In my recent visit to the LACM herpetology collection, I was interested to note that almost every croc, lizard, and snake vertebra I saw had a pair of neurovascular foramina on either side of the centrum, in “pleurocoel” position. You can see these in the baby Tomistoma tail, above. Some vertebrae have a big foramen, some have a small foramen, and some have no visible foramen at all. Somehow I’d never noticed this before.

This is particularly interesting in light of the observation from birds that pneumatic diverticula tend to follow nerves and vessels as they spread through the body. Maybe we find pneumatic features where we do in dinosaurs and pterosaurs because that’s where the blood vessels were going in the babies. Also, these neurovascular foramina in extant reptiles are highly variable in size and often asymmetric – sound familiar?

It should. Caudal pneumaticity in the tail of Giraffatitan MB.R.5000. Dark blue vertebrae are pneumatic on both sides, light blue vertebrae only have fossae on the right side. Wedel and Taylor (2013b: Figure 4).

I am starting to wonder if some of the variability we associate with pneumaticity is just the variability of soft tissue, full stop. Or if pneumaticity is variable because it developmentally follows in the footsteps of the blood vessels, which are themselves inherently variable. That seems like a promising line of inquiry. And also something I should have though of a lot sooner.

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WOW! I knew I was dragging a bit on getting around to this vertebral orientation problem, but I didn’t realize a whole month had passed. Yikes. Thanks to everyone who has commented so far, and thanks to Mike for getting the ball rolling on this. Previous posts in this series are here and here.

First up, this may seem like a pointlessly picky thing to even worry about. Can’t we just orient the vertebrae in whichever way feels the most natural, or is easiest? Do we have to think about this?

The alarmingly 3D pelvis of the mounted brontosaur at the AMNH. Note that sauropod pubes are usually illustrated lying flat, so what usually passes for ‘lateral’ view would be roughly from the point of view of the animal’s knee.

I think we do. For sauropods, vertebrae are usually oriented for illustration purposes in one of two ways. The first is however they sit most easily on their pallets. This is similar to the problem Mike and I found for ‘lateral’ views of sauropod pelvic elements when were on our AMNH/Yale trip in 2012. In an articulated skeleton, the pubes and ischia usually lean inward by 30-45 degrees from their articulations with the ilia, so they can meet on the midline, but when people illustrate the “lateral view” of a sauropod pubis or ischium, it’s often the ventro-lateral aspect that is face-up when the element is lying on a shelf or a pallet. Photographic lateral does not equal biological lateral for those elements. Similarly, if I’m trying to answer biological questions about vertebrae (see below), I need to know something about their orientation in the body, not just how they sit comfortably on a pallet.

The other way that vertebrae are commonly oriented is according to what we might call the “visual long axis” of the centrum—so for example, dorsoventrally tall but craniocaudally short proximal caudals get oriented with the centrum ‘upright’, whereas dorsoventrally short but craniocaudally long distal caudals get oriented with the centrum ‘horizontal’, even if they’re in the same tail and doing so makes the neural canals or articular faces be oriented inconsistently down the column. (I’m not going to name names, because it seems mean to pick on people for something I just started thinking about myself, but if you go plow through a bunch of sauropod descriptions, you’ll see what I’m talking about.)

Are there biological questions where this matters? You bet! There are some questions that we can’t answer unless we have the vertebrae correctly oriented first. One that comes to mind is measuring the cross-sectional area of the neural canal, which Emily Giffin did a lot of back in the 90s. Especially for the Snowmass Haplocanthosaurus, what counts as the cross-sectional area of the neural canal depends on whether we are looking at the verts orthogonal to their articular faces, or in alignment with the course of the canal. I think the latter is pretty obviously the way to go if we are measuring the cross-sectional area of the canal to try and infer the diameter of the spinal cord—we’d want to see the canal the same way the cord ‘sees’ it as it passes through—but it’s less obvious if we’re measuring, say, the surface area of the articular face of the vertebra to figure out, say, cartilage stress. It doesn’t seem unreasonable to me that we might want to define a ‘neural axis’ for dealing with spinal-cord-related questions, and a ‘biomechanical axis’ for dealing with articulation-related questions.

