The sauropod neck mass project: an experiment in open science

March 4, 2013

Brachiosaurus sp. BYU 12866 c5? in left lateral view with CT slices, some corrected for distortion.

Brachiosaurus sp. BYU 12866 c5? in left lateral view with CT slices, some corrected for distortion.

Last Tuesday Mike popped up in Gchat to ask me about sauropod neck masses.  We started throwing around some numbers, derived from volumetric estimates and some off-the-cuff guessing. Rather than tell you more about it, I should just paste our conversation, minimally edited for clarity and with a few hopefully helpful links thrown in.

Mike: Dud. Neck masses.
Matt: What about ’em?
Mike: Taylor (2009:803) measured the neck of Giraffatitan by GDI as 4117 liters.
Matt: k
Mike: I didn’t convert that to a mass, but I guess density of 0.5 is as good as any, which gives us (say) 2 tonnes.
Matt: That works for me.
Mike: That’s for an 8.5 m neck. So Supersaurus at 15 …
Matt: Yep. Almost twice as long, and not much more slender, and from what I’ve seen, ASP about the same.
Mike: Is 1.76 times as long. If it was isometric with the G. neck, it would be 5.5 times as heavy, which is 11 tonnes.
Matt: Oh.
Mike: So first: yeesh. Like, that is the mass of a whole freaking Diplo. Now we surely have to say isometry is unlikely.
Matt: Prolly.
Mike: But just multiplying out by length is unrealistic too. So maybe I should guess at mass =~ l^2? If I went with that, I’d get 6410 kg, which is elephant mass.
Matt: Something just occurred to me. Like, just now. For my 2006 poster, I calculated the mass of the cervical series in Giraffatitan, by summing over the CT slices from Brachiosaurus sp. BYU 12866 and multiplying by appropriate scale factors for the rest of the verts. We could “skin” that in muscle, and actually figure this out, for various muscle thicknesses, for one sauropod.
Mike: We should totally do that … if we had some idea how heavily muscled it was.
Matt: Well, obviously the thing to do is what Hutch et al. did for the tyrannosaurs, and put on several soft tissue envelopes. Crazy skinny, our best guess, markedly unfit, OMG, etc. It’s not that much more work. In fact, that could be my SVPCA talk this year.
Mike: Sure, but that’s just how to mitigate our ignorance. All we’d be doing at this point is taking n guesses instead of one. But, yeah, we should do it. Or you should if you prefer.
Matt: Let’s make it a Wedel and Taylor. I’ll crunch the numbers, but I want your input.
Mike: Works for me!
Matt: Good. Now let’s file it until April at least.
BYU 12613, a posterior cervical probably referable to Diplodocus, in dorsal (top), left lateral (left), and posterior (right) views. It compares most favourably with C14 of D. carnegii CM 84/94 (Hatcher 1901: plate 3) despite being less than half as large, with a centrum length of 270 mm compared to 642 mm for C14 of D. carnegii. From Wedel and Taylor (in press).

BYU 12613, a posterior cervical probably referable to Diplodocus, in dorsal (top), left lateral (left), and posterior (right) views. It most closely resembles C14 of D. carnegii CM 84/94 (Hatcher 1901: plate 3) despite being less than half as large, with a centrum length of 270 mm compared to 642 mm for C14 of D. carnegii. From Wedel and Taylor (in press).

