Here’s the jar of wasps sitting out on the table in our back garden:


OK, this is not so much an interesting specimen as a handy hint.

We hosted a picnic during the summer and it was absolutely infested with wasps. (One person was stung — everyone else had to look super-carefully at their sandwiches before each bite.) That made me realise we needed to get rid of all the wasps that haunt the garden, and this trap is the solution.

It could hardly be simpler: it’s an old jar with a tablespoon of jam in the bottom, topped up to half way with water. Then a tinfoil lid with a small hole poked through it with a teaspoon handle.

For some reason, wasps just can’t resist it: they crawl in, then drown themselves in the water trying to get to the jam. Then more wasps come. And they just keep coming, as you can see in the photo. We’re going to have to dig the wasps out and throw them away so that the trap has enough space for more.

The great thing about this is that it only seems to catch wasps: not bees, which simply don’t seem to see the appeal in jam-water.

This came out two months ago, and I should have blogged about it then, but as usual I am behind. I’m blogging about it now because it deals with a question that has been on my mind for about 10 years now. If you want to skip my blatherations and get on to the good stuff, here’s the paper (Martin and Palmer 2014).

An Unsolved Problem

Back in 2004 I realized that if one had CTs or other cross-sections of a pneumatic bone, it was possible to quantify how much of the cross-sectional space was bone, and how much was air, a ratio I called the Air Space Proportion (ASP). That was the subject of my 2004 SVP talk, and a big part–arguably the most important part–of my chapter in The Sauropods in 2005. Of course the same calculation works for marrow-filled bones as well, where you would refer to it as an MSP rather than an ASP. If you can quantify the areas of bone, air, and marrow, you can figure out how dense the element was. One-stop shopping for all the relevant (simple) math is in this post.

(From Wedel 2005)

(From Wedel 2005)

Sometimes in science you end up with data that you don’t know what to do with, and that was my situation in 2004. Since I had CTs and other cross-sectional images of sauropod vertebrae, I could calculate ASPs for them, but I didn’t know what those results meant, because I didn’t have anything to compare them to. But I knew where to get I could get comparative data: from limb bone cross-sections. John Currey and R. McNeill Alexander had published a paper in 1985 titled, “The thickness of the walls of tubular bones”. I knew about that paper because I’d become something of an R. McNeill Alexander junkie after reading his book, Dynamics of Dinosaurs and Other Extinct Giants (Alexander 1989). And I knew that it had data on the cross-sectional properties of the limb bones in a host of animals, including crocs, birds, mammals, and–prophetically–pterosaurs.

If you know the inner and outer radii of a tubular bone, it is trivial to convert that to an ASP. So I could take the data from Currey and Alexander (1985) and calculate ASPs for the pneumatic bird and pterosaur bones in their study. Cubo and Casinos (2000) had a much larger sample of bird limb bones, and those got fed into my 2005 paper as well.

I was alert to the possibility that a mid-shaft cross-section might not be representative of the whole bone, and I hedged a bit in describing the bird ASPs (Wedel 2005: p. 212):

For the avian long bones described above, data were only presented for a single cross sec- tion located at midshaft. Therefore, the ASP values I am about to discuss may not be representative of the entire bones, but they probably approximate the volumes (total and air) of the diaphyses. For tubular bones, ASP may be determined by squaring K (if r is the inner diameter and R the outer, then K is r/R, ASP is πr^2/πR^2 or simply r^2/R^2, and ASP = K^2). For the K of pneumatic bones, Currey and Alexander (1985) report lower and upper bounds of 0.69 and 0.86, and I calculate a mean of 0.80 from the data presented in their table 1. Using a larger sample size, Cubo and Casinos (2000) found a slightly lower mean K of 0.77. The equivalent values of ASP are 0.48 and 0.74, with a mean of 0.64, or 0.59 for the mean of Cubo and Casinos (2000). This means that, on average, the diaphysis of a pneumatic avian long bone is 59%–64% air, by volume.

Now, even though I hedged and talked about diaphyses (shafts of long bones) rather than whole bones, I honestly expected that the ASP of any given slice would not change much along the length of a bone. Long bones tend to be tubular near the middle, with a thick bony cortex surrounding the marrow or air space, and honeycombed near the ends, with much thinner cortices and lots of bony septa or trabeculae (for marrow-filled bones, this is called spongy or trabecular bone, and for air-filled bones it is best referred to as camellate pneumatic bone). I figured that the decrease in cortical bone thickness near the ends of the bone would be offset by the increase in internal bony septa, and that the bone-to-air ratio through the whole element would be under some kind of holistic control that would keep it about even between the middle of the bone and the ends.

It is fair to ask why I didn’t just go check. The answer is that research is to some extent a zero-sum game, in that every project you take on means another that gets left waiting in the wings or abandoned completely. I was mainly interested in what ASP had to say about sauropods, not birds, and I had other fish to fry.

So that’s me from 2004-2012: aware that mid-shaft cross-sections of bird and pterosaur long bones might not be representative of whole elements, but not sufficiently motivated to go check. Then at SVPCA in Oxford that fall, Liz Martin rocked my world.


Figure 1. CT scan images from two different regions of pterosaur first wing phalanx. A and B show the unmodified CT scans from A) the distal end of UP WP1 and B) the mid-shaft of UP WP1, while C and D show the modified and corrected images used in the calculation. Air space proportion (ASP) is calculated by determining the cross-sectional area of the internal, air filled cavity (the black centre of D) and dividing that by the total cross-sectional area, including the white cortical tissue and the black cavity. In areas with trabeculae, like C, the calculation of the air space includes the air found in individual trabeculae around the edges. Scale = 10 mm. doi:10.1371/journal.pone.0097159.g001 (From Martin and Palmer 2014)

A Paper in the Can

At SVPCA 2012, Liz Martin gave a talk titled, “A novel approach to estimating pterosaur bone mass using CT scans”, the result of her MS research with Colin Palmer at the University of Bristol. In that talk–the paper for which has been submitted to JVP–Liz and Colin were interested in using CT scans of pterosaur bones to quantify the volume of bone, in order to refine pterosaur mass estimates. I was fully on board, since estimating the masses of extinct animals is a minor obsession of mine. But what really caught my attention is that Liz and Colin had full stacks of slices spanning the length of each element–and therefore everything they needed to see how or if ASPs of pterosaur wing bones changed along their lengths.

