I have a new paper out:
Update June 6, 2012: the final version was formally published yesterday, so the rest of this paragraph is of historical interest only. Like Yates et al. on prosauropod pneumaticity, it is “out” in the sense that the manuscript has been through peer review, has been accepted for publication, and is freely available online at Acta Palaeontologica Polonica. Technically it is “in press” and not published yet, but all that formal publication will change is to make a prettier version of the paper available. All of the content is available now, and the paper doesn’t include any of those pesky nomenclatural acts, and so, as with the prosauropod pneumaticity paper, I don’t see any reason to pretend it doesn’t exist. Think of the accepted manuscript as the caterpillar to the published version’s butterfly: different look, but same genome.
This one came about because last summer I read a review of Richard Dawkins’s book, The Greatest Show on Earth: The Evidence for Evolution. The review mentioned that the book includes a lengthy discussion of the recurrent laryngeal nerve (RLN) in the giraffe, which is a spectacularly dumb piece of engineering and therefore great evidence against intelligent design creationism. It wasn’t the first time I’d heard of the RLN, of course. It’s one of the touchstones of both human anatomy and evolutionary biology; anatomy because of its clinical importance in thyroid surgery, known for more than two millennia, and evolutionary biology because it is such a great example of a developmental constraint. (Dawkins’s coverage of all of this is great, BTW, and you should read the book.)
No, the reason the book review inspired me to write the paper was not because the RLN was new to me, but because it was overly familiar. It is a cool piece of anatomy, and its fame is justly deserved–but I am sick and tired of seeing the stinkin’ giraffe trotted out as the ultimate example of dumb design. My beloved sauropods were way dumber, and it’s time they got some credit.
But first, let’s talk about that nerve, and how it got to be there.
No necks for sex? How about no necks for anybody!
Embryos are weird. When you were just a month old (counting from fertilization), you had a set of pharyngeal arches that didn’t look radically different from those of a primitive fish. These started out quite small, tucked up underneath your comparatively immense brain, and each pharyngeal arch was served by a loop of artery called an aortic arch. What we call the arch of the aorta in an adult human is a remnant of just one of these embryonic aortic arches, and as you’ve no doubt noticed, it’s down in your chest, not tucked up next to your brain. When you were in the embryonic stages I’m talking about, you didn’t yet have a neck, so your brain, pharyngeal arches, aortic arches, and the upper parts of your digestive system were all smooshed together at your front end.
One thing you did have at that stage was a reasonably complete peripheral nervous system. The nerve cell bodies in and near your central nervous system sent out axons into the rest of your body, including your extremities. Many of these axons did not persist; they failed to find innervation targets and their parent neurons died. Imagine your embryonic central nervous system sending out a starburst of axons in all directions, and some of those axons finding targets and persisting, and others failing and dying back. So the architecture of your nervous system is the result of a process of selection in which only some cells were successful.
Crucially, this radiation and die-off of axons happened very early in development, when a lot of what would become your guts was still hanging under your proportionally immense brain like the gondola on a blimp. This brings us to the recurrent laryngeal nerve.
Going back the way we came
The fates of your embryonic pharyngeal arches are complex and I’m not going to do a comprehensive review here (go here for more information). Suffice it to say that the first three arches give rise to your jaws and hyoid apparatus, the fourth and sixth form your larynx (voicebox), and fifth is entirely resorbed during development. Update: I made a pharyngeal arch cheat sheet.
There are two major nerves to the larynx, each of which is bilaterally paired. The nerve of the fourth pharyngeal arch becomes the superior laryngeal nerve, and it passes cranial to the fourth aortic arch. The nerve of the sixth pharyngeal arch becomes the inferior or recurrent laryngeal nerve, and it passes caudal to the sixth aortic arch. At the time that they form, both of these nerves take essentially straight courses from the brainstem to their targets, because you’re still in the blimp-gondola stage.
If you were a shark, the story would be over. The more posterior pharyngeal arches would persist as arches instead of forming a larynx, each arch would hold on to its artery, and the nerves would all maintain their direct courses to their targets.
But you’re not a shark, you’re a tetrapod. Which means that you have, among other things, a neck separating your head and your body. And the formation of your neck shoved your heart and its associated great vessels down into your chest, away from the pharyngeal arches. This was no problem for the superior laryngeal nerve, which passed in front of the fourth aortic arch and could therefore stay put. But the inferior laryngeal nerve passed behind the sixth aortic arch, so when the heart and the fourth and sixth aortic arches descended into the chest, the inferior laryngeal nerve went with them. Because it was still hooked up to the brainstem and the larynx, it had to grow in length to compensate.
