Finite Element Analysis of sauropod vertebrae
October 27, 2009
Earlier this month Daniela Schwarz-Wings and colleagues published the first finite element analysis (FEA) of sauropod vertebrae (Schwarz-Wings et al. 2009). Above is one of the figures showing some of their results. Following standard convention, stresses are shown on a gradient with cooler colors indicating lower stresses and hotter colors indicating higher stresses. I’m not going to dwell on the on the nuts-n-bolts of FEA in general or of this study in particular. Instead, I want to talk about how sauropod vertebrae are built.
In cross-section, sauropod vertebrae often have thick bone at the outer edges of the laminae and in the walls and especially the floor of the centrum, as shown in this Brachiosaurus cervical. The bone everywhere else is pretty thin. If you hit one of these vertebrae with some magical forumula that would dissolve away all the bone thinner than, say, 1 cm, all that would be left would be the various apophyses, the outer margins of the laminae connecting them, and probably the bottom half of the centrum. It would be like the outline of a vertebra constructed from tent poles, or tinkertoys.
This is weird because most pneumatic sauropod vertebrae have at least something approaching an I-beam shape in cross-section. You might think that the median septum would be mechanically important, but it’s usually very thin, sometimes perforated (see Hatcher’s [1901] Diplodocus cervicals, for example), and often asymmetrically deviated to one side or the other. Not what you would expect for a piece of bone that was doing any work.
And indeed, Schwarz-Wings et al. (2009) found that:
Comparative stresses are distributed evenly around the vertebrae and mainly on the bone cortex. Peak stresses occur only at points where the tendons and muscles are inserting because the insertion areas used were small resulting in extreme localized stresses. The interior of both vertebrae is nearly stress free. Almost no stresses occur around the cavities and in their bony walls (figure 3).
This reminds me not of I-beams but of the long bones of the limbs of terrestrial vertebrates. There’s a reason why you’ve got a big honkin’ marrow cavity running through the middle of your femur: the stresses are being borne by the walls of the bone. It makes sense that vertebrae would function similarly, especially sauropod cervicals which sometimes approximate limb bones in their proportions.
So how about that median septum? Why aren’t sauropod vertebrae just hollow tubes? My guess–and it is a guess–is that they got as close to being hollow tubes as their evolutionary and developmental origins allowed. The pneumatic diverticula invaded the centra from either side and pushed in lateral-to-medial, and I think the median septum is just the wimpy little bit of bone left in between the two sets of diverticula when they almost meet up in the middle.
Even if that’s correct, there’s another mystery: why don’t the diverticula just go ahead and erode away the median septum? I can think of two possible reasons. One is that, for reasons I don’t know and I’m not sure if anyone else does either, pneumatic diverticula are good at getting into bones but pretty lousy at getting back out. There are comparatively few cases of diverticula inside bones making foramina to get out into the surrounding tissue. It does happen–in humans, the mastoid air cells sometimes bust out and make subcutaneous pneumatocoels, basically bubbles of air under the skin (Anorbe et al. 2000)–but it seems to be rare. Maybe median septa fall under the same inscrutable rule.
(Incidentally, this makes the perforate laminae in Giraffatitan all the weirder.)
Another, more mundane possibility is that the median septa (and other oddly thin bits of bone) are not never loaded, just infrequently loaded. Not enough to make them straight, thick, or normal-lookin’, but enough to make sure they don’t get resorbed entirely.
Sauropod vertebrae are just loaded with these growth-and-form-related mysteries. Kudos to Schwarz-Wings et al. for pushing us a little farther down the road toward solving them.
References
- Anorbe, E., Aisa, P. and Saenz de Ormijana, J. 2000. Spontaneous pneumatocele and pneumocephalus associated with mastoid hyperpneumatization. European Journal of Radiology 36:158–160. [abstract only for free]
- Hatcher, J.B. 1901. Diplodocus (Marsh): its osteology, taxonomy and probable habits, with a restoration of the skeleton. Memoirs of the Carnegie Museum 1: 1-63 and plates I-XIII.