At the next available break I dashed up to Liz, opened up my notebook, and started scribbling and gesticulating and in general carrying on like a crazy person. It’s a wonder she didn’t flee in terror. The substance of my raving was that (1) there was this outstanding problem in the nascent field of ASP research, and (2) she had everything she needed to address it, all that was required was a little math using the data she already had (I say this as if running the analyses and writing the paper were trivial tasks–they weren’t). Fortunately Liz and Colin were sufficiently interested to pursue it. Their paper on ASPs of pterosaur wing bones was submitted to PLOS ONE this February, and published on May 9 (while their earlier paper continues to grind its way through JVP).

And I’m blogging about it because the results were not what I expected.

Pterosaur wing bone ASPs - Martin and Palmer 2014

Figure 2. Plot of air space proportion over the length in six pterosaur wing bones. These plots show a polynomial line fit for each bone to show the general shape distribution. Exact measurements can be seen in Table S1. (From Martin and Palmer 2014).

Here’s the graph that tells the tale. Each line traces the ASP per slice along the length of a single pterosaur wing bone. A few things jump out:

  • Almost all of the lines drop near the left end. This is expected–if you’re cutting slices of a bone and measuring the not-bone space inside, then as you approach the end of the bone, you’re cutting through progressively more bone and less space. A few of the lines also drop near the right. I’m puzzled by that–if my explanation is correct, the ASP should plunge about equally at both ends. And the humerus USNM 11925 doesn’t follow the same pattern as the rest. As Martin and Palmer write, “It is unknown if this is a general feature of humeri, or this single taxon and more investigation is needed.”
  • Almost all of the bones have MUCH lower ASPs at mid-shaft than near the ends, on the order of 10% or more. So mid-shaft cross-sections of pterosaur wing bones tend to significantly underestimate how pneumatic they were. It would be interesting to know if the same holds true for bird long bones, or for the vertebrae of pterosaurs, birds, and sauropods. As Martin and Palmer point out, more work is needed.
  • The variation in ASP along the length of a single bone is in some cases greater than the variation between elements and individuals. That’s pretty cool. On the happy side, it means that getting into the nitty-gritty of ASP is not just stamp-collecting; you really need to know what is going on along the length of a bone before you can say anything intelligent about ASP or the density of the element. On the less happy side, that’s going to be a righteous pain in the butt for sauropod workers, because vertebrae are tough to get good scans of, assuming they will fit through a CT scanner at all (most don’t).
  • Finally, pterosaurs turn out to be even more pneumatic than you would think from looking at the already-freakishly-thin-walled shafts of their long bones. That’s pretty awesome, and it dovetails nicely with the emerging picture that pneumaticity in ornithodirans was more prevalent and more interesting than even I had suspected–it’s in prosauropods (Yates et al. 2012) and brachiosaur tails (Wedel and Taylor 2013) and rebbachisaur hips (Fanti et al. 2013) and saltasaur shoulders (Cerda et al. 2012) and, er, a couple of places that I can’t mention just yet. So life is good.

A few last odds and ends:

You can read more of this story at Liz Martin’s blog, scattered over several recent posts.

If you have CTs of bones and you want to follow in the footsteps of Martin and Palmer, you can do a lot of the work, and maybe all of it, in BoneJ, a free plug-in for ImageJ, which is also free.

A final note: this is Liz Martin’s first published paper, so congratulations are in order. Well done, Liz!

Almost Immediate Update: As soon as I posted this, I sent the link to Liz to see if I’d missed anything important. She writes, “It may be worth mentioning that it’s a question that I am actively following up on in my PhD, and looking into it with birds too hopefully. And it is indeed all possible using ImageJ, as that’s how I did the whole thing!”


ASPs for Alamosaurus

January 4, 2010

A section of the cotyle of a presacral vertebra of Alamosaurus (Woodward and Lehman 2009:fig. 6A). The arrow will be explained in a future post!

Last year was good for sauropod pneumaticity. In the past few months we’ve had the publication of the first FEA of pneumatic sauropod vertebrae by Schwarz-Wings et al (2009), as well as a substantial section on pneumaticity in the big Alamosaurus histology paper by Woodward and Lehman (2009). I won’t repeat here everything that Woodward and Lehman have to say about pneumaticity, I just want to draw attention to a little piece of it. Their work is observant, up-to-date, and worth reading, so if you can get access to the paper, read it.

The major brake on the growth of our knowledge and understanding of pneumaticity is sample size. I harped on this in 2005 (Wedel 2005), and Mike just brought it up again in a comment on a previous post. In fact, what he had to say is so relevant that I’m going to just cut and paste it here:

How does degree of pneumatisation vary between individuals? Here are three more: how does it vary along the neck, how does it vary long the length of an individual vertebra, and how does it vary through ontogeny? Then of course there is variation between taxa across the tree. So what we have here is a five-and-half-dimensional space that we want to fill with observations so that we can start to deduce conclusions. Trouble is, there are, so far, 22 published observations (neatly summarised by Wedel 2005:table 7.2), which is not really enough to let us map out 5.5-space! That’s one reason why, at the moment, each observation is valuable — it adds 4% to the total knowledge in the world.

To be fair, there are a few more published observations. Schwarz and Fritsch (2006) published ASPs for cervicals of Giraffatitan and Dicraeosaurus, and I have a gnawing feeling that there are a couple here and there that I’ve seen but not remembered. I’ve got some more of my own data in the as-yet-unpublished fourth chapter of my diss, which I failed to get out as part of the Paleo Paper Challenge. And, getting back to the subject of the post, Woodward and Lehman (2009:819) have some tasty new data to report:

Digital images of sections of vertebrae and ribs were imported into ArcGIS 8.1 (Dangermond, 2001; for methods see Woodward, 2005). A unitless value for the total area of the image was calculated, using the outline of the bone as a perimeter. Subtracted from this was the area value taken up by bone, as determined by color differences (lighter areas are camellate cavities, darker areas are bone). Using this method, longitudinal sections of centra are estimated to be roughly 65% air filled. The amount of open space similarly calculated for the pneumatic proximal and medial rib sections is about 52%, whereas the cancellous spongiosa in distal rib transverse sections yields an average estimate of about 44% of their cross sectional area. Hence, the camellate cavities result in an appreciably lower bone volume compared to spongiosa.

