Folks,

You may know that the inaugral TetZooCon is set to take place next Saturday (12 July) at the London Wetland Centre. It’s an informal convention that’s condensed around occasional SV-POW!sketeer Darren Naish’s absurdly informative blog Tetrapod Zoology, and features a day of talks, a palaeoart workshop and a quiz. At £40 for the day, it’s a bit of a bargain.

Among the speakers is my own good self, and I will be talking about why giraffes are rubbish.

Taylor and Wedel 2013a: Figure 3. Necks of long-necked sauropods, to scale. Diplodocus, modified from elements in Hatcher (1901, plate 3), represents a “typical” long-necked sauropod, familiar from many mounted skeletons in museums. Puertasaurus, Sauroposeidon, Mamenchisaurus and Supersaurus modified from Scott Hartman’s reconstructions of Futalognkosaurus, Cedarosaurus, Mamenchisaurus and Supersaurus respectively. Alternating pink and blue bars are one meter in width. Inset shows Fig. 1 to the same scale.

Taylor and Wedel 2013a: Figure 3. Necks of long-necked sauropods, to scale. Diplodocus, modified from elements in Hatcher (1901, plate 3), represents a “typical” long-necked sauropod, familiar from many mounted skeletons in museums. Puertasaurus, Sauroposeidon, Mamenchisaurus and Supersaurus modified from Scott Hartman’s reconstructions of Futalognkosaurus, Cedarosaurus, Mamenchisaurus and Supersaurus respectively. Alternating pink and blue bars are one meter in width. Inset shows Fig. 1 to the same scale.

If that sounds like your idea of a good time, then you need to move fast! Booking closes at 4pm this evening. Better get on it now!

 

Emeus crassus mount

In a back room at the Field Museum, from my visit in 2012.

I took a lot of photos of the neck, which nicely records the transition in neural spine shape from simple to bifurcated–a topic of interest to sauropodophiles.

Emeus crassus neural spines

Are you a lover of sauropod necks?

Do you long to demonstrate to your friends and family how much better[1] they are than the necks of other long-necked critters?

Are you crazy for the Taylor and Wedel (2013a) paper on why sauropods had long necks; and why giraffes have short necks, but disappointed that it’s not, until now, been obtainable in T-shirt form?

front

back

If so, it’s your lucky day! You can now buy a T-shirt featuring Figure 1 on the front (necks of a human, giraffe, ostrich, Paraceratherium[2], Therizinosaurus, Gigantoraptor, Arambourgiania and Tanystropheus) and Figure 3 on the back (necks of Diplodocus, Puertasaurus, Sauroposeidon, Mamenchisaurus and Supersaurus).

And here it is in real life — sorry I couldn’t get a more photogenic model at short notice.

DSCN0800-front

DSCN0796-back

And here are the original figures as they appeared in the paper. The full captions, as reproduced here, are also on the shirts — just in case you need to check details while you’re out and about.

Figure 1. Necks of long-necked non-sauropods, to scale. The giraffe and Paraceratherium are the longest necked mammals; the ostrich is the longest necked extant bird; Therizinosaurus and Gigantoraptor are the largest representatives of two long-necked theropod clades; Arambourgiania is the longest necked pterosaur; and Tanystropheus has a uniquely long neck relative to torso length. Human head modified from Gray’s Anatomy (1918 edition, fig. 602). Giraffe modified from photograph by Kevin Ryder (CC BY, http://flic.kr/p/cRvCcQ). Ostrich modified from photograph by “kei51” (CC BY, http://flic.kr/p/cowoYW). Paraceratherium modified from Osborn (1923, figure 1). Therizinosaurus modified from Nothronychus reconstruction by Scott Hartman. Gigantoraptor modified from Heyuannia reconstruction by Scott Hartman. Arambourgiania modified from Zhejiangopterus reconstruction by Witton & Naish (2008, figure 1). Tanystropheus modified from reconstruction by David Peters. Alternating blue and pink bars are 1 m tall.