Matt: Oh!
Matt: Also.
Matt: You know that little Diplo cervical from BYU that we figure in our in-press paper?
Mike: I think I know the one, yeah.
Matt: I am SUCH a moron. I have CT scans of the whole thing.
Mike: Good.
Matt: I forgot that Kent and I scanned it back in 2008. Even blogged about it, fer cryin’ out loud.  So I can do the sum-over-slices, scale-for-other-verts thing for Diplodocus, too. Which is at least closer to Supes than JANGO is.
Mike: Remind me, is it from a juvenile?
Matt: Maybe, maybe not. It IS tiny, but the neural spine is fused, the internal structure is crazy complex, and it doesn’t have any obvious juvenile characters other than just being small. The ASP is about as high as it gets in diplodocids. Which, as you may remember, is not nearly as high as it gets in titanosauriforms–that’s another paper that needs writing. Damn it. To know all this stuff and not have told it yet is killing me.
Mike: PeerJ!
Matt: I know!
Mike: Bottom line, it’s nuts that no-one has ever even tried to weigh a sauropod neck.* We should definitely do it, even if we do a really crappy job, if only so that others feel obliged to rebut.
Matt: Quite. Let’s do it. For reals.
Mike: In April. Done.

* R. McNeill Alexander (1985, 1989) did estimate the mass of the neck of Diplodocus, based on the old Invicta model and assuming a specific gravity of 1.0. Which was a start, and waaay better than no estimate at all. Still, let’s pretend that Mike meant “tried based on the actual fossils and what we know now about pneumaticity”.

The stuff about putting everything off until April is in there because we have a March 31 deadline to get a couple of major manuscripts submitted for an edited thingy. And we’ve made a pact to put off all other sciencing until we get those babies in. But I want to blog about this now, so I am.

Another thing Mike and I have been talking a lot about lately is the relation between blogging and paper-writing. The mode we’ve seen most often is to blog about something and then repurpose or rewrite the blog posts as a paper. Darren paved the way on this (at least in our scientific circle–people we don’t know probably did it earlier), with “Why azhdarchids were giant storks“, which became Witton and Naish (2008). Then last year our string of posts (starting here) on neural spine bifurcation in Morrison sauropods became the guts–and most of the muscles and skin, too–of our in-press paper on the same topic.

But there’s another way, which is to blog parts of the science as you’re doing them, which is what Mike was doing with Tutorial 20–that’s a piece of one of our papers due on March 31.

Along the way, we’ve talked about John Hawks’ model of using his blog as a place to keep his notes. We could, and should, do more of that, instead of mostly keeping our science out of the public eye until it’s ready to deploy (which I will always favor for certain projects, such as anything containing formal taxonomic acts).

And I’ve been thinking that maybe it’s time for me–for us–to take a step that others have already taken, and do the obvious thing. Which is not to write a series of blog posts and then decide later to turn it into a paper (I wasn’t certain that I’d be writing a paper on neural spine bifurcation until I had written the second post in that series), but to write the paper as a series of blog posts, deliberately and from the outset, and get community feedback along the way. And I think that the sauropod neck mass project is perfect for that.

Don’t expect this to become the most common topic of our posts, or even a frequent one. We still have to get those manuscripts done by the end of March, and we have no shortage of other projects waiting in the wings. And we’ll still post on goofy stuff, and on open access, and on sauropod stuff that has nothing to do with this–probably on that stuff a lot more often than on this. But every now and then there will be a post in this series, possibly written in my discretionary blogging time, that will hopefully move the paper along incrementally.


24 Responses to “The sauropod neck mass project: an experiment in open science”

  1. On your BYU vert, just one question: have you considered Kateedocus siberi Tschopp & Mateus in press? Small, argued to be adult or near it. CV13 in SMA 0004 (holotype) compares well with your vert, aside from placement and degree of cranial inclination of neural spine, and that both may be experiencing a non-negligible amount of diagenetic distortion.

    That said, working out masses for verts should take into consideration the mass and nature of the m. longissimus colli and the various “nuchal” structures, especially if they rose in a “withers” or avian-like fashion well above the neural spines, which should accomodate several other sets of muscles above the spines.

  2. Matt Wedel Says:

    Solid suggestion on Kaatedocus–that’s a possibility we probably should have considered in the paper. Fortunately we said it was only probably referable to Diplodocus, and if it turns out to be Kaatedocus that would further support our point, which is that you can have small sauropods that are more skeletally mature–at least as measured by fusions of various joints–than large ones of the same taxon or of closely related taxa.