The ASP of 0.65 for centra is right in line with the numbers I’ve gotten for neosauropods, and with the results of Schwarz and Fritsch (2006) for Giraffatitan (Dicraosaurus had a much lower ASP, around 0.2 IIRC). The stuff about the ribs is particularly interesting. Using densities of 0.95 for bone marrow, 1.8 for avian (and sauropod) compact bone, and 1.9 for mammalian compact bone we get the following:

  • Pneumatic Alamosaurus vertebrae – ASP of 0.65, density of 0.63 g/cm^3.
  • Pneumatic Alamosaurus ribs – ASP of 0.52, density of 0.86 g/cm^3.
  • Apneumatic Alamosaurus ribs – MSP (marrow space proportion) of 0.44, density of 1.43 g/cm^3.
  • Pneumatic bird long bones – ASP of 0.59, density of 0.74 g/cm^3.
  • Apneumatic bird long bones – MSP of 0.42, density of 1.44 g/cm^3.
  • Apneumatic mammal long bones – MSP of 0.28, density of 1.63 g/cm^3.

ASPs and MSPs of bird and mammal bones are calculated from K values reported by Cubo and Casinos (2000) for birds and Currey and Alexander (1985) for mammals. I don’t know what the in vivo density of sauropod compact bone was; changing it from the avian value of 1.8 to the mammalian value of 1.9 would have a negligible effect on the outcome.

At least with the data in hand, we can make the following generalizations:

  • The apneumatic bones of birds are thinner-walled than those of mammals, on average. (This has been known for a long time.)
  • The apneumatic ribs of Alamosaurus were more similar in density to apneumatic bird bones than to apneumatic mammal bones.
  • In both birds and Alamosaurus, pneumatization reduces the amount of bone tissue present by 15-30% in the same elements (long bones for birds, ribs for Alamosaurus). Pneumatic bones are light not just because the marrow is replaced by air, but because there is less bone tissue than in apneumatic bones, as bird people have been observing for ages.

There’s loads more work to be done on this sort of thing, so I’m going to stop blogging now and get back to it. Stay tuned!


arborization of science

Modified from an original SEM image of branching blood vessels, borrowed from

I was reading a rant on another site about how pretentious it is for intellectuals and pseudo-intellectuals to tell the world about their “media diets” and it got me thinking–well, angsting–about my scientific media diet.

And then almost immediately I thought, “Hey, what am I afraid of? I should just go tell the truth about this.”

And that truth is this: I can’t tell you what forms of scientific media I keep up with, because I don’t feel like I am actually keeping up with any of them.

Papers – I have no systematic method of finding them. I don’t subscribe to any notifications or table of contents updates. Nor, to be honest, am I in the habit of regularly combing the tables of contents of any journals.

Blogs – I don’t follow any in a timely fashion, although I do check in with TetZoo, Laelaps, and a couple of others every month or two. Way back when we started SV-POW!, we made a command decision not to list any sites other than our own on the sideboard. At the time, that was because we didn’t want to have any hurt feelings or drama over who we did and didn’t include. But over time, a strong secondary motive to keep things this way is that we’re not forced to keep up with the whole paleo blogosphere, which long ago outstripped my capacity to even competently survey. Fortunately, those overachievers at Love in the Time of Chasmosaurs have a pretty exhaustive-looking set of links on their sidebar, so globally speaking, someone is already on that.

The contraction in my blog reading is a fairly recent thing. When TetZoo was on ScienceBlogs, I was over there all the time, and there were probably half a dozen SciBlogs that I followed pretty regularly and another dozen or so that I at least kept tabs on. But ScienceBlogs burned down the community I was interested in, and the Scientific American Blog Network is sufficiently ugly (in the UI sense) and reader-unfriendly to not be worth my dealing with it. So I am currently between blog networks–or maybe past my last one.

Social Media – I’m not on Twitter, and I tend to only log into Facebook when I get an interesting notice in my Gmail “Social” folder. Sometimes I’m not on FB for a week or two at a time. So I miss a lot of stuff that goes down there, including notices about new papers. I could probably fix that if I just followed Andy Farke more religiously.

What ends up happening – I mainly find papers relevant to specific projects as I execute those projects; each new project is a new front in my n-dimensional invasion of the literature. My concern is that in doing this, I tend to find the papers that I’m looking for, whereas the papers that have had the most transformative effect on me are the ones I was not looking for at the time.

Beyond that, I find out about new papers because the authors take it on themselves to include me when they email the PDF out to a list of potentially interested colleagues (and many thanks to all of you who are doing that!), or Mike, Darren, or Andy send it to me, or it turns up in the updates to my Google Scholar profile.

So far, this combination of ad hoc and half-assed methods seems to be working, although it does mean that I have unfairly outsourced much of my paper discovery to other people without doing much for them in return. When I say that it’s working, I mean that I don’t get review comments pointing out that I have missed important recent papers. I do get review comments saying that I need to cite more stuff,* but these tend to be papers that I already know of and maybe even cited already, just not in the right ways to satisfy the reviewers.**

* There is a sort of an arrow-of-inevitability thing here, in that reviewers almost always ask you to cite more papers rather than fewer. Only once ever have I been asked to cite fewer sources, and that is when I had submitted my dinosaur nerve paper (Wedel 2012) to a certain nameless anatomy journal that ended up not publishing it. One of the reviewers said that I had cited several textbooks and popular science books and that was poor practice, I should have cited primary literature. Apparently this subgenius did not realize that I was citing all of those popular sources as examples of publications that held up the recurrent laryngeal nerve of giraffes as evidence for evolution, which was part of the point that I was making: giraffe RLNs are overrated.