- Schwarz-Wings, D., Meyer, C.A., Frey, E., Manz-Steiner, H.-R., and Schumacher, R. 2009. Mechanical implications of pneumatic neck vertebrae in sauropod dinosaurs. Proceedings of the Royal Society B. doi: 10.1098/rspb.2009.1275
Sauropods were corn-on-the-cob, not shish kebabs
June 25, 2009
This is corn on the cob:

Corn on the cob, in cross section. Stolen from http://www.istockphoto.com/file_thumbview_approve/214165/2/istockphoto_214165-co rn-cob-cross-section.jpg
This is a shish kebab:
Most tetrapods are like shish kebabs: a whole lot of meat stuck on a proportionally tiny skeleton. If you don’t believe me, you can look at the human and cow neck torso cross-sections in Matt’s last post, or check out this ostrich-neck cross-section from his 2003 Paleobiology paper:
Remember that this is a freakin’ ostrich — of all extant animals, one of the ones with a most extreme long, skinny neck. And yet, if sauropods were muscled like ostriches, then their necks would have looked like this in cross section:

Putative shish kebab-style sauropod neck in cross section. Ostrich soft-tissue from Wedel (2003a: fig. 2), Diplodocus vertebra cross-section from Paul (1997: fig. 4) scaled to match size of ostrich vertebra
And soft-tissue reconstructions would have to look like this:
Which, happily, no-one is suggesting. Instead, published reconstructions of sauropod neck soft-tissue are startlingly emaciated. As exhibit A, I call this pair of Greg Paul cross-sections:

Diplodocus and Brachiosaurus neck cross-sections, showing very light musculature. From Paul (1997: fig. 4)
(Yes, the Diplodocus on the left is the one I used in the photoshopped ostrich cross-section above. It’s instructive to compare Paul’s original with the What If It Was Like A Big Ostrich version.)
Paul’s reconstructions seem to be widely considered too lightly muscled. But even the very careful and rigorous more recent reconstructions of Daniela Schwarz and her colleague show a neck much, much thinner than that of the ostrich:
Although Schwarz has put a lot more soft tissue onto the neck vertebrae than Paul did, it is still a tiny proportion of what we see in extant animals — even the ostrich, remember, which has a super-thin neck compared with pretty much anything else alive today. If sauropod necks were muscled as heavily as those of, say, cows, then the soft tissue would pretty much reach down to the ground. But they weren’t: they were more like corn on the cob, with a broad core of skeleton and relatively little in the way of delicious edibles festooned about it.
So why is this? Why does everyone agree that sauropod necks were much less heavily muscled than those of any extant animal?
It’s a simple matter of scaling. A really big ostrich might have a neck 1 m long. (Actually, ostriches don’t get that big, but let’s pretend they do because it makes the maths easier). If the x meter-long neck of a sauropod was just a scaled-up ostrich neck, then it would be x times longer, x times taller and x times wider, for a total of x^3 times as voluminous and therefore x^3 times as heavy. But the cross-sectional area of the tension members that support it is only x times taller and x times wider, for a total of x^2 times the strength. In total, then, the neck’s mass/strength is x^3/x^2 = x times as great as in the ostrich. (The sauropod neck’s mass also acts further out from the fulcrum by an additional factor of x, but that is cancelled by the fact that the tension in the neck also acts x times higher above the fulcrum.)
It seems intuitively obvious (which is is code for “I have no way to prove”) that you can’t reasonably expect the neck muscles of a giant ostrich to work ten times as hard as they do in their lesser cousins, which is what you’d need to do for the 10 m neck of, say, Sauroposeidon. So simple isometric scaling won’t get the job done, and you need to restructure the neck.
But how? Surely just reducing all the muscle around the vertebrae can’t help? No indeed — but that is not really what sauropods were doing. If you look at the typical sauropod-neck life restoration, you’ll see that the proportional thickness of the neck is actually not too dissimilar to that of an ostrich — rather thicker, in fact. If you scaled an ostrich neck up to sauropod size and compared it with a real sauropod neck, you would find not that the soft tissue was too fat, but that the vertebrae were too thin.
And so we come to it at last: rather than thinking of sauropods as having reduced the amount of soft-tissue hanging on the cervical vertebrae, we do better to think of them as having kept a roughly similar soft-tissue profile to that of an an ostrich, but enlarging the vertebrae within the soft-tissue envelope. Of course if you just blindly made the vertebrae taller and wider, they would become heavier in proportion, which would defeat the whole purpose of the exercise — but as everyone who reads this blog surely knows by now, sauropod cervicals were extensively lightened by pneumaticity. By bringing air into the center of the neck, they were effectively able to displace bone, muscle and ligament away from the centre, so that they acted with greater mechanical advantage: higher epaxial tension members, lower hypaxial compression members, and more laterally positioned paraxials.
