What does it cost to publish a paper with Elsevier?
July 9, 2012
What does it cost to publish a paper in a non-open access Elsevier journal? The immediate cost to the author is often zero (though page charges, and fees for colour illustrations mean this is not always true). But readers have to pay to see the paper, either directly in the case of private individuals or through library budgets in the case of university staff and students. What is the total cost to the world?
Previous attempts
It’s a calculation that I’ve taken a couple of stabs at in public forums, but in both cases space restraints meant that I couldn’t lay out the reasoning in the detail I’d like — and as a result I couldn’t get the kind of detailed feedback that would allow me to refine the numbers. So I am trying again here.
The first version of the calculation was in my article Open, moral and pragmatic at Times Higher Education:
According to Elsevier’s annual report for 2010, it publishes about “200,000 new science & technology research articles each year”. The same report reveals revenues for 2010 of £2.026 billion. This works out as £10,130 per article, each made available only to the tiny proportion of the world’s population that has access to a subscribing library.
As Kent Anderson pointed out in an otherwise misleading comment, that calculation was flawed in that I was using the total of Elsevier revenue rather than just the portion that comes from journal subscriptions. Trying to fix this, and using more up-to-date figures, I provided a better estimate in Academic Publishing Is Broken at The Scientist:
To publish in an Elsevier journal … appears to cost some $10,500. In 2011, 78 percent of Elsevier’s total revenue, or £1,605 million, was contributed by journal subscriptions. In the same year, Elsevier published 240,000 articles, making the average cost per article some £6,689, or about $10,500 US.
But this, it turns out, is also an over-estimate, because it’s 78% of Elsevier’s Scientific, Technical and Medical revenue that comes from journal subscriptions; the other half of Elsevier, their Health Sciences division, has its own revenues.
The data we have to work with
Here’s what I have right now — using data from 2010, the last complete year for which numbers are available.
Bear in mind that Elsevier is a publisher, and Reed Elsevier is a larger company that owns Elsevier and a bunch of other businesses such as Lexis Nexus. According to the notes from a Reed Elsevier investment seminar that took place on December 6, 2011 in London:
- Page 2: 34% of Reed Elsevier’s total 2010 revenue of £6,055M (i.e. £2058.7M) was from “Science and Medical”, which I take to mean Elsevier. This is in keeping with the total revenue number from Elsevier’s annual report.
- Page 8: Elsevier’s revenues are split 50-50 between the Scientific & Technical division and the Health Sciences division. 39% of total Elsevier revenue (i.e. £803M) is from research journals in the S&T sector. No percentage is given for research journal revenue in Health Sciences.
- Page 18: confirmation that 78% of Scientific & Technical revenue (i.e. 39% of total Elsevier revenue) is from research journals.
- Page 21: total number of articles published in 2010 seems to be about 258,000 (read off from the graph).
- Page 22 confirms “>230,000 articles per year”.
- Page 23, top half, says “>80% of revenue derived from subscriptions, strongly recurring revenues”. Bottom half confirms earlier revenue of 78% for research journals. I suppose that the “subscriptions” amounting to >80% must include database subscriptions.
The other important figure is the proportion of Elsevier journal revenue that comes from Gold OA fees rather than subscriptions. The answer is, almost none. Figures for 2010 are no longer on Elsevier’s Sponsored Articles page, but happily we quoted it in an older SV-POW! post:
691 Elsevier articles across some six hundred journals were sponsored in 2010. Sponsorship revenues from these articles amounted to less than 0.1% of Elsevier’s total revenues.
So for the purposes of these rough-and-ready calculations, we can ignore Elsevier’s Gold-OA revenue completely and assume that all research-journal revenue is from subscriptions.
The data we don’t have
The crucial piece of information we don’t have is this: how much of Elsevier Health Sciences revenue is from journal subscriptions? This information is not included in the investor report, and my attempts to determine it have so far been wholly unsuccessful. Back in March, I contacted Liz Smith (VP/Director of Global Internal Communications), Alicia Wise (Director of Universal Access), Tom Reller (VP of Global Corporate Relations), Ron Mobed (CEO of Scientific & Technical) and Michael Hansen (CEO of Health Sciences). Of these, only Tom Reller got back to me — he was helpful, and pointed me to the investor report that I cite heavily above — but wasn’t able to give me a figure.
If anyone knows the true percentage — or can even narrow the range a bit — I would love to know about it. Please leave a comment.
In the mean time, I will proceed with calculations on two different bases:
- That Health Sciences revenue is proportioned the same as Scientific & Technical, i.e. 78% comes from journal subscriptions;
- That Health Sciences has no revenue from journal subscriptions. This seems very unrealistic to me, but will at least give us a hard lower bound.
Calculation
It’s pretty simple.
If HS journal-subscription revenue is zero, then Elsevier’s total from journal subscriptions in 2010 was £803M. On the other hand, if HS revenue proportions are about the same as in S&T, then total journal-subscription revenue was twice this, £1606M.
Across the 258,000 or so articles published in 2010, that yields either £803M / 258,000 = £3112 per article, or £1606M / 258,000 = £6224 per article. At current exchange rates, that’s $4816 or $9632. My guess is that the true figure is somewhere between these extremes. If I had to give a single figure, I guess I’d split the difference and go with £4668, which is about $7224.
Remember: this is what it costs the academic world to get access to your article when you give it to an Elsevier journal. Those parts of the academic world that have access, that is — don’t forget that many universities and almost everyone outside a university won’t be able to access it at all.
This is less than my previous estimates. It’s still an awful lot.
Why this matters
Over on Tim Gowers’ blog, he’s recently announced the launch of a new open-access maths journal, Forum of Mathematics, to be published by Cambridge University Press. The new journal will have an article processing fee of £500 after the first three years, during which all fees will be waived. I’ve been shocked at the vehemence with which a lot of commenters have objected to the ideas of any article processing fee.
Here’s the thing. For each maths article that’s sent to an Elsevier journal, costing the worldwide maths community between £3112 and £6224, that same worldwide maths community could instead pay for six to twelve open-access articles in the new journal. And those articles would then be available to anyone who wanted them, not only people affiliated with subscribing institutions.
To me, the purely economic argument for open access is unanswerable. Even if you leave aside the moral argument, the text-mining argument, and so on, you’re left with a very stark financial equation. It’s madness to give research to subscription publishers.
In the middle of February, Times Higher Education ran a piece by Elsevier boycott originator Tim Gowers, entitled Occupy publishing. A week ago, they published a letter in response, written by Elsevier Senior VP David Clark, under the title If it ain’t broke, don’t bin it, in which he argued that “there is little merit in throwing away a system that works in favour of one that has not even been developed yet”.
Seeing the current journal system, with its arbitrary barriers, economic inefficiencies and distorted perspective on impact, described as “a system that works” was more than I could bear. So I sent a letter in response, and it’s published in today’s issue as Open, moral and pragmatic.
Space limitations of THE letters meant that I was only able to address one aspect — the economics. Based on numbers in their own annual report, I show that the cost of each article that Elsevier makes available to subscribers is twelve times the cost of each article that PLoS makes available to the world. And since Elsevier’s 200,000 articles per year are about a seventh of the total global output, the money paid to Elsevier alone would easily pay for every single paper to be published as open access. Easily.