** My usual sin is that I mentally categorize papers in one or two holes and forget that a given paper also mentioned C and D in addition to saying a lot about A and B. It’s something that vexes me about some of my own papers. I put so much stuff into the second Sauroposeidon paper (Wedel et al. 2000b) that some it has never been cited–although that paper has been cited plenty, it often does not come up in discussions where some of the data presented therein is relevant, I think because there’s just too much stuff in that paper for anyone (who cares about that paper less than I do) to hold in their heads. But that’s a problem to be explored in another post.

The arborization of science

Part of the problem with keeping up with the literature is just that there is so much more of it than there was even a few years ago. When I first got interested in sauropod pneumaticity back in the late 90s, you were pretty much up to speed if you’d read about half a dozen papers:

  • Seeley (1870), who first described pneumaticity in sauropods as such, even if he didn’t know what sauropods were yet;
  • Longman (1933), who first realized that sauropod vertebrae could be sorted into two bins based on their internal structures, which are crudely I-beam-shaped or honeycombed;
  • Janensch (1947), who wrote the first ever paper that was primarily about pneumaticity in dinosaurs;
  • Britt (1993), who first CTed dinosaur bones looking for pneumaticity, independently rediscovered Longman’s two categories, calling them ‘camerate’ and ‘camellate’ respectively, and generally put the whole investigation of dinosaur pneumaticity on its modern footing;
  • Witmer (1997), who provided what I think is the first compelling explanation of how and why skeletal pneumaticity works the way it does, using a vast amount of evidence culled from both living and fossil systems;
  • Wilson (1999), who IIRC was the first to seriously discuss the interplay of pneumaticity and biomechanics in determining the form of sauropod vertebrae.

Yeah, there you go: up until the year 2000, you could learn pretty much everything important that had been published on pneumaticity in dinosaurs by reading five papers and one dissertation. “Dinosaur pneumaticity” wasn’t a field yet. It feels like it is becoming one now. To get up to speed today, in addition to the above you’d need to read big swaths of the work of Roger Benson, Richard Butler, Leon Claessens, Pat O’Connor (including a growing body of work by his students), Emma Schachner (not on pneumaticity per se, but too closely related [and too awesome] to ignore), Daniela Schwarz, and Jeff Wilson (and his students), plus important singleton papers like Woodward and Lehman (2009), Cerda et al. (2012), Yates et al. (2012), and Fanti et al. (2013). Not to mention my own work, and some of Mike’s and Darren’s. And Andy Farke and the rest of Witmer, if you’re into cranial pneumaticity. And still others if you care about pneumaticity in pterosaurs, which you should if you want to understand how–and, crucially, when–the anatomical underpinnings of ornithodiran pneumaticity evolved. Plus undoubtedly some I’ve forgotten–apologies in advance to the slighted, please prod me in the comments.

You see? If I actually listed all of the relevant papers by just the authors I named above, it would probably run to 50 or so papers. So someone trying to really come to grips with dinosaur pneumaticity now faces a task roughly equal to the one I faced in 1996 when I was first trying to grokk sauropods. This is dim memory combined with lots of guesswork and handwaving, but I probably had to read about 50 papers on sauropods before I felt like I really knew the group. Heck, I read about a dozen on blood pressure alone.

(Note to self: this is probably a good argument for writing a review paper on dinosaur pneumaticity, possibly in collaboration with some of the folks mentioned above–sort of a McIntosh [1990] for the next generation.)

When I wrote the first draft of this post, I was casting about for a word to describe what is going on in science, and the first one that came to mind is “fragmentation”. But that’s not the right word–science isn’t getting more fragmented. If anything, it’s getting more interconnected. What it’s really doing is arborizing–branching fractally, like the blood vessels in the image at the top of this post. I think it’s pointless to opine about whether this is a good or bad thing. Like the existence of black holes and fuzzy ornithischians, it’s just a fact now, and we’d better get on with trying to make progress in this new reality.

How do I feel about all this, now that my little capillary of science has grown into an arteriole and threatens to become a full-blown artery? It is simultaneously exhilarating and worrying. Exhilarating because lots of people are discovering lots of cool stuff about my favorite system, and I have a lot more people to bounce ideas around with than I did when I started. Worrying because I feel like I am gradually losing my ability to keep tabs on the whole thing. Sound familiar?

Conclusion: Help a brother out

Having admitted all of this, it seems imperative that I get my act together and establish some kind of systematic new-paper-discovery method, beyond just sponging off my friends and hoping that they’ll continue to deliver everything I need. But it seems inevitable that I am either going to have to be come more selective about what I consume–which sounds both stupid and depressing–or lose all of my time just trying to keep up with things.

Hi, I’m Matt. I just arrived here in Toomuchnewscienceistan. How do you find your way around?


My camera had a possibly-fatal accident in the field at the end of the day on Saturday, so I didn’t take any photos on Sunday or Monday. From here on out, you’re either getting my slides, or photos taken by other people.

Powell Museum sauropod humerus

On Sunday we were at the John Wesley Powell River History Museum in Green River, Utah, for the Cretaceous talks. There were some fossils on display downstairs, including mounted skeletons of Falcarius and one or two ornithischians,* and this sauropod humerus from the Cedar Mountain Formation (many thanks to Marc Jones for the photo).

* A ceratopsian and Animantarx, maybe? They were in the same room as the sauropod humerus, so it’s no surprise that I passed them by with barely a glance.

There were loads of great talks in the Cretaceous symposium on Sunday, and I learned a lot, about everything from clam shrimp biostratigraphy to ankylosaur phylogeny to Canadian sauropod trackways. But I can’t show you any slides from those talks, so the rest of this post is the abstact from Darren’s and my talk, illustrated by a few select slides.

Wedel Naish 2014 Sauroposeidon and kin - slide 1 title

Sauroposeidon is a giant titanosauriform from the Early Cretaceous of North America. The holotype is OMNH 53062, a series of four articulated cervical vertebrae from the Antlers Formation (Aptian-Albian) of Oklahoma. According to recent analyses, Paluxysaurus from the Twin Mountain Formation of Texas is the sister taxon of OMNH 53062 and may be a junior synonym of Sauroposeidon. Titanosauriform material from the Cloverly Formation of Wyoming may also pertain to Paluxysaurus/Sauroposeidon. The proposed synonymy is based on referred material of both taxa, however, so it is not as secure as it might be.

