact that the answer changes as you vary the parameters is a feature, not a bug. Investigate a range of possibilities, report all of those results, and feel free to argue why you think some of the results are better than others. Give people enough information to replicate your results, and compare your results to those of other workers. Figure out where yours differ and why.

Try to think of more interesting things you could do with your results. Don Henderson went from digitally slicing critters (Henderson 1999) to investigating floating sauropods (Henderson 2004) to literally putting sauropods through their paces (Henderson 2006)–not to mention working on pterosaur flight and swimming giraffes and other cool stuff. I’m not saying you should run out and do those exact things, but rather that you’re more likely to come up with something interesting if you think about what you could do with your GDI results instead of treating them as an end in themselves.

How massive was GPIT1, really?

Beats me. I’m not the only one who has done a mass estimate based on that skeleton. Gunga et al. (2007) did not one but two volumetric mass estimates based on GPIT1, and Mallison (2010) did a whole series, and they published their models so we can see how they got there. (In fact, many of you have probably been reading this post in slack-jawed horror, wondering why I was ignoring those papers and redoing the mass estimate the hard way. Now you know!) I’m going to discuss the results of Gunga et al. (2007) first, and come back to Mallison (2010) at the end.

Here’s the “slender” model of Gunga et al. 2007 (their fig. 3):

and here’s their “robust” model (Gunga et al. 2007:fig. 4):

(These look a bit…inelegant, let’s say…because they are based on the way the physical skeleton is currently mounted; Heinrich’s model looks much nicer because of his virtual remount.)

For both mass estimates they used a density of 0.8, which I think is probably on the low end of the range for prosauropods but not beyond the bounds of possibility. They got a mass of 630 kg for the slender model and 912 kg for the robust one.

Their 630-kg estimate for the slender model is deceptively close to the upper end of my range; deceptive because their 630-kg estimate assumes a density of 0.8 and my 636-kg one assumes a density of 1.0. The volumes are more directly comparable: 636 L for mine, 790 L for their slender one, and 1140 L for their robust one. I think that’s pretty good correspondence, and the differences are easily explained. My version is even more skinnier than their slender version; I made it about as svelte as it could possibly have been. I did that deliberately, because it’s always possible to pack on more soft tissue but at some point the dimensions of the skeleton establish a lower bound for how voluminous a healthy (i.e., non-starving) animal could have been. The slender model of Gunga et al. (2007) looks healthier than mine, whereas their robust version looks, to my eye, downright corpulent. But not unrealistically so; fat animals are less common than skinny ones but they are out there to be found, at least in some times and places. It pays to remember that the mass of a single individual can fluctuate wildly depending on seasonal food availability and exercise level.

For GPIT1, I think something like 500 kg is probably a realistic lower bound and 900 kg is a realistic upper bound, and the actual mass of an average individual Plateosaurus of that size was somewhere in the middle. That’s a big range–900 kg is almost twice 500 kg. It’s hard to narrow down because I really don’t know how fleshy Plateosaurus was or what it’s density might have been, and I feel less comfortable making guesses because I’ve spent much less time working on prosauropods than on sauropods. If someone put a gun to my head, I’d say that in my opinion, a bulk somewhere between that of my model and the slender model of Gunga et al. is most believable, and a density of perhaps 0.85, for a result in the neighborhood of 600 kg. But those are opinions, not hypotheses, certainly not facts.

I’m happy to see that my results are pretty close to those of Mallison (2010), who got 740 L, which is also not far off from the slender model of Gunga et al. (2007). So we’ve had at least three independent attempts at this and gotten comparable results, which hopefully means we’re at least in the right ballpark (and pessimistically means we’re all making mistakes of equal magnitude!). Heinrich’s paper is a goldmine, with loads of interesting stuff on how the skeleton articulates, what poses the animal might have been capable of, and how varying the density of different body segments affects the estimated mass and center of mass. It’s a model study and I’d happily tell you all about it but you should really read it for yourself. Since it’s freely available (yay open access!), there’s no barrier to you doing so.

Conclusion

So: use GDI with caution, but do use it. It’s easy, it’s cool, it’s explicit, it will give you lots to think about and give us lots to talk about. Stay tuned for related posts in the not-too-distant future.

References

• Gunga, H.-C., Suthau, T., Bellmann, A., Friedrich, A., Schwanebeck, T., Stoinski, S., Trippel, T., Kirsch, K., Hellwich, O. 2007. Body mass estimations for Plateosaurus engelhardti using laser scanning and 3D reconstruction methods. Naturwissenschaften 94(8):623-630.
• Henderson, D.M. 1999. Estimating the mass and centers of mass of extinct animals by 3D mathematical slicing. Paleobiology 25:88-106.
• Henderson, D.M. 2004. Tipsy punters: sauropod dinosaur pneumaticity, buoyancy and aquatic habits. Proceedings: Biological Sciences 271 (Supplement):S180-S183.
• Henderson, D.M. 2006. Burly gaits: centers of mass, stability and the trackways of sauropod dinosaurs. Journal of Vertebrate Paleontology 26:907-921.
• Hurlburt, G. 1999. Comparison of body mass estimation techniques, using Recent reptiles and the pelycosaur Edaphosaurus boanerges. Journal of Vertebrate Paleontology 19:338–350.
• Jerison, H.J. 1973. Evolution of the Brain and Intelligence. Academic Press, New York, NY, 482 pp.
• Mallison, H., Hohloch, A., and Pfretzschner, H.-U. 2009. Mechanical digitizing for paleontology–new and improved techniques. Palaeontologica Electronica 12(2):4T, 41 pp.
• Mallison, H. 2010. The digital Plateosaurus I: Body mass, mass distribution, and posture assessed by using CAD and CAE on a digitally mounted complete skeleton. Palaeontologica Electroncia 13(2):8A, 26 pp.
• Motani, R. 2001. Estimating body mass from silhouettes: testing the assumption of elliptical body cross-sections. Paleobiology 27(4):735–750.
• Murray, P.F. and Vickers-Rich, P. 2004. Magnificent Mihirungs. Indiana University Press, Bloomington, IN, 410 pp.
• Taylor, M.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. 2007. What pneumaticity tells us about ‘‘prosauropods,’’ and vice versa. Special Papers in Palaeontology 77:207–222.

I have a new paper out:

Wedel, M.J. 2012. A monument of inefficiency: the presumed course of the recurrent laryngeal nerve in sauropod dinosaurs. Acta Palaeontologica Polonica 57(2):251-256.

Update June 6, 2012: the final version was formally published yesterday, so the rest of this paragraph is of historical interest only. Like Yates et al. on prosauropod pneumaticity, it is “out” in the sense that the manuscript has been through peer review, has been accepted for publication, and is freely available online at Acta Palaeontologica Polonica. Technically it is “in press” and not published yet, but all that formal publication will change is to make a prettier version of the paper available. All of the content is available now, and the paper doesn’t include any of those pesky nomenclatural acts, and so, as with the prosauropod pneumaticity paper, I don’t see any reason to pretend it doesn’t exist. Think of the accepted manuscript as the caterpillar to the published version’s butterfly: different look, but same genome.

This one came about because last summer I read a review of Richard Dawkins’s book, The Greatest Show on Earth: The Evidence for Evolution. The review mentioned that the book includes a lengthy discussion of the recurrent laryngeal nerve (RLN) in the giraffe, which is a spectacularly dumb piece of engineering and therefore great evidence against intelligent design creationism. It wasn’t the first time I’d heard of the RLN, of course. It’s one of the touchstones of both human anatomy and evolutionary biology; anatomy because of its clinical importance in thyroid surgery, known for more than two millennia, and evolutionary biology because it is such a great example of a developmental constraint. (Dawkins’s coverage of all of this is great, BTW, and you should read the book.)

No, the reason the book review inspired me to write the paper was not because the RLN was new to me, but because it was overly familiar. It is a cool piece of anatomy, and its fame is justly deserved–but I am sick and tired of seeing the stinkin’ giraffe trotted out as the ultimate example of dumb design. My beloved sauropods were way dumber, and it’s time they got some credit.

But first, let’s talk about that nerve, and how it got to be there.

No necks for sex? How about no necks for anybody!

Embryos are weird. When you were just a month old (counting from fertilization), you had a set of pharyngeal arches that didn’t look radically different from those of a primitive fish. These started out quite small, tucked up underneath your comparatively immense brain, and each pharyngeal arch was served by a loop of artery called an aortic arch. What we call the arch of the aorta in an adult human is a remnant of just one of these embryonic aortic arches, and as you’ve no doubt noticed, it’s down in your chest, not tucked up next to your brain. When you were in the embryonic stages I’m talking about, you didn’t yet have a neck, so your brain, pharyngeal arches, aortic arches, and the upper parts of your digestive system were all smooshed together at your front end.

Human embryo at three weeks. From http://education.yahoo.com/reference/gray/subjects/subject/135

One thing you did have at that stage was a reasonably complete peripheral nervous system. The nerve cell bodies in and near your central nervous system sent out axons into the rest of your body, including your extremities. Many of these axons did not persist; they failed to find innervation targets and their parent neurons died. Imagine your embryonic central nervous system sending out a starburst of axons in all directions, and some of those axons finding targets and persisting, and others failing and dying back. So the architecture of your nervous system is the result of a process of selection in which only some cells were successful.

Crucially, this radiation and die-off of axons happened very early in development, when a lot of what would become your guts was still hanging under your proportionally immense brain like the gondola on a blimp. This brings us to the recurrent laryngeal nerve.

Going back the way we came

The fates of your embryonic pharyngeal arches are complex and I’m not going to do a comprehensive review here (go here for more information). Suffice it to say that the first three arches give rise to your jaws and hyoid apparatus, the fourth and sixth form your larynx (voicebox), and fifth is entirely resorbed during development.