It’s a rather brilliant system — using the same volume of bone to achieve greater strength by displacing it outwards and filling the center with air (and, in doing so, also displacing soft tissue outwards). And it will be hauntingly familiar to anyone who loves birds, because it is of course exactly what birds (and pterosaurus) have done in their long bones: the hollow humeri of flying vertebrates famously allow them to attain greater strength — specifically, resistance to bending — for the same volume and mass of bone. It’s a neat trick when done with long bones, but it takes a truly awesome taxon to do it with the neck.
So maybe sauropods were not corn on the cob after all. Maybe they were Hostess Twinkies.

Hostess Twinkie. Not truly pneumatic, as the internal cavity is filled with adipose tissue rather than air, but do you have any idea how difficult it is to find good images of hollow junk food? Stolen from http://dixiedining.files.wordpress.com/2008/07/twinkie_070918_ms1.jpg
And now for something completely different
Now that I’ve finished my Ph.D at the University of Portsmouth, what am I going to do with the rest of my scientific life? I’ve always said that I have no intention of going into palaeo full time: my knowledge is far too narrow for that, so that even if paid jobs were not in insanely short supply, I wouldn’t stand much chance of getting one. And in any case, I’d hate to get into the all-too-common situation of being up against a friend for a position we both wanted. Throw in the fact that I really enjoy my computer-programming day-job and it seems pretty clear that what I need is an unpaid affiliation that lets me get on with lovely research.
Well: I am absolutely delighted to announce that, as of last month, I am an Honorary Research Associate in the Department of Earth Sciences at UCL. It’s not just that UCL is such a well-respected institution — see that Wikipedia article for some details — more importantly, it’s where Paul Upchurch hangs out, as Senior Lecturer in Palaeobiology. Sauropod fans will be familiar with Paul’s characteristically detailed and careful work, from his pioneering work on sauropod phylogeny (Upchurch 1995, 1998), through his and John Martin’s indispensible Cetiosaurus makeovers (Upchurch and Martin 2002, 2003) to the state-of-the art review that he lead-authored for Dinosauria II (Upchurch et al. 2004) and the Tokyo Apatosaurus monograph (Upchurch et al. 2005). What many of you won’t know is what an excellent collaborator he is — quick, conscientious, insightful and diplomatic. We’ve already collaborated on a few short papers (Upchurch et al. 2009 and a couple of Phylocode companion-volume chapters that are in press), and I hope there will be more in the future.
References
- Paul, Gregory S. 1997. Dinosaur models: the good, the bad, and using them to estimate the mass of dinosaurs. pp. 129-154 in: D. L. Wolberg, E. Stump, and G. D. Rosenberg (eds.), DinoFest International: Proceedings of a Symposium Sponsored by Arizona State University. Academy of Natural Sciences, Philadelphia.
- Paul, Gregory S. 1998. Terramegathermy and Cope’s Rule in the land of titans. Modern Geology 23: 179-217.
- Schwarz, Daniela, Eberhard Frey and Christian A. Meyer. 2007. Pneumaticity and soft-tissue reconstructions in the neck of diplodocid and dicraeosaurid sauropods. Acta Palaeontologica Polonica 52(1): 167-188.
- Upchurch, Paul. 1995. The evolutionary history of sauropod dinosaurs. Philosophical Transactions of the Royal Society of London Series B, 349: 365-390.
- Upchurch, Paul. 1998. The phylogenetic relationships of sauropod dinosaurs. Zoological Journal of the Linnean Society, 124: 43-103.
- Upchurch, Paul and John Martin. 2002. The Rutland Cetiosaurus: the anatomy and relationships of a Middle Jurassic British sauropod dinosaur. Palaeontology, 45(6): 1049-1074.
- Upchurch, Paul and John Martin. 2003. The anatomy and taxonomy of Cetiosaurus (Saurischia, Suaropoda) from the Middle Jurassic of England. Journal of Vertebrate Paleontology 23(1): 208-231.
- Upchurch, Paul, Paul M. Barrett and Peter Dodson. 2004. Sauropoda. pp. 259-322 in D. B. Weishampel, P. Dodson and H. Osmólska (eds.), The Dinosauria, 2nd edition. University of California Press, Berkeley and Los Angeles. 861 pp.
- Upchurch, Paul, Yukimitsu Tomida, and Paul M. Barrett. 2005. A new specimen of Apatosaurus ajax (Sauropoda: Diplodocidae) from the Morrison Formation (Upper Jurassic) of Wyoming, USA. National Science Museum Monographs No. 26. Tokyo. ISSN 1342-9574.