Figure 1. Necks of long-necked non-sauropods, to scale. The giraffe and Paraceratherium are the longest necked mammals; the ostrich is the longest necked extant bird; Therizinosaurus and Gigantoraptor are the largest representatives of two long-necked theropod clades; Arambourgiania is the longest necked pterosaur; and Tanystropheus has a uniquely long neck relative to torso length. Human head modified from Gray’s Anatomy (1918 edition, fig. 602). Giraffe modified from photograph by Kevin Ryder (CC BY, http://flic.kr/p/cRvCcQ). Ostrich modified from photograph by “kei51” (CC BY, http://flic.kr/p/cowoYW). Paraceratherium modified from Osborn (1923, figure 1). Therizinosaurus modified from Nothronychus reconstruction by Scott Hartman. Gigantoraptor modified from Heyuannia reconstruction by Scott Hartman. Arambourgiania modified from Zhejiangopterus reconstruction by Witton & Naish (2008, figure 1). Tanystropheus modified from reconstruction by David Peters. Alternating blue and pink bars are 1 m tall.

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Figure 3. Necks of long-necked sauropods, to scale. Diplodocus, modified from elements in Hatcher (1901, plate 3), represents a “typical” long-necked sauropod, familiar from many mounted skeletons in museums. Puertasaurus, Sauroposeidon, Mamenchisaurus and Supersaurus modified from Scott Hartman’s reconstructions of Futalognkosaurus, Cedarosaurus, Mamenchisaurus and Supersaurus respectively. Alternating pink and blue bars are one meter in width. Inset shows Fig. 1 to the same scale.

No doubt these will be all the rage at SVPCA this year!

So get your T-shirts!

Update (the same evening)

As suggested by Kevin, I’ve now made the shirt available in a selection of eight versions: four men’s shirt, two women’s, and two kids. I don’t really understand what the differences are between them all, but they seemed to be the saner choices among those offered by Cafe Press. You can get any or all of them here. The shirt modelled above is the one called simple “White T-Shirt”. Please be aware that unlike all the others, the “Value T-Shirt” has no printing on the back — only Figure 1 on the front.

Notes

[1] i.e. bigger.

[2] Not to be confused with Paramecium.

References

Taylor, Michael P., and Mathew J. Wedel. 2013. Why sauropods had long necks; and why giraffes have short necks. PeerJ 1:e36. doi:10.7717/peerj.36

Bird vertebra diagrams

January 10, 2014

bird neck note sheet

I made these back in the day. The idea was that you could print them out and have them along while dissecting bird necks, so you could draw on the muscles.

bird neck note sheet - LEFT - all three views

It’s basically one drawing of an ostrich vertebra, morphed in GIMP and stacked to simulate articulation. All of the ones in this post show the vertebrae in left lateral view. If you need right views, flip ‘em in GIMP or heck, I think even Windows Explorer will do that for you. The one above has dorsal views in the top row, lateral view in the middle row, and ventral views in the bottom row.

bird neck note sheet - LEFT - double lateral

Here’s a sheet with two rows in lateral view, the idea being that you draw on the more superficial multi-segment muscles on one row, and the deeper single- or two-segment muscles on the other row.

bird neck note sheet - LEFT - 12 cervicals

A version with 12 vertebrae, so you can map out the often complicated patterns of origins and insertions in the really long muscles. How complicated? Well, check out this rhea neck with the M. longus colli dorsalis and M. longus colli ventralis fanned out.

Rhea neck muscles fanned - full

That’s all. Have fun!

One aspect of sauropod neck cartilage that’s been overlooked — and this applies to all non-avian dinosaurs, not just sauropods — is the configuration of the cartilage in their necks. It’s not widely appreciated that birds’ necks differ from those of all other animals in this respect, and we don’t yet know whether sauropods resembled birds or mammals.

Here’s a classic sagittal view of a mammal neck — in this case a human — from The Basics of MRI (Joseph P. Hornak, 1996-2013):

sagittal-neck

You can see two distinct kinds of structure alternating along the neck: the big, square ones are vertebral centra (slightly hollow at each end), and the narrower lens-shaped ones are the intervertebral discs.