    I note that Kaatedocus has fused cervical ribs from C3 on back and bifid spines from C8 on back, whereas the much larger mounted D. carnegii has bifid spines as early as C6 (spines are missing in C3-C5), but no fused cervical ribs before C6. In isolation, these observations show that Kaatedocus and D. carnegii were not on the same ontogenetic trajectory and thus there is some biological basis for their taxonomic separation. I am being precise here because I know that there are other reasons to think that Kaatedocus is a separate, valid, taxon; my point is that you could throw those out and still have some justification for recognizing it as a new taxon.

    I suppose one could use a similar argument to say that BYU 12613 can’t be Diplodocus. But in the case of BYU 12613, all we know is that the neural arch fused when the individual was small–and I don’t know when neural arch fusion usually happens in Diplodocus (expect a post on that soonish). In the case of Kaatedocus, known ontogenetic characters (cervical rib fusion) and putative ontogenetic characters (neural spine bifurcation) are out of order with respect to Diplodocus. So BYU 12613 could be a Diplodocus that fused its spine and cervical ribs at small size, whereas the same simple acceleration cannot explain the morphology of Kaatedocus. (None of this contradicts the possibility that BYU 12613 is Kaatedocus–that is still a viable hypothesis.)

    Also, this is further evidence that you cannot just throw all of the Morrison diplodocoids into one bin and hope to sort out their ontogeny en masse, no matter what criteria you use. Diplodocus was developmentally different from Apatosaurus was developmentally different from Suuwassea was developmentally different from Kaatedocus. Heck, Apatosaurus alone is festival of contradictory skeletochronology (see this and this).

    And furthermore, it illustrates the perils of trying to figure out anything related to ontogeny based on isolated vertebrae. Is BYU 12613:
    – a small adult Diplodocus?
    – a juvenile Dipldocus that just fused its spine early?
    – a normal-sized adult Kaatedocus?
    – a juvenile Kaatedocus that just fused its spine early?

    Off the top of my head, I can’t falsify any of those possibilities. Which is a little scary.

    Finally, I’m not saying that sorting out sauropod skeletochronology is hopeless. I just want people to have a healthy respect for the magnitude of the problem.

  3. Matt Wedel Says:

    Oh, and also:

    That said, working out masses for verts should take into consideration the mass and nature of the m. longissimus colli and the various “nuchal” structures, especially if they rose in a “withers” or avian-like fashion well above the neural spines, which should accomodate several other sets of muscles above the spines.

    Yep. Interesting that you could get a lot of soft-tissue above the vertebrae either by having “withers” or by bowstringing of the epaxial muscles as in birds. I guess it is sort of two sides of the same thing–one could argue that the effect of withers is to force the muscles to bowstring. It’s just interesting that you can get the same effect without withers–and I think that point has been underappreciated in discussions of neck musculature and support in sauropods, and in dinosaurs more generally.

  4. Mike Taylor Says:

    Dude, pls. You can’t get more neck mass by bowstringing! You just elevate the soft-tissue mass you already have higher above the vertebrae. For the purposes of mass reconstruction, we can completely ignore bowstringing, and just work with a horizontal neck.

  5. Mike Taylor Says:

    Very tangential tangent, because I mentioned horizontal necks. We have argued that sauropods did not habitually hold their necks horizontally; but accepted that they did so from time to time when transitioning between the typical raised alert posture and the lowered drinking posture.

    It now occurs to me that ostriches never have horizontal necks. They transition sinuously, keeping the majority of the neck near-vertical throughout, and moving the ‘U’ of the neck up and down, “rolling” the neck through it.

    Maybe some sauropods did something similar. Of course it can’t be exactly the same, because sauropod necks were much longer than then ground-to-neck-base height — unlike the case in ostriches. But at least some sauropods may still have been able to avoid getting very close to horizontal.

  6. Matt Wedel Says:

    Dude, pls. You can’t get more neck mass by bowstringing! You just elevate the soft-tissue mass you already have higher above the vertebrae.