- Upchurch, Paul, John Martin, and Michael P. Taylor. 2009. Case 3472: Cetiosaurus Owen, 1841 (Dinosauria, Sauropoda): proposed conservation of usage by designation of Cetiosaurus oxoniensis Phillips, 1871 as the type species. Bulletin of Zoological Nomenclature 66(1): 51-55.
- Wedel, Mathew J. 2003. Vertebral pneumaticity, air sacs, and the physiology of sauropod dinosaurs. Paleobiology 29(2): 243-255.
Sauropods were tacos, not corn dogs
June 22, 2009
This is a taco.
This is a corn dog.
Here’s a cross-section of a human. In the terms of fast food, people are corndogs. Most of us even have an outer ring of yellow adipose ‘breading’.
Here’s a cross-section of a cow. In an example of function following form, cows are, and often become, corndogs.
Note that in both the human and the cow the spaces between the neural spine and transverse processes are completely filled with back muscles, which in fact bulge out beyond the tips of the neural spine, as we also saw here. This despite the common paleoart convention of presenting dinosaurs as thin layers of skin conforming perfectly to the underlying skeleton. Just Say No to shrink-wrapped sauropods!
Here is Figure 17 from Holland (1910), one of the most badass scientific smackdowns ever published, in which Holland wiped the floor with Hay, Tornier, and the idea of sprawling sauropods. On the left are torso skeletons of three lizards and a croc; on the right is an anterior dorsal with articulated ribs from Diplodocus. As you can see, it’s a taco, and its taconic form would be perfected if it could roll supine.
The point of the post is not that sauropods had deep, slab-sided bodies. We’ve covered that before. The point is that sauropod torsos are seriously weird. In mammals, the dorsal ribs arch up and out, away from the vertebra, before sweeping around to define the anterior body wall. In lizards, the proximal part of each rib sticks out sideways. In sauropods, the ribs point down. This is mainly because the vertebrae are FREAKIN’ HUGE compared to the size of the body. Whereas in the mammals and lizards the dorsal vertebrae are titchy little things that span a small fraction of the width of the torso, in Diplodocus and other sauropods the dorsal vertebrae account for about half. (The cow cross-section missed the transverse processes, so that vert looks narrower than it actually is.)
This is relevant when we think about the function of pneumaticity. When I write that pneumaticity lightened vertebrae, I usually mean relative to that same vertebra if it wasn’t pneumatized. But we could also ask if the pneumatic vertebra is lighter than a vertebra from a similar-sized animal that lacks pneumaticity–except that, for big sauropods, there are no similar-sized terrestrial animals without pneumaticity to compare.
Imagine that in a big sauropod the dorsal vertebrae are three times as wide and three times as tall as they would be in a similar-sized mammal. They should weigh nine times more. But let’s also assume that the vertebrae of the sauropod are 85% air by volume, which is in fact pretty typical for Early Cretaceous brachiosaurids. The mass of the dorsal column relative to that of the mammal is then 9 x 0.15 = 1.35, a little heavier, but not much (I’m assuming the length of the torso is the same in the two animals). Bigger bones mean better lever arms for the muscles and lower bending stresses on the ribs, which can function more like curtains and less like cantilevered beams.
I can’t think of much published discussion of this stuff as it relates to sauropods, but it seems like it might be important.
Reference
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.
Brachiosaurus and friends from here (hat tip to Ville Sinkkonen).
In an e-mail with explicit permission to quote, our colleague Casey Holliday sent the following thoughts about our new paper and the subsequent ten days of related blogging:
I don’t know guys. I like your blogs, and your papers are fine. And I liked this paper. And I’m a fan. But it looks to me that you blogged about far more data, in- or not in support of your paper than you actually presented in your paper. So,…wtf? The posts on Dinomorph far exceeded your (or any) published rebuke. Your explanation (and honorable erred parts) of the semicircular canal data also exceeded that actual published part too, with extra photos, description etc. (is that error going to be OA published too?) Also additional pix of necks (e.g., Nigersaurus), and not only from sauropods that would have
potentially bettered the original pub. So what’s fair? Why weren’t
these data also included in the publication? Maybe it’s not my business and was taken up in review…I don’t know. Frankly, none of this blog stuff really counts in the peer-reviewed world of “real” publications. Its not like this blogging and comments all count as Supplementary Data either. But also, I’m obviously here commenting on it, so also crossing into the fray…But who really cares about all this discussion? Its no different than the DML or any other noise in the internet world (or is it). Similar to what Paul Barrett was posting on Tet Zoo…what counts? Why take up arguments here, when they should (maybe?likely?) be taken up more formally and privately.If you’re going to air all this additional data and unreviewed
opinion, then I think this discussion is important.I think this phenomenon of the sauropod neck paper is really
interesting. We have 3 scientists that published a paper, and then, thanks to their current blogosphere cred, basically unleashed a hype not seen in this way previously that I can remember. Maybe that’s the interesting part? and kudos. But interestingly…we’re seeing this intersection of traditional publication (OA or not), blogosphere description, and perhaps, almost certainly, excellent self-promotion.I’m still a fan. I think this paper is generally solid. But I’m
particularly interested in this phenomenon and hope this is a fair
place to raise it.