Wedel Naish 2014 Sauroposeidon and kin - slide 34 Sauroposeidon characters

Top row, vertebrae of Paluxysaurus. From left to right, the centrum lengths of the vertebrae are 72cm, 65cm, and 45cm. Main image, the largest and most complete vertebra of the holotype of Sauroposeidon. Labels call out features that are present in every Sauroposeidon vertebra where they can be assessed, but consistently absent in Paluxysaurus. Evaluating the proposed synonymy of Paluxysaurus and Sauroposeidon is left as an exercise for the reader.

MIWG.7306 is a cervical vertebra of a large titanosauriform from the Wessex Formation (Barremian) of the Isle of Wight. The specimen shares several derived characters with the holotype of Sauroposeidon: an elongate cervical centrum, expanded lateral pneumatic fossae, and large, plate-like posterior centroparapophyseal laminae. In all of these characters, the morphology of MIWG.7306 is intermediate between Brachiosaurus and Giraffatitan on one hand, and Sauroposeidon on the other. MIWG.7306 also shares several previously unreported features of its internal morphology with Sauroposeidon: reduced lateral chambers (“pleurocoels”), camellate internal structure, ‘inflated’ laminae filled with pneumatic chambers rather than solid bone, and a high Air Space Proportion (ASP). ASPs for Sauroposeidon, MIWG.7306, and other isolated vertebrae from the Wessex Formation are all between 0.74 and 0.89, meaning that air spaces occupied 74-89% of the volume of the vertebrae in life. The vertebrae of these animals were therefore lighter than those of brachiosaurids (ASPs between 0.65 and 0.75) and other sauropods (average ASPs less than 0.65).

Wedel Naish 2014 Sauroposeidon and kin - slide 64 Mannion phylogeny

Check this out: according to at least some versions of the Mannion et al. (2013) tree, Sauroposeidon and Paluxysaurus are part of a global radiation of andesaurids in the Early and middle Cretaceous. Cool!

Sauroposeidon and MIWG.7306 were originally referred to Brachiosauridae. However, most recent phylogenetic analyses find Sauroposeidon to be a basal somphospondyl, whether Paluxysaurus and the Cloverly material are included or not. Given the large number of characters it shares with Sauroposeidon, MIWG.7306 is probably a basal somphospondyl as well. But genuine brachiosaurids also persisted and possibly even radiated in the Early Cretaceous of North America; these include Abydosaurus, Cedarosaurus, Venenosaurus, and possibly an as-yet-undescribed Cloverly form. The vertebrae of Abydosaurus have conservative proportions and solid laminae and the bony floor of the centrum is relatively thick. In these characters, Abydosaurus is more similar to Brachiosaurus and Giraffatitan than to Sauroposeidon or MIWG.7306. So not all Early Cretaceous titanosauriforms were alike, and whatever selective pressures led Sauroposeidon and MIWG.7306 to evolve longer and lighter necks, they didn’t prevent Giraffatitan-like brachiosaurs such as Abydosaurus and Cedarosaurus from persisting well into the Cretaceous.

Wedel Naish 2014 Sauroposeidon and kin - slide 65 Cloverly sauropods

The evolutionary dynamics of sauropods in the North American mid-Mesozoic are still mysterious. In the Morrison Formation, sauropods as a whole are both diverse and abundant, but Camarasaurus and an efflorescence of diplodocoids account for most of that abundance and diversity, and titanosauriforms, represented by Brachiosaurus, are comparatively scarce. During the Early Cretaceous, North American titanosauriforms seem to have radiated, possibly to fill some of the ecospace vacated by the regional extinction of basal macronarians (Camarasaurus) and diplodocoids. However, despite a flood of new discoveries in the past two decades, sauropods still do not seem to have been particularly abundant in the Early Cretaceous of North America, in contrast to sauropod-dominated faunas of the Morrison and of other continents during the Early Cretaceous.

Wedel Naish 2014 Sauroposeidon and kin - slide 66 acknowledgments

That final slide deserves some explanation. On the way back from the field on Saturday–the night before my talk–a group of us stopped at a burger joint in Hanksville. Sharon McMullen got a kid’s meal, and it came in this bag. We took it as a good omen that Sauroposeidon was the first dinosaur listed in the quiz.

For the full program and abstracts from both days of talks, please download the field conference guidebook here.

Currey Alexander 1985 fig 1

Figure 1 from Currey and Alexander (1985)

This post pulls together information on basic parameters of tubular bones from Currey & Alexander (1985), on ASP from Wedel (2005), and on calculating the densities of bones from Wedel (2009: Appendix). It’s all stuff we’ve covered at one point or another, I just wanted to have it all in one convenient place.


  • R = outer radius = r + t
  • r = inner radius = R – t
  • t = bone wall thickness = R – r

Cross-sectional properties of tubular bones are commonly expressed in R/t or K (so that r = KR). K is defined as the inner radius divided by the outer radius (r/R). For bones with elliptical or irregular cross-sections, it’s best to measure two radii at right angles to each other, or use a different measure of cross-sectional geometry (like second moment of area, which I’m not getting into here).

R/t and K can be converted like so:

  • R/t = 1/(1-K)
  • K = 1 – (1/(R/t))

ASP (air space proportion) and MSP (marrow space proportion) measure the cross-sectional area of an element not taken up by bone tissue. ASP and MSP are the same measurement–the amount of non-bone space in a bony element divided by the total–we just use ASP for air-filled bones and MSP for marrow-filled bones. See Tutorial 6 and these posts: one, two, three.

For tubular bones, ASP (or MSP) can be calculated from K:

  • ASP = πr^2/πR^2 = r^2/R^2 = (r/R)^2 = K^2

Obviously R/t and K don’t work for bones like vertebrae that depart significantly from a tubular shape. But if you had a vertebra or other irregular bone with a given ASP and you wanted to see what the equivalent tubular bone would look like, you could take the square root of ASP to get K and then use that to draw out the cross-section of that hypothetical tubular bone.