In mammals, and most animals, we find this distinct fibrocartilaginous element, the disc, between the centra of consecutive vertebrae. These discs have a complex structure of their own, consisting of an annulus fibrosus (fibrous ring), made of several layers of fibrocartilage, surrounding a nucleus pulposus (pulpy centre) with the consistency of jelly.

IntervertebralDisc

But in birds, uniquely among extant animals, there is no separate cartilaginous element. Instead, the articular surfaces of the bones are covered with layers of hyaline cartilage which articulate directly with one another, and are free to slide across each other. The adjacent articular surfaces are enclosed in synovial capsules similar to those that enclose the zygapophyseal joints. You can see this in the hemisected Rhea neck from last time:

Figure 18. Cartilage in the neck of a rhea. Joint between cervicals 11 (left) and 10 (right) of a rhea, sagittally bisected. Left half of neck in medial view. The thin layers of cartilage lining the C11 condyle and C10 cotyle are clearly visible.

Taylor and Wedel (2013c: Figure 18). Cartilage in the neck of a rhea. Joint between cervicals 11 (left) and 10 (right) of a rhea, sagittally bisected. Left half of neck in medial view. The thin layers of cartilage lining the C11 condyle and C10 cotyle are clearly visible.

The difference between these two constructions is very apparent in dissection: in birds, adjacent vertebrae come apart easily once the surrounding soft tissue is removed; but in mammals, it is very difficult to separate consecutive vertebrae, as they are firmly attached to the intervening intervertebral disc.

Figure 19. Alligator head and neck. Sagittally bisected head and neck of American alligator, with the nine cervical vertebrae indicated. Inset: schematic drawing of these nine vertebrae, from ([62]: figure 1), reversed.

Taylor and Wedel (2013c: Figure 19). Alligator head and neck. Sagittally bisected head and neck of American alligator, with the nine cervical vertebrae indicated. Inset: schematic drawing of these nine vertebrae, from ([62]: figure 1), reversed.

To complicate matters further, thin articular discs occur in the necks of some birds — for example, the ostrich (see illustration below), the swan, and the king penguin. But these discs do not occur in all birds — for example, they are absent in the turkey and the rhea. When they are present, these articular discs divide the synovial cavity and prevent the (cartilage-covered) bones on either side from ever articulating directly with each other, just like the articular discs in the human temporomandibular and sternoclavicular joints. These discs are thinner than the true intervertebral discs of mammals and crocodilians; and they are different in composition, lacking the annulus/nucleus structure and consisting of a simple sheet of fibrocartilage.

Taylor and Wedel (2013: Figure 4). Intervertebral articular discs of an ostrich (not to scale). Left: first sacral vertebra in anterior view, showing articular disc of joint with the last thoracic vertebra. Right: posterior view view of a cervical vertebra, with probe inserted behind posterior articular disc. The cervical vertebra is most relevant to the present study, but the the sacral vertebra is also included as it shows the morphology more clearly. These fibrocartilaginous articular discs divide the synovial cavity, like the articular discs in the human temporomandibular and sternoclavicular joints, and should not be confused with the true intervertebral discs of mammals and other animals, which consist of a nucleus pulposus and an annulus fibrosus.

Taylor and Wedel (2013: Figure 4). Intervertebral articular discs of an ostrich (not to scale). Left: first sacral vertebra in anterior view, showing articular disc of joint with the last thoracic vertebra. Right: posterior view view of a cervical vertebra, with probe inserted behind posterior articular disc. The cervical vertebra is most relevant to the present study, but the the sacral vertebra is also included as it shows the morphology more clearly. These fibrocartilaginous articular discs divide the synovial cavity, like the articular discs in the human temporomandibular and sternoclavicular joints, and should not be confused with the true intervertebral discs of mammals and other animals, which consist of a nucleus pulposus and an annulus fibrosus.