There are two major nerves to the larynx, each of which is bilaterally paired. The nerve of the fourth pharyngeal arch becomes the superior laryngeal nerve, and it passes cranial to the fourth aortic arch. The nerve of the sixth pharyngeal arch becomes the inferior or recurrent laryngeal nerve, and it passes caudal to the sixth aortic arch. At the time that they form, both of these nerves take essentially straight courses from the brainstem to their targets, because you’re still in the blimp-gondola stage.

If you were a shark, the story would be over. The more posterior pharyngeal arches would persist as arches instead of forming a larynx, each arch would hold on to its artery, and the nerves would all maintain their direct courses to their targets.

The normal fate of the aortic arches in humans. From http://education.yahoo.com/reference/gray/subjects/subject/135

But you’re not a shark, you’re a tetrapod. Which means that you have, among other things, a neck separating your head and your body. And the formation of your neck shoved your heart and its associated great vessels down into your chest, away from the pharyngeal arches. This was no problem for the superior laryngeal nerve, which passed in front of the fourth aortic arch and could therefore stay put. But the inferior laryngeal nerve passed behind the sixth aortic arch, so when the heart and the fourth and sixth aortic arches descended into the chest, the inferior laryngeal nerve went with them. Because it was still hooked up to the brainstem and the larynx, it had to grow in length to compensate.

Human laryngeal nerves, from http://www.healthcentral.com/ency/408/imagepages/19721.html

As you sit reading this, your inferior laryngeal nerves run down your neck into your chest, loop around the vessels derived from the fourth and sixth aortic arches (the subclavian artery on the right, and the arch of the aorta and ductus arteriosus on the left) and run back up your neck to your larynx. Because they do this U-turn in your chest and go back the way they came, the inferior laryngeal nerves are said to ‘recur’ to the larynx and are therefore more commonly referred to as the recurrent laryngeal nerves (RLNs).

An enlightening diversion

The RLN is the poster child for “unintelligent design” because it is pretty dumb. Your RLNs travel a heck of a lot farther to reach your larynx than they ought to, if they’d been designed. Surely an intelligent designer would have them take the same direct course as the superior laryngeal nerve. But evolution didn’t have that option. Tetrapod embryos could not be built from the ground up but had to be modified from the existing “sharkitecture” of ancestral vertebrates. The rules of development could not be rewritten to accommodate a shorter RLN. Hence Dawkins’s love affair with the RLN, which gets 7 pages in The Greatest Show on Earth. He also appeared on the giraffe episode of Inside Nature’s Giants, in which the RLN was dug out of the neck and the continuity of its ridiculous path was demonstrated–probably the most smack-you-in-the-face evidence for evolution that has ever been shown on television (said the rabid fan of large-tetrapod dissections).

Incidentally, the existence and importance of the RLN has been known since classical times. The RLN innervates the muscles responsible for speech, and on either side it passes right behind the thyroid gland, which is subject to goiters and tumors and other grotesque maladies. So a careless thyroidectomy can damage one or both of the RLNs; if one gets snipped, the subject will be hoarse for the rest of his or her life; if both are cut, the subject will be rendered mute. The Roman physician Galen memorably demonstrated this by dissecting the neck of an immobilized but unanesthetized pig and isolating the RLNs (Kaplan et al. 2009). One moment the poor pig was squealing its head off–as any of us would be if someone dug out our RLNs without anesthesia–and the next moment Galen severed the RLNs and the animal abruptly fell silent, still in unbelievable pain but now without a mechanism to vocally express its discomfort.

Galen versus pig. Figure 2 from Kaplan et al. 2009.

The name of the nerve also goes back to Galen, who wrote:

I call these two nerves the recurrent nerves (or reversivi) and those that come upward and backward on account of a special characteristic of theirs which is not shared by any of the other nerves that descend from the brain.

Like at least some modern surgeons, Galen does not seem to have been overly burdened by humility:

All these wonderful things, which have now become common property, I was the first of all to discover, no anatomist before me ever saw one of these nerves, and so all of them before me missed the mark in their anatomical description of the larynx.

Both of those quotes are from Kaplan et al. (2009), which is a fascinating paper that traces the knowledge of the recurrent laryngeal nerve from classical times to the early 20th century. If you’d like a copy and can’t get hold of one any other way, let me know and I’ll hook you up.

Share and share alike

By now you can see where this is going: all tetrapods have larynges, all tetrapods have necks, and all tetrapods have recurrent laryngeal nerves. Including giraffes, much to the delight of Richard Dawkins. And also including sauropods, much to the delight of yours truly.

Now, I cannot show you the RLN in a living sauropod, nor can I imagine a scenario in which such a delicate structure would be recognizably preserved as a fossil. But as tetrapods, sauropods were bound to the same unbreakable rules of development as everything else. The inference that sauropods had really long, really dumb RLNs is as secure as the inference that they had brainstems, hearts, and larynges.

Wedel (in press) Fig. 1. Course of the left vagus nerve and left recurrent laryngeal nerve in a human, a giraffe, and Supersaurus. The right recurrent laryngeal nerve passes caudal to the right subclavian artery rather than the aorta and ductus arteriosus, but otherwise its course is identical to that of the left.

Giraffes have necks up to 2.4 meters long (Toon and Toon 2003), so the neurons that make up their RLNs approach 5 meters in the largest indiividuals. But the longest-necked sauropods had necks 14 meters long, or maybe even longer, so they must have had individual neurons at least 28 meters long. The larynx of even the largest sauropod was probably less than 1 meter away from the brainstem, so the “extra” length imposed on the RLN by its recurrent course was something like 27 meters in a large individual of Supersaurus. Take that, Giraffa.

Inadequate giraffe is inadequate.

One way or another

It is possible to have a nonrecurrent laryngeal nerve–on one side, anyway. If you haven’t had the opportunity to dissect many cadavers, it may come as a surprise to learn that muscles, nerves, and blood vessels are fairly variable. Every fall in Gross Anatomy at WesternU, we have about 40 cadavers, and out of those 40 people we usually have two or three with variant muscles, a handful with unusual branching patterns of nerves, and usually half a dozen or so with some wackiness in their major blood vessels. Variations of this sort are common enough that the better anatomy atlases illustrate not just one layout for, say, the branching of the femoral artery, but 6-10 of the most common patterns. Also, these variations are almost always asymptomatic, meaning that they never cause any problems and the people who have them usually never know (ask Mike about his lonely kidney sometime). You–yes, you, gentle reader!–could be a serious weirdo and have no idea.

Variations in the blood vessels seem to be particularly common, possibly because the vessels develop in situ with apparently very little in the way of genetic control. Most parts of the body are served by more than one artery and vein, so if the usual vessel isn’t there or takes an unusual course, it’s often no big deal, as long as the blood gets there somehow. To wit: occasionally a person does not have a right subclavian artery. This does not mean that their right shoulder and arm receive no blood and wither away; usually it means that one of the segmental arteries branching off the descending aorta–which normally serve the ribs and their associated muscles and other soft tissues–is expanded and elongated to compensate, and looks for all the world like a normal subclavian artery with an abnormal connection to the aorta. But if the major artery that serves the forelimb comes from the descending aorta, and the 4th aortic arch on the right is completely resorbed during development, then there is nothing left on the right side to drag the inferior laryngeal nerve down into the torso. A person with this setup will have an inferior laryngeal nerve on the right that looks intelligently designed, and the usual dumb RLN on the left.

Can people have a nonrecurrent laryngeal nerve on the left? Sure, if they’ve got situs inversus, in which the normal bilateral asymmetry of the internal organs is swapped left to right. Situs inversus is pretty darned rare in the general population, occurring in fewer than 1 in 10,000 people. It is much more prevalent in television shows and movies, where the hero or villain may survive a seemingly mortal wound and then explain that he was born with his heart on the right side. (Pro tip: the heart crosses the midline in folks of both persuasions, so just shoot through the sternum and you’ll be fine. Or, if you’re worried about penetration, remember Rule #2 and put one on either side.) Anyway, take everything I wrote in the preceding paragraph, mirror-image it left to right, and you’ve got a nonrecurrent laryngeal nerve on the left. But just like the normally-sided person who still has an RLN on the left, a person with situs inversus and no remnant 4th aortic arch on the left (double variation alert!) still has an RLN looping around the aorta and ductus arteriosus on the right.

Bottom line: replumb the vessels to your arms, swap your organs around willy-nilly, you just can’t beat the aorta. If you have an aorta, you’ve got at least one RLN; if you don’t have an aorta, you’re dead, and no longer relevant to this discussion.

Nonrecurrent laryngeal nerves–a developmental Hail Mary?

But wait–how do we know that the inferior laryngeal nerve in embryonic sauropods didn’t get rerouted to travel in front of the fourth and sixth aortic arches, so it could be spared the indignity of being dragged into the chest later on?

First of all, such a course would require that the inferior laryngeal nerve take an equally dumb recurrent course in the embryo. Or maybe it should be called a procurrent course. Instead of simply radiating out from the central nervous system to its targets in the sixth pharyngeal arch, the axons that make up the RLN would have to run well forward of their normal course, loop around the fourth and sixth aortic arches from the front, and then run back down to the sixth pharyngeal arch. There is simply no known developmental mechanism that could make this happen.

Even if we postulated some hypothetical incentive that would draw those axons into the forward U-turn, other axons that took a more direct course from the central nervous system would get to the sixth pharyngeal arch first. By the time the forwardly-recurring axons finished their intelligently-routed course and finally arrived at the sixth pharyngeal arch, all of the innervation targets would be taken, and those axons would die off.

