arborization of science

Modified from an original SEM image of branching blood vessels, borrowed from http://blogs.uoregon.edu/artofnature/2013/12/03/fractal-of-the-week-blood-vessels/.

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?

References

As recently noted, it was my pleasure and privilege on 25 June to give a talk at the ESOF2014 conference in Copenhagen (the EuroScience Open Forum). My talk was one of four, followed by a panel discussion, in a session on the subject “Should science always be open?“.

 

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I had just ten minutes to lay out the background and the problem, so it was perhaps a bit rushed. But you can judge for yourself, because the whole session was recorded on video. The image is not the greatest (it’s hard to make out the slides) and the audio is also not all it could be (the crowd noise is rather loud). But it’s not too bad, and I’ve embedded it below. (I hope the conference organisers will eventually put out a better version, cleaned up by video professionals.)

Subbiah Arunachalam (from Arun, Chennai, India) asked me whether the full text of the talk was available — the echoey audio is difficult for non-native English speakers. It wasn’t but I’ve sinced typed out a transcript of what I said (editing only to remove “er”s and “um”s), and that is below. Finally, you may wish to follow the slides rather than the video: if so, they’re available in PowerPoint format and as a PDF.

Enjoy!

It’s very gracious of you all to hold this conference in English; I deeply appreciate it.

“Should science always be open?” is our question, and I’d like to open with one of the greatest scientists there’s ever been, Isaac Newton, who humility didn’t come naturally to. But he did manage to say this brilliant humble thing: “If I have seen further, it’s by standing on the shoulders of giants.”

And the reason I love this quote is not just because it’s insightful in itself, but because he stole it from something John of Salisbury said right back in 1159. “Bernard of Chartres used to say that we were like dwarfs seated on the shoulders of giants. If we see more and further than they, it is not due to our own clear eyes or tall bodies, but because we are raised on high and upborne by their gigantic bigness.”

Well, so Newton — I say he stole this quote, but of course he did more than that: he improved it. The original is long-winded, it goes around the houses. But Newton took that, and from that he made something better and more memorable. So in doing that, he was in fact standing on the shoulders of giants, and seeing further.

And this is consistently where progress comes from. It’s very rare that someone who’s locked in a room on his own thinking about something will have great insights. It’s always about free exchange of ideas. And we see this happening in lots of different fields.

Over the last ten or fifteen years, enormous advances in the kinds of things computers working in networks can do. And that’s come from the culture of openness in APIs and protocols, in Silicon Valley and elsewhere, where these things are designed.

Going back further and in a completely different field, the Impressionist painters of Paris lived in a community where they were constantly — not exactly working together, but certainly nicking each other’s ideas, improving each other’s techniques, feeding back into this developing sense of what could be done. Resulting in this fantastic art.

And looking back yet further, Florence in the Renaissance was a seat of all sorts of advances in the arts and the sciences. And again, because of this culture of many minds working together, and yielding insights and creativity that would not have been possible with any one of them alone.

And this is because of network effects; or Metcalfe’s Law expresses this by saying that the value of a network is proportional to the square of the number of nodes in that network. So in terms of scientific reasearch, what that means is that if you have a corpus of published research output, of papers, then the value of that goes — it doesn’t just increase with the number of papers, it goes up with the square of the number of papers. Because the value isn’t so much in the individual bits of research, but in the connections between them. That’s where great ideas come from. One researcher will read one paper from here and one from here, and see where the connection or the contradiction is; and from that comes the new idea.

So it’s very important to increase the size of the network of what’s available. And that’s why we have a very natural tendency, I think among scientists particularly, but I think we can say researchers in other areas as well, have a natural tendency to share.

Now until recently, the big difficulty we’ve had with sharing has been logistical. It was just difficult to make and distribute copies of pieces of research. So this [picture of a printing press] is how we made copies, this [picture of stacks of paper] was what we stored them on, and this was how we transmitted them from one researcher to another.

And they were not the most efficient means, or at least not as efficient as what we now have available. And because of that, and because of the importance of communication and the links between research, I would argue that maybe the most important invention of the last hundred years is the Internet in general and the World Wide Web in particular. And the purpose of the Web, as it was initially articulated in the first public post that Tim Berners-Lee made in 1991 — he explained not just what the Web was but what it was for, and he said: “The project started with the philosophy that much academic information should be freely available to anyone. It aims to allow information sharing within internationally dispersed teams, and the dissemination of information by support groups.”