Crucially, the extant phylogenetic bracket (EPB) does not help us to establish the nature of the intervertebral articulations in sauropods, as the two extant groups most closely related to them have different articulations. As noted, birds have synovial joints; but crocodilians, like mammals, have fibrocartilaginous intervertebral discs. So their most recent common ancestor, the ur-archosaur, could equally have had either condition, and so could its various descendants.

vertebral-joint-type-cladogram

This seems like a mystery well worth solving. For one thing,  in the wholly inadequate database that we assembled for the paper, the birds had much thinner cartilage than the other animals. Since they are also the only animals with synovial neck joints, thin cartilage correlates with this kind of joint — at least across that tiny database. Is that correlation reliable? Does it hold out across a bigger sample? Is there a causation? If so, then finding out what kind of intervertebral joints sauropods had would help us to determine how thick their cartilage was, and so what their actual neutral posture was.

But we can’t tell this directly unless we find sensationally well preserved specimens that let us see the structure of the cartilage. We might speculate that since birds have unique saddle-shaped joints and sauropods have ball-and-socket joints like those of mammals and crocs, they’d be more likely to resemble the latter in this respect, too, but that’s rather hand-wavey.

Can we do better?

If we can, it will be through osteological correlates: that is, features of the bones (which are preserved in fossils) that are consistently correlated with features of the soft tissues (which are not). We’d want to find out from analysis of extant animals what correlates might exist, then go looking for them in the bones of extinct animals.

A couple of times now, I’ve pitched this as an abstract for a Masters project, hoping someone at Bristol will work on it with me as co-supervisor, but so far no-one’s bitten. Maybe next year. It would be a very specimen-based project, which I’d think would be a plus in most people’s eyes.

Figure 8. Cervical vertebra 7 from a turkey. Anterior view on the left; dorsal, left lateral and ventral views in the middle row; and posterior on the right.

Taylor and Wedel (2013: Figure 8). Cervical vertebra 7 from a turkey. Anterior view on the left; dorsal, left lateral and ventral views in the middle row; and posterior on the right.

Anyway, the awful truth is that at the moment we know spectacularly little about the cartilage in the necks of sauropods. We don’t know whether they had true intervertebral discs. If not, we don’t know whether they had articular discs like those of ostriches. We don’t know how thick these elements, if present, were. We don’t know how thick the hyaline cartilage on the bones’ articular surfaces was, or how evenly it covered its those surfaces.

And until we know those things, we don’t really know anything about neck posture or range of movement.

There’s lots of work to be done here!

Last time, we looked at how including intervertebral cartilage changes the neutral pose of a neck — or, more specifically, of the sequence of cervical vertebrae. The key finding (which is inexplicably missing from the actual paper, Taylor and Wedel 2013c) is that adding cartilage of thickness x between vertebrae whose zygapophyses are height y above the mid-height of the centra elevates the joint’s neutral posture by x/y radians.

Figure 14. Geometry of opisthocoelous intervertebral joints. Hypothetical models of the geometry of an opisthocoelous intervertebral joint compared with the actual morphology of the C5/C6 joint in Sauroposeidon OMNH 53062. A. Model in which the condyle and cotyle are concentric and the radial thickness of the intervertebral cartilage is constant. B. Model in which the condyle and cotyle have the same geometry, but the condyle is displaced posteriorly so the anteropos- terior thickness of the intervertebral cartilage is constant. C. the C5/C6 joint in Sauroposeidon in right lateral view, traced from the x-ray scout image (see Figure 12); dorsal is to the left. Except for one area in the ventral half of the cotyle, the anteroposterior separation between the C5 cotyle and C6 condyle is remarkably uniform. All of the arrows in part C are 52 mm long.

Figure 14. Geometry of opisthocoelous intervertebral joints. Hypothetical models of the geometry of an opisthocoelous intervertebral joint compared with the actual morphology of the C5/C6 joint in Sauroposeidon OMNH 53062. A. Model in which the condyle and cotyle are concentric and the radial thickness of the intervertebral cartilage is constant. B. Model in which the condyle and cotyle have the same geometry, but the condyle is displaced posteriorly so the anteroposterior thickness of the intervertebral cartilage is constant. C. the C5/C6 joint in Sauroposeidon in right lateral view, traced from the x-ray scout image (see Figure 12); dorsal is to the left. Except for one area in the ventral half of the cotyle, the anteroposterior separation between the C5 cotyle and C6 condyle is remarkably uniform. All of the arrows in part C are 52 mm long.