As you sit reading this, your inferior laryngeal nerves run down your neck into your chest, loop around the vessels derived from the fourth and sixth aortic arches (the subclavian artery on the right, and the arch of the aorta and ductus arteriosus on the left) and run back up your neck to your larynx. Because they do this U-turn in your chest and go back the way they came, the inferior laryngeal nerves are said to ‘recur’ to the larynx and are therefore more commonly referred to as the recurrent laryngeal nerves (RLNs).
An enlightening diversion
The RLN is the poster child for “unintelligent design” because it is pretty dumb. Your RLNs travel a heck of a lot farther to reach your larynx than they ought to, if they’d been designed. Surely an intelligent designer would have them take the same direct course as the superior laryngeal nerve. But evolution didn’t have that option. Tetrapod embryos could not be built from the ground up but had to be modified from the existing “sharkitecture” of ancestral vertebrates. The rules of development could not be rewritten to accommodate a shorter RLN. Hence Dawkins’s love affair with the RLN, which gets 7 pages in The Greatest Show on Earth. He also appeared on the giraffe episode of Inside Nature’s Giants, in which the RLN was dug out of the neck and the continuity of its ridiculous path was demonstrated–probably the most smack-you-in-the-face evidence for evolution that has ever been shown on television (said the rabid fan of large-tetrapod dissections).
Incidentally, the existence and importance of the RLN has been known since classical times. The RLN innervates the muscles responsible for speech, and on either side it passes right behind the thyroid gland, which is subject to goiters and tumors and other grotesque maladies. So a careless thyroidectomy can damage one or both of the RLNs; if one gets snipped, the subject will be hoarse for the rest of his or her life; if both are cut, the subject will be rendered mute. The Roman physician Galen memorably demonstrated this by dissecting the neck of an immobilized but unanesthetized pig and isolating the RLNs (Kaplan et al. 2009). One moment the poor pig was squealing its head off–as any of us would be if someone dug out our RLNs without anesthesia–and the next moment Galen severed the RLNs and the animal abruptly fell silent, still in unbelievable pain but now without a mechanism to vocally express its discomfort.
The name of the nerve also goes back to Galen, who wrote:
I call these two nerves the recurrent nerves (or reversivi) and those that come upward and backward on account of a special characteristic of theirs which is not shared by any of the other nerves that descend from the brain.
Like at least some modern surgeons, Galen does not seem to have been overly burdened by humility:
All these wonderful things, which have now become common property, I was the first of all to discover, no anatomist before me ever saw one of these nerves, and so all of them before me missed the mark in their anatomical description of the larynx.
Both of those quotes are from Kaplan et al. (2009), which is a fascinating paper that traces the knowledge of the recurrent laryngeal nerve from classical times to the early 20th century. If you’d like a copy and can’t get hold of one any other way, let me know and I’ll hook you up.
Share and share alike
By now you can see where this is going: all tetrapods have larynges, all tetrapods have necks, and all tetrapods have recurrent laryngeal nerves. Including giraffes, much to the delight of Richard Dawkins. And also including sauropods, much to the delight of yours truly.
Now, I cannot show you the RLN in a living sauropod, nor can I imagine a scenario in which such a delicate structure would be recognizably preserved as a fossil. But as tetrapods, sauropods were bound to the same unbreakable rules of development as everything else. The inference that sauropods had really long, really dumb RLNs is as secure as the inference that they had brainstems, hearts, and larynges.
Giraffes have necks up to 2.4 meters long (Toon and Toon 2003), so the neurons that make up their RLNs approach 5 meters in the largest indiividuals. But the longest-necked sauropods had necks 14 meters long, or maybe even longer, so they must have had individual neurons at least 28 meters long. The larynx of even the largest sauropod was probably less than 1 meter away from the brainstem, so the “extra” length imposed on the RLN by its recurrent course was something like 27 meters in a large individual of Supersaurus. Take that, Giraffa.
One way or another
It is possible to have a nonrecurrent laryngeal nerve–on one side, anyway. If you haven’t had the opportunity to dissect many cadavers, it may come as a surprise to learn that muscles, nerves, and blood vessels are fairly variable. Every fall in Gross Anatomy at WesternU, we have about 40 cadavers, and out of those 40 people we usually have two or three with variant muscles, a handful with unusual branching patterns of nerves, and usually half a dozen or so with some wackiness in their major blood vessels. Variations of this sort are common enough that the better anatomy atlases illustrate not just one layout for, say, the branching of the femoral artery, but 6-10 of the most common patterns. Also, these variations are almost always asymptomatic, meaning that they never cause any problems and the people who have them usually never know (ask Mike about his lonely kidney sometime). You–yes, you, gentle reader!–could be a serious weirdo and have no idea.