No doubt there are errors in some of the numbers, which are necessarily estimates; and the calculation is overly simplistic. But even allowing for that, there is plenty enough slop in the figures that the conclusion stands. If we stopped paying Elsevier subscriptions alone — we can keep Wiley, Springer and the rest — the money we save would pay for all our work to be available to the whole world, with hundreds of millions of pounds left over to fund more research.
Worried about the lack of jobs in palaeontology? Concerned that universities are reducing the number of tenure-track positions? Disturbed by the elimination of curators and preparators from museums? We need to cut the inefficient, profiteering publishers out of the loop.
Who is publishing how many open-access papers?
February 8, 2012
How many open-access papers are getting published these days? And who’s doing it? Inspired by a tweet from @labroides (link at the end so as not to give away the punchline), I went looking for numbers.
We’ll start with our old friends Elsevier, since they are the world’s largest academic publisher by volume and by revenue. One often reads statements such as “Elsevier is committed to Universal Access, Quality and Sustainability … Elsevier wants to enable the broadest possible access to quality research content in sustainable ways that meet our many constituents’ needs” (from their page Elsevier’s position on Access). Even their submission to the OSTP call for comments begins by saying “One of Elsevier’s primary missions is to work towards providing universal access to high-quality scientific information in sustainable ways. We are committed to providing the broadest possible access to our publications.”
The most important way Elsevier does this is by allowing authors to pay a fee, currently $3000, to “sponsor” their articles, so that they are made freely available to readers (though we still don’t know under what specific licence!). While that fee is more than twice the $1350 that PLoS ONE charges, it’s comparable to the $2900 PLoS Biology fee and identical to Springer’s $3000 fee. Elsevier have rather a good policy in connection with their “sponsored article” fee: “Authors can only select this option after receiving notification that their article has been accepted for publication. This prevents a potential conflict of interest where a journal would have a financial incentive to accept an article.”
According to the page linked above, “691 Elsevier articles across some six hundred journals were sponsored in 2010. Sponsorship revenues from these articles amounted to less than 0.1% of Elsevier’s total revenues.” (And indeed, 691 × $3000 = $2.073 M, which is about 0.065% of their 2010 revenue of £2026 M ≈ $3208 M.) As Elsevier publishes 2639 journals in all, that amounts to just over a quarter of one open-access article per journal across the year.
I find that disappointing.
In the other corner (I won’t call it red or blue because of the political implications of those colours, which by the way are the opposite way around on different sides of the Atlantic. Anyway …) In the other corner, we have PLoS ONE. According to its Advanced Search engine, this journal alone published 6750 open-access articles in 2010 — about ten times as many as all Elsevier journals combined. Indeed, in the last month of that year alone, PLoS ONE’s 847 articles comfortably exceeded Elsevier’s output for the year. That’s one journal, in one month, up against a stable of 2639 journals across a whole year.
What can we take away from this? Maybe not very much: Elsevier offer their sponsored-article option to all authors, after all, and they can hardly be blamed if the authors don’t take them up on it.
But why don’t they? Tune in next time for some thoughts on that.
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And, finally, here is the tweet that started this line of thought:
@labroides Joshua Drew
@PublicAccessYAY@PLoSOne published more#OA articles in Dec ’10 than ALL of #elsevier‘s journals had the entire year
Food for thought.
Economics of open-access publishing
October 22, 2011
[This post is mostly a rehash of a comment I made on the last one, but I guess more people see posts than comments. Oh, and I will try to post something about sauropod vertebrae Real Soon Now.]
—
Last time out, Michael Richmond suggested that one way towards an open-access world is pointing out to decision makers that open-access publishing/reading is cheaper, and commented “that approach will only work if the open-access journals are much less expensive. Are they?”
As I’ve noted elsewhere, the difficulty in shifting to author-pays open access is that universities’ libraries and research departments are funded separately, so that when the extra costs to the latter result in savings for the former, it doesn’t look like a good deal (in the short term) for the research departments.
But let’s ignore that for now, and imagine a perfect economy where universities could shift money from the subscriptions that libraries buy to the publication fees that departments pay. If we could reassign all that money, would the universities spend more or less in total?
The answer may surprise you. A recent article on the Poetic Economics blog shows that Elsevier’s 2009 profits of more than $2.075 billion, divided by the world’s total scholarly output of 1.5 million articles per year, comes out to $1383 per article.
Now as it happens, PLoS ONE’s publication fee is $1350 — $33 less.
So think about it. That means the money that Elsevier alone takes out of academia — not its turnover but its profits, which are given to shareholders who have nothing to do with scholarly work — is enough to fund every research article in every field in the world as open access at PLoS ONE’s rate.
(And remember that PLoS is now making a profit at that rate — no longer living off the grants that helped to get it started. At a rate of $1350 per article, it’s not just surviving but flourishing, so we know that that’s a reasonable commercial rate to charge for handling an open-access academic article with no limits on length or on number of high-resolution colour figures.)
Isn’t that … astonishing?
Isn’t it … scandalous?
ONE COMMERCIAL PUBLISHER is taking out of the system enough money for everything to be open to the world. Everything. In the world. Open to the world.
if we all stopped buying Elsevier journals — just Elsevier, no other publisher — and if we threw away the proportion of the savings that Elsevier spends on costs, including salaries; then the profits alone would have been sufficient to fund every single research article in the world to be published in PLoS ONE — freely available to the whole world.
What would this mean? Dentists would be able to keep up with the relevant literature. Small businesses would be able to make plans with full information. The Climate Code Foundation would have a sounder and more up-to-date scientific basis for its work. Patient groups would be able to understand their diseases and give informed consent for treatment. Medical charities, amateur palaeontologists, ornithologists and so many more would have access to the information they need. Researchers in third-world countries could have the information they need to cope with life-threatening issues of health, food and water.
We can have all that for our $2.075 billion per year. Or we can keep giving it to Elsevier’s shareholders. Giving it, remember: not buying something with it. Don’t forget, this is not the money that Elsevier absorbs as its costs: salaries, rent, connectivity, what have you. This is their profit. It’s pure profit. This is the money that is taken out of the system.
So, yes, open access is cheaper. Stupidly cheaper. Absurdly, ridiculously, appallingly cheaper.
Update (later the same day)
In an article posted just an hour ago, Cambridge research-group head Peter Murray-Rust comes right out and says it: closed access means people die. That’s the bottom line. Follow his syllogism:
- Information is a key component of health-care
- Closed access publishers make money by restricting access to information.
- The worse the medicine and healthcare, etc. the more people die.
Are any of those statements false? And if not, is there any way to construe them that doesn’t lead by simply logic to the conclusion that closed access means people die? I don’t see one.
CORRECTION (Monday 24th)
Please see Jeff Hecht’s comment below for an important correction: Elsevier’s annual profits are “only” 60% of the figure originally cited. Which means we’d need to throw in Springer’s profits, too, in order to open-access everything. My bad — thanks for the correction, Jeff.