Also, at what point in the evolution of long necks would this forwardly-looping course supposedly be called into existence? Ostriches and giraffes have RLNs that take the same recurrent course as those of humans, pigs, and all other tetrapods. The retention of the recurrent course in extant long-necked animals is further evidence that the developmental constraint cannot be broken.

Finally, the idea that a non-recurrent laryngeal nerve would need to evolve in a long-necked animal is based on the perception that long nerve pathways are somehow physiologically taxing or otherwise bad for the animals in which they occur. But almost every tetrapod that has ever lived has had much longer neurons than those in the RLN, and we all get on just fine with them.

In dire extremity

Probably you seen enough pictures of neurons to know what one looks like: round or star-shaped cell body with lots of short branches (dendrites) and one very long one (the axon), like some cross between an uprooted tree–or better yet, a crinoid–and the Crystalline Entity. When I was growing up, I always imagined these things lined up nose to tail (or, rather, axon to dendrite) all down my spinal cord, arms, and legs, like boxcars in a train. But it ain’t the case. Textbook cartoons of neurons are massively simplified, with stumpy little axons and only a few to a few dozen terminals. In reality, each neuron in your brain is wired up to 7000 other neurons, on average, and you have about a hundred billion neurons in your brain. (Ironically, 100 billion neurons is too many for your 100 billion neurons to visualize, so as a literal proposition, the ancient admonition to “know thyself” is a non-starter.)

Back to the axons. Forget the stumpy little twigs you’ve seen in books and online. Except for the ganglia of your autonomic nervous system (a semi-autonomous neural network that runs your guts), all of the cell bodies of your neurons are located in your central nervous system or in the dorsal root ganglia immediately adjacent to your spinal cord. The nerves that branch out into your arms and legs, across your face and scalp, and into your larynx are not made of daisy chains of neurons. Rather, they are bundles of axons, very long axons that connect muscles, glands, and all kinds of sensory receptors back to the nerve cell bodies in and around your brain and spinal cord.

Indulge me for a second and wiggle your toes. The cell bodies of the motor neurons that caused the toe-wiggling muscles to fire are located in your spinal cord, at the top of your lower back. Those motor neurons got orders transmitted down your spinal cord from your brain, and the signals were carried to the muscles of your feet on axons that are more than half as long as you are tall.

Some of your sensory neurons are even longer. Lift your big toe and then set it down gently, just hard enough to be sure that it’s touching down on the floor or the sole of your shoe, but not hard enough to exert any pressure. When you first felt the pad of your toe touch down, that sensation was carried to your brain by a single neuron (or, rather, by several neurons in parallel) with receptor terminals in the skin of your toe, axon terminals in your brainstem, and a nerve cell body somewhere in the middle (adjacent to your sacrum and just a bit to one side of your butt crack, if you want the gory details). That’s right: you have individual sensory neurons that span the distance from your brainstem to your most distal extremity. And so does every other vertebrate, from hagfish to herons to hippos. Including, presumably, sauropods.

I had you set your toe down gently instead of pushing down hard because the neurons responsible for sensing pressure do not travel all the way from toe-tip to brainstem; they synapse with other neurons in the spinal cord and those signals have been through a two-neuron relay by the time they reach your brainstem. Ditto for sensing temperature. But the neurons responsible for sensing vibration and fine touch go all the way.

If you want to experience everything I’ve discussed in this post in a single action, put your fingertips on your voicebox and hum. You are controlling the hum with signals sent from your brain to your larynx through your recurrent laryngeal nerves, and sensing the vibration through individual neurons that run from your fingertips to your brainstem. Not bad, eh?

Wedel (in press) Fig. 2. The longest cells in the bodies of sauropods were sensory neurons that connected receptors in the skin of the extremities with interneurons in the brainstem, a pattern of neural architecture that is present in all extant vertebrates. The nerve cell bodies would have been located in the dorsal root ganglia adjacent to the spinal cord. The diagram of the neuron is based on Butler and Hodos (1996: fig. 2–1B).

Getting back to big animals: the largest giraffes may have 5-meter neurons in their RLNs, but some of the sensory neurons to their hindfeet must be more like 8 meters long. I don’t think anyone’s ever dissected one out, but blue whales must have sensory neurons to the tips of their flukes that are almost 30 meters (98 feet) long (subtract the length of the skull, but add the lateral distance from body midline to fluke-tip). And Supersaurus, Amphicoelias, and the like must have had neurons that were approximately as long as they were, minus only the distance from the snout-tip to the back of the skull. I could be wrong, and if I am I’d love to be set straight, but I think these must have been the longest cells in the history of life.

Oh, one more thing: up above I said that almost every tetrapod that has ever lived has had much longer neurons than those in the RLN. The exceptions would be animals for which the distance from brainstem to base of neck was longer than the distance from base of neck to tip of limb or tail, so that twice the length of the neck would be longer than the distance from base of skull to most distal extremity. In that case, the neurons that contribute to the RLN would be longer than those running from brainstem to tail-tip or toe-tip. Tanystropheus and some of the elasmosaurs probably qualified; who else?

Parting Thoughts

In this post I’ve tried to explain the courses that these amazingly long cells take in humans and other vertebrates. I haven’t dealt at all with the functional implications of long nerves, for which please see the paper. The upshot is that big extant animals get along just fine with their crazy-long nerves, and there’s no reason to assume that sauropods were any more troubled. So why write the paper, then? Well, it was fun, I learned a lot (dude: axoplasmic streaming!), and most importantly I got to steal a little thunder from those silly poseurs, the giraffes.

Department of Frivolous Nonsense: yes, I titled the paper after those TV ads for Chili’s hamburgers from a few years back. If you never saw them, the ads compared mass-produced, machine-stamped fast-food burgers with restaurant burgers painstakingly built by hand, and concluded with, “Chili’s Big-Mouth Burgers: monuments of inefficiency!”

Update: All of this is out of date now that the paper has been formally published. Department of Good Karma: since the paper is at the “accepted manuscript” stage, I still have the chance to make (hopefully minor) changes when I get the proofs. As is always, always, always the case, I caught a few dumb errors only after the manuscript had been accepted. Here’s what I’ve got so far, please feel free to add to the list:

• Page 1, abstract, line 3: pharyngeal, not pharyngial
• Page 1, abstract, line 8: substitute ‘made up’ for ‘comprised’
• Page 6, line 12: substitute ‘make up’ for ‘comprise’
• Page 9, line 5: citation should be of Carpenter (2006:fig. 3), not fig. 2
• Page 10, line 7: “giant axons of squid are”, not ‘ares’
• Page 12, entry for Butler and Hodos should have year (1996)
• Page 12, entry for Carpenter has ‘re-evaluation misspelled
• Page 16, entry for Woodburne has ‘mammalian’ misspelled

(Notes to self: stop trying to use ‘comprise’, lay off the ‘s’ key when typing bibliography.)

References

• Butler, A.B., and Hodos, W. 1996. Comparative Vertebrate Neuroanatomy: Evolution and Adaptation. 514 pp. Wiley–Liss, New York.
• Kaplan, E.L, Salti, G.I., Roncella, M., Fulton, N., and Kadowaki, M. 2009. History of the recurrent laryngeal nerve: from Galen to Lahey. World Journal of Surgery 33:386-393. DOI 10.1007/s00268-008-9798-z
• Toon, A., and Toon, S.B. 2003. Okapis and giraffes. In: M. Hutchins, D. Kleiman, V. Geist, and M. McDade (eds.), Grzimek’s Animal Life Encyclopedia, 2nd ed. Vol 15: Mammals IV, 399–409. Gale Group, Farmington Hills.
• Wedel, M.J. 2012. A monument of inefficiency: the presumed course of the recurrent laryngeal nerve in sauropod dinosaurs. Acta Palaeontologica Polonica 57(2):251-256.

In a new comment on an oldish post, Peter Adlam asked:

I recently happened upon a picture of the late Jim Jenson standing beside the huge front leg of “Ultrasauros”, which leads me to ask a few questions. Did he really find a complete forelimb? Was the leg from Brachiosaurus altithorax? If that leg is valid at actual size how tall/long was the whole animal? It looks to be about 40% to 50% taller than the berlin Giraffatitan, I am guessing the leg is a constructed representation of how the leg would look rather than a cast of the actual leg because if the whole front leg was found they would probably be the most talked about sauropod bones in the world and the fact is I’ve heard pretty much nothing about these remains for years.

I answered this in a followup comment, but because the answer involved a few nice images, I thought it ought to be promoted into a post of its own.  So here it is, in expanded form.

I believe I know the picture Peter was talking about: it was either the one on the right, of Jensen working on the limb in the lab, or the one below of the same limb, again with Jensen, this time out in the desert.

As an aside: based on a post by ReBecca Hunt-Foster (scroll down to the 12th picture), it looks like this forelimb may have ended up in the New Mexico Museum of Natural History and Stuff (NMMNHS).

Anyway, the bad news is that, no, this is not a complete forelimb fossil. The worse news is that the limb is not even partly cast from real material: it’s a pure sculpture, based presumably on the forelimb of Giraffatitan brancai, but scaled up according to Jensen’s idea of how big “Ultrasauros” was. The only part of the model that probably was cast from real material is not part of the limb proper, but the scapulocoracoid — which is the only real brachiosaur element that Jensen found and described from the Dry Mesa quarry.  In fact, the scap in these photos (and in ReBecca’s) does look very much like BYU 9462, the element that Jensen meant to designate as the “Ultrasauros” holotype, but didn’t, instead plumping for … ah, you all know the story.

"Ultrasauros" scapulocoracoid BYU 9462 (almost certainly a cast), with Graeme Elliott for scale.