Variations in the blood vessels seem to be particularly common, possibly because the vessels develop in situ with apparently very little in the way of genetic control. Most parts of the body are served by more than one artery and vein, so if the usual vessel isn’t there or takes an unusual course, it’s often no big deal, as long as the blood gets there somehow. To wit: occasionally a person does not have a right subclavian artery. This does not mean that their right shoulder and arm receive no blood and wither away; usually it means that one of the segmental arteries branching off the descending aorta–which normally serve the ribs and their associated muscles and other soft tissues–is expanded and elongated to compensate, and looks for all the world like a normal subclavian artery with an abnormal connection to the aorta. But if the major artery that serves the forelimb comes from the descending aorta, and the 4th aortic arch on the right is completely resorbed during development, then there is nothing left on the right side to drag the inferior laryngeal nerve down into the torso. A person with this setup will have an inferior laryngeal nerve on the right that looks intelligently designed, and the usual dumb RLN on the left.
Can people have a nonrecurrent laryngeal nerve on the left? Sure, if they’ve got situs inversus, in which the normal bilateral asymmetry of the internal organs is swapped left to right. Situs inversus is pretty darned rare in the general population, occurring in fewer than 1 in 10,000 people. It is much more prevalent in television shows and movies, where the hero or villain may survive a seemingly mortal wound and then explain that he was born with his heart on the right side. (Pro tip: the heart crosses the midline in folks of both persuasions, so just shoot through the sternum and you’ll be fine. Or, if you’re worried about penetration, remember Rule #2 and put one on either side.) Anyway, take everything I wrote in the preceding paragraph, mirror-image it left to right, and you’ve got a nonrecurrent laryngeal nerve on the left. But just like the normally-sided person who still has an RLN on the left, a person with situs inversus and no remnant 4th aortic arch on the left (double variation alert!) still has an RLN looping around the aorta and ductus arteriosus on the right.
Bottom line: replumb the vessels to your arms, swap your organs around willy-nilly, you just can’t beat the aorta. If you have an aorta, you’ve got at least one RLN; if you don’t have an aorta, you’re dead, and no longer relevant to this discussion.
Nonrecurrent laryngeal nerves–a developmental Hail Mary?
But wait–how do we know that the inferior laryngeal nerve in embryonic sauropods didn’t get rerouted to travel in front of the fourth and sixth aortic arches, so it could be spared the indignity of being dragged into the chest later on?
First of all, such a course would require that the inferior laryngeal nerve take an equally dumb recurrent course in the embryo. Or maybe it should be called a procurrent course. Instead of simply radiating out from the central nervous system to its targets in the sixth pharyngeal arch, the axons that make up the RLN would have to run well forward of their normal course, loop around the fourth and sixth aortic arches from the front, and then run back down to the sixth pharyngeal arch. There is simply no known developmental mechanism that could make this happen.
Even if we postulated some hypothetical incentive that would draw those axons into the forward U-turn, other axons that took a more direct course from the central nervous system would get to the sixth pharyngeal arch first. By the time the forwardly-recurring axons finished their intelligently-routed course and finally arrived at the sixth pharyngeal arch, all of the innervation targets would be taken, and those axons would die off.
Also, at what point in the evolution of long necks would this forwardly-looping course supposedly be called into existence? Ostriches and giraffes have RLNs that take the same recurrent course as those of humans, pigs, and all other tetrapods. The retention of the recurrent course in extant long-necked animals is further evidence that the developmental constraint cannot be broken.
Finally, the idea that a non-recurrent laryngeal nerve would need to evolve in a long-necked animal is based on the perception that long nerve pathways are somehow physiologically taxing or otherwise bad for the animals in which they occur. But almost every tetrapod that has ever lived has had much longer neurons than those in the RLN, and we all get on just fine with them.
In dire extremity
Probably you seen enough pictures of neurons to know what one looks like: round or star-shaped cell body with lots of short branches (dendrites) and one very long one (the axon), like some cross between an uprooted tree–or better yet, a crinoid–and the Crystalline Entity. When I was growing up, I always imagined these things lined up nose to tail (or, rather, axon to dendrite) all down my spinal cord, arms, and legs, like boxcars in a train. But it ain’t the case. Textbook cartoons of neurons are massively simplified, with stumpy little axons and only a few to a few dozen terminals. In reality, each neuron in your brain is wired up to 7000 other neurons, on average, and you have about a hundred billion neurons in your brain. (Ironically, 100 billion neurons is too many for your 100 billion neurons to visualize, so as a literal proposition, the ancient admonition to “know thyself” is a non-starter.)