So that’s what the Web is for; and here’s why it’s important. I’m quoting here from Cameron Neylon, who’s great at this kind of thing. And again it comes down to connections, and I’m just going to read out loud from his blog: “Like all developments of new communication networks, SMS, fixed telephones, the telegraph, the railways, and writing itself, the internet doesn’t just change how well we can do things, it qualitatively changes what we can do.” And then later on in the same post: “At network scale the system ensures that resources get used in unexpected ways. At scale you can have serendipity by design, not by blind luck.”

Now that’s a paradox; it’s almost a contradiction, isn’t it? Serendipity by definition is what you get by blind luck. But the point is, when you have enough connections — enough papers floating around the same open ecosystem — all the collisions happening between them, it’s inevitable that you’re going to get interesting things coming out. And that’s what we’re aiming towards.

And of course it’s never been more important, with health crises, new diseases, the diminishing effectiveness of antibiotics, the difficulties of feeding a world of many billions of people, and the results of climate change. It’s not as though we’re short of significant problems to deal with.

So I love this Jon Foley quote. He said, “Your job” — as a researcher — “Your job is not to get tenure! Your job is to change the world”. Tenure is a means to an end, it’s not what you’re there for.

So this is the importance of publishing. Of course the word “publish” comes from the same root as the word “public”: to publish a piece of research means to make that piece of research public. And the purpose of publishing is to open research up to the world, and so open up the world itself.

And that’s why it’s so tragic when we run into this [picture of a paywalled paper]. I think we’ve all seen this at various times. You go to read a piece of research that’s valuable, that’s relevant to either the research you’re doing, or the job you’re doing in your company, or whatever it might be. And you run into this paywall. Thirty five dollars and 95 cents to read this paper. It’s a disaster. Because what’s happened is we’ve got a whole industry whose existence is to make things public, and who because of accidents of history have found themselves doing the exact opposite. Now no-one goes into publishing with the intent of doing this. But this is the unfortunate outcome.

So what we end up with is a situation where we’re re-imposing on the research community barriers that were necessarily imposed by the inadequate technology of 20 or 30 years ago, but which we’ve now transcended in technological terms but we’re still strugging with for, frankly, commercial reasons. This is why we’re struggling with this.

And I don’t like to be critical, but I think we have to just face the fact that there is a real problem when organisations, for many years have been making extremely high profits — these [36%, 32%, 34%, 42%] are the profit margins of the “big four” academic publishers which together hugely dominate the scholarly publishing market — and as you can see they’re in the range 32% to 42% of revenue, is sheer profit. So every time your university library spends a dollar on subscriptions, 40% of that goes straight out of the system to nowhere.

And it’s not surprising that these companies are hanging on desperately to the business model that allows them to do that.

Now the problem we have in advocating for open access is that when we stand against publishers who have an existing very profitable business model, they can complain to governments and say, “Look, we have a market that’s economically significant, it’s worth somewhere in the region of 10-15 billion US dollars a year.” And they will say to governments, “You shouldn’t do anything that might damage this.” And that sounds effective. And we struggle to argue against that because we’re talking about an opportunity cost, which is so much harder to measure.

You know, I can stand here — as I have done — and wave my hands around, and talk about innovation and opportunity, and networks and connections, but it’s very hard to quantify in a way that can be persuasive to people in a numeric way. Say, they have a 15 billion dollar business, we’re talking about saving three trillion’s worth of economic value (and I pulled that number out of thin air). So I would love, if we can, when we get to the discussions, to brainstorm some way to quantify the opportunity cost of not being open. But this is what it looks like [picture of flooding due to climate change]. Economically I don’t know what it’s worth. But in terms of the world we live in, it’s just essential.

So we’ve got to remember the mission that we’re on. We’re not just trying to save costs by going to open access publishing. We’re trying to transform what research is, and what it’s for.

So should science always be open? Of course, the name of the session should have been “Of course science should always be open”.

 

photo1

I was at the Natural History Museum of Los Angeles County yesterday to do some research in the ornithology collection. After lunch I was working on this pelican skeleton and I thought, “Geez, there is just no way to do this thing justice with still photos. I should make a video.” Here it is. You’ll want to see it full-screen–this being my first time out making a video, I didn’t realize that I was holding the phone the wrong way for efficient viewing on other devices.