Why we do mass estimates
Mass estimates are a big deal in paleobiology. If you want to know how much an animal needed in terms of food, water, and oxygen, or how fast it could move, or how many offspring it could produce in a season, or something about its heat balance, or its population density, or the size of its brain relative to its body, then at some point you are going to need a mass estimate.
All that is true, but it’s also a bit bogus. The fact is, people like to know how big things are, and paleontologists are not immune to this desire. We have loads of ways to rationalize our basic curiosity about the bigness of extinct critters. And the figuring out part is both very cool and strangely satisfying. So let’s get on with it.
Two roads diverged
There are two basic modes for determining the mass of an extinct animal: allometric, and volumetric. Allometric methods rely on predictable mathematical relationships between body measurements and body mass. You measure a bunch of living critters, plot the results, find your regression line, and use that to estimate the masses of extinct things based on their measurements. Allometric methods have a couple of problems. One is that they are absolutely horrible for extrapolating to animals outside the size range of the modern sample, which ain’t so great for us sauropod workers. The other is that they’re pretty imprecise even within the size range of the modern sample, because real data are messy and there is often substantial scatter around the regression line, which if faithfully carried through the calculations produces large uncertainties in the output. The obvious conclusion is that anyone calculating extinct-animal masses by extrapolating an allometric regression ought to calculate the 95% confidence intervals (e.g. “Argentinosaurus massed 70000 kg, with a 95% confidence interval of 25000-140000 kg), but, oddly, no-one seems to do this.
Volumetric methods rely on creating a physical, digital, or mathematical model of an extinct animal, determining the volume of the model, multiplying by a scale factor to get the volume of the animal in life, and multiplying that by the presumed density of the living animal to get its mass. Volumetric methods have three problems: (1) many extinct vertebrates are known from insufficient material to make a good 3D model of the skeleton; (2) even if you have a complete skeleton, the method is very sensitive to how you articulate the bones–especially the ribcage–and the amount of flesh you decide to pack on, and there are few good guidelines for doing this correctly; and (3) relatively small changes in the scale factor of the model can produce big changes in the output, because mass goes with the cube of the linear measurement. If your scale factor is off by 10%, you mass will be off by 33% (1.1^3=1.33).
On the plus side, volumetric mass estimates are cheap and easy. You don’t need hundreds or thousands of measurements and body masses taken from living animals; you can do the whole thing in your kitchen or on your laptop in the space of an afternoon, or even less. In the old days you’d build a physical model, or buy a toy dinosaur, and use a sandbox or a dunk tank to measure the volume of sand or water that the model displaced, and go from there. Then in the 90s people started building digital 3D models of extinct animals and measuring the volumes of those.
But you don’t need a physical model or a dunk tank or even a laptop to do volumetric modeling. Thanks to a method called graphic double integration or GDI, which is explained in detail in the next section, you can go through the whole process with nothing more than pen and paper, although a computer helps.
Volumetric methods in general, and GDI in particular, have one more huge advantage over allometric methods: they’re more precise and more accurate. In the only published study that compares the accuracy of various methods on extant animals of known mass, Hurlburt (1999) found that GDI estimates were sometimes off by as much as 20%, but that allometric estimates were much worse, with several off by 90-100% and one off by more than 800%. GDI estimates were not only closer to the right answers, they also varied much less than allometric methods. On one hand, this is good news for GDI afficionados, since it is the cheapest and easiest of all the mass estimation methods out there. On the other hand, it should give us pause that on samples of known mass, the best available method can still be off by as much as a fifth even when working with complete bodies, including the flesh. We should account for every source of error that we can, and still treat our results with appropriate skepticism.
Graphic Double Integration
GDI was invented by Jerison (1973) to estimate the volumes of cranial endocasts. Hurlburt (1999) was the first to apply it to whole animals, and since then it has been used by Murray and Vickers-Rich (2004) for mihirungs and other extinct flightless birds, yours truly for small basal saurischians (Wedel 2007), Mike for Brachiosaurus and Giraffatitan (Taylor 2009), and probably many others that I’ve missed.
GDI is conceptually simple, and easy to do. Using orthogonal views of a life restoration of an extinct animal, you divide the body into slices, treat each slice as an ellipse whose dimensions are determined from two perspectives, compute the average cross-sectional area of each body part, multiply that by the length of the body part in question, and add up the results. Here’s a figure from Murray and Vickers-Rich (2004) that should clarify things:
One of the cool things about GDI is that it is not just easy to separate out the relative contributions of each body region (i.e., head, neck, torso, limbs) to the total body volume, it’s usually unavoidable. This not only lets you compare body volume distributions among animals, it also lets you tinker with assigning different densities to different body parts.
An Example: Plateosaurus
Naturally I’m not going to introduce GDI without taking it for a test drive, and given my proclivities, that test drive is naturally going to be on a sauropodomorph. All we need is an accurate reconstruction of the test subject from at least two directions, and preferably three. You could get these images in several ways. You could take photographs of physical models (or toy dinosaurs) from the front, side, and top–that could be a cool science fair project for the dino-obsessed youngster in your life. You could use the white-bones-on-black-silhouette skeletal reconstructions that have become the unofficial industry standard. You could also use orthogonal photographs of mounted skeletons, although you’d have to make sure that they were taken from far enough away to avoid introducing perspective effects.
For this example, I’m going to use the digital skeletal reconstruction of the GPIT1 individual of Plateosaurus published by virtual dino-wrangler and frequent SV-POW! commenter Heinrich Mallison (Mallison et al 2009, fig. 14). I’m using this skeleton for several reasons: it’s almost complete, very little distorted, and I trust that Heinrich has all the bits in the right places. I don’t know if the ribcage articulation is perfect but it looks reasonable, and as we saw last time that is a major consideration. Since Heinrich built the digital skeleton in digital space, he knows precisely how big each piece actually is, so for once we have scale bars we can trust. Finally, this skeleton is well known and has been used in other mass estimate studies, so when I’m done we’ll have some other values to compare with and some grist for discussion. (To avoid accidental bias, I’m not looking at those other estimates until I’ve done mine.)
Of course, this is just a skeleton, and for GDI I need the body outline with the flesh on. So I opened the image in GIMP (still free, still awesome) and drew on some flesh. Here we necessarily enter the realm of speculation and opinion. I stuck pretty close to the skeletal outline, with the only major departures being for the soft tissues ventral to the vertebrae in the neck and for the bulk of the hip muscles. As movie Boromir said, there are other paths we might take, and we’ll get to a couple of alternatives at the end of the post.
This third image is the one I used for actually taking measurements. You need to lop off the arms and legs and tote them up separately from the body axis. I also filled in the body outlines and got rid of the background so I wouldn’t have any distracting visual clutter when I was taking measurements. I took the measurements using the measuring tool in GIMP (compass icon in the toolbar), in orthogonal directions (i.e., straight up/down and left/right), at regular intervals–every 20 pixels in this case.
One thing you’ll have to decide is how many slices to make. Ideally you’d do one slice per pixel, and then your mathematical model would be fairly smooth. There are programs out there that will do this for you; if you have a 3D digital model you can just measure the voxels (= pixels cubed) directly, and even if all you have is 2D images there are programs that will crank the GDI math for you and measure every pixel-width slice (Motani 2001). But if you’re just rolling with GIMP and OpenOffice Calc (or Photoshop and Excel, or calipers and a calculator), you need to have enough slices to capture most of the information in the model without becoming unwieldy to measure and calculate. I usually go with 40-50 slices through the body axis and 9 or 10 per limb.