But in fact, the scapulocoracoid in the whole-forelimb pictures above looks much too small in comparison with the other elements; or to put it the right way round, since only the scap is based on an actual fossil, all the other elements are too big — which suggests that Jensen exaggerated the sizes of the sculpted limb bones well beyond what the scapulocoracoid warranted.  (In any case, the idea that this scap represents a much larger brachiosaurid than any previously known specimen was shown by Curtice et al. (1996) to be mistaken — it’s from an animal pretty similar in size to, and probably a little smaller than, the largest known Tendaguru specimens.)

But the good news is, Peter’s sense of awe is not misplaced. Real brachiosaur forelimbs are actually not much less impressive than this. See for example me next to the right forelimb of the Berlin Giraffatitan mount, which is real bone — as shown in our classic post Shedloads Of Awesome:

Or here I am again, this time with the Chicago Brachiosaurus mount. (The Chicago mount is a cast, based on a hybrid of real Brachiosaurus elements, some bits of Giraffatitan, and some sculptures, but the scaling is good.)

My rule of thumb, based on a lot of posing for photos around the Chicago mount, is that if I stand next to the forelimb and reach up, I can just rest my hand on the top of the ulna without stretching.  I’m about six feet tall, if that helps.

Jim Jensen was 4% taller than me — 6’3″.  Bearing that in mind, and looking at the second photograph above (the first one is useless because of the forced perspective), Jensen’s inability to reach close to the top of the ulna suggests that his model is inflated by maybe 30%.  Which means that it represents an animal about 1.3^3 = 2.2 times as voluminous and heavy as it should be.  But let’s not forget that among the Giraffatitan material in Berlin is the isolated fibula XV 2, which at 134 cm in length is 12.6% longer than the 119 cm tibia of S II.  So that is from animal about half way between S II and Jensen’s Imaginary Monster in size.

So.  Real brachiosaurs are awesome enough.

Vanessa Graff and I spent yesterday working in the herpetology and ornithology collections at the Natural History Museum of Los Angeles County (LACM). The herpetology collections manager, Neftali Comacho, pointed us to this skull of Alligator mississippiensis. It’s not world’s biggest gator–about which more in a second–but it’s the biggest I’ve seen in person. Normally it lives in a big rubbermaid tub in the collections area, but this Sunday it will be out on display for Reptile and Amphibian Appreciation Day (RAAD) at the LACM. RAAD will include guest talks, tours of the collections, and live animal demonstrations. If you’re in SoCal and you’re into herps–or have kids, grandkids, nephews or nieces that are into herps–it will be well worth checking out. While you’re there, don’t neglect the newly renovated Age of Dinosaurs and Age of Mammals halls, which are frankly phenomenal: spacious, well-lit, loads of actual material on display, skeletons you can walk all the way around, informative but unobtrusive signage, tasteful integration with existing architecture…I could go on. Better if you just go and see for yourself.

About that gator. First the bad news.  It came to the LACM from another collection, and has no data–no locality, no date collected, nothing. The skull is also missing all of its teeth, the left retroarticular process, the back end of the braincase and the occipital condyle. I think the latter losses were probably caused by a foramen of Winchester.*

Now, the awesome news. The length from the snout tip to the end of the articulars was 680mm and from the snout to the end of the quadrates was 590mm. Irritatingly I did not get a dorsal head length, which is the gold standard for comparative croc skull measurements, because I only reread Darren’s giant croc skull post after I got home last night. Going from the photos, I think the dorsal head length was right around 50 cm (beware, the yardstick in the photos is marked off in inches).

Darren’s post led me to this one, which has some very useful measurements (yay!) of giant croc skulls. The table at the end of that post lists alligator skulls with dorsal head lengths of 58, 60, and 64 cm, so the big LACM gator is nowhere near being the world’s largest. In fact, the 64 cm skull would be a quarter again as large, which is a truly horrifying thought. Still, it’s a big damn skull from a big damn gator.

You might get the impression that here in the Wedel lab we are shamelessly obsessed with giant saurians. And that is in fact true. But we also look at tiny ones, too. Here I’m playing with the skull of a little Tomistoma, the false gharial. Tomistoma is notable because another individual of the genus produced the longest skull of any known extant crocodilian–a whopping 84 cm dorsal head length (photos of this monster are in both of the giant croc skull posts linked above).

The moral of the story? If the sign says don’t go swimming, don’t go swimming. Go to RAAD instead, and see the giant alligator skull, and a ton of other cool stuff besides. And if you’re into gator skulls or just like geeking out on awesome anatomy, check out the 3D Alligator Skull site, a joint project of the Holliday lab and Witmer lab. Have fun!

* bullet hole

Left: the Queen of England, 163 cm. Middle, the Oklahoma apatosaur dorsal, 135 cm. Right, classic "big Apatosaurus" dorsal, 106 cm. To scale.

Something I’ve always intended to do but never gotten around to is posting on some of the immense Apatosaurus elements from the Oklahoma panhandle. Here’s one of the most impressive, OMNH 1670, an isolated dorsal. Notice that the tip of the neural spine is ever-so-shallowly bifurcated, which in Apatosaurus indicates a D4, D5, or D6. The low parapophyses and fat transverse processes are similar to D4, but Apatosaurus D4s usually have somewhat broader spines, so I’m guessing this thing is a D5. These things vary and I could easily be off by a position in either direction.

Next to it is D5 of CM 3018, the holotype specimen of Apatosaurus louisae (from Gilmore 1936: plate 25), which has served as the basis for many of the published mass estimates of the genus Apatosaurus. OMNH 1670 is 135 cm tall, compared to 106 cm for D5 of CM 3018. If the rest of the animal scaled the same way, it would have been 1.27^3 = 2 times as massive. Mass estimates for CM 3018 are all over the map, from about 18 tons up to roughly twice that, so the big Oklahoma Apatosaurus was probably in Supersaurus territory, mass-wise, and may have rivaled some of the big titanosaurs (Update: see the two giant diplodocids square off in a cool follow-up post by Supersaurus wrangler Scott Hartman). Here’s a fun rainy-day activity: take any skeletal reconstruction of Apatosaurus, clone it in Photoshop or GIMP, scale it up by 27%, and park it next to the original. It looks a lot bigger. So I’m continually surprised that Apatosaurus is so rarely mentioned in the various roundups of giant sauropods, both in the technical literature and in popular articles online. This vertebra was figured by Stovall (1938)–if I get inspired, I’ll dig up that figure and post it another day.

Fun fact: in Apatosaurus the tallest (most posterior) dorsals are 1.3-1.5 times as tall as D5 (Gilmore 1936: 201). So D10 from this individual was probably between 1.7 and 2 meters tall–not quite in Amphicoelias fragillimus territory but getting closer than I’ll bet most people suspected.

NB: if you try to use the scale bar lying on the centrum of OMNH 1670 to check my numbers, you will get a wonky answer. The problem is that the vertebra is so large that it is almost impossible to get far enough back from it (above it, in this case, since it is lying on a padded pallet) to get a shot free from distortion due to parallax. For this shot, the pallet with the vert was on the floor, and I was standing on top of the tallest ladder in the OMNH collections, leaning out over the vert to get centered over the prezygapophyses, and shooting straight down–in other words, I had done everything possible to minimize the visual distortion. But it still crept in. Anyway, trust the measurements, which I–and presumably Gilmore–made with a good old reliable tape measure.

References

• Gilmore, C.W. 1936. Osteology of Apatosaurus with special reference to specimens in the Carnegie Museum. Memoirs of the Carnegie Museum 11:175-300.
• Stovall, J.W. 1938. The Morrison of Oklahoma and its dinosaurs. Journal of Geology 46:583-600.

In the recent post on OMNH 1670, a dorsal vertebra of a giant Apatosaurus from the Oklahoma panhandle, I half-promised to post the only published figure of this vertebra, from Stovall (1938: fig. 3.3). So here it is:

And in the second comment on that post, I promised a sketch from one of my notebooks, showing how much of the vertebra is reconstructed. Here’s a scan of the relevant page from my notebook. Reconstructed areas of the vert are shaded (confusingly, using strokes going in opposite directions on the spine and centrum, and the dark shaded areas on the front of the transverse processes are pneumatic cavities), and measurements are given in mm.

Next item: is this really a fifth dorsal vertebra?

Apatosaurus louisae CM 3018 D4 and D5, in anterior (top), left lateral, and posterior views, from Gilmore (1936: plate 25).

Here are D4 and D5 of A. louisae CM 3018. They sort of bracket OMNH 1670 in terms of morphology. D4 has a broader spine, and D5 has a narrower one. The spine of D5 lacks the slight racquet-shaped expansion seen in OMNH 1670, but the overall proportions of the spine are more similar. On the other hand, the transverse processes of D4 taper a bit in anterior and posterior view, as in OMNH 1670, and unlike the transverse processes of D5 with their more parallel dorsal and ventral margins. But honestly, neither of these verts is a very good match (and the ones on either side, D3 and D6, are even worse).

Apatosaurus parvus UWGM 15556 (formerly A. excelsus CM 563) D4 (left) and D3 (right) in anterior (top), right lateral, and posterior views, from Gilmore (1936: plate 32).

Here are D3 and D4 of A. parvus UWGM 15556. D3 is clearly a poor match as well–it is really striking how much the vertebral morphology changes through the anterior dorsals in most sauropods, and Apatosaurus is no exception. D3 looks like a dorsal in lateral view, but in anterior or posterior view it could almost pass for a posterior cervical. If I was going to use the term “cervicodorsal”, indicating one of the vertebrae from the neck/trunk transition, I would apply it as far back as D3, but not to D4. That thing is all dorsal.