Back to the axons. Forget the stumpy little twigs you’ve seen in books and online. Except for the ganglia of your autonomic nervous system (a semi-autonomous neural network that runs your guts), all of the cell bodies of your neurons are located in your central nervous system or in the dorsal root ganglia immediately adjacent to your spinal cord. The nerves that branch out into your arms and legs, across your face and scalp, and into your larynx are not made of daisy chains of neurons. Rather, they are bundles of axons, very long axons that connect muscles, glands, and all kinds of sensory receptors back to the nerve cell bodies in and around your brain and spinal cord.
Indulge me for a second and wiggle your toes. The cell bodies of the motor neurons that caused the toe-wiggling muscles to fire are located in your spinal cord, at the top of your lower back. Those motor neurons got orders transmitted down your spinal cord from your brain, and the signals were carried to the muscles of your feet on axons that are more than half as long as you are tall.
Some of your sensory neurons are even longer. Lift your big toe and then set it down gently, just hard enough to be sure that it’s touching down on the floor or the sole of your shoe, but not hard enough to exert any pressure. When you first felt the pad of your toe touch down, that sensation was carried to your brain by a single neuron (or, rather, by several neurons in parallel) with receptor terminals in the skin of your toe, axon terminals in your brainstem, and a nerve cell body somewhere in the middle (adjacent to your sacrum and just a bit to one side of your butt crack, if you want the gory details). That’s right: you have individual sensory neurons that span the distance from your brainstem to your most distal extremity. And so does every other vertebrate, from hagfish to herons to hippos. Including, presumably, sauropods.
I had you set your toe down gently instead of pushing down hard because the neurons responsible for sensing pressure do not travel all the way from toe-tip to brainstem; they synapse with other neurons in the spinal cord and those signals have been through a two-neuron relay by the time they reach your brainstem. Ditto for sensing temperature. But the neurons responsible for sensing vibration and fine touch go all the way.
If you want to experience everything I’ve discussed in this post in a single action, put your fingertips on your voicebox and hum. You are controlling the hum with signals sent from your brain to your larynx through your recurrent laryngeal nerves, and sensing the vibration through individual neurons that run from your fingertips to your brainstem. Not bad, eh?
Getting back to big animals: the largest giraffes may have 5-meter neurons in their RLNs, but some of the sensory neurons to their hindfeet must be more like 8 meters long. I don’t think anyone’s ever dissected one out, but blue whales must have sensory neurons to the tips of their flukes that are almost 30 meters (98 feet) long (subtract the length of the skull, but add the lateral distance from body midline to fluke-tip). And Supersaurus, Amphicoelias, and the like must have had neurons that were approximately as long as they were, minus only the distance from the snout-tip to the back of the skull. I could be wrong, and if I am I’d love to be set straight, but I think these must have been the longest cells in the history of life.
Oh, one more thing: up above I said that almost every tetrapod that has ever lived has had much longer neurons than those in the RLN. The exceptions would be animals for which the distance from brainstem to base of neck was longer than the distance from base of neck to tip of limb or tail, so that twice the length of the neck would be longer than the distance from base of skull to most distal extremity. In that case, the neurons that contribute to the RLN would be longer than those running from brainstem to tail-tip or toe-tip. Tanystropheus and some of the elasmosaurs probably qualified; who else?
In this post I’ve tried to explain the courses that these amazingly long cells take in humans and other vertebrates. I haven’t dealt at all with the functional implications of long nerves, for which please see the paper. The upshot is that big extant animals get along just fine with their crazy-long nerves, and there’s no reason to assume that sauropods were any more troubled. So why write the paper, then? Well, it was fun, I learned a lot (dude: axoplasmic streaming!), and most importantly I got to steal a little thunder from those silly poseurs, the giraffes.
Department of Frivolous Nonsense: yes, I titled the paper after those TV ads for Chili’s hamburgers from a few years back. If you never saw them, the ads compared mass-produced, machine-stamped fast-food burgers with restaurant burgers painstakingly built by hand, and concluded with, “Chili’s Big-Mouth Burgers: monuments of inefficiency!”
Update: All of this is out of date now that the paper has been formally published. Department of Good Karma: since the paper is at the “accepted manuscript” stage, I still have the chance to make (hopefully minor) changes when I get the proofs. As is always, always, always the case, I caught a few dumb errors only after the manuscript had been accepted. Here’s what I’ve got so far, please feel free to add to the list:
- Page 1, abstract, line 3: pharyngeal, not pharyngial
- Page 1, abstract, line 8: substitute ‘made up’ for ‘comprised’
- Page 6, line 12: substitute ‘make up’ for ‘comprise’
- Page 9, line 5: citation should be of Carpenter (2006:fig. 3), not fig. 2
- Page 10, line 7: “giant axons of squid are”, not ‘ares’
- Page 12, entry for Butler and Hodos should have year (1996)
- Page 12, entry for Carpenter has ‘re-evaluation misspelled
- Page 16, entry for Woodburne has ‘mammalian’ misspelled
(Notes to self: stop trying to use ‘comprise’, lay off the ‘s’ key when typing bibliography.)