The specimen is LACM Ornithology 86262. I’m posting this video with the knowledge and kind permission of the ornithology collection staff.

For previous things in this vein, please see:

If you like it that stuff like this exists, please support your local natural history museum, especially the LACM, which has some really fantastic education and outreach programs.

Supersaurus vs Brachiosaurus - BYU 9024 and FMNH P25107

This was inspired by an email Mike sent a couple of days ago:

Remind yourself of the awesomeness of Giraffatitan:
http://svpow.files.wordpress.com/2008/11/mike-by-jango-elbow.jpeg

Now think of this. Its neck is 8.5m long. Knock of one measly meter — for example, by removing one vertebra from the middle of the neck — and you have 7.5 m.

Supersaurus’s neck was probably TWICE that long.

Holy poo.

I replied that I was indeed freaked out, and that it had given me an idea for a post, which you are now reading. I didn’t have a Giraffatitan that was sufficiently distortion-free, so I used my old trusty Brachiosaurus. The vertebra you see there next to Mike and next to the neck of Brachiosaurus is BYU 9024, the longest vertebra that has ever been found from anything, ever.

Regarding the neck length of Supersaurus, and how BYU 9024 came to be referred to Supersaurus, here’s the relevant chunk of my dissertation (Wedel 2007: pp. 208-209):

Supersaurus is without question the longest-necked animal with preserved cervical material. Jim Jensen recovered a single cervical vertebra of Supersaurus from Dry Mesa Quarry in western Colorado. The vertebra, BYU 9024, was originally referred to “Ultrasauros”. Later, both the cervical and the holotype dorsal of “Ultrasauros” were shown to belong to a diplodocid, and they were separately referred to Supersaurus by Jensen (1987) and Curtice et al. (1996), respectively.

BYU 9024 has a centrum length of 1378 mm, and a functional length of 1203 mm (Figure 4-3). At 1400 mm, the longest vertebra of Sauroposeidon is marginally longer in total length [see this post for a visual comparison]. However, that length includes the prezygapophyses, which overhang the condyle, and which are missing from BYU 9024. The centrum length of the largest Sauroposeidon vertebra is about 1250 mm, and the functional length is 1190 mm. BYU 9024 therefore has the largest centrum length and functional length of any vertebra that has ever been discovered for any animal. Furthermore, the Supersaurus vertebra is much larger than the Sauroposeidon vertebrae in diameter, and it is a much more massive element overall.

Neck length estimates for Supersaurus vary depending on the taxon chosen for comparison and the serial position assumed for BYU 9024. The vertebra shares many similarities with Barosaurus that are not found in other diplodocines, including a proportionally long centrum, dual posterior centrodiapophyseal laminae, a low neural spine, and ventrolateral flanges that connect to the parapophyses (and thus might be considered posterior centroparapophyseal laminae, similar to those of Sauroposeidon). The neural spine of BYU 9024 is very low and only very slightly bifurcated at its apex. In these characters, it is most similar to C9 of Barosaurus. However, theproportions of the centrum of BYU 9024 are more similar to those of C14 of Barosaurus, which is the longest vertebra of the neck in AMNH 6341. BYU 9024 is 1.6 times as long as C14 of AMNH 6341 and 1.9 times as long as C9. If it was built like that of Barosaurus, the neck of Supersaurus was at least 13.7 meters (44.8 feet) long, and may have been as long as 16.2 meters (53.2 feet).

Based on new material from Wyoming, Lovelace et al. (2005 [published as Lovelace et al. 2008]) noted potential synapomorphies shared by Supersaurus and Apatosaurus. BYU 9024 does not closely resemble any of the cervical vertebrae of Apatosaurus. Instead of trying to assign its serial position based on morphology, I conservatively assume that it is the longest vertebra in the series if it is from an Apatosaurus-like neck. At 2.7 times longer than C11 of CM 3018, BYU 9024 implies an Apatosaurus-like neck about 13.3 meters
(43.6 feet) long.

Supersaurus vs Diplodocus BYU 9024 and USNM 10865 - Gilmore 1932 pl 6

Bonus comparo: BYU 9024 vs USNM 10865, the mounted Diplodocus longus at the Smithsonian, modified from Gilmore 1932 (plate 6). For this I scaled BYU 9024 against the 1.6-meter femur of this specimen.