But how thick was the intervertebral cartilage in sauropods?

At the moment, no-one really knows. As Kent Stevens (2013) points out in his contribution to the PLOS ONE sauropod gigantism collection:

Determining the ONP of a sauropod’s cervical vertebral column given only its bones requires is necessarily speculative since the cartilage, and thus the intervertebral spacing, is unknown.

Part of the our goal in our own PLOS collection paper (Taylor and Wedel 2013c) was to take some very tentative first steps towards estimating the cartilage thickness. To do this, we used two approaches. First, we looked at CT scans of articulated vertebrae; and second, we measured the cartilage thickness in a selection of extant animals and thought about what we could extrapolate.

Since the CT scans were Matt’s domain, I’m going to pass over those for now, in the hope that he’ll blog about that part of the paper. Here, I want to look at the extant-animal survey.

Figure 18. Cartilage in the neck of a rhea. Joint between cervicals 11 (left) and 10 (right) of a rhea, sagittally bisected. Left half of neck in medial view. The thin layers of cartilage lining the C11 condyle and C10 cotyle are clearly visible.

Figure 18. Cartilage in the neck of a rhea. Joint between cervicals 11 (left) and 10 (right) of a rhea, sagittally bisected. Left half of neck in medial view. The thin layers of cartilage lining the C11 condyle and C10 cotyle are clearly visible.

The first thing to say is that our survey is inadequate in many ways. We worked with the specimens we could get hold of, in the state we had them. This means that:

  • we have a very arbitrary selection of different animals,
  • they are at different ontogenetic stages, and
  • their cartilage thickness was measured by a variety of methods.

Our goal was not at all to reach anything like a definitive answer, but just to get the question properly asked, and so hopefully to catalyse much a more detailed survey.

With that proviso out of the way, here are our main results (from Table 4 of the paper, though here I have removed the sauropod CT-scan rows since we’ll be writing about those separately).

Taxon Thickness Reference Notes
Turkey 4.56% This study Difference in measurements of intact neck and articulated sequence of cleaned, degreased and dried vertebrae.
Ostrich 6.30% Cobley et al. (2013) Difference in measurements of individual vertebrae with and without cartilage.
Rhea 2.59% This study Measurement of in situ cartilage in bisected neck.
Alligator 14.90% This study Measurement of in situ cartilage from photograph of cross section.
Horse 6.90% This study Measurement of in situ cartilage from photograph of cross section.
Camel 13.00% This study Crude measurement from condyle margin to cotyle lip of lateral-view X-ray. This is an interim measurement, which we hope to improve on when we obtain better images.
Dog 17.00% This study Measurement of intervertebral gaps in lateral-view X-ray, uncorrected for likely concavity of cotyles.
Giraffe 24.00% This study Difference in measurement of intact neck and closely articulated sequence of cleaned vertebrae. Young juvenile specimen.
Muraenosaurus 14.00% Evans (1993) Measurement of in situ cartilage in fossils.
Cryptoclidus 20.00% Evans (1993) Measurement of in situ cartilage in fossils.

We’ve expressed the measurements as a ratio between cartilage thickness and the length of the bone itself — that is, cartilage/bone. Another way to think of this is that the percentage is a correction factor which you need to add onto bone length to get whole-segment length. Note that this is not the same ratio as the proportion of total segment length that consists of cartilage: that would be (cartilage thickness + bone length) / bone length.

(We also tossed in some measurements of plesiosaur neck cartilage that Mark Evans made way back when. Get that thing properly published, Mark!)

Even this small survey throws up some interesting points.

First, there is a huge range of proportional cartilage thicknesses: almost an order of magnitude from the 2.59% of the Rhea up to the 24% of the juvenile giraffe — or, even if you discard that because of its ontogenetic stage, up to 17% for the dog. And note that the 17% for the dog is probably an under-estimate, since we were working from an X-ray that doesn’t show the concavity of the vertebral cotyles.