To estimate the density of an element (at least near the point of a given cross-section), multiply the proportional areas of bone and air, or bone and marrow, by the specific gravities of those materials. According to Currey and Alexader (1985: 455), the specific gravities of fatty marrow and bone tissue are 0.93 and 2.1, respectively.

For a marrow-filled bone, the density of the element (or at least of the part of the shaft the section goes through) is:

  • 0.93MSP + 2.1(1-MSP)

Air is matter and therefore has mass and density, but it is so light (0.0012-0.0013 g/mL) that we can effectively ignore it in these calculations. So the density of a pneumatic element is: 2.1(1-ASP) For the three examples in the figure at the top of the post, the ASP/MSP values and densities are:

  • (b) alligator femur (marrow-filled), K = 0.35, MSP = K^2 = 0.12, density = (0.93 x 0.12) + (2.1 x 0.88) = 1.96 g/mL
  • (c) camel tibia (marrow-filled), K = 0.57, MSP = K^2 = 0.32, density = (0.93 x 0.32) + (2.1 x 0.68) = 1.73 g/mL
  • (d) Pteranodon first phalanx (air-filled), K = 0.91, ASP = K^2 = 0.83, density = (2.1 x 0.17) = 0.36 g/mL

What if we switched things up, and imagined that the alligator and camel bones were pneumatic and the Pteranodon phalanx was marrow-filled? The results would then be:

  • (b) alligator femur (hypothetical air-filled), K = 0.35, ASP = K^2 = 0.12, density = (2.1 x 0.88) = 1.85 g/mL
  • (c) camel tibia (hypothetical air-filled), K = 0.57, ASP = K^2 = 0.32, density = (2.1 x 0.68) = 1.43 g/mL
  • (d) Pteranodon first phalanx (hypothetical marrow-filled), K = 0.91, MSP = K^2 = 0.83, density = (0.93 x 0.83) + (2.1 x 0.17) = 1.13 g/mL

In the alligator femur, the amount of non-bone space is so small that it does much matter whether that space is filled by air or marrow–replacing the marrow with air only lowers the density of the element by 5-6%. The Pteranodon phalanx is a lot less dense than the alligator femur for two reasons. First, there is much less bony tissue–the hypothetical marrow-filled phalanx is 42% less dense as the alligator femur. Second, the marrow is replaced by air, which reduces the density by an additional 40% relative to the alligator.

Next time: how to write punchier endings for tutorial posts.


Things to Make and Do

January 31, 2010

We like to keep you busy with arts-and-crafts projects :)

For some reason, these posts always make the think of a fictional book entitled Things a Boy Can Do that crops up in one of Richmal Crompton’ Just William stories.

A section of the cotyle of a presacral vertebra of Alamosaurus (Woodward and Lehman 2009:fig. 6A).

The last time we talked about Alamosaurus, I promised to explain what the arrow in the above image is all about. The image above is a section through the cotyle (the bony socket of a ball-and-socket joint) at the end of one of the presacral vertebra. The external bone surface would have been over on the left; it was either very thin (which happens) or a bit eroded, or both. The arrow is pointing at something weird–a plate of bone inside the vertebra that forms a sort of shadow cotyle deep to the articular surface.

This is weird for a couple of reasons. First, once camellate (small-chambered) vertebrae get above a certain level of complexity, it’s hard to make any sense of the orientation of individual bony struts. Possibly I haven’t seen enough vertebrae, or played with enough 3D models, to figure it out. You would certainly expect that the struts would be oriented to resist biomechanical loads, just like the struts in the long bones of your limbs; the fact that sauropod verts were filled with air whereas your long bones are filled with marrow shouldn’t make any difference. Back in the day, Kent Sanders–who is second author on that super-important paper on unidirectional air flow in croc lungs that you’ve probably heard about (Farmer and Sanders 2010)–speculated to me that the complex of laminae we see in the vertebrae of most sauropods are still there in the inflated-looking vertebrae of titanosaurs and birds, they’re just incarnated in internal struts rather than external laminae. Cool hypothesis for somebody to test.

The other reason that this is weird is that the plate of bone is parallel to the articular surface. One place where I have seen some regularity in terms of strut orientation is in zygapophyses, where in both camerae and camellate vertebrae the internal struts are oriented at right angles to the articular surfaces of the zygs, like beams propping up a wall. In this Alamosaurus section, there are indeed smaller struts that run at right angles to both the cotyle and the internal plate, but I have no idea why they’re so wimpy and the plate is so thick; a priori I would have expected the reverse.

It turns out that this isn’t even the first time that an internal “shadow” of the cotyle has been figured–check out this figure that I redrew from Powell’s (1992:fig. 16) Saltasaurus osteology. But don’t credit me with the discovery. I’d looked at this section a hundred times and even drawn it and never noticed the shadow cotyle, until it was pointed out by Woodward and Lehman (2009)–another reason to read that paper if you haven’t yet. Kudos to Holly Woodward for spotting this and making the connection.

Now that I’ve drawn attention to the weirdness and given credit where it’s due, this is one of those times I’m going to throw up my hands in confusion and open the floor for comments.


  • Farmer, C.G., and Sanders, K. 2010. Unidirectional airflow in the lungs of alligators. Science 327:338-340.
  • Powell, J.E. 1992. Osteologia de Saltasaurus loricatus (Sauropoda – Titanosauridae) del Cretacico Superior del noroeste Argentino; pp. 165-230 in J.L. Sanz and A.D. Buscalioni (editors), Los Dinosaurios y Su Entorno Biotico: Actas del Segundo Curso de Paleontologia in Cuenca. Institutio Juan de Valdes.
  • Woodward, H.N.,  and Lehman, T.M. 2009. Bone histology and microanatomy of Alamosaurus sanjuanensis (Sauropoda: Titanosauria) from the Maastrichtian of Big Bend National Park, Texas. Journal of Vertebrate Paleontology 29(3):807-821.