And it’s a very interesting dorsal from the perspective of identifying OMNH 1670. It has fairly short, tapering transverse processes. The neural spine is a bit shorter and broader, but it has a similar racquet-shaped distal expansion. I’m particularly intrigued by the pneumatic fossae inscribed into the anterior surface of the neural spine–in Gilmore’s plate they make a broken V shapen, like so \ / (or maybe devil eyes). Now, OMNH 1670 doesn’t have devil eyes on its spine, but it does have a couple of somewhat similar pneumatic fossae cut into the spine just below the distal racquet–perhaps a serially modified iteration of the same pair of fossae as in the A. parvus D4. It’s a right sod that D5 from this animal has its spine blown off–but it still has its transverse processes, and they are short and tapering as in OMNH 1670.

Apatosaurus sp. FMNH P25112, dorsal vertebrae 1-10 and sacrals 1 and 2, Riggs (1903: plate 46)

Here are all the dorsals and the first couple sacrals of FMNH P25112, which was originally described as A. excelsus but in the specimen-level analysis of Upchurch et al. 2005) comes out as the sister taxon to the A. ajax/A. parvus/A. excelsus clade. Note the striking similarity of the D5 here with D4 of the A. parvus specimen in Gilmore’s plate (until the careful phylogenetic work up Upchurch et al. 2005, that A. parvus specimen, once CM 563 and now UWGM 15556, was considered to represent A. excelsus as well). But  also notice the striking similarity of D6 to OMNH 1670. It’s not quite a dead ringer–the transverse processes are longer and have weird bent-down “wingtips” (XB-70 Valkyrie, anyone?)–but it’s pretty darned close, especially in the shape of the neural spine.

So what does this all mean? First, that trying to specify the exact serial position of an isolated vertebra is nigh on to impossible, unless it’s something that is one-of-a-kind like an axis. Second, after doing all these comparos I think it’s unlikely that OMNH 1670 is a D4–those are a bit too squat across the board–but it could plausibly be either a D5 or a D6. Third, I’m really happy that it doesn’t seem to match any particular specimen better than all the rest. What I don’t want to happen is for someone to see that this vertebra looks especially like specimen X and therefore decide that it must represent species Y. As I said in the comments of the previous post, what this Oklahoma Apatosaurus material needs is for someone to spend some quality time seeing, measuring, and photographing all of it and then doing a phylogenetic analysis. That sounds like an ambitious master’s thesis or the core of a dissertation, and I hope an OU grad student takes it on someday.

If you were intrigued by my suggestion that the big Oklahoma Apatosaurus rivaled Supersaurus in size, and wanted to see a technical comparison of the two, I am happy to report that Scott Hartman has done the work for you. Here’s one of his beautiful Apatosaurus skeletal reconstructions, scaled to the size of OMNH 1670, next to his Supersaurus silhouette. This is just a small teaser–go check out his post on the subject for a larger version and some interesting (and funny) thoughts on how the two animals compare.

References

• Gilmore, C.W. 1936. Osteology of Apatosaurus with special reference to specimens in the Carnegie Museum. Memoirs of the Carnegie Museum 11:175-300.
• Riggs, E.S. 1903. Structure and relationships of opisthocoelian dinosaurs, part I: Apatosaurus Marsh. Field Columbian Museum Publications, Geological Series 2(4): 165–196.
• Stovall, J.W. 1938. The Morrison of Oklahoma and its dinosaurs. Journal of Geology 46:583-600.

Today sees the publication, on arXiv (more on that choice in a separate post), of Mike and Matt’s new paper on sauropod neck anatomy. In this paper, we try to figure out why it is that sauropods evolved necks six times longer than that of the world-record giraffe — as shown in Figure 3 from the paper (with a small version of Figure 1 included as a cameo to the same scale):

Figure 3. Necks of long-necked sauropods, to the same scale. Diplodocus, modified from elements in Hatcher (1901, plate 3), represents a “typical” long-necked sauropod, familiar from many mounted skeletons in museums. Puertasaurus modified from Wedel (2007a, figure 4-1). Sauroposeidon scaled from Brachiosaurus artwork by Dmitry Bogdanov, via commons.wikimedia.org (CC-BY-SA). Mamenchisaurus modified from Young and Zhao (1972, figure 4). Supersaurus scaled from Diplodocus, as above. Alternating pink and blue bars are one meter in width. Inset shows Figure 1 to the same scale.

This paper started life as a late-night discussion over a couple of beers, while Matt was over in England for SVPCA back in (I think) 2008. It was originally going to be a short note in PaleoBios, just noting some of the oddities of sauropod cervical architecture — such as the way that cervical ribs, ventral to the centra, elongate posteriorly but their dorsal counterparts the epipophyses do not.

As so often, the tale grew in the telling, so that a paper we’d initially imagined as a two-or-three-page note became Chapter 5 of my dissertation under the sober title of “Vertebral morphology and the evolution of long necks in sauropod dinosaurs”, weighing in at 41 1.5-spaced pages. By now the manuscript had metastatised into a comparison between the necks of sauropods and other animals and an analysis of the factors that enabled sauropods to achieve so much more than mammals, birds, other theropods and pterosaurs.

(At this point we had one of our less satisfactory reviewing experiences. We sent the manuscript to a respected journal, where is wasn’t even sent out to reviewers until more than a month had passed. We then had to repeatedly prod the editor before anything else happened. Eventually, two reviews came back: one of them careful and detailed; but the other, which we’d waited five months for, dismissed our 53-page manuscript in 108 words. So two words per page, or about 2/3 of a word per day of review time. But let’s not dwell on that.)

Figure 6. Basic cervical vertebral architecture in archosaurs, in posterior and lateral views. 1, seventh cervical vertebra of a turkey, Meleagris gallopavo Linnaeus, 1758, traced from photographs by MPT. 2, fifth cervical vertebra of the abelisaurid theropod Majungasaurus crenatissimus Depéret, 1896,UA 8678, traced from O’Connor (2007, figures 8 and 20). In these taxa, the epipophyses and cervical ribs are aligned with the expected vectors of muscular forces. The epipophyses are both larger and taller than the neural spine, as expected based on their mechanical importance. The posterior surface of the neurapophysis is covered by a large rugosity, which is interpreted as an interspinous ligament scar like that of birds (O’Connor, 2007). Because this scar covers the entire posterior surface of the neurapophysis, it leaves little room for muscle attachments to the spine. 3, fifth cervical vertebra of Alligator mississippiensis Daudin, 1801, MCZ 81457, traced from 3D scans by Leon Claessens, courtesy of MCZ. Epipophyses are absent. 4, eighth cervical vertebra of Giraffatitan brancai (Janensch, 1914) paralectotype HMN SII, traced from Janensch (1950, figures 43 and 46). Abbreviations: cr, cervical rib; e, epipophysis; ns, neural spine; poz, postzygapophysis.

This work made its next appearance as my talk at SVPCA 2010 in Cambridge, under the title Why giraffes have such short necks. For the talk, I radically restructured the material into a form that had a stronger narrative – a process that involved a lot of back and forth with Matt, dry-running the talk, and workshopping the order in which ideas were presented. The talk seemed to go down well, and we liked the new structure so much more than the old that we reworked the manuscript into a form that more closely resembled the talk.

That’s the version of the manuscript that we perfected in New York when we should have been at all-you-can-eat sushi places. It’s the version that we submitted on the train from New York to New Haven as we went to visit the collections of the Yale Peabody Museum. And it’s the version that was cursorily rejected from mid-to-low ranked palaeo journal because a reviewer said “The manuscript reads as a long “story” instead of a scientific manuscript” — which was of course precisely what we’d intended.

Needless to say, it was deeply disheartening to have had what we were convinced was a good paper rejected twice from journals, at a cost of three years’ delay, on the basis of these reviews. One option would have been to put the manuscript back into the conventional “scientific paper” straitjacket for the second journal’s benefit. But no. We were not going to invest more work to make the paper less good. We decided to keep it in its current, more readable, form and to find a journal that likes it on that basis.

At the moment, the plan is to send it to PeerJ when that opens to submissions. (Both Matt and I are already members.) But that three-years-and-rolling delay really rankles, and we both felt that it wasn’t serving science to keep the paper locked up until it finally makes it into a journal — hence the deposition in arXiv which we plan to talk about more next time.

Table 3. Neck-elongation features by taxon.

In the paper, we review seven characteristics of sauropod anatomy that facilitated the evolution of long necks: absolutely large body size; quadrupedal stance; proportionally small, light head; large number of  cervical vertebrae; elongation of cervical vertebrae; air-sac system; and vertebral pneumaticity. And we show that giraffes have only two of these seven features. (Ostriches do the next best, with five, but they are defeated by their feeble absolute size.)

The paper incorporates some material from SV-POW! posts, including Sauropods were corn-on-the-cob, not shish kebabs. In fact, come to think of it, we should have cited that post as a source. Oh well. We do cite one SV-POW! post: Darren’s Invading the postzyg, which at the time of writing is the only published-in-any-sense source for pneumaticity invading cervical postzygapogyses from the medial surface.

As for the non-extended epipophyses that kicked the whole project off: we did illustrate how they could look, and discussed why they would seem to make mechanical sense:

Figure 10. Real and speculative muscle attachments in sauropod cervical vertebrae. 1, the second through seventeenth cervical vertebrae of Euhelopus zdanskyi Wiman, 1929 cotype specimen PMU R233a-δ(“Exemplar a”). 2, cervical 14 as it actually exists, with prominent but very short epipophyses and long cervical ribs. 3, cervical 14 as it would appear with short cervical ribs. The long ventral neck muscles would have to attach close to the centrum. 4, speculative version of cervical 14 with the epipophyses extended posteriorly as long bony processes. Such processes would allow the bulk of both the dorsal and ventral neck muscles to be located more posteriorly in the neck, but they are not present in any known sauropod or other non-avian dinosaur. Modified from Wiman (1929, plate 3).