Figure 22. Dog neck in X-ray. Neck of a dog (dachsund), in X-ray, with the seven cervical vertebrae indicated. This photo has been used with permission from the Cuyahoga Falls Veterinary Clinic.

Figure 22. Dog neck in X-ray. Neck of a dog (dachsund), in X-ray, with the seven cervical vertebrae indicated. This photo has been used with permission from the Cuyahoga Falls Veterinary Clinic.

(Two reviewers expressed scepticism that this is the usual condition for dogs, but this X-ray is consistent with those of other dogs illustrated in the veterinary literature.)

The second thing to note is that the cartilage measurements for birds (average 4.5%) are are much lower than those of crocodilians (14.9%) or mammals (15.2%). What does this mean? Among these groups, sauropods are most closely related to birds; but birds and crocs form the extant phylogenetic bracket, so we can’t tell from phylogeny alone whether to expect them to more closely approach the avian or crocodilian condition. Furthermore, in being opisthocoelous (condyle in front, cotyle at the back) sauropod cervicals most closely resemble those of mammals in gross structure — and they have the thickest cartilage of all.

The third thing to note is that there is considerable variation within groups. Although the cartilage is proportionally thin for all three birds, it’s more than twice as thick in the ostrich as in the rhea (although some of this could be due to the different measurement methods used for these two birds). More interestingly, among mammals the cartilage is twice as thick in camels as in horses. In the horse, the condyles are deeply inserted into the cotyles of the preceding vertebrae; but in camels, they don’t reach even the lip of the cotyle. This should worry us, as horse and camel cervicals are grossly similar, and no osteological correlates have been identified that would allow us to determine from the bones alone how very different the cartilage is between these two mammals. So it seems possible that there were similarly dramatic differences in the neck-cartilage thickness of different sauropods.

Note: I said that no osteological correlates have been identified. That doesn’t mean they don’t exist. One thing I would love to see is a serious attempt to analyse cartilage thickness across a broad range of mammals, and to examine the corresponding dry bones to see whether in fact there are correlates that could be informative in this respect. One lesson that Matt and I have learned over and over again is that there’s often plenty of data in places that are out in the open, but where no-one’s thought to look.

Next time: more on searching for osteological correlates of cartilage. Then, measurements of sauropod-neck cartilage from CT scans, and likely implications for cartilage thickness in life.

References

As I mentioned a few days ago, Matt and I have a couple of papers in the new PLOS ONE Sauropod Gigantism collection. We were each lead author on one and second author on the other, so for convenience’s sake we’ll refer to them as my paper (Taylor and Wedel 2013c on neck cartilage) and Matt’s paper (Wedel and Taylor 2013b on caudal pneumaticity.)

Mine is very simple in concept (although it ended up at 17 pages and 23 figures). It’s all about addressing one of the overlooked variables in reconstructing the postures of the necks of sauropods (and indeed of all tetrapods). That is, the spacing between consecutive vertebrae, and the effect this has on “neutral pose”.

The concept of “neutral pose” goes back to the DinoMorph work of Stevens and Parrish (1999). They defined it (p. 799) as follows: “We determined the neutral poses for each animal, wherein the paired articular facets of the postzygapophyses of each cervical vertebra were centered over the facets of the prezygapophyses of its caudally adjacent counterpart.”

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Taylor and Wedel (2013c: Figure 3). Articulated sauropod vertebrae. Representative mid-cervical vertebra of Giraffatitan brancai, articulating with its neighbours. The condyle (ball) on the front of each vertebra’s centrum fits into the cotyle (socket) at the back of the preceding one, and the prezygapophyses articulate with the preceding vertebra’s postzygapophyses. These vertebrae are in Osteological Neutral Pose, because the pre- and postzygapophyseal facets overlap fully.

One of the more fundamental flaws in Stevens and Parrish (1999) is the assumption that animals habitually rest their necks in neutral pose — an assumption that is unsupported by evidence and, as it turns out, false (Vidal et al. 1986, Taylor et al. 2009). But let’s leave that aside for the moment, and consider what neutral pose actually represents.