Caudal 3 of the Snowmass Haplocanthosaurus, hemisected 3D model.

With all that in mind, here are some points.

To me, asking “how do we know if a vertebra is horizontal” is an odd phrasing of the problem, because “horizontal” doesn’t have any biological meaning. I think it makes more sense to couch the question as, “how do we define cranial and caudal for a vertebra?” Normally both the articular surfaces and the neural canal are “aimed” head- and tail-wards, so the question doesn’t come up. Our question is, how do we deal with vertebrae for which the articular surfaces and neural canal give different answers?

For example. Varanus komodoensis caudal.

(And by the way, I’m totally fine using “anterior” and “posterior” for quadrupedal animals like sauropods. I don’t think it causes any confusion, any more than people are confused by “superior” and “inferior” for human vertebrae. But precisely because we’re angling for a universal solution here, I think using “cranial” and “caudal” makes the most sense, just this once. That said, when I made the image above, I used anterior and posterior, and I’m too lazy now to change it.)

I think if we couch the question as “how do we define cranial and caudal”, it sets up a different set of possible answers than Mike proposed in the first post in this series: (1) define cranial and caudal according to the neural canal, and then describe the articular surfaces as inclined or tilted relative to that axis; (2) vice versa—realizing that using the articular surfaces to define the anatomical directions may admit a range of possible solutions, which might resurrect some of the array of possible methods from our first-draft abstract; (3) define cranial and caudal along the long axis of the centrum, which is potentially different from either of the above; (4) we can imagine a range of other possibilities, like “use the zygs” or “make the transverse processes horizontal” (both of which are subsets of Mike’s method C) but I don’t think most of those other possibilities are sufficiently compelling to be worthy of lengthy discussion.

IF we accept “neural canal”, “articular surfaces”, and “centrum long axis” as our strongest contenders, I think it makes most sense to go with the neural canal, for several reasons:

  • In a causative sense, the neural tube/spinal cord does define the cranial/caudal axis for the developing skeleton. EDIT: Actually, that’s a bit backwards. It’s the notochord, which is later replaced by the vertebral column, that induces the formation of the brain and spinal cord from the neural plate. But it’s still true that the vertebrae form around the spinal cord, so it’s not wrong to talk about the spinal cord as a defining bit of soft tissue for the developing vertebrae to accommodate.
  • The neural canal works equally well for isolated vertebrae and for articulated series. Regardless of how the vertebral column is oriented in life, the neural canal is relatively smooth—it may bend, but it doesn’t kink. So if we line up a series of vertebrae so that their neural canals are aligned, we’re probably pretty close to the actual alignment in life, even before we look at the articular surfaces or zygs.
  • The articulated tails of Opisthocoelicaudia and big varanids show that sometimes the articular surfaces simply are tilted to anything that we might reasonably consider to be the cranio-caudal axis or long axis of the vertebra. In those cases, the articular surfaces aren’t orthogonal to horizontal OR to cranio-caudal. So I think articular surfaces are ruled out because they break down in the kinds of edge cases that led us to ask the question in the first places.

Opistocoelicaudia caudals 6-8, stereopair, Borsuk-Bialynicka (1977:plate 5).

“Orient vertebrae, isolated or in series, so that their neural canals define the cranio-caudal axis” may seem like kind of a ‘duh’ conclusion (if you accept that it’s correct; you may not!), but as discussed up top, often vertebrae from a single individual are oriented inconsistently in descriptive works, and orientation does actually matter for answering some kinds of questions. So regardless of which conclusion we settle on, there is a need to sort out this problem.

That’s where I’m at with my thinking. A lot of this has been percolating in my hindbrain over the last few weeks—I figured out most of this while I was writing this very post. Is it compelling? Am I talking nonsense? Let me know in the comments.