- Butler, A.B., and Hodos, W. 1996. Comparative Vertebrate Neuroanatomy: Evolution and Adaptation. 514 pp. Wiley–Liss, New York.
- Kaplan, E.L, Salti, G.I., Roncella, M., Fulton, N., and Kadowaki, M. 2009. History of the recurrent laryngeal nerve: from Galen to Lahey. World Journal of Surgery 33:386-393. DOI 10.1007/s00268-008-9798-z
- Toon, A., and Toon, S.B. 2003. Okapis and giraffes. In: M. Hutchins, D. Kleiman, V. Geist, and M. McDade (eds.), Grzimek’s Animal Life Encyclopedia, 2nd ed. Vol 15: Mammals IV, 399–409. Gale Group, Farmington Hills.
- Wedel, M.J. 2012. A monument of inefficiency: the presumed course of the recurrent laryngeal nerve in sauropod dinosaurs. Acta Palaeontologica Polonica 57(2):251-256.
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.
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.
- 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.
February 19, 2010
Lovers of fine sauropods will be well aware that, along with the inadequately described Indian titanosaur Bruhathkayosarus, the other of the truly super-giant sauropods is Amphicoelias fragillimus. Known only from a single neural arch of a dorsal vertebra, which was figured and briefly described by Cope (1878) and almost immediately either lost or destroyed, it’s the classic “one that got away”, the animal that sauropod aficionados cry into their beer about late at night.
I’m not going to write about A. fragillimus in detail here, because Darren’s so recently covered it in detail over at Tetrapod Zoology — read Part 1 and Part 2 right now if you’ve not already done so. The bottom line is that it was a diplodocoid roughly twice as big as Diplodocus in linear dimension (so about eight times as heavy). That makes it very very roughly 50 m long and 100 tonnes in mass.
But Mike!, you say, Isn’t it terribly naive to go calculating masses and all from a single figure of part of a single bone?
Why, yes! Yes, it is! And that is what this post is about.
As I write, the go-to paper on A. fragillimus is Ken Carpenter’s (2006) re-evaluation, which carefully and tentatively estimated a length of 58 m, and a mass of around 122,400 kg.
As it happens, Matt and a colleague submitted a conference abstract a few days ago, and he ran it past me for comments before finalising. In passing, he’d written “there is no evidence for sauropods larger than 150 metric tons and it is possible that the largest sauropods did not exceed 100 tons”. I replied:
I think that is VERY unlikely. [...] the evidence for Amphicoelias fragillimus looks very convincing, Carpenter’s (2006) mass estimate of 122.4 tonnes is conservative, being extrapolated from Greg Paul’s ultra-light 11.5 tonne Diplodocus.
Carpenter’s estimate is based on a reconstruction of the illustrated vertebra, which when complete he calculated would have been 2.7 m tall. That is 2.2 times the height of the corresponding vertebra in Diplodocus, and the whole animal was considered as it might be if it were like Diplo scaled up by that factor. Here is his reconstruction of the vertebra, based on Cope’s figure of the smaller but better represented species Amphicoelias altus:
Matt’s answer to me was:
First, Paul’s ultra-light 11.5 tonne Dippy is not far off from my 12 tonne version that you frequently cite, and mine should be lighter because it doesn’t include large air sacs (density of 0.8 instead of a more likely 0.7). If my Dippy had an SG of 0.7, it would have massed only 10.25 tonnes. Second, Carpenter skewed [...] in the direction of large size for Amphicoelias. I don’t necessarily think he’s wrong, but his favoured estimate is at the extreme of what the data will support. Let’s say that Amphicoelias was evenly twice as large as Dippy in linear terms; that could still give it a mass as low as 90 tonnes. And that’s not including the near-certainty that Amphicoelias had a much higher ASP than Diplodocus. If Amphicoelias was to Diplodocus as Sauroposeidon was to Brachiosaurus—pneumatic bones about half as dense—then 1/10 of its volume weighed ½ as much as it would if it were vanilla scaled up Dippy, and we might be able to knock off another 5 tonnes.
There’s lots of good stuff here, and there was more back and forth following, which I won’t trouble you with. But what I came away with was the idea that maybe the scale factor was wrong. And the thing to do, I thought, was to make my own sealed-room reconstruction and see how it compared.
