Dinosaurs in motion – computer modeling of dinosaur biomechanics – Cover Story
Computer scientists and paleontologists are joining forces to get the very largest of Earth’s extinct giants moving again, this time the right way.
The great extinct giants left behind nothing but their fossils as testament to their lives. And while paleontologists can easily toy with the slender bones of an extinct bat or fish to get a handle on how its body worked, the sheer size of sauropod bones makes such hands-on playtime impossible.
Technology, though, has created a way to twirl a sauropod on your fingertips, and dinosaur-obsessed computer scientists are showing the paleontologists how: put the ghost of the beast inside a machine–create a virtual sauropod that can be used to test ideas about how these animals threw around their spectacular weight.
One of these helpful outsiders is the chief technology officer at Microsoft, a brilliant polymath named Nathan Myhrvold. Myhrvold graduated high school at age 14; by 23 he had a Ph.D. in theoretical physics from Princeton. Within three more years he had set up a software company that was bought by Bill Gates, who later put him in charge of basic research at Microsoft. Now, at 38, Myhrvold advises Gates on what computers will be like in the future.
As a boy, Myhrvold had a typical, visceral affection for dinosaurs; these days, while his appreciation of the beasts is undiminished, it is changed in character. Now they represent for him an intriguingly difficult intellectual problem. “The total evidence you have to look at for these animals is shockingly small,” he explains, “because they are so different in terms of their scale and their habits. You’re able to extrapolate less well than you could if you found a giant turtle. There’s an enormous amount of debate about just about everything.” For several years Myhrvold has been doing his part to further these debates through a long volley of dinosaurian e-mail with Phil Currie, a paleontologist at Canada’s Royal Tyrrell Museum of Palaeontology in Drumheller, Alberta. Not long ago, their exchanges convinced Myhrvold that he could use computers to test some of the more hotly argued ideas making the rounds.
“For most things you do in paleontology, computers are only marginally useful,” he admits. “They’re nowhere near as useful as burlap and plaster, for wrapping fossils up; they’re not even as good as a shovel. But as you try to reconstruct the lives of dinosaurs in detail, there are lots of areas where modeling can be a helpful tool. It has the advantage of letting you check things that would be hard to argue otherwise. If you are making a claim and people say no, you can show that your argument is reasonable.”
Sauropods offered Myhrvold and Currie a fit subject for digital analysis. When nineteenth-century paleontologists first unearthed these fossil giants in Europe and the United States, they hardly knew what to make of their own discoveries. In the 420 million years that animals have walked on land, nothing else has come close to sauropodian length and weight. Only some whales have grown bigger, but their buoyancy in water makes them virtually weightless. And unlike more recent minor giants like mastodons and ground sloths, sauropods didn’t package their weight in a reasonably compact form; frontward and backward they stretched to biblical proportions–their necks were as cedars, their tails snaking rivers of flesh and bone. It hardly seemed possible that a body could support such unwieldy mass without some help, and for decades paleontologists assumed that the bodies of sauropods couldn’t: the animals must have been like hippos, they reasoned, submerged in lakes or swamps, feeding on aquatic plants and relying on the water to relieve the great gravitational burden of their bodies.
Eventually the discovery of many long trackways on dry land demonstrated that the assumptions were wrong, that sauropods didn’t need water to hold up their bulk. By the 1970s a radically different image of the giants had begun to take shape: a number of researchers were convinced by the shape of sauropod bones that these dinosaurs were not torpid, boggy animals but erect and lively. Judging from the observation that sauropod footprints were rarely accompanied by tail marks, paleontologists raised the animals’ tails, setting them stiffly in the horizontal plane. The necks they raised also, until some sauropod species assumed towering, giraffe-like stances. Robert Bakker, the most zealous and passionate of the lively reconstructionists, even argued that the spines of some sauropods showed that they could boost themselves onto their hind legs, using their tail to create a tripod base. In such a pose, they could lift their heads to the tops of five-story trees.