The area of a circle is pi*r^2, and the area of an ellipse is pi*r*R, where r and R are the radii of the minor and major axes. So enter the widths and heights of the body segments in pixels in two columns (we’ll call them A and B) in your spreadsheet, and create a third column with the function 3.14*A1*B1/4. Divide by four because the pixel counts you measured on the image are diameters and the formula requires radii. If you forget to do that, you are going to get some wacky numbers.
One obvious departure from reality is that the method assumes that all of the body segments of an animal have elliptical cross-sections, when that is often not exactly true. But it’s usually close enough for the coarse level of detail that any mass estimation method is going to provide, and if it’s really eating you, there are ways to deal with it without assuming elliptical cross-sections (Motani 2001).
For each body region, average the resulting areas of the individual slices and multiply the resulting average areas by the lengths of the body regions to get volumes. Remember to measure the lengths at right angles to your diameter measurements, even when the body part in question is curved, as is the tail of Heinrich’s Plateosaurus.
For sauropods you can usually treat the limbs as cylinders and just enter the lateral view diameter twice, unless you are fortunate enough to have fore and aft views. It’s not a perfect solution but it’s probably better than agonizing over the exact cross sectional shape of each limb segment, since that will be highly dependent on how much flesh you (or some other artist) put on the model, and the limbs contribute so little to the final result. For Plateosaurus I made the arm circular, the forearm and hand half as wide as tall, the thigh twice as long as wide, and the leg and foot round. Don’t forget to double the volumes of the limbs since they’re paired!
We’re not done, because so far all our measurements are in pixels (and pixels cubed). But already we know something cool, which is what proportion each part of the body contributes to the total volume. In my model based on Heinrich’s digital skeleton, segmented as shown above, the relative contributions are as follows:
- Head: 1%
- Neck: 3%
- Trunk: 70%
- Tail: 11%
- Forelimbs (pair): 3%
- Hindlimbs (pair): 12%
Already one of the great truths of volumetric mass estimates is revealed: we tend to notice the extremities first, but really it is the dimensions of the trunk that drive everything. You could double the size of any given extremity and the impact on the result would be noticeable, but small. Consequently, modeling the torso accurately is crucial, which is why we get worried about the preservation of ribs and the slop inherent in complex joints.
Scale factor
The 170 cm scale bar in Heinrich’s figure measures 292 pixels, or 0.582 cm per pixel. The volume of each body segment must be multiplied by 0.582 cubed to convert to cubic cm, and then divided by 1000 to convert to liters, which are the lingua franca of volumetric measurement. If you’re a math n00b, your function should look like this: volume in liters = volume in pixels*SF*SF*SF/1000, where SF is the scale factor in units of cm/pixel. Don’t screw up and use pixels/cm, or if you do, remember to divide by the scale factor instead of multiplying. Just keep track of your units and everything will come out right.
If you’re not working from an example as perfect as Heinrich’s digital (and digitally measured) skeleton, you’ll have to find something else to use for a scale bar. Something big and reasonably impervious to error is good. I like the femur, if nothing else is available. Any sort of multi-segment dimension like shoulder height or trunk length is going to be very sensitive to how much gloop someone thought should go between the bones. Total length is especially bad because it depends not only on the intervertebral spacing but also on the number of vertebrae, and even most well-known dinos do not have complete vertebral series.
Density
Finally, multiply the volume in liters by the assumed density to get the mass of each body segment. Lots of people just go with the density of water, 1.0 kg/L, which is the same as saying a specific gravity (SG) of 1. Depending on what kind of animal you’re talking about, that may be a little bit off or it may be fairly calamitous. Colbert (1962) found SGs of 0.81 and 0.89 for an extant lizard and croc, which means an SG of 1.0 is off by between 11% and 19%. Nineteen percent–almost a fifth! For birds, it’s even worse; Hazlehurst and Rayner (1992) found an SG of 0.73.
Now, scroll back up to the diagram of the giant moa, which had a mass of 257.5 kg “assuming a specific gravity of 1”. If the moa was as light as an extant bird–and its skeleton is highly pneumatic–then it might have had a mass of only 188 kg (257.5*0.73). Or perhaps its density was higher, like that of a lizard or a croc. Without a living moa to play with, we may never know. Two points here: first, the common assumption of whole-body densities of 1.0 is demonstrably incorrect* for many animals, and second, since it’s hard to be certain about the densities of extinct animals, maybe the best thing is to try the calculation with several densities and see what results we get. (My thoughts on the plausible densities of sauropods are here.)
* Does anyone know of actual published data indicating a density of 1.0 for a terrestrial vertebrate? Or is the oft-quoted “bodies have the same density as water” basically bunk? (Note: I’m not disputing that flesh has a density close to that of water, but bones are denser and lungs and air spaces are lighter, and I want to know the mean density of the whole organism.)
Back to Plateosaurus. Using the measurements and calculations presented above, the total volume of the restored animal is 636 liters. Here are the whole body masses (in kg) we get using several different densities:
- SG=1.0 (water), 636 kg
- SG=0.89 (reptile high), 566 kg
- SG=0.81 (reptile low), 515 kg
- SG=0.73 (bird), 464 kg
I got numbers. Now what?
I’m going to describe three possible things you could do with the results once you have them. In my opinion, two of them are the wrong the thing to do and one is the right thing to do.
DON’T mistake the result of your calculation for The Right Answer. You haven’t stumbled on any universal truth. Assuming you measured enough slices and didn’t screw up the math, you know the volume of a mathematical model of an organism. If you crank all the way through the method you will always get a result, but that result is only an estimate of the volume of the real animal the model was based on. There are numerous sources of error that could plague your results, including: incomplete skeletal material, poorly articulated bones, wrong scale factor, wrong density, wrong amount of soft tissue on the skeleton. I saved density and gloop for last because you can’t do much about them; here the strength of your estimate relies on educated guesses that could themselves be wrong. In short, you don’t even know how wrong your estimate might be.
Pretty dismal, eh?
DON’T assume that the results are meaningless because you don’t know the actual fatness or the density of the animal, or because your results don’t match what you expected or what someone else got. I see this a LOT in people that have just run their first phylogenetic analysis. “Why, I could get any result I wanted just by tinkering with the input!” Well, duh! Like I said, the method will always give you an answer, and it won’t tell you whether the answer is right or not. The greatest advantage of explicit methods like cladistics and GDI is that you know what the input is, and so does everyone else if you are honest about reporting it. So if someone disagrees with your character coding or with how much the belly sags on your model sauropod, you can have a constructive discussion and hopefully science as a whole gets closer to the right answer (even if we have no way of knowing if or when we arrive, and even if your pet hypothesis gets trampled along the way).
DO be appropriately skeptical of your own results without either accepting them as gospel or throwing them out as worthless. The fact that the answer changes as you vary the parameters is a feature, not a bug. Investigate a range of possibilities, report all of those results, and feel free to argue why you think some of the results are better than others. Give people enough information to replicate your results, and compare your results to those of other workers. Figure out where yours differ and why.
