This was an interesting exercise. It was my first time generating a poster to be delivered at a conference since 2006. Scientific communication has evolved a lot in the intervening decade, which spans a full half of my research career to date. So I had a chance to take the principles that I say that I admire and try to put them into practice.

It helped that I wasn’t working alone. Jann and Brian both provided strong, simple images to help tell the story, and Mike and I were batting ideas back and forth, deciding on what we could safely leave out of our posters. Abstracts were the first to go, literature cited and acknowledgments were next. We both had the ambition of cutting the text down to just figure captions. Mike nailed that goal, but my poster ended up being slightly more narrative. I’m cool with that – it’s hardly text-heavy, especially compared with most of my efforts from back when. Check out the text-zilla I presented at SVP back in 2006, which is available on FigShare here. I am happier to see, looking back, that I’d done an almost purely image-and-caption poster, with no abstract and no lit cited, as early as 1999, with Kent Sanders as coauthor and primary art-generator – that one is also on FigShare.

I took 8.5×11 color printouts of both my poster and Mike’s, and we ended up passing out most of them to people as we had conversations about our work. That turned out to be extremely useful – I had a 30-minute conversation about my poster at a coffee break the day before the posters even went up, precisely because I had a copy of it to hand to someone else. Like Mike, I found that presenting a poster resulted in more and better conversations than giving a talk. And it was the most personally relaxing SVPCA I’ve ever been to, because I wasn’t staying up late every night finishing or practicing my talk.

I have a lot of stuff to say about the conference, the field trip, the citability of abstracts and posters (TL;DR: I’m for it), and so on, but unfortunately no time right now. I’m just popping in to get this posted while it’s still fresh. Like Mike’s poster, this one is now published alongside my team’s abstract on PeerJ PrePrints.

I will hopefully have much more to say about the content in the future. This is a project that Jann, Brian, and I first dreamed up over a decade ago, when we were grad students at Berkeley. Mike provided the impetus for us to get it moving again, and kindly stepped aside when I basically hijacked his related but somewhat different take on ontogeny and serial homology. When my fall teaching is over, I’m hoping that the four of us can take all of this, along with additional examples found by Mike that didn’t make it into this presentation, and shape it into a manuscript. I’ll keep you posted on that. In the meantime, the comment field is open. For some related, previously-published posts, see this one for the baby sauropod verts, this one for CM 555, and this one for Plateosaurus.

Flying over Baffin Island on the way home.

And finally, since I didn’t put them into the poster itself, below are the full bibliographic references. Although we didn’t mention it in the poster, the shell apex theory for inferring the larval habits of snails was first articulated by G. Thorson in 1950, which is referenced in full here.

Literature Cited

Plateosaurus is comical

September 5, 2013

Back in 2008, Matt and I were at the Museum Für Naturkunde Berlin. We spent some time down in the collections, where we were particularly pleased to see the much-admir’d C8 of Giraffatitan‘s paralectotype, MB.R.2181 (previously known as HMN SII).

While we were down there, we found a C8 from Plateosaurus, too, so we put that next to the Giraffatitan vertebra and shot them together:


I’m just sayin’, is all.

Note: after having written this post, I now see that I wrote an essentially identical one, with an essentially identical image, earlier this year. My memory is definitely going. Oh well: since I’ve written this, I may as well post it anyway.

Plateosaurus is pathetic

January 16, 2013


This photograph is of what I consider the closest thing to the Platonic Ideal sauropod vertebra: it’s the eighth cervical of our old friend the Giraffatitan brancai paralectotype MB.R.2181. (previously known as “Brachiosaurusbrancai HM S II — yes, it’s changed genus and specimen number, both recently, but independently.)

And if you look very carefully, down at the bottom, you can see the same vertebra, C8, of the prosauropod Plateosaurus. Pfft.

This photo was taken down in the basement of the Museum für Naturkunde Berlin, on the same 2008 trip where Matt took the “Mike in Love” photo from two days ago. For anyone who didn’t recognise the specific vertebra I was in love with in that picture, shame on you! It is of course our old friend the ?8th dorsal vertebra of the same specimen, which we’ve discussed in detail here on account of its unique spinoparapophyseal laminae, its unexpectedly missing infradiapophyseal lamina and its bizarre perforate anterior centroparapophyseal laminae.