If you’d like to gaze upon BYU 9024 without distraction, or put it into a composite of your own, here you go:

Supersaurus cervical BYU 9024

References

 

Today, available for the first time, you can read my 2004 paper A survey of dinosaur diversity by clade, age, place of discovery and year of description. It’s freely available (CC By 4.0) as a PeerJ Preprint. It’s one of those papers that does exactly what it says on the tin — you should be able to find some interesting patterns in the diversity of your own favourite dinosaur group.

Fig. 1. Breakdown of dinosaur diversity by phylogeny. The number of genera included in each clade is indicated in parentheses. Non-terminal clades additionally have, in square brackets, the number of included genera that are not also included in one of the figured subclades. For example, there are 63 theropods that are neither carnosaurs nor coelurosaurs. The thickness of the lines is proportional to the number of genera in the clades they represent.

Taylor (2014 for 2004), Figure 1. Breakdown of dinosaur diversity by phylogeny. The number of genera included in each clade is indicated in parentheses. Non-terminal clades additionally have, in square brackets, the number of included genera that are not also included in one of the figured subclades. For example, there are 63 theropods that are neither carnosaurs nor coelurosaurs. The thickness of the lines is proportional to the number of genera in the clades they represent.

“But Mike”, you say, “you wrote this thing ten years ago?”

Yes. It’s actually the first scientific paper I ever wrote (bar some scraps of computer science) beginning in 2003. It’s so old that all the illustrations are grey-scale. I submitted it to Acta Palaeontologica Polonica way back on on 24 October 2004 (three double-spaced hard-copies in the post!) , but it was rejected without review. I was subsequently able to publish a greatly truncated version (Taylor 2006) in the proceedings of the 2006 Symposium on Mesozoic Terrestrial Ecosystems, but that was only one tenth the length of the full manuscript — much potentially valuable information was lost.

My finally posting this comes (as so many things seem to) from a conversation with Matt. Off work sick, he’d been amusing himself by re-reading old SV-POW! posts (yes, we do this). He was struck by my exhortation in Tutorial 14: “do not ever give a conference talk without immediately transcribing your slides into a manuscript”. He bemoaned how bad he’s been at following that advice, and I had to admit I’ve done no better, listing a sequence of old my SVPCA talks that have still never been published as papers.

The oldest of these was my 2004 presentation on dinosaur diversity. Commenting on this, I wrote in email: “OK, I got the MTE four-pager out of this, but the talk was distilled from a 40ish-page manuscript that was never published and never will be.” Quick as a flash, Matt replied:

If I had written this and sent it to you, you’d tell me to put it online and blog about how I went from idea to long paper to talk to short paper, to illuminate the process of science.

And of course he was right — hence this preprint.

Fig. 2. Breakdown of dinosaurian diversity by high-level taxa. "Other sauropodomorphs" are the "prosauropods" sensu lato. "Other theropods" include coelophysoids, neoceratosaurs, torvosaurs (= megalosaurs) and spinosaurs. "Other ornithischians" are basal forms, including heterodontosaurs and those that fall into Marginocephalia or Thyreophora but not into a figured subclade.

Taylor (2014 for 2004), Figure 2. Breakdown of dinosaurian diversity by high-level taxa. “Other sauropodomorphs” are the “prosauropods” sensu lato. “Other theropods” include coelophysoids, neoceratosaurs, torvosaurs (= megalosaurs) and spinosaurs. “Other ornithischians” are basal forms, including heterodontosaurs and those that fall into Marginocephalia or Thyreophora but not into a figured subclade.

I will never update this manuscript, as it’s based on a now wildly outdated database and I have too much else happening. (For one thing, I really ought to get around to finishing up the paper based on my 2005 SVPCA talk!) So in a sense it’s odd to call it a “pre-print” — it’s not pre anything.

Despite the data being well out of date, this manuscript still contains much that is (I think) of interest, and my sense is that the ratios of taxon counts, if not the absolute numbers, are still pretty accurate.

I don’t expect ever to submit a version of this to a journal, so this can be considered the final and definitive version.

References

 

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.

journal.pone.0097159.g001

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!”

References

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!

 

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