    We-ell. Yes, that’s true, unless some of the muscles are permanently bowstringed, as they are in animals with withers. For example, many folks have been following Greg Paul in restoring brachiosaurs with a lot of soft tissue up above the cervicals. That bothers me less than it used to, because although I am skeptical about the presence of a big nuchal ligament in brachiosaurs, I am not skeptical about the presence of bowstringed cervical muscles. If they can occur in animals as phylogenetically and morphologically distant as ducks and deer, and they make intuitive mechanical sense, I think we should assume that they were present in sauropods.

    The question then is, does the neck have more muscle in it because of the bowstringing? At the level that it is practiced by big ungulates, I’d have to say yes, in that if you do a soft-tissue-envelope drawing that does not take them into account, you will seriously underestimate the amount of muscle in the neck. For ducks it’s not so clear, because I don’t know where the bowstringing stops.

    Anyway, in agreeing with Jaime I only meant that this is something we can’t just ignore. We need to address it, even if all we do with it is say in the paper, “we assume that none of the tension members were bowstringed when the neck was horizontal, and therefore ignore the possibility of extra neck tissue imposed by mammalian-style nuchal ligaments and cervical muscles. If such tissues were present, it should be possible to investigate their effects by building on the results presented herein”. Cool?

  7. dudes, Christian and various cos never estimated neck mass? You sure?

    Also, I have some very nice ideas for how to do this neatly in 3D; let me dig out the K. scans and run a test…

  8. emanuel tschopp Says:

    concerning the possibility of BYU 12613 being Kaatedocus, this actually struck me as well as probable, for a few reasons:
    there’s no distinct dorsal capping of the spinodiapophyseal fossa, as present in diplodocus (with the distinct horizontal ridge just ventral to the spine top), there’s no distinct elongate fossa posteroventral to the “normal” posterior pneumatic fossa and i also think to recognize the autapomorphic transverse sulcus just behind the prezygap facets.
    I guess that won’t change much for your neck mass project, just fyi!

  9. Awesome stuff.

    The reason I used “withers” here has more to do with Scott’s recent updating storm on sauropods, placing higher and deeper tissues above the neural spines on the way to the skull. These raise the issue of the form that this musculature and tendons would take, so that rather than there simply being an assumption on the avian style structure as found in ratites and applying it to sauropods, we note that for some birds, this structure and set up differs tremendously: Some birds hold their necks in a U, including some parrots, owls, and the ever rambunctious skimmer, which employs a longer, broader, and more “robust” cervical series and a very complex tendon system for its neck, including the epaxial system. Even if these birds should straighten out, as I am sure most could, during those times the soft-tissue should rise a significant portion above the bone, perhaps as much as a vertebra in height (as perhaps more — and no, I do not have dissection studies at hand to follow this, though I wish my library was more complete to keep abreast on the topic).

    Mammalian withers involve a true nuchal structure which attaches to intervening verts, and forms a sheet onto which muscles of the neck attach, but for birds the epaxial tendons seem to be relatively muscle light (duh!), suggesting that, as crocs are largely silent on this issue, the best inference is for birds. But this doesn’t mean mammals cannot offer insight, and suggest a higher muscle mass above the verts due to the presence of specialized dorsal verts, such as Scott reconstructs for Alamosaurus and Nothronychus, where a “peak” occurs where longissimus colii and other basal neck or epaxial neck muscles may attach. There may further be a fundamental error in assuming sauropod necks, even if horizontal, were scaled up versions of rhea or ostrich necks, given that the two groups have substantially different vertebral architecture, cervical ribs formed from ossified tendons suggesting a different loading regime for the neck than in the much, much smaller animals, and so forth.

    As Heinrich notes, some work has occurred from the Sauropod guys over in Germany on muscle mass and reconstruction, including the relevance of loading on vertebrae and their influence on attitude (and thus posture, but of course with the caveat that it refers to an absolute maximum).