Thanks to everyone who’s engaged with yesterday’s apparently trivial question: what does it mean for a vertebra to be “horizontal”? I know Matt has plenty of thoughts to share on this, but before he does I want to clear up a couple of things.

This is not about life posture

First, and I really should have led with this: the present question has nothing to do with life posture. For example, Anna Krahl wrote on Twitter:

I personally find it more comprehensible if the measurements relate to something like eg. the body posture. This is due to my momentary biomech./functional work, where bone orientation somet is difficult to define.

I’m sympathetic to that, but we really need to avoid conflating two quite different issues here.

Taylor, Wedel and Naish (2009), Figure 1. Cape hare Lepus capensis RAM R2 in right lateral view, illustrating maximally extended pose and ONP: skull, cervical vertebrae 1-7 and dorsal vertebrae 1-2. Note the very weak dorsal deflection of the base of the neck in ONP, contrasting with the much stronger deflection illustrated in a live rabbit by Vidal et al. (1986: fig. 4). Scalebar 5 cm.

If there’s one thing we’ve learned in the last couple of decades, it’s that life posture for extinct animals is controversial — and that goes double for sauropod necks. Heck, even the neck posture of extant animals is terribly easy to misunderstand. We really can’t go changing what we mean by “horizontal” for a vertebra based on the currently prevalent hypothesis of habitual posture.

Also, note that the neck posture on the left of the image above is close to (but actually less extreme than) the habitual posture of rabbits and hares: and we certainly wouldn’t want to illustrate vertebrae as “horizontal” when they’re oriented directly upwards, or even slightly backwards!

Instead, we need to imagine the animal’s skeleton laid out with the whole vertebral column in a straight line — sort of like Ryder’s 1877 Camarasaurus, but with the tail also elevated to the same straight line.

Ryder’s 1877 reconstruction of Camarasaurus, the first ever made of any sauropod, modified from Osborn & Mook (1921, plate LXXXII).

Of course, life posture is more important, and more interesting, question than that of what constitutes “horizontal” for an individual vertebra — but it’s not the one we’re discussing right now.

In method C, both instances are identically oriented

I’m not sure how obvious this was, but I didn’t state it explicitly. In definition C (“same points at same height in consecutive vertebrae”), I wrote:

We use two identical instances of the vertebrae, articulate them together as well as we can, then so orient them that the two vertebrae are level

What I didn’t say is that the two identical instances of the vertebrae have to be identically oriented. Here’s why this is important. Consider that giraffe C7 that we looked at last time, with its keystoned centrum. if you just “articulate them together as well as we can” without that restriction, you end up with something like this:

Which is clearly no good: there’s no way to orient that such that for any given point on one instance, the corresponding point on the other is level with it. What you need instead is something like this:

In this version, I’ve done the best job I can of articulating the two instances in the same attitude, and arranged them such that they are level with each other — so that the attitude shown here is “horizontal” in sense C.

As it happens, this is also just about horizontal in sense B — the floor of the neural canal is presumably at the same height as the top of the centrum as it meets the neural arch.

But “horizontal” in sense A (posterior articular surface vertical) fails horribly for this vertebra:

To me, this image alone is solid evidence that Method A is just not good enough. Whatever we mean by “horizontal”, it’s not what this image shows.

References

I was lucky enough to have Phil Mannion as one of the peer-reviewers for my recent paper (Taylor 2018) showing that Xenoposeidon is a rebbachisaurid. During that process, we got into a collegial disagreement about one of the autapomorphies that I proposed in the revised diagnosis: “Neural arch slopes anteriorly 30°–35° relative to the vertical”. (This same character was also in the original Xenoposeidon paper (Taylor and Naish 2007), in the slightly more assertive form “neural arch slopes anteriorly 35 degrees relative to the vertical”: the softening to “30°–35°” in the newer paper was one of the outcomes of the peer-review.)