Bakker’s vision was certainly more entertaining than the old image of swamp-bound reptiles (and Steven Spielberg, not surprisingly, adopted it for Jurassic Park). But was it true? Bakker and his fellow enthusiasts based their arguments on broad similarities between the sauropods and living animals. When they invoked biomechanics, they used only simple models in which the entire backbone was reduced to a single beam rather than a flexible linked chain of vertebrae. Of course, at the time they didn’t have much choice–any model more complex was too hard to calculate. But software has now become so sophisticated that, in the industrial world, engineers can test detailed models of cranes, backhoes, bridges, and other structures on laptop computers. And, as Nathan Myhrvold realized, a dinosaur fanatic could use the same software to simulate a sauropod. “I was going to design my own program,” he says. “Instead I just went out and bought one.”
He commenced his new career in “cyberpaleontology,” as he calls it, with the question of what purpose was served by the absurdly tapered lengths of sauropod tails. Apatosaurus (formerly known as Brontosaurus), for example, had a 41-foot-long tail, the last 6 feet of which were the diameter of a garden hose. The tail’s whiplike look has inspired some to suggest that it might have been used in some manner as a weapon. But as with so many ideas in paleontology, it was difficult to do anything with this notion other than suggest it.
Myhrvold set out to test it, comparing whips and tails on a computer to see how similarly they behaved. First, though, he explains, “I had to learn a hell of a lot about whips. It turns out the Internet is a great place to learn about them–although you learn about a lot of other things too”–one of which was that most people who are interested in whips are not likely to be paleontologists. “I discovered that there are very few people who make whips anymore, and one of the greatest living whip makers lives here in Seattle. The various Web sites that recommended him–most of them were S&M sites–said you had to make up a story, because he was very conservative and wouldn’t sell you a whip if it was for something he considered to be perverse.
“So I get my story all lined up, that I’m interested in Western culture or some such. I come in and he says, `Well, what’ll you be wanting a whip for?’
“And I just blurt out, `Dinosaurs.’
“The guy gives me this look, this pathetic look. Not only does he assume I’m some kind of pervert, but I must be the stupidest pervert he’s ever encountered because I have the worst story. Dinosaurs? It would have gone very badly if not for the fact that a guy came out from around the back and said, `Hi, Nathan.’ It turned out to be his son, who works at Microsoft, and he was able to convince him that I was sincere about dinosaurs.”
Back home, as Myhrvold snapped his new bullwhip around, he observed its elegant demonstration of Newton’s laws of motion. When he flicked the handle, he created a wave that traveled down the whip’s length; its energy remained constant as it moved except for what little was lost in friction. But since the whip got increasingly narrower down its length, the farther the wave traveled, the faster it moved. By the time the wave got to the tip, it was moving more than 787 miles an hour–faster than the speed of sound. What we hear as the crack of a whip is in fact a small sonic boom.
Tapping away on his laptop during business flights, Myhrvold found that he could tailor his engineering software to simulate a whip’s movements quite accurately. Then he turned to one of the best-preserved sauropod tails, that of Apatosaurus louisae, which is on display at the Carnegie Museum of Natural History in Pittsburgh. He worked out and estimate of the mass of the tail and found that it weighed about 3,200 pounds. That’s unquestionably a lot of weight to propel to the speed of sound. But most of that weight, he saw, was close to the hips–half of it in the first four feet alone. The last four feet of tail weighed only three-quarters of a pound.
Myhrvold then set the tail moving on his computer. Fossils suggest that Apatosaurus could bend its tail as much as 30 degrees at the joints between the vertebrae, but to err on the conservative side Myhrvold also tried out tails that could bend as little as 9 degrees. Over that entire range, he found that with very little energy–less than a fifth of the amount a sauropod used to walk–he could drive the tip of the tail above the speed of sound. It would have been easy, he concluded, for Apatosaurus to crack its tail like a whip.
Why would it have done so? Myhrvold doesn’t put much stock in the idea that sauropods ever used their whipping tails as weapons against predators. The tips, where most of the energy would have been released, were so slender that they couldn’t have hurt an attacker–they would likely have done more harm to the sauropods themselves. However, Myhrvold certainly doesn’t want to downplay the majesty of a sauropod tail. The crack of its tip would have released 2,000 times more energy than comes off a bullwhip, and the sound would have been over 200 decibels, a cannonlike boom traveling across the Mesozoic landscape for miles. So what was the purpose of this great extravagance? The sauropods used their tails, Myhrvold thinks, not for war but for love. “Most of the outlandish things that animals have are due to sexual selection–it’s why moose have big antlers, and peacocks have their wonderful tails,” he says. Rather than getting into titanic–and probably fatal–battles over females, male sauropods might have dueled each other conically, seeing who could create the most fearsome racket. One test of Myhrvold’s idea would be to see if signs of scarring appear on the tips of only male sauropod tails–but that would require knowing how to sex a fossil sauropod, which is, not surprisingly, a matter of great debate.