The comment field is open, and we SV-POW!sketeers are going to refrain from commenting for a couple of days to let the conversation develop unfettered.
We are genuinely curious to know what you think.
What heads tell us about necks, redux
June 5, 2009
I Cannot Brain Today, I Have the Dumb
Man, I hate making mistakes. The only thing worse than making mistakes is making them in public, and the only thing worse than that is finding them in published papers when it’s too late to do anything about them. About the only consolation left–if you’re lucky–is getting to be the one to rat yourself out (we have to do this a lot). So here goes.
In our figure 4 (from Taylor et al. 2009) we showed the skulls of three sauropodomorphs, Massospondylus, Camarasaurus, and Diplodocus, posed with horizontal semicircular canals (HSCCs) level, angled 30 degrees above horizontal, and angled 20 degrees below horizontal, as it is written (by Duijm 1951). We also showed the angle of the occipital condyle when the HSCCs are level; if the craniocervical joint was in osteologically neutral pose (ONP), that line would indicate the angle of the anterior cervicals.
Trouble is, we put the neck lines for Diplodocus and Camarasaurus in the wrong places.
As any idiot can see from Sereno et al. (2008: fig 1), the brain, brainstem, and occipital condyle form a line that runs from roughly the upper part of the orbit (in lateral see-through view) out the back of the head. Now if you look at our fig. 4 you’ll see that the ONP lines for Camarasaurus and Diplodocus are much too inclined, so that if the brain was in line with the anterior neck–which it should be, in ONP–it would be sticking out the back of the head.
If that doesn’t make sense, just look at the above illustration, imagine the brain and spinal cord in a straight line parallel to the black neck line but also dorsal to it, and you’ll see that the brain would be outside the skull. Those incorrect neck lines don’t represent impossible postures, but they don’t represent ONP, either.
Here’s a corrected up version of the figure to show what I mean. The black lines are still the ONP neck lines, and now I’ve put in shadowy necks at +30 and -20 to go with the shadowy heads. The 50 degree spans marked out by the shadowy necks are the ranges within which the neck could articulate in ONP with skulls stuck in the 50-degree “Duijm window”.
Caution: it is very easy to misread the shadowy necks as showing a range of movement within an individual; in fact, the neck lines are ‘anchored’ to the skulls in ONP as the skulls rotate through the 50 degrees allowed by the HSCCs. They are not individual movement but the possible range of taxonomic variation in HSCC orientation according to Duijm (1951).
Worth noting here is the likelihood that Massospondylus had a more elevated neck than any of the neosauropods studied so far–certainly a finding at odds with the traditional depictions of basal sauropodomorphs. (It is just a likelihood, though, since the top, neck-wise, of Massospondylus’s Duijm window overlaps with the windows of the other taxa a bit.)
In this version I’ve gone one step farther and included Nigersaurus (modified from Sereno et al. (2008: fig 1). Nigersaurus differs from Diplodocus in the angle of the face from the HSCCs and occipital condyle, not in the angle between the HSCCs and the occipital condyle, which is remarkably similar in Camarasaurus, Diplodocus, and Nigersaurus. This suggests that Nigersaurus held its head differently than other sauropods, but not necessarily its neck.
Keep in mind, though, that the difference in facial angle between Diplodocus and Nigersaurus is less than 50 degrees, and that some of the head postures in the respective Duijm windows of the two taxa are identical. So we can’t say for certain that Nigersaurus held its head differently than Diplodocus; it is possible that they held their heads at the same angle and that Nigersaurus just carried its HSCCs at a different angle. If that were the case, the neck of Nigersaurus would have been more inclined than that of Diplodocus. I’m not arguing that that’s likely–it seems perfectly plausible that the two taxa might have held their necks similarly and their heads differently, as suggested above–I’m just pointing out the very wide range of possibilities allowed by the data. To reiterate one of the points of the paper, HSCCs aren’t useless for determining habitual head posture, they just can’t narrow things down very far on their own.