The reason this is interesting is because the slope of the neural arch is measured relative to the vertical, which of course is 90˚ from the horizontal — but Phil’s comments (Mannion 2018) pushed me to ask myself for the first time: what actually is “horizontal”? We all assume we know horizontality when we see it, but what precisely do we mean by it?

Three notions of “horizontal”

The idiosyncratic best-preserved caudal vertebra of the Snowmass Haplocanthosaurus MWC 8028, illustrating three different versions of “horizontal”. A. horizontality defined by vertical orientation of the posterior articular surface. B. horizontality defined by horizontal orientation of the roof of the neural canal (in this case, rotated 24˚ clockwise relative to A). C. horizontality defined by optimal articulation of two instances of the vertebra, oriented such the a line joining the same point of both instances is horizontal (in this case, rotated 17˚ clockwise relative to A). Red lines indicate exact orthogonality according to the specified criteria. Green line indicate similar but diverging orientations: that of the not-quite-vertical anterior articular surface (A) and of the not-quite-horizontal base of the neural canal (B).

There are at least three candidate definitions, which we can see yield noticeably different orientations in the case of the Snowmass Haplocanthosaurus vertebra that Matt’s been playing with so much recently.

Definition A: articular surfaces vertical

In part A, I show maybe the simplest — or, at least, the one that is easiest to establish for most vertebrae. So long as you have a reasonably intact articular surface, just rotate the vertebra until that surface is vertical. If, as is often the case, the surface is not flat but concave or convex, then ensure the top and bottom of the surface are vertically aligned. This has the advantage of being easy to do — it’s what I did with Xenoposeidon — but it conceals complexities. Most obviously, what to do when the anterior and posterior articular surfaces are not parallel, in the 7th cervical vertebra of a giraffe?

Cervical vertebra 7 of Giraffa camelopardalis FMNH 34426, in left lateral view. Note that the centrum is heavily “keystoned” so that the anterior and posterior articular surfaces are 15-20˚ away from being parallel.

Another difficulty with this interpretation of horizontality is that it can make the neural canal jagged. Consider a sequence of vertebrae oriented as in part A, all at the same height: the neural canal would rise upwards along the length of each vertebra, before plunging down again on transitioning from the front of one to the back of the next. This is not something we would expect to see in a living animal: see for example the straight line of the neural canal in our hemisected horse head(*).

Definition B: neural canal horizontal

Which leads us to the second part of the illustration above. This time, the vertebra is oriented so that the roof of the neural canal is horizontal, which gives us a straight neural canal. Nice and simple, except …

Well, how do we define what’s horizontal for the neural canal? As the Haplocanthosaurus vertebra shows nicely, the canal is not always a nice, neat tube. In this vertebra, the floor is nowhere near straight, but dishes down deeply — which is why I used to the roof, rather than the floor of the canal. Rather arbitrary, I admit — especially as it’s often easier to locate the floor of the canal, as the dorsal margin is often confluent with fossae anteriorly, posteriorly or both.

And as we can see, it makes a difference which we choose. The green line in Part B of the illustration above shows the closest thing to “horizontal” as it would be defined by the ventral margin of the neural canal — a straight line ignoring the depression and joining the anteriormost and posteriormost parts of the base of the canal. As you can see, it’s at a significantly different angle from the red line — about 6.5˚ out.

And then you have human vertebrae, where the dorsal margin of the neural canal is so convex in lateral view that you really can’t say where the anteriormost or posteriormost point is.

Left sides of hemisected human thoracic vertebrae, medial view. Note how ill-defined the dorsal margin of the neural canal is.

So can we do better? Can we find a definition of “horizontal” that’s not dependent of over-interpreting a single part of the vertebra?

Definition C: same points at same height in consecutive vertebrae

I’ve come to prefer a definition of horizontal that uses the whole vertebra — partly in the hope that it’s less vulnerable to yielding a distorted result when the vertebra is damaged. With this approach, shown in part C of the illustration above, we use two identical instances of the vertebrae, articulate them together as well as we can, then so orient them that the two vertebrae are level — that a line drawn between any point on one vertebra and its corresponding point on the other is horizontal. We can define that attitude of the vertebra as being horizontal.