    First things first: Getting muscle homology and placement correct.

  10. Mike Taylor Says:

    Heinrich asks: “dudes, Christian and various cos never estimated neck mass? You sure?”

    OK, there is Gunga et al. 2008 (and indeed Gunga et al. 1999 if you insist, but let’s all pretend that never happened). It gives a rather generous volume estimate of 7.3 m^3 and implies a mass of 5.84 tonnes (since the only density value it gives is 0.8 as the average across the whole animal). But that paper doesn’t make even a nominal attempt to reconstruct neck profile from anatomy, it just wraps an oval-cross-sectioned tube around the bones and calls it done.

    Or is there a much better paper that I’ve not seen?

  11. Mike Taylor Says:

    Jaime writes (among much else which is helpful): “First things first: Getting muscle homology and placement correct.”

    Do you not trust the reconstruction of Wedel and Sanders (2002)? (It’s helpfully reproduced, in glorious open-access colour, as part of Taylor and Wedel 2013.)

  12. Mike, I do not know – otherwise I wouldn’t have posted a question, but a citation! (or do you think me such a smart ass?)

    I do know that Andreas bandies a lot of numbers, including masses, around in his talks, and looking at bending resistance etc. requires mass estimates for the segments. Thus, double-check, and why not email him?

  13. Mike Taylor Says:

    OK, thanks, will do!

  14. Mike asks:

    Do you not trust the reconstruction of Wedel and Sanders (2002)? (It’s helpfully reproduced, in glorious open-access colour, as part of Taylor and Wedel 2013.)

    In a word, no.

    Nor do I trust any muscle homology placement in extinct animals, including my own for oviraptorid skulls. We are dealing with what are often a one-taxon comparison, with regards to bird to sauropod, and not any real bracketing argument. Even then, the EPB is only useful when novelty isn’t invoked, and sauropod verts are filled with novelty (as indeed are pterosaur verts). Consider, for example, the extremely long cervical ribs/ossified tendons, and the relationship of loading on bone surfaces to their likely placement — things which may help indicate placements for muscle attachment. Texture, knobs, and homology of placement are one thing, but deeper-tissue relationships is another. (I’m not saying you’re not doing this at all, mind.)

  15. Matt Wedel Says:

    Mike asks:

    Do you not trust the reconstruction of Wedel and Sanders (2002)? (It’s helpfully reproduced, in glorious open-access colour, as part of Taylor and Wedel 2013.)

    In a word, no.

    Me neither. I’ve been meaning to blog about this, but that diagram sort of implies that every vertebra serves as the origin and insertion for all of those muscles, and at least in birds it just ain’t so. For example, anterior cervical vertebrae have longus colli dorsalis inserting but not originating. So there is variation along the column in which muscles attach, and in the relative sizes of the attachments.

    So that figure is sort of a diagrammatic summary of the topological attachments of bird neck muscles as mapped onto sauropod vertebrae, but it doesn’t take into account serial variation or the relative size and importance of the various muscles or the likelihood that sauropod cervical muscles were not just like those of birds or the near-certainty that cervical muscles were not uniform across Sauropoda.

    Still, y’know. It’s a start.

  16. Yes, exactly, Matt! It’s a start. It was my intention to provoke this, that generalization here is the bane of precision. Generalization -> precision as a process, though, is what I’m getting at. And we get there by correctly noting the cervical regionalization that occurs in birds, crocs, even mammals, and use this to help discriminate regionalization of muscle origin and insertions. Yes, this means a paper devoted solely to mapping probable homologies by vertebrae in a single neck, but gosh durnit, gotta start somewhere. And make that a single paper, much like I am trying to make a presentation of oviraptorid jaw muscles.

  17. Nathan Myers Says:

    Neck mass estimation is all very well, but mechanically the torque that such mass/weight applies at the base of the neck has to be a limiting factor. Each kg is multiplied by its horizontal distance from that point. How much torque did/could it sustain, and how? Will we find that supey could only have rolled its neck, ostrich-wise, because a horizontal neck could not but buckle the proximal-most cervical?