Try to think of more interesting things you could do with your results. Don Henderson went from digitally slicing critters (Henderson 1999) to investigating floating sauropods (Henderson 2004) to literally putting sauropods through their paces (Henderson 2006)–not to mention working on pterosaur flight and swimming giraffes and other cool stuff. I’m not saying you should run out and do those exact things, but rather that you’re more likely to come up with something interesting if you think about what you could do with your GDI results instead of treating them as an end in themselves.
How massive was GPIT1, really?
Beats me. I’m not the only one who has done a mass estimate based on that skeleton. Gunga et al. (2007) did not one but two volumetric mass estimates based on GPIT1, and Mallison (2010) did a whole series, and they published their models so we can see how they got there. (In fact, many of you have probably been reading this post in slack-jawed horror, wondering why I was ignoring those papers and redoing the mass estimate the hard way. Now you know!) I’m going to discuss the results of Gunga et al. (2007) first, and come back to Mallison (2010) at the end.
Here’s the “slender” model of Gunga et al. 2007 (their fig. 3):
and here’s their “robust” model (Gunga et al. 2007:fig. 4):
(These look a bit…inelegant, let’s say…because they are based on the way the physical skeleton is currently mounted; Heinrich’s model looks much nicer because of his virtual remount.)
For both mass estimates they used a density of 0.8, which I think is probably on the low end of the range for prosauropods but not beyond the bounds of possibility. They got a mass of 630 kg for the slender model and 912 kg for the robust one.
Their 630-kg estimate for the slender model is deceptively close to the upper end of my range; deceptive because their 630-kg estimate assumes a density of 0.8 and my 636-kg one assumes a density of 1.0. The volumes are more directly comparable: 636 L for mine, 790 L for their slender one, and 1140 L for their robust one. I think that’s pretty good correspondence, and the differences are easily explained. My version is even more skinnier than their slender version; I made it about as svelte as it could possibly have been. I did that deliberately, because it’s always possible to pack on more soft tissue but at some point the dimensions of the skeleton establish a lower bound for how voluminous a healthy (i.e., non-starving) animal could have been. The slender model of Gunga et al. (2007) looks healthier than mine, whereas their robust version looks, to my eye, downright corpulent. But not unrealistically so; fat animals are less common than skinny ones but they are out there to be found, at least in some times and places. It pays to remember that the mass of a single individual can fluctuate wildly depending on seasonal food availability and exercise level.
For GPIT1, I think something like 500 kg is probably a realistic lower bound and 900 kg is a realistic upper bound, and the actual mass of an average individual Plateosaurus of that size was somewhere in the middle. That’s a big range–900 kg is almost twice 500 kg. It’s hard to narrow down because I really don’t know how fleshy Plateosaurus was or what it’s density might have been, and I feel less comfortable making guesses because I’ve spent much less time working on prosauropods than on sauropods. If someone put a gun to my head, I’d say that in my opinion, a bulk somewhere between that of my model and the slender model of Gunga et al. is most believable, and a density of perhaps 0.85, for a result in the neighborhood of 600 kg. But those are opinions, not hypotheses, certainly not facts.
I’m happy to see that my results are pretty close to those of Mallison (2010), who got 740 L, which is also not far off from the slender model of Gunga et al. (2007). So we’ve had at least three independent attempts at this and gotten comparable results, which hopefully means we’re at least in the right ballpark (and pessimistically means we’re all making mistakes of equal magnitude!). Heinrich’s paper is a goldmine, with loads of interesting stuff on how the skeleton articulates, what poses the animal might have been capable of, and how varying the density of different body segments affects the estimated mass and center of mass. It’s a model study and I’d happily tell you all about it but you should really read it for yourself. Since it’s freely available (yay open access!), there’s no barrier to you doing so.
Conclusion
So: use GDI with caution, but do use it. It’s easy, it’s cool, it’s explicit, it will give you lots to think about and give us lots to talk about. Stay tuned for related posts in the not-too-distant future.
References
- Gunga, H.-C., Suthau, T., Bellmann, A., Friedrich, A., Schwanebeck, T., Stoinski, S., Trippel, T., Kirsch, K., Hellwich, O. 2007. Body mass estimations for Plateosaurus engelhardti using laser scanning and 3D reconstruction methods. Naturwissenschaften 94(8):623-630.
- Hazlehurst, G.A., and Rayner, J.M. 1992. Flight characteristics of Triassic and Jurassic Pterosauria: an appraisal based on wing shape. Paleobiology 18(4):447-463.
- Henderson, D.M. 1999. Estimating the mass and centers of mass of extinct animals by 3D mathematical slicing. Paleobiology 25:88-106.
- Henderson, D.M. 2004. Tipsy punters: sauropod dinosaur pneumaticity, buoyancy and aquatic habits. Proceedings: Biological Sciences 271 (Supplement):S180-S183.
- Henderson, D.M. 2006. Burly gaits: centers of mass, stability and the trackways of sauropod dinosaurs. Journal of Vertebrate Paleontology 26:907-921.
- Hurlburt, G. 1999. Comparison of body mass estimation techniques, using Recent reptiles and the pelycosaur Edaphosaurus boanerges. Journal of Vertebrate Paleontology 19:338–350.
- Jerison, H.J. 1973. Evolution of the Brain and Intelligence. Academic Press, New York, NY, 482 pp.
- Mallison, H., Hohloch, A., and Pfretzschner, H.-U. 2009. Mechanical digitizing for paleontology–new and improved techniques. Palaeontologica Electronica 12(2):4T, 41 pp.
- Mallison, H. 2010. The digital Plateosaurus I: Body mass, mass distribution, and posture assessed by using CAD and CAE on a digitally mounted complete skeleton. Palaeontologica Electroncia 13(2):8A, 26 pp.
- Motani, R. 2001. Estimating body mass from silhouettes: testing the assumption of elliptical body cross-sections. Paleobiology 27(4):735–750.
- Murray, P.F. and Vickers-Rich, P. 2004. Magnificent Mihirungs. Indiana University Press, Bloomington, IN, 410 pp.
- Taylor, M.P. 2009. A re-evaluation of Brachiosaurus altithorax Riggs 1903 (Dinosauria, Sauropoda) and its generic separation from Giraffatitan brancai (Janensch 1914). Journal of Vertebrate Paleontology 29(3):787-806.
- Wedel, M.J. 2007. What pneumaticity tells us about ‘‘prosauropods,’’ and vice versa. Special Papers in Palaeontology 77:207–222.
How big were the biggest sauropod trackmakers?
October 13, 2009
UPDATE December 3, 2009
I screwed up, seriously. Tony Thulborn writes in a comment below to correct several gross errors I made in the original post. He’s right on every count. I have no defense, and I am terribly sorry, both to Tony and to everyone who ever has or ever will read this post.
He is correct that the paper in question (Thulborn et al 1994) does discuss track length, not diameter, so my ranting about that below is not just immoderate, it’s completely undeserved. I don’t know what I was thinking. I did reread the paper before I wrote the post, but I got the two switched in my mind, and I assigned blame where none existed. In particular, it was grossly unfair of me to tar Tony’s careful work with the same brush I used to lament the confused hodgepodge of measurements reported in the media (not by scientists) for the Plagne tracks.