Note that, while we use two “copies” of the vertebra in this method, we are nevertheless determining the horizontality of a single vertebra in isolation: we don’t need a sequence of consecutive vertebrae to have been preserved, in fact it doesn’t help if we do have them.

One practical advantage of this definition is that its unambiguous as regards what part of the vertebra is used: all of it; or any point on it, at the measurement stage. By contrast, method A requires us to choose whether to use the anterior or posterior articular surface, and method B requires a choice of the roof or floor of the neural canal.

Discussion

I have three questions, and would welcome any thoughts:

  1. Which of these definitions do you prefer, and why?
  2. Can you think of any other definitions that I missed?
  3. Does anyone know of any previous attempts to formalise this? Is it a solved problem, and Matt and I somehow missed it?

Answers in the comments, please!

References

(*) Yes, of course we have a hemisected horse head. What do you think we are, savages?

Down in flames

August 25, 2018

I first encountered Larry Niven’s story/essay “Down in Flames” in the collection N-Space in high school. This was after I’d read Ringworld and most of Niven’s Known Space stories, so by the time I got to “Down in Flames” I had the context to get it. (You can read the whole thing for free here.)

Here’s the idea, from near the start:

On January 14, 1968, Norman Spinrad and I were at a party thrown by Tom & Terry Pinckard. We were filling coffee cups when Spinny started this whole thing.

“You ought to drop the known space series,” he said. “You’ll get stale.” (Quotes are not necessarily dead accurate.) I explained that I was writing stories outside the “known space” history, and that I would give up the series as soon as I ran out of things to say within its framework. Which would be soon.

“Then why don’t you write a novel that tears it to shreds? Don’t just abandon known space. Destroy it!”

“But how?” (I never asked why. Norman and I think alike in some ways.)

The rest of the piece is just working out the details.

“Down in Flames” brain-wormed me. Other than Ray Bradbury’s “A Sound of Thunder” I doubt if there is another short story I’ve read as many times. Mike once described the act of building something complex and beautiful and then destroying it as “magnificently profligate”, and that’s the exact quality of “Down in Flames” that appeals to me.

I also think it is a terrific* exercise for everyone who is a scientist, or who aspires to be one.

* In both the modern sense of “wonderful” and the archaic sense of “causing terror”.

Seriously, try it. Grab a piece of paper (or open a new doc, or whatever) and write down the ideas you’ve had that you hold most dear. And then imagine what it would take for all of them to be wrong. (When teams and organizations do this for their own futures, it’s called a pre-mortem, and there’s a whole managerially-oriented literature on it. I’d read “Down in Flames” instead.)

It feels like this! Borrowed from here.

Here are some questions to help you along:

  • Which of your chains of reasoning admit more than one end-point? If none of them might lead other places, then either you are the most amazing genius of all time (even Newton and Einstein made mistakes), or you are way behind the cutting edge, and your apparent flawlessness comes from working on things that are already settled.
  • If there is a line of evidence that could potentially falsify your pet hypothesis, have you checked it? Have you drawn any attention to it? Or have you gracefully elided it from your discussions in hopes that no-one will notice, at least until after you’re dead?
  • If there’s no line of evidence that could falsify your pet hypothesis, are you actually doing science?
  • Which of your own hypotheses do you have an emotional investment in?
  • Are there findings from a rival research team (real or imagined) that you would not be happy to see published, if they were accurate?
  • Which hypotheses do you not agree with, that you would be most dismayed to see proven correct?

[And yes, Karl, I know that according to some pedants hypotheses are never ‘proven’. It’s a theoretical exercise already, so just pretend they can be!]

I’ll close with one of my favorite quotes, originally published in a couple of tweets by Angus Johnson in May of 2017 (also archived here):

If skepticism means anything it means skepticism about the things you WANT to be true. It’s easy to be a skeptic about others’ views. Embracing a set of claims just because it happens to fit your priors doesn’t make you a skeptic. It makes you a rube, a mark, a schnook.