The fact that there is even such a thing as neutral articulation between two consecutive vertebrae is due to there being three points of contact between those vertebra: as with the legs of a tripod, three points is the minimum number you need to fix an object in three-dimensional space. Two of these points are at the zygapophyses, as noted in the original definition above. The third point is the articulation between the centra.

The centrum has been curiously overlooked in discussions of neutral pose, but needless to say its length is crucial in establishing what is neutral. In the image above, if the centrum was longer, then the angle between the consecutive vertebrae would need to be raised in order to keep the zygapophyses articulated.

And of course it was longer in life, because of the cartilage in between the consecutive centra. (The use of the more specific term “osteological neutral pose” goes some way to recognising that tissues other than bone have been overlooked, but the problem has not really been addressed or even properly acknowledged in published works before our paper.)

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Taylor and Wedel (2013c: Figure 5). Intervertebral gaps in camel necks. Head and neck of dromedary camels. Top: UMZC H.14191, in right lateral view, posed well below habitual posture, with apparently disarticulated C3/C4 and C4/C5 joints. Photograph taken of a public exhibit at University Museum of Zoology, Cambridge, UK. Bottom: OUMNH 17427, in left lateral view, reversed for consistency with Cambridge specimen. Photograph taken of a public exhibit at Oxford University Museum of Natural History, UK. Inset: detail of C4 of the Oxford specimen, showing articulations with C3 and C5. The centra are separated by thick pads of artificial ‘‘cartilage’’ to preserve spacing as in life.

You simply can’t ignore cartilage when modelling neck postures and expect to get anything resembling a meaningful result. That is, presumably, the reason why the habitual posture of rabbits in life exceeds the most extended posture we were able to obtain when manipulating dry vertebrae of a hare: compare Vidal et al. (1986: fig. 4) with Taylor et al. (2009: fig. 1).

How big is the effect? That depends on the thickness of the cartilage and the height of the zygapophyses above the center of rotation. Here is an illustration that we should have put in the paper, but which inexplicably neither of us thought of:

figNEW-angle-at-zygs

Influence of intervertebral cartilage on vertebral articulation angle. Consider the posterior vertebra (black) as fixed. The blue vertebra represents neutral pose of the preceding vertebra with centra abutting and zygapophyseal facets maximally overlapped. The red vertebra indicates neutral pose once intervertebral cartilage is added between the vertebra (where else?) The green lines show the angle by which the more anterior vertebra must be inclined in order to accommodate the cartilage, and the magenta line shows the height of the zygapophyseal articulation above the center of rotation between the two vertebrae.

Here’s some elementary trigonometry. Suppose the intervertebral cartilage is x distance thick at mid-height of the centra, and that the height of the zygs above this mid-height point (the magenta line) is y. The triangle between the middle of the condyle of the posterior vertebra, the middle of the cotyle of the anterior one and the zygapophyseal articulation is near enough a right-angled triangle as makes no odds.

Consider the angle θ between the green lines. Sin(θ) = opposite/hypotenuse = x/y, and by similarity, the additional angle of inclination of the anterior vertebra is also θ.

But for small angles (and this is generally a small angle), sin(θ) ≈ θ. So the additional inclination in radians = cartilage thickness divided by zygapophyseal height. For example, in vertebrae where the zygs are 23 cm above the mid-height of the centra, adding 4 cm of intervertebral cartilage adds about 4/23 = 0.174 radians = 10 degrees of extra inclination. (That’s pretty similar to the angle in the illustration above. Eyeballing the cartilage thickness and zyg height in the illustration suggests that 23:4 ratio is about right, which is a nice sanity-check of this method.)

millionaire-stupid-contestant4

At this point, I am cursing my own stupidity for not putting this diagram, and the very simple calculation, into the paper. I guess that can happen when something is written in a hurry (which to be honest this paper was). The formula is so simple — and accurate enough within tolerances of inevitable measurement error — that we really should have used it all over the place. I guess that will have to go in a followup now.

Anyway — next time, we’ll address this important related question: how thick, in fact, was the cartilage between the cervicals of sauropods?

References

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