I am also sorry that I criticized the 1994 paper and implied that the work was incomplete. I was way out of line.
I regard this post as the most serious mistake in my professional career. I want very badly to somehow unmake it. I am adding corrections to the post below and striking out but not erasing my mistakes; they will stand as a reminder of my fallibility and a warning against being so high-handed and unfair in the future.
I’m sorry. I beg forgiveness from Tony, from all of our readers, and from the broader vertebrate paleontology community. Please forgive me.
–Mathew Wedel
You might have seen a story last week about some huge sauropod tracks discovered in Upper Jurassic deposits from the Jura plateau in France, near the town of Plagne. According to the news reports, the tracks are the largest ever discovered. Well, let’s see.
The Guardian (from which I stole the image above) says the prints are “up to 2 metres (6ft 6 in) in diameter”, but ScienceDaily says “up to 1.5 m in total diameter”. Not sure how ‘total diameter’ is different from regular diameter, but that’s science reporting for you. The BBC clarifies that, “the depressions are about 1.5m (4.9ft) wide”, which might be the key here (see below), but then mysteriously continues, “corresponding to animals that were more than 25m long and weighed about 30 tonnes.” I find it rather unlikely that a pes track 1.5 m wide indicates an animal only as big as Giraffatitan (hence this post).
So there’s some uncertainty with respect to the diameter of the tracks–half a meter of uncertainty, to be precise. But sauropod pes tracks are usually longer than wide, and a print 1.5 m wide might actually be 2 m long.
Not incidentally, Thulborn (1994) described some big sauropod tracks from the Broome Sandstone in Australia, with pes prints up to 1.5 m. Although the photos of the tracks are not as clear as one might wish, they do appear to show digit impressions and are probably not underprints. [See Tony Thulborn’s comment below regarding footprints vs underprints.]
I’ll feel a lot better about the Plagne tracks when the confusion about their dimensions is cleared up and when some evidence is presented that they also are not underprints. In any case, the only dimension with any orientation cited for the Plagne tracks is the 1.5 m width reported by the BBC, so we’ll go with that. So the Plagne tracks might only tie, but not beat, Thulborn’s tracks.
…Then again, Thulborn only said that the biggest tracks were up to 150 cm in diameter. What does that mean–length? Width? Are the tracks perfect circles? Does no one who works on giant sauropod tracks know how to report measurements? These questions will have to wait, because despite the passing of a decade and a half, the world’s (possibly second-) biggest footprints–from anything! ever!–have not yet merited a follow-up paper. [Absolutely wrong and unfair; please see the apology at top and Tony Thulborn’s comment below.]
Nevertheless, for the remainder of this post we’ll accept that at least some sauropods were leaving pes prints a meter and a half wide. Naturally, it occurs to me to wonder how big those sauropods were. I don’t know of any studies that attempt to rigorously estimate the size of a sauropod from its tracks or vice versa, so in the finest tradition of the internet in general and blogging in particular, I’m going to wing it.
How Big?
First we need some actual measurements of sauropod feet. When Mike and I were in Berlin last fall (gosh, almost a year ago!), we measured the feet (pedes) of the mounted Giraffatitan and Diplodocus for this very purpose. The Diplodocus feet were both 59 cm wide, and the Giraffatitan feet were 68 and 73 cm wide. The Diplodocus feet are trustworthy, the Giraffatitan bits less so. Unfortunately, the pes is the second part of the skeleton of Giraffatitan that is less well known than I would like (after the cervico-dorsal neural spines). The reconstructed feet look believable, but “believability” is hard to calibrate and probably a poor predictor of reality when working with sauropods.
One thing I won’t go into is that Giraffatitan (HM SII) probably massed more than twice what Diplodocus (CM 84/94) did, but on the other hand G. bore more of its weight on its forelimbs. It would be interesting to calculate whether the shifted center of mass would be enough to even out the pressure exerted by the hindfeet of the two animals; Don Henderson may have done this already.
Anyway, let’s say for the sake of argument that the hindfeet of the mounted Giraffatitan are sized about right. The next problem is figuring out how much soft tissue surrounded the bones. In other words, how much wider was the fleshy foot–deformed under load!–than the articulated pes skeleton? I am of two minds on this. On one hand, sauropods probaby had a big heel pad like that of elephants, and it seems reasonable that the heel pad plus the normal skin, fat, and muscle might have expanded the fleshy foot considerably beyond the edges of the bones. On the other hand, the pedal skeleton is widest across the distal ends of the phalanges, and in well-preserved tracks like the one below the fleshy foot is clearly not much wider than that (thanks, Brian, for the photo!).
Bear in mind that a liberal estimate of soft tissue will give a conservative estimate of the animal’s size, and vice versa. Looking at the AMNH track pictured above, it seems that the width added by soft tissue could possibly be as little as 5% of the width of the pes skeleton. Skewing hard in the opposite direction, an additional 20% or more does not seem unreasonable for other animals (keep in mind this would only be 10% on either side of the foot). Using those numbers, Diplodocus (CM 84/94) would have left tracks as narrow as 62 cm or as wide as 71 cm. For Giraffatitan (HM SII) I’ll use the wider of the two pes measurements, because the foot is expected to deform under load and the 73 cm wide foot looked just as believable as the 68 cm foot (for whatever that’s worth). Applying the same scale factors (1.05 and 1.20) yields a pes track width of 77-88 cm.
These numbers are like pieces of legislation, or sausages: the results are more pleasant to contemplate than the process that produced them. They’re ugly, and possibly wrong. But they give us someplace to start from in considering the possible sizes of the biggest sauropod trackmakers. Something with a hindfoot track 1.5 meters wide would be, using these numbers, conservatively more than twice as big as (2.11x) the mounted Carnegie Diplodocus or 170% the size of the mounted Berlin Giraffatitan. That’s right into Amphicoelias fragillimus/Bruhathkayosaurus territory. The diplo-Diplodocus would have been 150 feet long, and even assuming a very conservative 10 tons for Vanilla Dippy (14,000L x 0.7 kg/L = 9800 kg), would have had a mass of 94 metric tons (104 short tons). The monster Giraffatitan-like critter would have been “only” 130 feet long, but with a 14.5 meter neck and a mass of 113 metric tons (125 short tons; starting from a conservative 23 metric tons for HM SII).
Keep in mind that these are conservative estimates, for both the size of the trackmakers and the masses of the “known” critters. If we use the conservative soft tissue/liberal animal size numbers, the makers of the 1.5 meter tracks were 2.4 times as big as the mounted Diplodocus or almost twice as big as the mounted Giraffatitan, in which case masses in the blue whale range of 150-200 tons become not just probable but inevitable.
Mike measuring Giraffatitan's naughty bits. Check out the hindfeet. Also note the sauropod vertebrae in the background--titular obligation fulfilled!
Too Big?