So, don’t be that rube. Burn down your house of ideas – or at least, mentally sift through the rubble and ashes and imagine how it might have burned down. And then be honest about that, minimally with yourself, and ideally with the world.

If you’re a true intellectual badass, blog the results. I will. It’s not fair to give you all homework – painful homework – and not take the medicine myself, so I’m going to do a “Down in Flames” on my whole oeuvre in the next a future post. Stay tuned!

tornado debris

Hey, look, there goes my future!

One thing that always bemuses me is the near-absolute serendipity of the academic job market. To get into research careers takes at least a decade of very deliberate, directed work, and then at the end you basically toss your diploma into a whirlwind and see where it lands. After all of that careful planning, almost all of us end up where we do based on the random (to us) set of jobs available in the narrow window in which we’re searching.

Did you dream of being curator at Museum X, or professor at University Y? Well, tough, those jobs went to Dr. Graduated-Two-Years-Sooner and Lucky Nature Paper, PhD, and they’re not retiring for three or four decades. Or maybe your dream job comes open right after you, your spouse, and your kids get settled in at your new acceptable-but-not-quite-dream job. Uproot or stay the course? Or what would be your dream job finally comes open but they’re looking for new junior faculty and you just got tenure at Tolerable State U.

This drastic mismatch between carefulness of preparation and randomness of outcome was present even pre-2008. The craptastic academic job market since then has only whetted the central irony’s keen edge. Getting grants and getting jobs is now basically a lottery. I’m not saying that good jobs don’t go to good people – they almost always do – but there are a lot of good people in jobs they never imagined having. And, sadly, plenty of good people who are now working outside of the field they prepared for because of the vicissitudes of the job market. A handful of years sooner or later and they might be sitting pretty.

This is on my mind because I recently had lunch with a physician friend from work and he was talking about applying for jobs as a doctor. “The first thing everyone tells you,” he said, “is decide what part of the country you want to live in first, then apply for the jobs that are there.” Doctors can do that because there are more than 800,000 of them active in the US. Paleontologists are mighty rarified by comparison – it’s hard to say how many of us there are, but probably not more than 2000 active in vert paleo. So the usual advice for budding biologists and paleontologists is exactly opposite that for physicians: “Forget about living where you want. Go wherever the job is and make the best of it.”

Oddly enough, I don’t remember this ever coming up in grad school. It’s something Vicki and I figured out at the end, as we started the process of applying for positions. There are alternate universes where we are at Marshall (they offered us both jobs, but not as attractive as UC Merced at the time), or at Northern Arizona (which is bittersweet because we have totally fallen in love with Flagstaff just in the past three years), or other places. If I were choosing a job site based on everything other than the institution, I’d spring for somewhere in Arizona or the intermountain west in a heartbeat.

IMG_5787

But with all that said, we are happy here. It’s funny, when we got the job offers down here I thought, “LA? Crap, there goes the outdoor part of my life.” But Claremont has lots of parks, it’s tucked up against the San Gabriels and I can get into the mountains in 30 minutes, or out to the desert in 90. I’m spending more time outdoors than I have since I was a kid growing up in rural Oklahoma.

So I’m not complaining about my personal situation. Vicki and I both landed on our feet – and the fact that we both managed to stick the landing at the same institution is little short of miraculous. But we still had to step into the job market hurricane to get here.

If you’re a grad student and you’re reading this, I didn’t write it to freak you out. Just to let you know that it’s coming, and there are things you can do to improve your chances. Be aggressively curious. Write. Publish. Give good talks (and give lots of talks so you can become good at it). Broaden your skill set – if you’re going into paleo, knowing how to teach human anatomy probably doubles or triples the number of available jobs at any one time, even if many of them are not the jobs you’ve been dreaming of.

Then, at the end, pour yourself one stiff drink and cast your fortune to the winds.