Also note that some of the neck postures allowed by the Duijm window have the anterior cervicals running down, below horizontal, not up. And many of the allowed neck postures for the neosauropods are close to horizontal. So, we were wrong and HSCCs + occipital condyles show that most sauropods held their necks close to level and not strongly elevated after all, right?
Onward and Upward, or Down in Flames?
Not so fast. Remember that all of the neck lines in the above figures show the angle of the anterior neck if the neck was in ONP with the skull. But Vidal et al. (1986) found that the skull is habitually flexed on the neck, even in lizards, and we have since verified this for salamanders, turtles, and more. And sometimes the flexion is dramatic.
Our figure 1 (from Taylor et al. 2009) shows the cranium, cervicals, and first few dorsals from a hare in ONP and in the posture shown by Vidal et al. (1986: fig. 4b). The difference between the anteriorly-directed ONP pose and the backward-leaning Vidal-compliant pose is striking. I measured the angle between the cervical column and the maxillary toothrow to be ~110 degrees in the ONP pose and ~70 degrees in the Vidal-compliant pose (try it yourself with Paint or Photoshop, or download some free image manipulation software). That means the head is flexed on the neck by 40 degrees! That is a big angle. If sauropods did the same, you could take the neck lines shown above and crank them down by 40 degrees (remember that the heads are “fixed” into the 50-degree Duijm windows allowed by the HSCCs), which would make Mike’s elevated Diplodocus look not just achievable, but perhaps even conservative.
Where does all that leave us? In sauropods for which HSCC orientation is known, putting the HSCCs level the anterior neck is still inclined, and even with the HSCCs angled 20 degrees down the ONP neck would only be slightly below horizontal, and if the head was Vidal-compliant (strongly flexed on the neck), the neck would have to be above horizontal. So heads still tell us about necks, and in particular they tell us that the necks angled up. Our neck lines for Camarasaurus and Diplodocus are not correct for ONP, but probably represent attainable postures. My first head ‘n necks post has the angles too exaggeraged for ONP, too, but again all of those poses are not just possible but likely if the head was flexed on the neck.
Miscellanea
We owe mad props to Brian Engh, a.k.a. The Historian, who burst on the paleo-rap scene with a rap video about crocodilian predation and almost certainly the first ever kung-fu rap video to name-check titanosaurs. Brian stumbled across Mike’s extra goodies page for the new paper about week before the paper was due out, and kindly suppressed the information until after D-Day. You can and should download his entire album, Earth Beasts Awaken (open access, yo), and kick it old school.
Congratulations to Francisco “Paco” Gasco, who just got funding for a PhD to do a complete morphological and paleobiological workup on the giant Spanish sauropod Turiasaurus. You’ll be hearing more about Paco in the not-too-distant future, we promise.
Finally, here’s that video of an elephant grabbing an ostrich by the neck that you ordered.
The End of the Beginning?
This brings us to the end of ten solid days of new posts, which is a new record for us and one not likely to be broken for a long time, if ever. We never planned to do all this; in the beginning we each were going to contribute one post and that would have been that. But we kept finding things that we felt needed to be discussed.
As all of us have been saying in every available medium, this is not the end of anything. The sauropod neck posture debate is not over; in a few years we may look back and see that in 2009 we were still stumbling to the real starting line. We don’t think this stuff is unimportant or unknowable, and we’re going to keep working on it, and we hope lots of others do as well.
We’ll see you out there.
References
- Duijm, M. 1951. On the head posture in birds and its relation to some anatomical features. II. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series C 54: 260–271.
- Sereno, Paul C., Jeffrey A. Wilson, Lawrence M. Witmer, John A. Whitlock, Abdoulaye Maga, Oumarou Ide and Timothy A. Rowe. 2007. Structural Extremes in a Cretaceous Dinosaur. PLoS ONE 2 (11): e1230 (9 pages). doi:10.1371/journal.pone.0001230
- Taylor, M.P., Wedel, M.J., and Naish, D. 2009. Head and neck posture in sauropod dinosaurs inferred from extant animals. Acta Palaeontologica Polonica 54 (2): 213–220.
Unstated precision and undemonstrated accuracy: two more reasons why we don’t trust DinoMorph
June 2, 2009
Because the appearance of accuracy has an irresistible allure, non-specialists frequently treat these estimates as factual.
–Graur and Martin (2004: p.80)
Prologue: Why We Hatin’?