Weren’t we just discussing the problem of keeping up with all the good stuff on da intert00bz? The other day Rebecca Hunt-Foster, a.k.a. Dinochick, posted a “mystery photo” that is right up our alley here at SV-POW!, but, lazy sods that we are, we missed it until just now. Here’s the pic:


I flipped it 90 degrees so that you can see more clearly what is going on. This is a cut and polished section of a pneumatic sauropod vertebra–the bottom half of the mid-centrum of a dorsal vertebra, to be precise. Cervicals usually have concave ventral surfaces, and sacrals are usually either wider and flatter or narrower and V-shaped in cross sections, so I am pretty confident that this slice is from a dorsal. Compare to the classic anchor cross-section in this Camarasaurus dorsal:

camarasaurus-internal-structure(You may remember this image from Xenoposeidon week–almost two years ago now!)

Naturally as soon as I saw ReBecca’s shard of excellence, I wondered about its ASP, so after a bit of GIMPing, voila:

IMG_7857 ASP

As usual, bone is black, air is white, and everything else is gray. And the ASP is:

461080 white pixels/(461080 white + 133049 black pixels) = 0.78

So, we know what this is, and we know the ASP of this bit of it, and we can even figure out the in vivo density of this bit. The density of cortical bone ranges from about 1.8  g/cm^3 for some birds to about 2.0 for most mammals. For the sake of this example–and so I can hurry back to writing my lecture about the arse–let’s call it 1.9. The density is then the fraction of bone multiplied by the density of bone, full stop. If it was an apneumatic bone, we’d have to add the fraction of marrow multiplied by the density of marrow, but the density of air is negligible so we can skip that step here. The answer is 0.22 x 1.9 = 0.42 g/cm^3, which is pretty darned light. Keep in mind, though, that some slices of Sauroposeidon (and ‘Angloposeidon’, as it turns out) have ASPs of 0.89, and thus had an in vivo density half that of the above slice (0.11 x 1.9 = 0.21 g/cm^3).

What’s that in real money? Well, your femora are roughly 60% bone and 40% marrow, with a density of ((0.6 x 2.0)+(0.4 x 0.93)) = 1.6 g/cm^3, four times as dense as the bit of vertebra shown above, and eight times as dense as some slices of Sauroposeidon and ‘Angloposeidon’. If that doesn’t make you self-conscious about your heavy thighs, I don’t know what will.

Yes, that was a lame joke, and yes, I’m going out on it.

Hat tip to Dinochick.

P.S. It’s the 40th anniversary of the first moon landing today. Hoist a brew for Neil and Buzz, wouldja?


By now you’ll recognize this as NHM 46870, a minor celebrity in the world of pneumatic sauropod vertebrae. Darren has covered the history of the specimen before, and in the last post he showed photographs of both this chunk and its other half. He also briefly discussed the Air Space Proportion (ASP) of the specimen, and I’ll expand on that now.

People have mentioned the weight-saving properties of sauropod vertebrae from the very earliest discoveries of sauropods. But as far as I know, no one tried to quantify just how light they might have been until 2003.

That fall I was starting my third year of PhD work at Berkeley, and I was trying to think of everything that could possibly be investigated about pneumaticity in sauropod vertebrae. I came up with a list of four things:

  • external traces of pneumaticity (foramina, fossae, tracks, laminae)
  • form and complexity of internal spaces (camerae, camellae, branching patterns)
  • ratio of bone to air space within a pneumatic element
  • distribution of postcranial skeletal pneumaticity (PSP) in the body

That list of four things formed the outline for my first dissertation chapter (Wedel 2005), and for my dissertation itself. In fact, all of my papers that have anything to do with pneumaticity can be classified into one or more of those four bins:

That list is not exhaustive. It’s every aspect of PSP that I was able to think of back in 2003, but there are lots more. For example, I’ve only ever dealt with the internal complexity of sauropod vertebrae in a qualitative fashion, but the interconnections among either chambers or bony septa could be quantified, as Andy Farke has done for the frontal sinuses of hartebeests (Farke 2007). External traces on vertebrae and the distribution of PSP in the body can also be quantified, and were shortly after I drew up the list–see Naish et al. (2004) for a simple, straightforward approach to quantifying the extent of external pneumatic fossae, and O’Connor (2004, 2009) for a quantitative approach to the extent of pneumaticity in the postcranial skeletons of birds. There are undoubtedly still more parameters waiting to be thought of and measured. All of these papers are first steps, at least as applied to pneumaticity, and our work here is really just beginning.

Also, it took me an embarrassingly long time to “discover” ASPs.  I’d had CT slices of sauropod vertebrae since January, 1998, and it took me almost six years to realize that I could use them to quantify the amount of air inside the bones. I later discovered that Currey and Alexander (1985) and Casinos and Cubo (2000) had done related but not identical work on quantifying the wall thickness of tubular bones, and I was able to translate their results into ASPs (and MSPs for marrow-filled bones).


The procedure is pretty simple, as Mike has shown here before. Open up the image of interest in Photoshop (or GIMP if you’re all open-sourcey, like we are), make the bone one color, the air space a second color, and the background a third color. Count pixels, plug ’em into a simple formula, and you’ve got the ASP. I always colored the bone black, the air space white, and the background gray, so

ASP = (white pixels)/(black + white pixels)

For the image above, that’s 460442/657417 = 0.70.

Two quick technical points. First, most images are not just black, white, and one value of gray. Because of anti-aliasing, each black/white boundary is microscopically blurred by a fuzz of pixels of intermediate value. I could have used some kind of leveling threshold thing to bin those intermediate pixels into the bone/air/background columns, but I wanted to keep the process as fast and non-subjective as possible, so I didn’t. My spreadsheet has columns for black, white, gray, and everything else. The everything else typically runs 1-3%, which is not enough to make a difference at the coarse level of analysis I’m currently stuck with.