So I extracted the A.f. figure from Osborn and Mook, and deleted their dotted reconstruction lines. Then I went and did something else for a while, so that any memory of where those lines might have been had a chance to fade. I was careful not look at Carpenter’s reconstruction, so I could be confident mine would be indepedent. Then I photoshopped the cleaned A. fragillimus figure into a copy the A. altus figure, scaled it to fit the best as I saw it, and measured the results. Here it is:
As you can see, when I measured my scaled-to-the-size-of-A.f. Amphicoelias vertebra, it was “only” 2293 mm tall, compared with 2700 mm in Ken’s reconstruction. In other words, mine is only 85% as tall, which translates to 0.85^3 = 61% as massive. So if this reconstruction is right, the big boy is “only” 1.87 times as long as Diplodocus in linear dimension — maybe 49 meters long — and would likely come in well below the 100-tonne threshhold. Using Matt’s (2005) 12-tonne estimate for Diplodocus, we’d get a mere 78.5 tonnes for Amphicoelias fragillimus. So maybe Matt called that right.
Folks — please remember, the punchline is not “Amphicoelias fragillimus only weighed 78.5 tonnes rather than 122.4 tonnes”. The punchline is “when you extrapolate the mass of an extinct animal of uncertain affinities from a 132-year-old figure of a partial bone which has not been seen in more than a century, you need to recognise that the error-bars are massive and anything resembling certainty is way misplaced.”
- Carpenter, Kenneth. 2006. Biggest of the big: A critical re-evalustion of the mega-sauropod Amphicoelias fragillimus Cope, 1878. pp. 131-137 in J. Foster and S. G. Lucas (eds.), Paleontology and Geology of the Upper Jurassic Morrison Formation. New Mexico Museum of Natural History and Science Bulletin 36.
- Cope, Edward Drinker. 1878. Geology and Palaeontology: a new species of Amphicoelias. The American Naturalist 12 (8): 563-566.
- Osborn, Henry Fairfield, and Charles C. Mook. 1921. Camarasaurus, Amphicoelias and other sauropods of Cope. Memoirs of the American Museum of Natural History, n.s. 3:247-387, and plates LX-LXXXV.
November 12, 2009
Get on over to Art Evolved and scope out the sauroponderous Sauropod Gallery. It’s brobdingnaginormous. I don’t want to seem biased, but there’s a lot of hot brachiosaurian action on display. I’m happy to say that the other clades are not ignored–diplodocids, dicraeosaurids, titanosaurs, mamenchisaurids, basal eusauropods, and even a basal sauropodomorph are all in the mix.
Normally my brachiosaurcentricity would lead me to steal one of the numerous brachiosaur images–perhaps the awesome parade of brachiosaurs that includes both Sauroposeidon and the Archbishop (!!)–BUT my laziness led me to choose another piece by the same artist, Nima Sassani. That would be the Puertasaurus reconstruction shown at top, which includes vertebrae and thus fulfills our titular mandate. That means I can stop writing now and get back to gawking. Go do likewise.
…oh, and don’t forget to stop by Dracovenator and congratulate Adam Yates on his new critter, Aardonyx. You’ll be hearing more about Aardonyx here at SV-POW! in the hopefully not-too-distant future. I can say no more for now…
October 20, 2009
At the 2007 SVP meeting in Austin, Texas, I noticed that the suffix “-ass” was ubiquitiously used as a modifier: where an Englishman such as myself might say “This beer is very expensive”, a Texan would say “That is one expensive-ass beer” — and the disease seemed to spread by osmosis through the delegates, so that by my last day in Austin is was seemingly impossible to hear an adjective without the “-ass” suffix.
All of which is by way of introducing the fact that Futalognkosaurus really was a big-ass sauropod, as this photo of its sacrum (with articulated ilia) shows:
A version of this photograph (in black and white and with the background chopped out) appeared in Ferdinand Novas’s recent book (Novas 2009) and attracted some discussion on the Dinosaur Mailing List.
Although in the past, we have complained about the lack of measurements in the two papers describing Futulognkosaurus (Calvo et al. 2007, 2008), this photo demonstrates a lower bound on its size: we know that it was, at least, Darned Big. (I would attempt to calculate some measurements from this photo using Porfiri as my scale-bar, but we all know how variable human proportions are, so it’s probably better to refrain.) The great news here is that, as explained by Ruben Juarez Valieri in a comment on an earlier article, a third article is on the way that will contain all the measurements we want.
Anyway, here are some more of Calvo’s awesome Futalognkosaurus photos, all used with grateful permission:
(That is an insanely tall cervical.)
How on Earth did they get that jacket out the ground and back to the museum?!