Between the first DinoMorph post and this one, it may seem like we have it in for DinoMorph, like we’re trying to discredit the method or bury it. We’re not anti-DinoMorph at all. We really want it to work, because 3D modeling is probably going to be the only way to explore some problems we care about (like the breathing mechanics of an articulated sauropod torso), and so far DinoMorph seems to be farther along than any of the alternatives. It is also worth remembering that building 3D digital dinos for scientific purposes is still in its infancy, and that the VP community has barely gotten started exploring the possibilities. The field has great promise. But we also have to be realistic about limitations in the source data (see Mike’s post) and about the accuracy and precision of the results (this post). We hope that these posts will start constructive conversations and inspire more work to improve the science.
Intro: Accuracy and Precision
Accuracy is how close to the real value a measurement is, and precision is how close repeated measurements are to each other. Say it’s 100 degrees F outside, which it may be for some of you. If you have four thermometers and they read 90, 95, 105, and 110, then the mean is 100. The accuracy of the aggregate setup is high, but the precision is low (big error bars). If, on the other hand, your thermometers read 94.2, 93.8, 94.6, and 93.4, then they are precise (tight grouping) but inaccurate (not centered on the real value)
Oh Error Bars, Where Art Thou?
Here’s what 2 degrees (angular, not temperature) looks like:
It’s not a big measurement. If I was measuring the range of movement (ROM) of a single joint in one individual, like an elbow or shoulder, and I got a precision of plus or minus 2 degrees over repeated movements, I’d be pretty happy. If I got that level of precision on, say, the left knee, in ten different people, I’d start worrying that I was in the Matrix.
All eusauropods have at least 12 cervical vertebrae, and diplodocids have at least 15 (Barosaurus probably has 16, but there are no complete necks so it’s hard to be sure). What happens if we propagate an error of plus or minus 2 degrees down the neck of Diplodocus?
None of these are supposed to correspond to any particular pose in life. I just lined up all the cervicals as straight as I could get them, and then rotated each joint between C3 and C15 by 2 degrees. I left the occipital condyle and C1-C3 in a straight line because I felt the point was made, but the head could be rotated up or down by another 6 degrees if one so chose. Again, this is not an ROM, this is just an error of plus or minus 2 degrees across each of 12 intervertebral joints.
Now let’s look back at the neutral pose and estimated ROM of the neck in the CM 84/94 composite skeleton of Diplodocus (Stevens 2002: fig. 6a):
Notice that the model poses are shown with perfect precision, and no allowance for error. Now, look back up at the first picture to get an idea of what 2 degrees of error looks like, and then try to mentally apply it to each of those three poses. It’s not easy to picture, but in my mind’s eye the three neck poses dissolve into a fuzz of probabilities, like the electron cloud around the nucleus of an atom.
How precise is DinoMorph? Or rather, given that the guts of the program probably allow for Jupiter flyby levels of precision, how precise is any given result, based on the interaction of raw data, necessary but unverified controlling assumptions (see below), and the algorithm itself? Can we really rule out an error of plus or minus 2 degrees per joint? What about 1 degree per joint? What about 5? This is a problem of precision, and it would still exist even with an absolutely perfect neck that was 100% complete and entirely undistorted (which we ain’t got).
It’s possible that the current version of the program doesn’t allow these kinds of error calculations. That’s fine–I realize that DinoMorph, like all of science, is a work in progress. But I’d like to know up front that there is no provision for determining the precision, so I could delay asking the question. And at some point, it will have to be answered.
Maybe it would be better to shift gears and ask: when DinoMorph is applied to extant animals, does it accurately predict the neutral pose and ROM?
Ground Truthiness
It might be better to ask that question, but there are no published answers. From the first DinoMorph paper, where the method is justified (Stevens and Parrish 1999: p. 798):
Our manipulation of muscle and ligament preparations of extant bird necks indicated that synovial capsules constrain movement such that paired pre- and postzygapophyses could only be displaced to the point where the margin of one facet reaches roughly the midpoint of the other facet, at which point the capsule is stretched taut (20). In other words, one facet could slip upon the other until their overlap was reduced to about 50%. In vivo, muscles, ligaments, and fascia may have further limited movement (20); thus, the digital manipulations reported here represent a “best case” scenario for neck mobility.
The reference supporting all this is number 20 (remember how much I like numbered references?), and here’s the full text (Stevens and Parrish 1999: p. 800):
20. J. M. Parrish and K. Stevens, unpublished data.
Those data are still unpublished. But at least one of the basic assumptions–the 50% zyg overlap bit–is contradicted by Stevens and Parrish (2005b: p. 191 [not to mention by Taylor et al. 2009]).