Going the other way, I can think of only a handful of ways that the “conservative” trackmaker estimates might still be too big:
First, the pes of Giraffatitan might have been bigger than reconstructed in the mounted skeleton. Looking at the photo above, I can image a pes 10% wider that wouldn’t do any violence to the “believability” of the mount. That would make the estimated track of HM SII 10% wider and the estimated size of the HM-SII-on-steroids correspondingly smaller. But that wouldn’t affect the scaled up Diplodocus estimate, and the feet of Giraffatitan would have to be a LOT bigger than reconstructed to avoid the reality of an animal at least half again as big as HM SII.
Second, the amount of soft tissue might have been greater than even the liberal soft tissue/conservative size estimate allows. But I think that piling on 20% more soft tissue than bone is already beyond what most well-preserved tracks would justify, so I’m not worried on that score. (What scares me more is the thought that the conservative estimates are too conservative, and the real trackmakers even bigger.)
Third, I suppose it is possible that sauropod feet scaled allometrically with size and that big sauropods left disproportionately big tracks. I’m also not worried about this. For one thing, when they’ve been measured sauropod appendicular elements tend to scale isometrically, and it would be weird if feet were the undiscovered exception. For another, the allometric oversizing of the feet would have to be pronounced to make much of a dent in the estimated size of the trackmakers. I find the idea of 100-ton sauropods more palatable than the idea of 70-ton sauropods with clown shoes.
Fourth, the meta-point, what if the Broome and Plagne tracks are underprints? [Please see Tony Thulborn’s comment below regarding footprints and underprints.] I’ve seen some tracks-with-undertracks where the magnification of the apparent track size in the undertracks was just staggering. The Broom tracks have gotten one brief note and The Plagne tracks have not been formally described at all, so all of this noodling around about trackmaker size could go right out the window. Mind you, I don’t have any evidence that the either set are underprints, and at least for the Broome tracks the evidence seems to go the other way, I’m just trying to cover all possible bases.
Conclusions
So. Sauropods got big. As usual, we can’t tell exactly how big. Any one individual can leave many tracks but only one skeleton, so we might expect the track record to sample the gigapods more effectively than the skeletal record. Interestingly, the largest fragmentary skeletal remains (i.e., Amphicoelias and Bruhathkayosaurus, assuming they’re legit) and the largest tracks (i.e., Plagne and Broome) point to animals of roughly the same size.
It’s also weird that some of the biggest contenders in both categories have been so little published. I mean, if I had access to Bruhathkayosaurus or a track 1.5 m wide, you can bet that I’d be dropping everything else like a bad habit until I had the gigapod evidence properly written up. What gives? [The implication that the Broome tracks were not properly written up is both wrong and unfair; please see the apology at top.]
Finally, IF the biggest fragmentary gigapods and the biggest tracks are faithful indicators of body size, they suggest that gigapods were broadly distributed in space and time (and probably phylogeny). I wonder if these were representatives of giga-taxa, or just extremely large individuals of otherwise vanilla sauropods. Your thoughts are welcome.
Epilogue: What About Breviparopus?
It’s past time someone set the record straight about damn Breviparopus. The oft-quoted track length of 115 cm is (A) much smaller than either the Broome or Plagne tracks, and (B) the combined length of the manus and pes prints together; I know, I looked it up (Dutuit and Ouazzou 1980). Why anyone would report track “length” that way is beyond me, but what is more mysterious is why anyone was taken in by it, since the width of 50 cm (pathetic!) is usually quoted along with the 115 cm “length”, indicating an animal smaller than Vanilla Diplodocus (track length is much more likely than width to get distorted by foot motions during locomotion) [This part is wrong; see the update below.]. But people keep stumbling on crap (thanks, Guiness book!) about how at 157 feet long (determined how, exactly?) Breviparopus was possibly the largest critter to walk the planet. Puh-leeze. If there’s one fact that everyone ought to know about Breviparopus, it’s that it was smaller than the big mounted sauropods at museums worldwide. The only thing super-sized about it is the cloud of ignorance, confusion, and hype that clings to the name like cheap perfume. Here’s the Wikipedia article if you want to do some much-needed revising.
UPDATE (Nov 17 2009): The width of the Breviparopus pes tracks is 90 cm, not 50 cm. The story of the 50 cm number is typically convoluted. Many thanks to Nima Sassani for doing the detective work. Rather than steal his thunder, I’ll point you to his explanation here. Point A above is still valid: Breviparopus was dinky compared to the Broome and Plagne trackmakers.
Parting Shot
You know I ain’t gonna raise the specter of a beast 1.7 times the size of HM SII without throwing in a photoshopped giant cervical. So here you go: me with C8 of Giraffatitan blown up to 170% (the vert, not me). Compare to unmodified original here.
References
- Dutuit, J.M., and A. Ouazzou. 1980. Découverte d’une piste de Dinosaure sauropode sur le site d’empreintes de Demnat (Haut-Atlas marocain). Mémoires de la Société Géologique de France, Nouvelle Série 139:95-102.
- Thulborn, R.A., T.Hamley and P.Foulkes. 1994. Preliminary report on sauropod dinosaur tracks in the Broome Sandstone (Lower Cretaceous) of Western Australia. Gaia 10:85-96.
How tallweird was Sauroposeidon?
August 7, 2009
In an email, Vladimir Socha drew my attention to the fact that Tom Holtz’s dinosaur encyclopaedia estimates the maximum height of Sauroposeidon as 20 meters plus, and asked whether that was really possible. Here’s what Tom actually wrote: “Sauroposeidon was one of the largest of all dinosaurs. At perhaps 98 to 107 feet (30 to 32.5 meters) long and weighing 70 to 80 tons […] Sauroposeidon would have been the tallest of all dinosaurs. […] If it could crane its neck up, it might have been able to hold its head 66 to 69 feet (20 to 21 meters) high or more” (Holtz and Rey 2007:207). Vladimir was understandably skeptical. But can it be true?
Wedel and Cifelli (2005: fig. 15) shows Matt’s best skeletal reconstruction of Sauroposeidon, with Boring Old Brachiosaurus and a human for scale:
Sauroposeidon with Boring Old Brachiosaurus and human for scale and 20 m height indicated. Lightly modified from Wedel and Cifelli (2005: fig. 15)
Amazingly, those dummies didn’t include an actual scalebar; but apparently the human figure is 1.8 m tall, so by measuring pixels and cross-scaling, I determined that in this image, Sauroposeidon is a mere 13.43 m tall. I took the liberty of adding in a marker for the 20 m height proposed by Holtz, and as things stand you’d have to say that it doesn’t look probable.
But let’s see what we can do. We’ll begin with the classic brachiosaur skeleton of Paul (1988), which shows the well represented species Brachioaurus brancai:
Brachiosaurus brancai skeletal reconstruction in left lateral view. From Paul (1988:fig. 1)
(Some other time, we should take a moment to discuss the differences between this and the Wedel brachiosaur reconstruction; but it will not be this day.)