Second, I prefer transverse sections to longitudinal, because most of the internal chambers are longitudinally oriented. That means that longitudinal sections, whether sagittal or horizontal, are likely to cut through a chamber wall on its long axis, which makes the walls look unnaturally thick. For example, in the image above the median septum looks 5-10 times thicker than the outer walls of the bone, which would be a first–usually the outer walls are thicker than the internal septa, as you can see here. I don’t think the median septum really is that thick; I strongly suspect that a very thin plate of bone just happened to lie in the plane of the cut. It takes some work to get used to thinking about how a 2D slice can misrepresent 3D reality. When I first started CT scanning I was blown away by how thick the bone is below the pre- and postzygapophyses. I was thinking, “Wow, those centrozygapophyseal laminae must have been way more mechanically important than anyone thinks!” It took me a LONG time to figure out that if you take a transverse slice through a vertical plate of bone, it is going to look solid all the way up, even if that plate of bone is very thin.

Even apart from those considerations, there is still a list of caveats here as long as your arm. You may not get to choose your slice. That’s almost always true of broken or historically sectioned material, like NHM 46870. It’s even true in some cases for CT scans, because some areas don’t turn out very clearly, because of mineral inclusions, beam-hardening artifacts, or just poor preservation.

The slice you get, chosen or not, may not be representative of the ASP of the vertebra it’s from. Even if it is, other elements in the same animal may have different ASPs. Then there’s variation: intraspecific, ontogenetic, etc. So you have to treat the results with caution.

Still, there are some regularities in the data. From my own work, the mean of all ASP measurements for all sauropods is about 0.60. That was true when I had only crunched my first six images, late on the evening of October 9, 2003. It was true of the 22 measurements I had for Wedel (2005), and now that I have over a hundred measurements, it’s still true. More data is not shifting that number at all. And Woodward (2005) and Schwartz and Fritsch (2006) got very similar numbers, using different specimens.

This is cool for several reasons. It’s always nice when results are replicated–it decreases the likelihood that they’re a fluke, and in this case it suggests that although the limitations listed above are certainly real, they are not deal-killers for answering broad questions (we are at this point seeing the forest more clearly than the trees, though).

More importantly, the mean 0.60 ASP for all sauropod vertebrae is very similar to the numbers that you get from the data of Currey and Alexander (1985) and Cubo and Casinos (2000): 0.64 and 0.59, respectively. So sauropod vertebrae were about as lightly built as the pneumatic long bones of birds, on average.

Naturally, there are some deviations from average. Although I didn’t have enough data to show it in 2005, brachiosaurids tend to have higher ASPs than non-brachiosaurids. And Early Cretaceous brachiosaurids from the US and England are especially pneumatic–the mean for all of them, including Sauroposeidon, ‘Angloposeidon’, some shards of excellence from the Isle of Wight, and assorted odds and ends, is something like 0.75-0.80, higher even than Brachiosaurus. So there’s probably a combined phylogenetic/functional story in there about the highly pneumatic, hyper-long-necked brachiosaurids of the Early Cretaceous of Laurasia. Another paper waiting to be written.

Chondrosteosaurus broken face

Here’s another shard of excellence, referred to Chondrosteosaurus, NHM R96. As Mike had discussed here before, there’s no good reason to believe that it actually is Chondrosteosaurus, and the internal structure looks considerably more subdivided than in NHM 46870. This is an anterior view, and normally you’d be seeing a nice hemispherical condyle, but all of the cortical bone is gone and the internal structure is revealed. The little black traces are bone and the brownish stuff is rock matrix filling the pneumatic cavities.

Chondrosteosaurus broken face ASP

A few years ago, Mike asked me to look at that photo and guess the ASP, and then run the numbers and see how close I got. I guessed about 78%, then did the calculation, and lo and behold, the answer was 78%. So I’m pretty good at guessing ASPs.

Except I’m not, because as any of you armed with photo software can tell, that picture has 24520 black pixels and 128152 white ones, so the ASP is actually 128152/(128152+24520) = 0.84. The moral of the story is check your homework, kids! Especially if you seem to be an unnaturally good estimator.

ASP-ESP aside, I think ASP is cool and has some interesting potential at the intersection of phylogeny and biomechanics. But the method is severely limited by sample size, which is severely limited by how much of a pain in the butt preparing the images is. In most cases you can’t just play with levels or curves to get a black and white image that faithfully represents the morphology, or use the magic wand, or any of the other myriad shortcuts that modern imaging programs offer. Believe me, I’ve tried. Hard. But inevitably you get some matrix with the bone, or some bone with the matrix, and you end up spending an impossible amount of time fixing those problems (note that this is not a problem if you use perfect bones from extant animals, which is sadly not an option for sauropod workers). So almost all of my ASP images were traced by hand, which is really time-consuming. I could pile up a lot more data if I just sat around for a few weeks processing images, but every time I’ve gotten a few free weeks there has been something more important demanding my attention, and that may always be the case. Fortunately I’m not the only one doing this stuff now, and hopefully in the next few years we’ll get beyond these first few tottering steps.

Side Note: Does NHM 46870 represent a juvenile, or a dwarf?

This came up amongst the SV-POW!sketeers and we decided it should be addressed here. Darren noted that the vert at top is pretty darned small, ~23 cm for the preserved part and probably only a foot and a half long when it was complete, which is big for an animal but small for a sauropod and dinky for a brachiosaurid (if that’s what it is). Mike made the counter-observation that the internal structure is pretty complex, citing Wedel (2003b:fig. 12) and surrounding text, and suggested that it might be an adult of a small or even dwarfed taxon. And I responded:

I’m not at all certain that it is dwarfed. It matters a lot whether the complex internal structure is polycamerate or camellate. I was agnostic for a long time about how different those two conditions are, but there is an important difference that is relevant in this case: the two internal structures develop differently. Polycamerate verts really do get progressively more complex through development, as illustrated–there are at least two great series that show this, that I need to publish one of these days. But I think camellate vertebrae may be natively complex right from the get-go; i.e., instead of a big simple diverticulum pushing in from the side and making a big camera first, a bunch of smaller diverticula may remodel the small marrow spaces into small air spaces with no prior big cavities. At least, that’s how birds seem to do it. This needs more testing from sauropods–a good ontogenetic sequence from Brachiosaurus would be clutch here–but it’s my working hypothesis. In which case NHM 46870 may be a juvenile of a camellate taxon, rather than an adult of a polycamerate taxon.

The whole camerate-vs-camellate problem deserves a post of its own, and this post is already too long, so we’ll save that for another day.