And finally — if you’ll forgive the flagrant appendicularity:
And now for something completely different:
Open Access Week
I’m pleased to say that this week (October 19-23) is Open Access Week. Get over to the site for statistics about the rise of open access. Particularly impressive is a sequence of institutions that are introducing open-access mandates, i.e. requiring that all research produced by its staff is made freely available to the world. We’re on the way!
- Calvo, J.O., Porfiri, J.D., Gonzalez-Riga, B.J., and Kellner, A.W.A. 2007. A new Cretaceous terrestrial ecosystem from Gondwana with the description of a new sauropod dinosaur. Anais da Academia Brasileira de Ciencias 79(3):529-541.
- Calvo, J.O., Porfiri, J.D., Gonzalez-Riga, B.J., and Kellner, A.W.A. 2008. Anatomy of Futalognkosaurus dukei Calvo, Porfiri, Gonzalez-Riga & Kellner, 2007 (Dinosauria, Titanosauridae) from the Neuquen Group (Late Cretaceous), Patagonia, Argentina. Arquivos do Museu Nacional, Rio de Janeiro 65(4):511-526.
- Novas, F. 2009. The Age of Dinosaurs in South America. Indiana University Press (Life of the Past series). 480 pages.
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.
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.
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.
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.
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.
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.
- 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.
September 20, 2009
Just checking: no-one’s bored of brachiosaurs yet, are they?
Thought not. Right, then, here we go!
Greg Paul’s (1988) study of the two “Brachiosaurus” species — the paper that proposed the subgenus Giraffatitan for the African species — noted that the trunk is proportionally longer in Brachiosaurus than in Giraffatitan due to the greater length of its dorsal centra. Paul (p. 7) stated that the difference is “25%-30%” on the basis of his figure 2.
Having seen the dorsal vertebrae of the type specimens of both species, my gut reaction was that the difference was nowhere near this great, so I recalculated it for myself (Taylor 2009:table 3). Dorsal column length is the sum of the “functional length” of the centra of the dorsal vertebrae, where functional length is the length of the centrum not counting the condyle (which of course is nestled in the preceding vertebra’s cotyle when the column is articulated). For Brachiosaurus, Riggs (1904) did not give this measurement, but did give total heights, and using these for scale I was able to measure the functional lengths from his plate LXXII. For Giraffatitan, Janensch’s (1950:44) superbly comprehensive table supplied measurements for D4 and D8; for D11 and D12 I was able to determine the length by measuring from Janensch’s (1950:fig. 62) figure, knowing the height from his table; and for D5-D7, D9 and D10, I interpolated linearly between the measurements that I had. Summing the functional lengths of D6-D12, I got 226 cm for Brachiosaurus and 183 cm for Giraffatitan. So Brachiosaurus is 226/183 = 1.23 times as long as Giraffatitan — in other words, 23% longer, which is pretty much what Greg Paul said. So I learned something there.
So: is a 23% longer torso a big deal? Back when I was trying to answer that question for myself, I figured it would help to take an image of a familiar animal and stretch it — so here is a horse, stolen from here and stretched:
To me, that second picture is wrong enough to hurt my eyes a little; your mileage may vary, but I suspect those among you who love horses will feel ill when you look at it. This image was one of the reasons — one of many — that I concluded that generic separation was unavoidable.
But here’s an odd thing: tonight, for this blog post, I did the same thing to a human body, expecting it to seem even more horrible in light of how familiar we are with our own bodies. Here it is:
To my surprise, the elongated human doesn’t look appallingly wrong to me. It doesn’t look right, of course, but it seems within the realms of, for example, what might appear as a representation of a human body in the early issues of Fantastic Four. I am not sure what to make of that fact. I don’t believe I have a more finely tuned sense of horse anatomy than human anatomy: it might be that I am more used to badly drawn humans than badly drawn horses; or that there is more variation in human proportions than in horse proportions; or maybe weirdness just looks less weird when it’s upright than when it’s horizontal. I’ll be interested to hear in the comments whether the Long Horse or the Long Human looks most wrong to readers.
(By the way, I casually talk about the type specimens of both “Brachiosaurus” species: while the situation is simple in the case of Brachiosaurus altithorax, whose holotype is FMNH P25107, things are more complex in the case of Giraffatitan brancai. Janensch nominated “Skelett S” as the holotype of his new species “Brachiosaurus” brancai, but that turned out to be a chimera, composed of the two skeletons which he subsequently designated SI and SII — but Janensch never designated one of these as the type, and so far as I’ve been able to determine, neither has anyone else done so. SI is represented by cranial elements and the first seven cervicals, but that’s all; SII is a much larger animal and is represented by most of the skeleton, and has been informally treated as though it were the type specimen most of the while, so I formally proposed HMN SII as the lectotype of the species (Taylor 2009:788) — just a bit of housekeeping.)