This reconstruction is in a nice erect-necked posture which, in light of our own recent paper, is probably not too extreme. Since all the neural arches and processes are missing from the only known posterior cervicals of this species, we don’t know how much flexibility they allowed, and so in light of how the rest of the animal is built (high shoulders and all) it seems reasonable to allow a lot of extension at the base of the neck. So let’s assume that the pose offered by Paul is correct. By measuring my scan of that figure, and I see that the 2.13 m humerus is 306 pixels long. The entire reconstruction, from tip of cranial crest down to forefoot, is 1999 pixels tall, which is 1999/306 = 6.53 times as long as the humerus, which scales to 6.53*2.13 = 13.91 m — a little taller than Sauroposeidon (not Brachiosaurus) in Matt’s reconstruction, which seems about right if we imgine Matt’s Brachiosaurus raising its neck into a Paul-compliant posture.
Now Paul’s reconstruction is based on the Berlin mounted skeleton HMN S II. Cervical 8 is very well preserved in that animal, and has a centrum length of 98 cm (Janensch 1950a:44). By contrast, the centrum of C8 of Sauroposeidon OMNH 53062 (the only known specimen) is 125 cm long (Wedel et al. 2000a: 110). So if Sauroposeidon is merely an elongated Brachiosaurus brancai, then it’s 125/98 = 1.28 times as long and tall, which would be 17.74 m.
But wait: it seems that Sauroposeidon is to Brachiosaurus brancai as Barosaurus is to Diplodocus — similar overall but more elongate. And it turns out that Barosaurus has at least 16, maybe 17 cervicals (McIntosh 2005:45) compared with Diplodocus‘s 15. So maybe Sauroposeidon also added cervicals from the brachiosaur base-state — in fact, that would hardly be surprising given that Brachiosaurus brancai has so few cervicals for a long-neck: 13, compared with 15 in most diplodocids, 16 or 17 in Barosaurus, and 19 in Mamenchisaurus. If you reconstruct Sauroposeidon with two more C8-like cervicals in the middle of the neck, that adds 2*125 = 250 cm, which would give us a total height of 17.74+2.5 = 20.24 m.
So I don’t think Tom Holtz’s estimate is completely unrealistic, even for the one Sauroposeidon specimen we have now — and remember that the chances of that individual being the biggest that species got are vanishingly small.
On the other hand, maybe Sauropodseidon‘s neck was the only part of it that was elongated in comparison to Brachiosaurus brancai — maybe its forelimbs were no longer than those of its cousin, so that only the neck elongation contributed to greater height. And maybe it had no additional cervicals, so its neck was “only” 1.28 times as long as that of Brachiosaurus brancai — 1.28*8.5 = 10.88 m, which is 2.38 m longer; so the total height would be 13.91+2.38 = 16.29 m (assuming the additional neck length was vertical). And maybe the neck couldn’t get very close to vertical, so that the true height was lower still.
All of this just goes to show the perils of reconstructing an animal based only on a sequence of four cervicals. (Reconstructing on the basis of a single partial mid-to-posterior dorsal, on the other hand, is a much more exact science.)
Finally: Matt’s reconstruction of Sauroposeidon is really rather conservative, and looks very much like a scaled-up vanilla brachiosaur. Just to see how it looks, I’ve made a reconstruction of the putative (and very possible) elongated, attenuated version of Sauroposeidon, showing the legs and cervicals 28% longer than in B. brancai, and with two additional cervicals. I made this by subjecting Greg Paul’s 1988 brachiosaur to all sorts of horrible and half-arsed distortions, so apologies to Greg. But remember, folks: this is just as likely correct as Matt’s version!
A different view of Sauroposeidon, based on elongation of the cervicals and legs of Brachiosaurus brancai and the insertion of two additional cervicals. Heavily and carelessly modified from Paul (1988: fig. 1)
References
- Holtz, Thomas R., Jr., and Luis Rey. 2007. Dinosaurs: The Most Complete, Up-to-Date Encyclopedia for Dinosaur Lovers of All Ages. Random House, New York. 428 pages.
- Janensch, Werner. 1950. Die Wirbelsaule von Brachiosaurus brancai. Palaeontographica (Suppl. 7) 3: 27-93.
- McIntosh, John S. 2005. The Genus Barosaurus Marsh (Sauropoda, Diplodocidae). pp. 38-77 in Virginia Tidwell and Ken Carpenter (eds.), Thunder Lizards: the Sauropodomorph Dinosaurs. Indiana University Press, Bloomington, Indiana. 495 pages.
- Paul, Gregory S. 1988. The brachiosaur giants of the Morrison and Tendaguru with a description of a new subgenus, Giraffatitan, and a comparison of the world’s largest dinosaurs. Hunteria 2 (3): 1-14.
- Wedel, Mathew J., and Richard L. Cifelli. 2005. Sauroposeidon: Oklahoma’s Native Giant. Oklahoma Geology Notes 65 (2): 40-57.
- Wedel, Mathew J., Richard L. Cifelli and R. Kent Sanders. 2000a. Sauroposeidon proteles, a new sauropod from the Early Cretaceous of Oklahoma. Journal of Vertebrate Paleontology 20(1): 109-114.
- Wedel, Mathew J., Richard L. Cifelli and R. Kent Sanders. 2000b. Osteology, paleobiology, and relationships of the sauropod dinosaur Sauroposeidon. Acta Palaeontologica Polonica 45(4): 343-388.
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ASP target of opportunity
July 20, 2009
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:
(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:
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?
NHM 46870 Strikes Back: ASP
July 18, 2009
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:
- external traces: Wedel (2005, 2007)
- internal complexity: Wedel et al. (2000a, 2000b), Wedel (2003b)
- bone/air ratio: Wedel (2005)
- distribution in the body: Wedel (2003a, 2006, 2009)
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.
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.
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.
References
- Cubo, J., and Casinos, A. 2000. Incidence and mechanical significance of pneumatization in the long bones of birds. Zoological Journal of the Linnean Society 130: 499–510.
- Currey, J. D., and Alexander, R. McN. 1985. The thickness of the walls of tubular bones. Journal of Zoology 206:453–468.
- Farke, A. A. 2007. Morphology, constraints, and scaling of frontal sinuses in the hartebeest, Alcelaphus buselaphus (Mammalia: Artiodactlya, Bovidae). Journal of Morphology 268:243-253.
- Naish, D., Martill, D. M., Cooper, D. & Stevens, K. A. 2004. Europe’s largest dinosaur? A giant brachiosaurid cervical vertebra from the Wessex Formation (Early Cretaceous) of southern England. Cretaceous Research 25:787-795.
- O’Connor, P.M. 2004. Pulmonary pneumaticity in the postcranial skeleton of extant Aves: a case study examining Anseriformes. Journal of Morphology 261:141-161.
- O’Connor, P. M. 2009. Evolution of archosaurian body plans: Skeletal adaptations of an air-sac-based breathing apparatus in birds and other archosaurs. Journal of Experimental Zoology DOI: 10.1002/jez.548
- Schwarz D, Fritsch G. 2006. Pneumatic structures in the cervical vertebrae of the Late Jurassic Tendaguru sauropods Brachiosaurus brancai and Dicraeosaurus. Eclogae Geologicae Helvetiae 99:65–78.
- Woodward, H. 2005. Bone histology of the titanosaurid sauropod Alamosaurus sanjuanensis from the Javelina Formation, Texas. Journal of Vertebrate Paleontology 25 (Supplement to No. 3):132A.
Sauropod Vertebra Picture of the Week 