But we found and explained some good reasons why this apparently appealing arrangement would not work. You’ll need to read the paper for details.

Sadly, we were not able to include this slide from the talk illustrating the consequences:

Anyway, go and read the paper! It’s freely available, of course, like all arXiv depositions, and in particular uses the permissive Creative Commons Attribution (CC BY) licence. We have assembled related information over on this page, including full-resolution versions of all the figures.

In the fields of maths, physics and computer science, where deposition in arXiv is ubiquitous, standard practice is to go right ahead and cite works in arXiv as soon as they’re available, rather than waiting for them to appear in journals. We will be happy for the same to happen with our paper: if it contains information that’s of value to you, then feel free to cite the arXiv version.

Reference

• Taylor, Michael P., and Mathew J. Wedel. 2012. Why sauropods had long necks; and why giraffes have short necks. arXiv:1209.5439. 39 pages, 11 figures, 3 tables. [Full-resolution figures]

From Jensen (1987, page 604):

“In 1985 I found the proximal third of an extremely large sauropod femur (Figs. 8A, 12A) in a uranium miner’s front yard in southern Utah.  The head of this femur is 1.67 m (5’6″) in circumference and was collected from the Recapture Creek Member of the the Morrison Formation in Utah near the Arizona border.  It is the largest bone I have ever seen.”

Jensen included not one but two figures of this immense shard of excellence. Here they are:

Jensen 1987, Figure 8

Jensen 1987, Figure 12

The specimen was heavily reconstructed, as you can see from the big wodge of unusually smooth and light-colored material in the photo. So we can’t put much stock in that part of the specimen.

Unfortunately, the only measurement of the specimen that Jensen gives in the paper is that circumference; there are no straight-line linear measurements, and the figures both have the dreaded scale bars. Why dreaded? Check this out:

As you can see, when the scale bars are set to the same size, the bones are way off (the scale bar in the drawing is 50 cm). This is not an uncommon problem. I make the Fig 8 version 30% bigger in max mediolateral width of the entire proximal end, and still 17% bigger in minimum diameter across the femoral head, as measured from the slight notch on the dorsal surface (on the right in this view).

Can we figure out which is more accurate based  on the internal evidence of the paper? For starters, the Fig 12 version is a drawing (1), that does not match the outline from the photo (2), and the hand-drawn scale bar (3) does not actually coincide with any landmarks (4), and that’s plenty of reasons for me not to trust it.

What about that circumference Jensen mentioned? Unfortunately, he didn’t say exactly where he took it, just that the head of the femur had a circumference of 1.67 meters. Is that for the entire proximal end, or for the anatomical head that fits in the acetabulum, er wot? I’m afraid the one measurement given in the paper is no help in determining which of the figures is more accurately scaled.

The obvious thing to do would be to see if this bone is in the BYU collections, and just measure the damn thing. More on that at the end of the post.

In the meantime, Jensen said that the shape of the Recapture Creek femur was most similar to the femur of Alamosaurus, or to that of Brachiosaurus among Morrison taxa, and he referred it to Brachiosauridae. So how does this thing–in either version–compare with the complete femur of FMNH P25107, the holotype of Brachiosaurus altithorax?

The Recapture Creek femur fragment compared to the complete femur of the Brachiosaurus altithorax holotype FMNH P25107

The first thing to notice is that the drawn outline from Figure 12 is a much better match for the Brachiosaurus altithorax femur–enough so that I wonder if Jensen drew it from the Recapture Creek specimen, or just traced the B.a. proximal femur and scaled it accordingly (or maybe not accordingly, since the scale bars don’t match).

But let’s get down to business: how long would the complete femur have been?

Using the scale bar in the photograph from Figure 8 (on the left in above image), I get a total femur length of 2.36 meters. Which is long, but only 7.7% longer than the 2.19-meter femur of FMNH P25107, and therefore only 25% more massive. So, 35 tonnes to Mike’s 28-tonne B.a., or maybe 45 tonnes to a more liberal 36-tonne B.a. Big, yeah, but not world-shattering.

Using the scale bar in the drawing from Figure 12 (on the right in the above image)–which, remember, is 50 cm, not 1 meter–I get a total femur length of about 1.9 meters, which is considerably smaller than the B.a. holotype. That is very much at odds with Jensen’s description of it as “the largest bone I have ever seen”, and given that we have many reasons for not trusting the scale bar in the drawing, it is tempting to just throw it out as erroneous.

So it would seem that unless Jensen got both scale bars too big, the Recapture Creek brachiosaur was at most only a shade bigger than the holotype specimen of Brachiosaurus altithorax.

But wait–is the Recapture Creek brachiosaur a brachiosaur at all? Jensen didn’t list any characters that pushed him toward a brachiosaurid ID, and I don’t know of any proximal femur characters preserved in the specimen that would separate Brachiosaurus from, say, Camarasaurus. And in fact a camarasaur ID has a lot to recommend it, in that Camarasaurus femora have very offset heads (the ball- or cylinder-like articular surface at the top end sticks out a big more to engage with the hip socket–see Figure 12 up near the top of the post), moreso than in many other Morrison sauropods, and that would make them better matches for the Recapture Creek femur photo. Here’s what the comparo looks like:

The Recapture Creek femur fragment compared with a complete femur of Camarasaurus.

I make that a 2.07-meter femur using the photo on the left, and a 1.66-meter femur using the drawing on the right. The one decent femur in the AMNH 5761 Camarasaurus supremus collection is 1.8 meters long, so these results are surprisingly similar to those for the B. althithorax comparison–the drawing gives a femur length shorter than the largest known specimens, and the photo gives a length only slightly longer. A camarasaur with a 2.07 meter femur would be 15% larger than the AMNH C. supremus in linear terms, and  assuming isometric scaling, 1.5 times as massive–maybe 38 tonnes to AMNH 5761′s estimated 25. A big sauropod to be sure, but not as big as the largest apatosaurs, and not nearly as big as the largest titanosaurs.

I have always been surprised that the Recapture Creek femur frag has attracted so little attention, given that “Dinosaur Jim” himself called it the biggest bone he had ever seen. But it appears that the lack of attention is justified–whether it was a brachiosaur or a camarasaur, and using the most liberal estimates the scale bars allow, it simply wasn’t that big.

Update about half an hour later: Okay, maybe I was a little harsh here. IF the photo scale bar is right, the Recapture Creek femur might still represent the largest and most massive macronarian from the Morrison Formation (Edit: only if it’s a brachiosaur and not a camarasaur; see this comment), which is something. I suppose I was particularly underwhelmed because I was expecting something up in OMNH 1670-to-Argentinosaurus territory, and so far, this ain’t it. I’ll be interested to see what the actual measurements say (read on).

The Moral of This Story

So, if it wasn’t that big after all, and if no-one has made a stink about it being big before now, why go to all this trouble? Well, mostly just to satisfy my own curiosity. If there was a truly gigantic brachiosaur from the Morrison, it would be relevant to my interests, and it was past time I crunched the numbers to find out.

But along the way something occurred to me: this should be a cautionary tale for anyone who gets all wound up about the possible max size of Amphicoelias fragillimus. As with A. fragillimus, for the Recapture Creek critter we have part of one bone, and at least for this exercise I was working only from published illustrations with scale bars. And as with A. fragillimus, the choice of a reference taxon is not obvious, and the size estimates are all over the place, and some of them just aren’t that big.

It always amuses me when A. fragillimus comes up and people (well, trolls) accuse us of being big ole’ wet blankets that just don’t want to believe in 200-tonne sauropods. It amuses me because it’s wrong on so many levels. Believe me, when we have our sauropod fanboy hats on, we most definitely do want to believe in 200-tonne sauropods. That would rock. But when we put our scientist hats on, wanting and belief go right out the window. We have to take a cold, hard look at the data, and especially at its limitations.

Oh, the other moral is to go buy a tape measure, and use it. Sheesh!

Coda

As I said above, the obvious thing to do would be to just track down the bone and measure it. It does still exist, it’s in the BYU collections, and Brooks Britt has kindly offered to send along some measurements when he gets time. So we should have some real answers before long (and here they are). But I wanted to work through this example without them, to illustrate how much uncertainty creeps in when trying to estimate the size of a big sauropod from published images of a single partial bone.

Reference

Jensen, J.A. 1987. What I did on my holidaysNew brachiosaur material from the Late Jurassic of Utah and Colorado. Great Basin Naturalist 47(4): 592-608.

If you’re just joining us, this post is a follow-up to this one, in which I considered the possible size and identity of the Recapture Creek femur fragment, which “Dinosaur Jim” Jensen (1987: page 604) said was “the largest bone I have ever seen”.

True to his word, Brooks Britt at BYU got back to me with measurements of the Recapture Creek femur fragment in practically no time at all:

Length 1035 mm, width 665 mm.  However, you cannot trust the measurements because Jensen put a lot of plaster on the proximal half of the bone.

Now, taking plaster off a bone is not going to make it any larger. So the plastered-up specimen is the best case scenario for the RC femur to represent a gigapod. And I know the stated width of 665 mm is the max width of the proximal end, because I sent Brooks a diagram showing the measurements I was requesting. The length is a little less than anticipated, and doesn’t quite jibe with the max proximal width–I suspect a little might have broken off from the distal end where the preservation looks not-so-hot.

Based on those measurements, it looks like Jensen got the scale bar in Figure 8 in his 1987 paper approximately right–if anything, the scale bar is a little undersized, but only by 5% or so, which is actually pretty good as these things go (scale bars without measurements are still dag-nasty evil, though). By overlapping Jensen’s photo with the femur of the Brachiosaurus altithorax holotype (FMNH P25107) to estimate the size of the element when complete, I get a total length of 2.2 meters–exactly the same size as the Brachiosaurus holotype. If the Recapture Creek femur is from a Camarasaurus, which I don’t think we can rule out, it was 2 meters long when complete, or 11% longer and 37% more massive than the big C. supremus AMNH 5761–about 35 tonnes or maybe 40 on the outside. So it’s a big bone to be sure, but it doesn’t extend the known size range of Morrison sauropods.