Here’s our old friend, the 8th cervical vertebra of HMN II, in a rare posterodorsal aspect, showing just how thin and, well, lamina-like the spinopostzygapophyseal laminae are. All that space in between them? Filled with diverticula, mostly. Amazing.
Meanwhile some good news:
Remember the good news and bad news about the all-dinosaurs special volume of The Anatomical Record? Well, since we posted that, the entire issue has been made open access! Fantastic stuff there: details from D. Schachne of the Wiley-Blackwell Communications Team. It’s not clear why the articles were all paywalled when originally posted, but all’s well that ends well.
And finally …
There’s been a gratifying amount of discussion in the comments on recent articles. It can be hard to keep track of, but it helped a lot when I found an RSS feed for comments, which is what I now use. For anyone else who wants it, it’s at http://svpow.wordpress.com/comments/feed/
Janensch, Werner. 1950. Die Wirbelsaule von Brachiosaurus brancai. Palaeontographica (Suppl. 7) 3: 27-93.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.Taylor, Michael 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.Vesalius, A. 1543. Andreae Vesalii Bruxellensis, Scholae medicorum Patauinae professoris, de Humani corporis fabrica Libri septem [facsimile]. Ex Officina Ioannis Oporini, Basel, 659 pp.Wilson, Jeffrey A. 2006. Anatomical nomenclature of fossil vertebrates: standardized terms or “lingua franca”? Journal of Vertebrate Paleontology 26(3): 511-518.
- Janensch, Werner. 1950. Die Wirbelsaule von Brachiosaurus brancai. Palaeontographica (Suppl. 7) 3: 27-93.
- 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.
- Taylor, Michael 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.
- Vesalius, A. 1543. Andreae Vesalii Bruxellensis, Scholae medicorum Patauinae professoris, de Humani corporis fabrica Libri septem [facsimile]. Ex Officina Ioannis Oporini, Basel, 659 pp.
- Wilson, Jeffrey A. 2006. Anatomical nomenclature of fossil vertebrates: standardized terms or “lingua franca”? Journal of Vertebrate Paleontology 26(3): 511-518.
September 2, 2009
Here’s a skeletal reconstruction of Alamosaurus modified from Lehman and Coulson (2002:fig. 11). I cloned the neck and rotated it a few degrees to see where it would put the head.
The skeleton in the figure is scaled to the size of the individuals in the Smithsonian and at UT Austin. The scale bar is 1 meter, which by my calculations gives that individual the following dimensions:
- Total length: 15.8 meters (52 feet)
- Neck length: 5.2 meters (17 feet)
- Shoulder height: 4 meters (13 feet)
- Head height (with neck raised): 8.4 meters (27.5 feet)
Here are a couple of articles on a giant sauropod found in Big Bend in 1999. This critter is generally assumed to be Alamosaurus but it could be something new (I have no evidence either way); the material is currently under study at the Dallas Museum of Nature and Science.
According to the articles, 10 cervical vertebrae were found in a string 23 feet long. From the pictures, those ten vertebrae look like the ten largest, which should account for almost all of the neck except for the first few cervicals behind the head. Let’s assume that this big individual therefore had a neck just a little longer than 23 feet, and we find that it is almost exactly 1.5 times bigger than the one listed above. If its proportions follow those of the Lehman and Coulson recon, its measurements would be:
- Total length: 24 meters (79 feet)
- Neck length: 7.8 meters (25.5 feet)
- Shoulder height: 6 meters (19.5 feet)
- Head height: 12.6 meters (41 feet)
In the second article Homer Montgomery speculates that the complete neck would have been more than 30 feet long. That’s certainly not impossible, since 30-foot-plus necks are known for the largest individuals in several clades (e.g., Mamenchisaurus, Supersaurus, Sauroposeidon, probably Puertasaurus, possibly Futalognkosaurus, but probably not Aegyptosaurus) If so, then you could just about double all of the proportions from the first individual described above, which would give a truly prodigious animal. The 52-foot animal probably had a mass around 15 tons, so the 79-footer would have been about 50 tons (1.5^3 = 3.375), and the hypothetical 100-footer would have been 120 tons, which is up in Amphicoelias/Bruhathkayosaurus territory. For what it’s worth, I think the numbers for the 79-foot animal are more plausible, but who knows. Anytime you’ve got a partial neck that is longer than the complete neck of Diplodocus, you’re dealing with a wacky big animal.
Lehman, T.M. & Coulson, A.B. 2002. A juvenile specimen of the sauropod Alamosaurus sanjuanensis from the Upper Cretaceous of Big Bend National Park, Texas. Journal of Paleontology 76(1): 156-172.