Good luck.

OLYMPUS DIGITAL CAMERA

Last night, I submitted a paper for publication — for the first time since April 2013. I’d almost forgotten what it felt like. But, because we’re living in the Shiny Digital Future, you don’t have to wait till it’s been through review and formal publication to read it. I submitted to PeerJ, and at the same time, made it available as a preprint (Taylor 2014).

It’s called “Quantifying the effect of intervertebral cartilage on neutral posture in the necks of sauropod dinosaurs”, and frankly the results are weird. Here’s a taste:

Taylor (2014:figure 3). Effect of adding cartilage to the neutral pose of the neck of Apatosaurus louisae CM 3018. Images of vertebra from Gilmore (1936:plate XXIV). At the bottom, the vertebrae are composed in a horizontal posture. Superimposed, the same vertebrae are shown inclined by the additional extension angles indicated in Table 1. If the slightly sub-horizontal osteological neutral pose of Stevens and Parrish (1999) is correct, then the cartilaginous neutral pose would be correspondingly slightly lower than depicted here, but still much closer to the elevated posture than to horizontal. (Note that the posture shown here would not have been the habitual posture in life: see discussion.)

Taylor (2014:figure 3). Effect of adding cartilage to the neutral pose of the neck of Apatosaurus louisae CM 3018. Images of vertebra from Gilmore (1936:plate XXIV). At the bottom, the vertebrae are composed in a horizontal posture. Superimposed, the same vertebrae are shown inclined by the additional extension angles indicated in Table 1. If the slightly sub-horizontal osteological neutral pose of Stevens and Parrish (1999) is correct, then the cartilaginous neutral pose would be correspondingly slightly lower than depicted here, but still much closer to the elevated posture than to horizontal. (Note that the posture shown here would not have been the habitual posture in life: see discussion.)

A year back, as I was composing a blog-post about our neck-cartilage paper in PLOS ONE (Taylor and Wedel 2013c), I found myself writing down the rather trivial formula for the additional angle of extension at an intervertebral joint once the cartilage is taken into account. In that post, I finished with the promise “I guess that will have to go in a followup now”. Amazingly it’s taken me a year to get that one-pager written and submitted. (Although in the usual way of things, the manuscript ended up being 13 pages long.)

To summarise the main point of the paper: when you insert cartilage of thickness t between two vertebrae whose zygapophyses articulate at height h above the centra, the more anterior vertebra is forced upwards by t/h radians. Our best guess for how much cartilage is between the adjacent vertebrae in an Apatosaurus neck is about 10% of centrum length: the image above shows the effect of inserting that much cartilage at each joint.

And yes, it’s weird. But it’s where the data leads me, so I think it would be dishonest not to publish it.

I’ll be interested to see what the reviewers make of this. You are all of course welcome to leave comments on the preprint itself; but because this is going through conventional peer-review straight away (unlike our Barosaurus preprint), there’s no need to offer the kind of detailed and comprehensive comment that several people did with the previous one. Of course feel free if you wish, but I’m not depending on it.

References

Gilmore Charles W. 1936. Osteology of Apatosaurus, with special reference to specimens in the Carnegie Museum. Memoirs of the Carnegie Museum 11:175–300 and plates XXI–XXXIV.

Stevens, Kent A., and J. Michael Parrish. 1999. Neck posture and feeding habits of two Jurassic sauropod dinosaurs. Science 284(5415):798–800. doi:10.1126/science.284.5415.798

Taylor, Michael P. 2014. Quantifying the effect of intervertebral cartilage on neutral posture in the necks of sauropod dinosaurs. PeerJ PrePrints 2:e588v1 doi:10.7287/peerj.preprints.588v1

Taylor, Michael P., and Mathew J. Wedel. 2013c. The effect of intervertebral cartilage on neutral posture and range of motion in the necks of sauropod dinosaurs. PLOS ONE 8(10):e78214. 17 pages. doi:10.1371/journal.pone.0078214