It’s been a decade. There have been three subsequent papers on this stuff (Stevens 2002, Stevens and Parrish 2005a, b). The DinoMorph results have been the foundation for sauropod depictions in the biggest dinosaur documentary ever made and for an exhibit at the biggest natural history museum in the world. And we have no idea if the method is accurate, because the supporting data have never been published.
Sadly, this is not that uncommon in paleontology, particularly when it comes to sauropods, and especially when it comes to necks. Someone comes up with a totally new method, and right out of the gate it gets applied to a thorny paleontological problem, before it’s been demonstrated to work on extant animals. It’s exciting, it’s seductive, and it’s hard to screw up, because when you apply an unproven method to an unsolved problem, it’s impossible to get the wrong answer. In fact, the results are “not even wrong“; it’s impossible to get an answer of any value whatsoever, because there is no way of judging its correctness.
In contrast, the work of Christian and Dzemski (2007) on neck posture in Brachiosaurus warrants serious consideration, not because of the particular answer they got for Brachiosaurus, but because they got the right answers when they applied their method to extant long-necked animals (ostriches and camels; Dzemski and Christian 2007). Don Henderson and Ryosuke Motani, among others, have also been religious about ground-truthing their methods on extant animals before applying them to fossil taxa. That shouldn’t be exceptional. It should be expected. It should be the minimum requirement for being included in the discussion.
Conclusion: Let’s move forward
I can’t accuse the makers of Walking With Dinosaurs or the designers of Dinosaurs: Ancient Fossils, New Discoveries of drinking the DinoMorph Kool-Aid. I don’t know that it is Kool-Aid. It might be fine wine. There’s red stuff in the cup, but no one has tasted it.
If you get nothing else from this post, please understand that I’m not saying the results of DinoMorph are either good or bad. I’m saying that there is currently no objective way of knowing. I want DinoMorph to work, but I want a DinoMorph made rigorous by the publication of supporting data from extant animals demonstrating its accuracy, and ranges of error demonstrating its precision.
If someone has a novel method they want to apply to dinosaurs or any other extinct animal, the burden of proof is on them to show that the method works. And if that evidence is not forthcoming, you–reviewers, editors, readers, science journalists, museum exhibit designers, documentary producers, netizens, laypeople–have the right to ask for it. And until you get that supporting evidence, you don’t have to take the results of the method seriously. Asking “how do you know that?” is the basis of science; it ought to be reflexive.
In the immortal words of Tom Holtz, “Sorry if that makes some people feel bad, but I’m not in the ‘make people feel good business’; I’m a scientist.”
References
- Christian, A. and Dzemski, G. 2007. Reconstruction of the cervical skeleton posture of Brachiosaurus brancai Janensch, 1914 by an analysis of the intervertebral stress along the neck and a comparison with the results of different approaches. Fossil Record 10: 38–49. (subscription required)
- Dzemski, G., and Christian, A. (2007) Flexibility along the neck of the ostrich (Struthio camelus) and consequences for the reconstruction of dinosaurs with extreme neck length. Journal of Morphology 268(8):701-714. (subscription required)
- Graur, D., and Martin, W. 2004. Reading the entrails of chickens: molecular timescales of evolution and the illusion of precision. Trends in Genetics 20:80-86.
- Stevens, K.A. 2002. DinoMorph: Parametric modeling of skeletal structures. Senckenbergiana Lethaea 82(1): 23-34.
- Stevens, K.A. and Parrish, J.M. 1999. Neck posture and feeding habits of two Jurassic sauropod dinosaurs. Science 284: 798–800. (subscription required)
- Stevens, K.A. and Parrish, J.M. 2005a. Neck posture, dentition, and feeding strategies in Jurassic sauropod dinosaurs. In: V. Tidwell and K. Carpenter (eds.), Thunder−Lizards: The Sauropodomorph Dinosaurs, 212–232. Indiana University Press, Bloomington, Indiana.
- Stevens, K.A. and Parrish, J.M. 2005b. Digital reconstructions of sauropod dinosaurs and implications for feeding. In: K.A. Curry Rogers and J.A. Wilson (eds.), The Sauropods: Evolution and Paleobiology, 178–200. University of California Press, Berkeley, California.
- Taylor, M.P., Wedel, M.J. and Naish, D. 2009. Head and neck posture in sauropod dinosaurs inferred from extant animals. Acta Palaeontologica Polonica 54(2): 213-220.




