So, as before, caveat estimator when working from scaled illustrations of single partial bones of possibly immense sauropods.

Now, here’s a weird thing. Let’s assume for the sake of this discussion that the Recapture Creek femur is from a brachiosaur. That gives us three individual Late Jurassic brachiosaurids–the Recapture Creek animal, the Brachiosaurus altithorax holotype, and the mounted Giraffatitan brancai–that are almost exactly the same size in limb bone dimensions (although B.a. had a longer torso). But we know that brachiosaurids got bigger, as evidenced by the XV2 specimen of Giraffatitan, and based on the lack of scapulocoracoid fusion in both FMNH P25107 and the mounted Giraffatitan. So why do we keep finding these (and smaller) subadults, and so few that were XV2-sized? I know that there gets to be a preservation bias against immense animals (it’s hard to bury a 50-tonne animal all in one go), but I would not think the 13% linear difference between these subadults and XV2-class adults would be enough to matter. Your thoughts?

Reference

Jensen, J.A. 1987. New brachiosaur material from the Late Jurassic of Utah and Colorado. Great Basin Naturalist 47(4): 592-608.

At the top: our old friend BYU 9024 — the cervical vertebra that’s part of the Supersaurus vivianae holotype. At the bottom, C2 (the longest cervical) of Giraffa camelopardalis angolensis FMNH 34426.

The Supersaurus vertebra is 138 cm long. We don’t know which cervical it is, but there’s no reason to think it’s the longest. The giraffe vertebra is 31 cm long. Not only is the Supersaurus vertebra four times as long as that of the giraffe, it’s one of more than twice as many cervicals as the giraffe has.

Did we cheat by using an unusually small giraffe? Not really. When we articulated all seven cervicals as best we could, the sequence measured 171 cm, which is a fairly healthy 71% of the 2.4 m neck of the world-record giraffe. It’s not a monster, but it’s a decent-sized adult.

Bottom line, giraffes are just lame.

Here’s an update from the road–get ready for some crappy raw images, because that’s all I have the time or energy to post (with one exception).

Here’s OMNH 1331. It’s just the slightly convex articular end off a big vertebra, collected near Kenton, Oklahoma, in 1930s by one of J. Willis Stovall’s field crews. I measured the preserved width at 45 cm using a tape measure, and at 44.5 in GIMP using the scale bar in the photo, which is up on a piece of styrofoam so it’s about the same distance from the camera as the rim of the vertebra (i.e, about 8 feet–as high as I could get and still shoot straight down). So whether your distrust runs to tape measures or scale bars in photos, I am prepared to argue that this sucker is roughly 45 cm wide.

There’s admittedly not a ton of morphology here, but the size and the fact that the other side is hollow and has a midline bony septum show that it is a pneumatic vertebra from a sauropod, and given that the quarry it’s from was chock-full of Apatosaurus, and liberally salted with gigantic Apatosaurus, I feel pretty good about calling it Apatosaurus.

To figure out how wide the articular face was when it was intact, I duplicated the image and reversed it left-to-right in GIMP, which yields an intact max width of about 49 cm. That is friggin’ immense.

If we make the maximally conservative assumption that this is the largest centrum in the whole skeleton of a big Apatosaurus, then it has to be part of a dorsal vertebra. Here are the max diameters of the largest dorsal centra in some big mounted apatosaurs, taken from Gilmore (1936). The number in parentheses is how many percent bigger OMNH 1331 is.

• A. louisae CM 3018 – 36.5 cm (34%)
• A. parvus UWGM 15556 – 36.5 cm (34%)
• A. sp. FMNH P25112 – 41 cm (20%)

However, this might not be part of a dorsal vertebra. For one thing, it’s pretty convex, and Apatosaurus dorsals sometimes have a little bump but they’re pretty close to amphiplatyan, at least in the posterior half of the series. For another, I think that smooth lower margin on the right in the photo above is part of the rim of a big pneumatic foramen, but it’s waaay up high and pretty medial on the centrum, opening more dorsally than laterally, which I have seen a lot in anterior caudal vertebrae. Finally, Jack McIntosh went through the OMNH collections years ago and his identifications formed the basis for a lot of the catalogue IDs, and this thing is catalogued as the condyle off the back end of a proximal caudal.

Here are the max diameters of the largest caudal centra in those same mounted apatosaurs, again taken from Gilmore (1936). Once again, the number in parentheses is how many percent bigger OMNH 1331 is.

• A. louisae CM 3018 – 30 cm (63%)
• A. parvus UWGM 15556 – 32.5 cm (51%)
• A. sp. FMNH P25112 – 39 cm (26%)

(Aside: check out the skinny rear end on A. louisae. ‘Sup with that?)

So whatever vert it’s part of, OMNH 1331 is damn big bone from a damn big Apatosaurus. There are lots of other big Apatosaurus vertebrae in the OMNH collections, like OMNH 1670, but OMNH 1331 is the largest centrum that I know of in this museum. Which is why you’re getting a post about most of one end of a centrum in the wee hours of the morning–it’s most of one end of an awesome centrum. And it pains me when people do comparison figures of big sauropod vertebrae, or lists of the “Top 10 Largest Sauropods”, and put in stuff like Argentinosaurus and Puertasaurus and Supersaurus, but leave out Apatosaurus. It was legitimately huge, and it’s time the world realized that.

For more on the giant Oklahoma Apatosaurus, see:

• The giant Oklahoma Apatosaurus: OMNH 1670
• The giant Oklahoma Apatosaurus: OMNH 1670 redux

Reference

Gilmore, C.W. 1936. Osteology of Apatosaurus with special reference to specimens in the Carnegie Museum. Memoirs of the Carnegie Museum 11:175-300.

We jumped the gun a bit in asking How fat was Camarasaurus? a couple of years ago, or indeed How fat was Brontosaurus? last year. As always, we should have started with extant taxa, to get a sense of how to relate bones to live animals — as we did with neck posture.

So here we go. I give you a herd of Indian elephants, Elephas maximus (from here):

You will notice, from this conveniently-close-to-anterior view, that their torsos bulge out sideways, much further than the limbs.

Now let’s take a look at the skeleton of the same animal in the Oxford University Museum of Natural History (downloaded from here but for some reason the photo has now gone away):

The rib-cage is tiny. It doesn’t even extend as far laterally as the position of the limb bones.

(And lest you think this is an oddity, do go and look at any mounted elephant skeleton of your choice, Indian or African. They’re all like this.)

What’s going on here?

Is Oxford’s elephant skeleton mounted incorrectly? More to the point, are all museums mounting their elephants incorrectly? Do elephants’ ribs project much more laterally in life?

Do elephants have a lot of body mass superficial to the rib-cage? If so, what is that mass? It’s hard to imagine they need a huge amount of muscle mass there, and it can’t be guts. Photos like this one, from the RVC’s televised elephant dissection on Inside Nature’s Giants, suggest the ribs are very close to the body surface:

I’m really not sure how to account for the discrepancy.

Were sauropods similarly much fatter than their mounted skeletons suggest? Either because we’re mounting their skeletons wrongly with the ribs too vertical, or because they had a lot of superficial body mass?

Consider this mounted Camarasaurus skeleton in the Dinosaur Hall at the Arizona Museum of Natural History (photo by N. Neenan Photography, CC-BY-SA):

Compare the breadth of its ribcage with that of the elephant above, and then think about how much body bulk should be added.

This should encourage palaeoartists involved in the All Yesterdays movement to dramatically bulk up at least some of their sauropod restorations.

It should also make us think twice about our mass estimates.

You’ve probably seen a lot of yapping in the news about a new “world’s largest dinosaur”, with the standard photos of people lying down next to unfeasibly large bones. Here’s my favorite–various versions of it have been making the rounds, but I grabbed this one from Nima’s post on his blog, The Paleo King.

The first point I need to make here is that photos like these are attention-grabbing but they don’t really tell you much. Partly because they’re hard to interpret, and partly because they almost always look more impressive than they really are. For example, I am 6’2″ tall (1.88 meters). If I lie down next to a bone that is 7’2″ (219 cm) 6’8″ (203 cm) long, it is going to look ungodly huge–a full half a foot longer than I am tall. But that is the length of the femur of the Brachiosaurus holotype–we’ve known of sauropod femora that big for a century now. People get tripped up by this sort of thing all the time–even scientists. Update: even me! Somehow I had gotten it into my head that the Brachiosaurus femur was 219 cm, when it is actually 203 cm. That goof doesn’t affect any of what follows, because from here on down I used Argentinosaurus as the point of reference.

Second point: at least some of the reporting on this new find has been unusually–and refreshingly–nuanced. The first news story I read about it was this one, which gives Paul Barrett plenty of airtime to explain why we should be cautious about jumping to any conclusions regarding the size of the new animal. That will turn out to be prophetic.

But let’s get back to that photo. Just eyeballing it, it looks like the femur is about half again as long as the dude is tall (the dude, BTW, is Pablo Puerta, for whom Puertasaurus is named). I was reading Nima’s post and he guessed that the femur was in the neighborhood of 3 meters, which would be a significant size increase over the next-biggest sauropod known from fossils that still exist (i.e., not including semi-apocraphyal gigapods like Amphicoelias fragillimus and Bruhathkayosaurus). The current based-on-existing-fossils record-holder is Argentinosaurus–there is a partial femur that would have been about 2.5 meters long when complete. So a 3-meter femur would be a wonderful thing. But alas, it just ain’t so–or at least the one in the photo isn’t anywhere near that big. Allow me to demonstrate.