We’re off to Oxford next week for SVPCA, so things may be quiet around here for a few days. Catch you on the flip side.

Plateosaurus trossingensis AMNH 6810 sacrum and pelvis in left dorsolateral view

We’ve shown a lot of sauropod sacra around here lately (for example here, here, and here), so here’s a little look back down the tree.

You haven’t heard from me much lately because I’ve been busy teaching anatomy. Still, I get to help people dissect for a living, so I can’t complain.

Further bulletins as events warrant.

Plateosaurus engelhardti (originally P. trossingensis) SMNS 13200 cervical vertebrae 3-8 in left lateral view. C8 is roughly 15 cm long.

In the recent post on serial variation in sauropod cervicals, I wrote:

Even in ‘adult’ sauropods like the big mounted Apatosaurus and Diplodocus skeletons, the anterior cervicals are less complex than the posterior ones. Compared to posterior cervicals, anterior cervicals tend to have simpler pneumatic fossae and foramina, fewer laminae, and unsplit rather than bifid spines. In all of these things the anterior cervicals are similar to those of juveniles of the same taxa, and to those of adults of more basal taxa. This is also true in prosauropods–in Plateosaurus, the full complement of vertebral laminae is not present until about halfway down the neck.

I was working from memory there and actually understated things a bit. Plateosaurus presacral vertebrae don’t have well-developed spinal laminae, but they do eventually get the four major diapophyseal laminae–the anterior centrodiapophyseal lamina (ACDL), posterior centrodiapophyseal lamina (PCDL), prezygodiapophyseal lamina (PRDL), and postzygodiapophyseal lamina (PODL–please see the lamina tutorial if you need a refresher on these and the other 15 commonly identified laminae). But they aren’t all present halfway down the neck–the ACDL doesn’t really show up until the cervicodorsal transition. The other three kick in sequentially down the neck, as shown in the above image. I think that’s pretty cool, that you get different character states expressed at different points along the neck, in one individual organism, at one time. And possibly also at different times–in sauropods, the anterior cervicals tend to look more ‘juvenile’ or ‘primitive’, even in adult animals, so all of the cervicals go through a juvenile stage, but not all of them grow out of it. I don’t know if there’s a word for that–some kind of serial heterochronotopomorphy or the like–but hopefully someone will enlighten me.

I took the original photo in the collections at the Staatliches Museum für Naturkunde Stuttgart in the spring of 2004. Markus Moser and Rainer Schoch were wonderful hosts during my visit. Mike did all the work of turning the raw photo into a figure, so thanks to him for getting this off my hard drive and out into the world.

UPDATE April 16, 2012: The paper is officially published now. I’ve updated the citation and link below accordingly.

More new goodies:

Yates, A.M., Wedel, M.J., and Bonnan, M.F. 2012. The early evolution of postcranial skeletal pneumaticity in sauropodomorph dinosaurs. Acta Palaeontologica Polonica 57(1):85-100. doi:

This is only kinda sorta published. The accepted manuscript is now posted on the APP website, and it has a DOI, but it’s not formatted or available in print yet. But after discussing it amongst ourselves, we authors agreed that (1) the paper is globally available and it’s silly to pretend otherwise, (2) there are no nomenclatural ramifications of that fact, and (3) we’re tired of not being able to talk about this stuff. So we’re gonna, starting…now.

A brief tale of Serendipity in Science (TM):

Back in 2004 I was in my third year of grad school at Berkeley. My fellow grad student, Brian Kraatz, gave me a heads up about the 19th International Congress of Zoology coming up in Beijing. Attendees could submit 500-word abstracts or 2000-word short papers. I didn’t plan on doing either one, until the night before they were due, when I changed my mind and wrote almost all of what would become this paper in a single six-hour session (don’t be too impressed; I’ve been trying to replicate that feat for seven years with no success).

That summer, I met up with Brian in Beijing a week before the congress, and we spent the extra time working in the collections of the Institute of Vertebrate Paleontology and Paleoanthropology (IVPP). Paul Barrett was there, working on prosauropods, and he and I had some long and fascinating conversations. We also gave our talks in the same session at the congress. Paul must have decided I was not a complete moron because he invited me to give a talk in the basal sauropodomorph symposium at SVP in 2005.