While Myhrvold has been engrossed in the tail end of sauropods, University of Oregon computer scientist Kent A. Stevens has been busy at their front end, trying to figure out how they Stevens is another scientist for whom computers are stock-in-trade; he studies how we see in three dimensions–that is, how we perceive depth from textures and contours–and his basic research often involves experiments that use 3-D computer graphics. The information he collects helps him in his other lines of research, such as enabling robots to see and making virtual reality systems feel less virtual and more real.
While watching Jurassic Park in 1993, Stevens was surprised by the forward-facing eyes that had been given to Tyrannosaurus rex. As an expert on depth perception, he knew that if the depiction was accurate, the dinosaurs might have had stereovision like our own. “That started me on some formal research on vision in many species of dinosaurs,” he says. In particular, he looked at the variety of binocular vision among predatory dinosaurs: some, he found, had a wide overlap in their two fields of vision, like a cat. With their wide binocular field, these dinosaurs would have been good at navigating three-dimensional space–they could have been catlike stalkers. Other dinosaurs had a narrow overlap of visual fields and would have relied on their stereovision only when the prey was close. They would have been more like crocodiles, lying in wait for their prey and then lunging or sprinting forward for the kill.
Soon afterward Stevens wanted to show one of his computer science classes how to build a piece of software from scratch. With dinosaurs now on his mind, he constructed software that could model dinosaur skeletons. At about the same time, he became friends with Michael Parrish, a paleontologist at the University of Northern Illinois, and Parrish encouraged him in his modeling by telling him that his program could be scientifically groundbreaking.
“I’ve been frustrated by a lot of the studies of dinosaur functional morphology,” says Parrish. He had done his Ph.D. work on the biomechanics of some extinct species of crocodile-like reptiles. They were small enough that he could easily handle the bones, finding the way they fit together naturally, and thus discover their normal poses and ranges of motion. Such is not the case with the gigantic sauropods–to move a single thighbone takes at least a whole crew of strong backs, and more commonly a forklift–but with Stevens’s software, Parrish realized, it would be possible to heft the giant skeletons around effortlessly. It would also be possible to correct the shapes of the bones, which often get distorted during their eons in the ground.
Stevens and Parrish wanted to see what kind of movements sauropods could make with their necks. In their basic architecture, sauropod vertebrae are much like those in the backbones of any other terrestrial vertebrate. Below the spinal canal is a barrel-shaped section called the centrum. In sauropod necks, each centrum has a domed front end that fits into a bowl-shaped recess on the back of the previous vertebra, with a pad of cartilage cushioning the joint. Above the centrum and the spinal canal is a complex piece of bone called the neural arch. A prong may extend vertically from the arch, and there may be two others reaching out on either side. All these spars act as anchors for muscles that run along a sauropod’s neck, back, and tail.
The neural arch puts limits on the range of a spine’s movement with pairs of interlocking tabs known as zygapophyses. At the front and back end of each neural arch are two zygapophyses; the rear ones reach out over the front zygapophyses on the next vertebra. Each pair of overlapping zygapophyses are held together inside a fluid-filled capsule of ligament much like the one that keeps the ball and socket of your shoulder in place. As unobtrusive as they may look, zygapophyses play a huge role in determining how far an animal can flex its back and neck. The zygapophyses press against each other when the spine tries to move in certain directions, and the capsule of fluid keeps the bony tabs from grinding against each other.
In a camel’s neck, for example, the zygapophyses stick out on stalks and can thus slide around a great deal. That’s why a camel has such a flexible neck. But on a rhino the zygapophyses are stout and buttressed against the neural arches–making its neck rigid and sturdy enough to hold up its enormous head.
In their general anatomy, the necks of sauropods are, not surprisingly, more like those of camels than those of rhinos. But in their details, their zygapophyses offer a bizarre variety of shapes ranging from curved potato chip-size surfaces to giant flat wedges. Even small differences in their shape can radically change the flexibility of an animal’s neck.