Here’s another copy of the photo with some measurements applied. There is no actual scale bar in the picture, but we can use the dimensions of the things we can see to figure some stuff out.

For starters, there is a lot of perspective distortion going on here. Pallet B is 350 pixels wide at the near end, 280 pixels at the far end–a difference of 20%. I didn’t put the far-end measurement for Pallet A into the picture, but from corner to corner it is 295 pixels.

Shipping pallets vary in size around the world, but in the US the most common size is 48 x 40 inches. Other countries use different sizes, mostly smaller; I am unaware of any standard shipping pallets larger than 48×40. So assuming that the ones in the picture are that size is actually a liberal assumption that will lead to large estimates–if the pallets are smaller than 48×40, then all of the dimensions I’m about to calculate will be smaller as well. Obviously the pallets have their narrow ends facing us, which is nice because 40 inches is almost exactly 1 meter. So we can divide other things in the picture by pallet length and get their dimensions in meters.

The near side of the femur is pretty much in line with the stringer running left-to-right down the middle of Pallet A. From the measurements of the ends of that pallet, we’d expect the middle-distance width to be about 330 pixels, and in fact I got 335. The 830-pixel line I drew on the near side is not the total length of the bone–you could add a bit more for the femoral head, to a max of maybe 860 or 870 pixels. Divide that by 335 and you get a max length of about 2.6 meters.

The 800-pixel line for the far side of the femur goes from the top of the head to the bottom of the medial condyle, so there’s no extending needed there. That line is at about the mid-point of Pallet B, or about 315 pixels. If Pallet B is a meter wide, the femur is 2.5 meters long.

We can also check things by trying to figure out how tall Pablo Puerta is. At first that looks more encouraging for the possibility that this is a record-breaker. If we assume the femur really is 3 meters long, and compare the 800-pixel femur line to the 500-pixel Pablo line, Pablo is 62.5% the length of the femur, or 1.87 meters–about the same height as me. That would be pretty tall for an Argentinian, but it’s certainly plausible.

But that’s not a legit comparison, because Pablo is farther from the camera than is the femur. Look at Pallet A–we can use the slats as perspective guides to help figure out where the proximal end of the femur ought to be if projected back to Pablo’s distance from the camera. If we do that at both ends, the length of the femur if placed where Pablo is lying would be 750 pixels or fewer, which would make Pablo at least 2 meters tall. People get a lot taller than that, but it would make him unusually tall, and if you’re trying to emphasize how big your sauropod is, you probably won’t pick the tallest person in the room to pull a Jensen. If we assume Pablo’s about 5’8″–average height for an Argentinian male–then the femur is about 2.6 meters long, which is consistent with the estimates from the pallets. He could well be shorter, in which the case the femur might also be shorter.

There are of course vast amounts of uncertainty in all of this. I have heard the number 2.4 meters thrown around in the media, which is within the margin of error of my crude estimates here–I deliberately skewed large at most decision points to give the hypothesized 3-meter femur the best possible chance. I have to emphasize that this is not how you do science–I’m deliberately doing this quick and dirty. But even using these admittedly flawed and somewhat goofy methods, it’s easy to show that the femur isn’t 3 meters long, or anywhere near it.

So, three last points:

1. As the post title implies, the new Argentine titanosaur is about the same size as Argentinosaurus. That shouldn’t be too surprising, since the mass estimates that have been quoted in the media are within a few percent of the mass estimates for Argentinosaurus. The new critter might be a hair bigger, but it doesn’t “smash” the record, and when we get actual measurements it could end up being smaller than Argentinosaurus in linear dimensions. I note that the size trumpeted in the media is a mass estimate based on femoral fatness, not femoral length. You’d think that if the biggest femur was demonstrably longer than the 2.5-meter Argentinosaurus femur, they’d lead with that. So the reporting so far is also consistent with an animal about the same size as Argentinosaurus.
2. That is in no way a disappointing result! That biggest Argentinosaurus femur is incomplete, so the 2.5-meter length is an estimate. Even if the big femur shown here is only (only!) 2.4 meters long, it’s still the longest complete limb bone from anything, ever. And even if the new animal is identical to Argentinosaurus in size, there’s still a lot more of it, so we’ll get a better idea of what these super-gigantic titanosaurs looked like. That’s a big win.
3. Finally, this is not a case of MYDD. There’s no paper yet, and I don’t blame the team for not making the measurements public until the work is done. I also don’t blame them for publicizing the find. So far, this seems to be exactly what they’re saying it is–an animal about the size of Argentinosaurus, and maybe just a hair bigger. That’s cool. I wish them the best of luck writing it up. I almost wrote “I can’t wait to see the paper” but actually I can–something like this, I’d rather they take their time and do it right. It may not be a record-smasher, but it’s a solid, incremental advance, and science needs those, too.

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.

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

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:

(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):

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:

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.

This was inspired by an email Mike sent a couple of days ago:

Remind yourself of the awesomeness of Giraffatitan:
http://svpow.files.wordpress.com/2008/11/mike-by-jango-elbow.jpeg

Now think of this. Its neck is 8.5m long. Knock of one measly meter — for example, by removing one vertebra from the middle of the neck — and you have 7.5 m.

Supersaurus’s neck was probably TWICE that long.

Holy poo.

I replied that I was indeed freaked out, and that it had given me an idea for a post, which you are now reading. I didn’t have a Giraffatitan that was sufficiently distortion-free, so I used my old trusty Brachiosaurus. The vertebra you see there next to Mike and next to the neck of Brachiosaurus is BYU 9024, the longest vertebra that has ever been found from anything, ever.

Regarding the neck length of Supersaurus, and how BYU 9024 came to be referred to Supersaurus, here’s the relevant chunk of my dissertation (Wedel 2007: pp. 208-209):

Supersaurus is without question the longest-necked animal with preserved cervical material. Jim Jensen recovered a single cervical vertebra of Supersaurus from Dry Mesa Quarry in western Colorado. The vertebra, BYU 9024, was originally referred to “Ultrasauros”. Later, both the cervical and the holotype dorsal of “Ultrasauros” were shown to belong to a diplodocid, and they were separately referred to Supersaurus by Jensen (1987) and Curtice et al. (1996), respectively.

BYU 9024 has a centrum length of 1378 mm, and a functional length of 1203 mm (Figure 4-3). At 1400 mm, the longest vertebra of Sauroposeidon is marginally longer in total length [see this post for a visual comparison]. However, that length includes the prezygapophyses, which overhang the condyle, and which are missing from BYU 9024. The centrum length of the largest Sauroposeidon vertebra is about 1250 mm, and the functional length is 1190 mm. BYU 9024 therefore has the largest centrum length and functional length of any vertebra that has ever been discovered for any animal. Furthermore, the Supersaurus vertebra is much larger than the Sauroposeidon vertebrae in diameter, and it is a much more massive element overall.

Neck length estimates for Supersaurus vary depending on the taxon chosen for comparison and the serial position assumed for BYU 9024. The vertebra shares many similarities with Barosaurus that are not found in other diplodocines, including a proportionally long centrum, dual posterior centrodiapophyseal laminae, a low neural spine, and ventrolateral flanges that connect to the parapophyses (and thus might be considered posterior centroparapophyseal laminae, similar to those of Sauroposeidon). The neural spine of BYU 9024 is very low and only very slightly bifurcated at its apex. In these characters, it is most similar to C9 of Barosaurus. However, theproportions of the centrum of BYU 9024 are more similar to those of C14 of Barosaurus, which is the longest vertebra of the neck in AMNH 6341. BYU 9024 is 1.6 times as long as C14 of AMNH 6341 and 1.9 times as long as C9. If it was built like that of Barosaurus, the neck of Supersaurus was at least 13.7 meters (44.8 feet) long, and may have been as long as 16.2 meters (53.2 feet).

Based on new material from Wyoming, Lovelace et al. (2005 [published as Lovelace et al. 2008]) noted potential synapomorphies shared by Supersaurus and Apatosaurus. BYU 9024 does not closely resemble any of the cervical vertebrae of Apatosaurus. Instead of trying to assign its serial position based on morphology, I conservatively assume that it is the longest vertebra in the series if it is from an Apatosaurus-like neck. At 2.7 times longer than C11 of CM 3018, BYU 9024 implies an Apatosaurus-like neck about 13.3 meters
(43.6 feet) long.

Bonus comparo: BYU 9024 vs USNM 10865, the mounted Diplodocus longus at the Smithsonian, modified from Gilmore 1932 (plate 6). For this I scaled BYU 9024 against the 1.6-meter femur of this specimen.

If you’d like to gaze upon BYU 9024 without distraction, or put it into a composite of your own, here you go:

References

• Gilmore, C. W. 1932. On a newly mounted skeleton of Diplodocus in the United States National Museum. Proceedings of the United States National Museum 81, 1-21.
• Lovelace, David M., Scott A. Hartman and William R. Wahl. 2008. Morphology of a specimen of Supersaurus (Dinosauria, Sauropoda) from the Morrison Formation of Wyoming, and a re-evaluation of diplodocid phylogeny. Arquivos do Museu Nacional, Rio de Janeiro, 65 (4): 527-544.
• Wedel, M.J. 2007. Postcranial pneumaticity in dinosaurs and the origin of the avian lung. PhD dissertation, University of California, Berkeley, Department of Integrative Biology, 303 pp.

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)

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)

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.

References

• 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.
•  Mazzetta, G.V., Christiansen, P., and Farina, R.A. 2004. Giants and bizarres: body size of some southern South American Cretaceous dinosaurs. Historical Biology 2004:1-13.