  18. Michael Richmond Says:

    Physicist here. If you guys do make a detailed physical model for the neck (which I can understand :-), I’ll gladly compute all the torques you want. Just ask.

  19. Nathan Myers Says:

    In support of the rolling notion, can we say anything about the minimum bending radius of the neck, based on cotyle/centrum/condyle geometry? If they lowered their heads to drink by rolling, the torque at the base of the neck would remain constant throughout the motion. Its magnitude would depend on that radius.

    For those readers not totally up on torque, the crushing force on that proximal cervical vertebra is at least the whole weight M of the neck, when it is vertical, and must be many times that, NxM, when the neck is fully extended horizontally. The multiplier N depends on the ratio of the neck length to the separation between the centrum and the supporting tendon, so can be quite large.

    The total area of compressible bone in a cross section of that vertebra (at the point where it is least) should indicate an upper bound on what that force could be. (Is there a standard figure, somewhere, for the crushing strength of solid bone?) If it’s less than NxM, then anybody who insists sauropods could fully extend their (respective) necks needs to propose some other way to support the weight.

    I would enjoy a reconstruction of a supersaur drinking with its neck in an inverted “U” shape, suggestive of those hangers that socks come wrapped round.

  20. Mike Taylor Says:

    Nathan, I don’t think any of the calculations you suggest have been done. It would be great if someone did do them. I’d like to do it myself, but I can’t think of a way to do it that wouldn’t either (A) involve a lot of time-consuming modelling, or (B) involve so many assumptions that the results were more or less worthless. It’s a tough project to take on, but it would make a great Ph.D for someone with appropriate interests and expertise.

  21. Nathan Myers Says:

    The standard figure for the weight dense bone can support seems to top out at 130 MPa, corresponding to ~133 kg per square cm. A neck that weighs in at 6 tons needs a minimum vertebral cross-section of 45 sq cm just to hold the neck perfectly still vertically. Motion alone introduces additional forces, maybe 1.5x? Rolling the head to ground level puts maybe 3 tons at a distance at least 2m away, so assuming a 1m lever arm, we have 1.5x(3×2+3)=13.5 tons, for ~100 sq cm. That doesn’t seem like so much.

    The cross section through a medial vert like I seem to recall seeing here doesn’t tell us anything about the density of a proximal vert. Do we have any of the latter CT-scanned?

  22. Matt Wedel Says:

    The cross section through a medial vert like I seem to recall seeing here doesn’t tell us anything about the density of a proximal vert. Do we have any of the latter CT-scanned?

    Yes! Schwarz and Fritsch (2006) scanned C2-C4 of Giraffatitan SI and found that the following Air Space Proportions:
    C2 – 0.50
    C3 – 0.47
    C4 – 0.60

    So, these are all a bit lower than the numbers I found for Brachiosauru sp. BYU 12866 and other brachiosaurids or basal titanosauriforms, which were usually above 0.70. BUT the Schwarz and Fritsch numbers include the neural spines, which I lopped off for ASP work because it’s hard to know how much air filled the spaces between the laminae.* So their numbers might be a bit lower than mine for purely methodological, rather than biological, reasons. In any case, it wouldn’t be hugely surprising if the most anterior vertebrae were a bit more robustly built, since they are so much physically smaller than the rest of the column and probably have to maintain a certain absolute cross-section of bone to support the head.

    * Laminae only constrain the size of the diverticula on one side. Were the laminae covered by a thin skein of air and had a lot of muscles or other tissues building in between the laminae, or did the diverticula just fill the spaces between the laminae and no more, or did the diverticula actually bulge out into the surrounding tissues? When I think of a way to answer that question, I’ll certainly let people know.

  23. […] least, this is catalogued as Diplodocus. Jaime Headden suggested, and Emanuel Tschopp corroborated, the idea that it’s more likely […]

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