A brief aside: many of the animals I grew up calling prosauropods ended up outside of the monophyletic Prosauropoda that is anchored on Plateosaurus. Some are now basal sauropods, some are closer to sauropods than to Plateosaurus but outside of Sauropoda, and some are outside of Prosauropoda + Sauropoda. The phylogenetically correct term encompassing all of the nonsauropods is  ‘basal sauropodomorphs’, and it means roughly what ‘prosauropods’ did until a decade or so ago. I often slip into informally using ‘prosauropods’, but I try to remember to put the term in quotes so as not to mislead anyone.

I had been to England in 2004 and 2005 and seen the putatively pneumatic vertebrae of Erythrosuchus and what was then known as Thecodontosaurus caducus (and is currently trading under the name Pantydraco caducus for reasons that it would be otiose, for the moment, to rehearse)–and, not incidentally, had finally met Mike in person, although we’d been corresponding since 2000. I’d also been to Stuttgart primarily to see the appendicular material of Janenschia and ended up spending some quality time with Plateosaurus. (Since the theme here is serendipity, note that the Janenschia work–my raison d’etre for going to Germany–died on the table, whereas I’ve now been an author on three ‘prosauropod’ papers and have more in the works. Weird!)

Anyway, with all of that accidental experience with ‘prosauropods’ and other interesting critters like Erythrosuchus, I found that I actually had something to say in 2005 SVP symposium. I titled my talk, ‘What pneumaticity tells us about “prosauropods”, and vice versa’, and it turned into the 2007 paper of the same title.

None of this would have happened if Brian hadn’t hounded me about going to Beijing, and if I hadn’t ended up talking so much with Paul on that trip, and if I hadn’t finished up with Janenschia on my first day in Stuttgart and spent the rest of the week playing with Plateosaurus. And so on. Science is unpredictable, especially for scientists.

When I sent around the PDF of the paper to friends and colleagues, I included this quip: “Were prosauropods pneumatic? The fossils don’t say. Somehow I stretched that out to 16 pages.” Mike claims that because of this quip he’s never been able to take that paper seriously. But it is my favorite among my solo efforts. It includes loads of stuff on the origins of air sacs and pneumaticity that I wasn’t able to get into my earlier papers, either because it wasn’t directly relevant or because some reviewer forced me to excise it.


Almost immediately after the paper came out, Adam Yates and Matt Bonnan went and found roughly a zillion pneumatic ‘prosauropods’, which was a bit embarrassing since I’d just concluded that the evidence for ‘prosauropod’ pneumaticity was thin to nonexistent. So it is a damn good thing for me that I was already on friendly terms with both of them, because instead of taking the opportunity to smack me down, they invited me on board. Which led to Adam’s talk at SVP in Bristol in 2009, and to the new paper.

And actually, the depth of my incorrectness was even greater than I had thought. I reckon that literally millions of people have seen the mounted Plateosaurus skeleton in the AMNH, and any of them who have looked closely have seen this:

(Click for full size, unlabeled version.)

You see the problem here, I’m sure: the semi-big, semi-obvious fossa divided by an accessory lamina, not consistent with a muscle attachment point or fat pad or cartilage or infection, but very consistent in both form and location with the pneumatic fossae of other, more derived sauropodomorphs. On the lateral face of the vertebra, probably seen by millions, obvious to anyone who cares to look. A pneumatic prosauropod, in other words, right out in public for decades and decades (this time I don’t have to use the scare quotes because Plateosaurus actually IS a prosauropod sensu stricto). I didn’t even notice the first time I visited the AMNH back in 2006. I took the above photos, which are the basis for Figure 4 in the paper, in 2009.

So: ‘prosauropods’ were pneumatic. Some of them. A little bit. If you’d like to know more, please read the paper–it’s free.

Finally, a big thank-you to Adam and Matt for inviting me to be part of this. I think it’s pretty cool stuff, and I’m sure I’ll have more to say about it in the future. They might too–you should be reading their blogs, Dracovenator and Jurassic Journeys, anyway.

We’re still not done with Brontomerus, by the way. If nothing else, there’s the long-overdue post on how sauropod ilia change (or rather fail to change) through ontogeny. But that’s something we’ll have to get back to next week. Stay tuned.

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.


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.


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.