“It’s very difficult to eyeball these things and say, `Okay, this shape will give me this much flexibility,'” says Stevens. “You really have to put it in the machine.” He and Parrish have visited museums around the United States and Europe over the past two years, recording the dimensions of sauropod vertebrae. Hovering in cherry pickers or crawling around dusty basement collections, they have made dozens of measurements of each bone, sometimes making rubbings of the zygapophyses as if they were gravestones. Back in Oregon, Stevens feeds the numbers into his computer and has it build the dinosaurs.
The program lets Stevens find the natural position for each sauropod’s neck by calculating the stance in which its zygapophyses fit snugly against each other. From there he can explore the range of movement they were capable of by pulling their necks until the zygapophyses either press against each other or slide too far apart. As a rule, an animal’s zygapophyses can move about 50 percent off center before the capsule holding them together begins to stretch dangerously. Any further and a sauropod might do itself serious harm.
What’s most surprising about the results Stevens and Parrish are getting is how different the biomechanics of sauropod species are, despite their similar appearance. Take, for example, Apatosaurus and its close relative, Diplodocus. Paleontologists have often thought of Diplodocus, at 11 tons, as little more than a slender variation of the 30-ton Apatosaurus. Stevens has found that the neutral poses of their necks are about the same–not gently sloping upward as you’ll see in museums or textbooks, but tilted downward. Apatosaurus would normally have held its head just a few feet off the ground; Diplodocus’s head would have hung down like the head of a hammer, hovering just inches above the ground. In their necks’ mobility, however, the two animals are quite distinct. Apatosaurus could lift its head 17 feet into the air and move it 13 feet to the right or left. It could bend its 16-foot neck in a U shape so that it could look directly behind itself. It could even twist its neck into a forward-facing S. Diplodocus, though it had a longer, 20-foot neck, was far stiffer. It could lift its head only 12 feet above the ground and could bend only 7 feet or so to either side.
The other sauropods that Stevens and Parrish have studied show a similar split between the contortionists and the straitjackets. A small Chinese sauropod called Euhelopus, for example, was so flexible in the side-to-side plane that it could turn its neck three-quarters of a circle–so far, in fact, that it could almost touch the side of its rib cage with its nose. The stocky, 59-foot-long Camarasaurus may have been able to hold its neck almost vertically–which, according to Stevens, is actually a rare pose for sauropods. If you have an image of sauropods holding their towering necks high like giraffes, you’re probably thinking of the much-painted 80-foot-long Brachiosaurus from the American West. Yet Stevens has shown that such a pose is beyond its ability. It normally held its 30-foot neck at about 20 degrees above horizontal, its head only 18 feet above the ground. It could move only some 9 feet to either side.
For now Stevens and Parrish are reconstructing as many sauropods as they can, leaving the full interpretation of their results for later. Still, they can’t help wondering whether the biomechanical variety they’re finding will help solve the ecological puzzle of sauropods. Sauropods were incredibly diverse for herbivores of their size: at Dinosaur National Monument in Utah, for example, four different genera of sauropods (each of which may have included several species) lived side by side 150 million years ago. Imagine an African savanna packed with four different species of elephant instead of one, and then multiply the weight of each elephant by ten. It’s hard to picture so many sauropod species feeding together without either driving one another into extinction through competition for resources or coming to a truce by specializing in different ecological niches.
The results of Stevens and Parrish’s work suggest that sauropods may have divided up their Mesozoic ecosystems in part by being able to maneuver their heads differently. “What you end up with in Brachiosaurus,” says Stevens, “is a neck that is straight out and high but that can’t flex much. It’s like one of the staircases you wheel up to an airplane. You wheel up to some vegetation, munch on it, and move on to the next.” Meanwhile Apatosaurus, with its flexible neck, could have lived as a jack-of-all-trades, able to maneuver its mouth to all sides of a fern or cycad. Diplodocus, with its rigid, downward-sloping neck and its head close to the ground, might have spent most of its time feeding like a grazing cow on ground-hugging vegetation.
One of the oddest results to come out of Stevens’s computer is the extent to which some sauropods could reach down. The lowest that Brachiosaurus–the airplane-stairway dinosaur–could get its head was about five feet off the ground. It might have faced the same troubles trying to drink water that giraffes face today, but whether it splayed its legs apart like a giraffe is anybody’s guess. Apatosaurus and Diplodocus had no such difficulties: when Stevens brings their necks down as far as the zygapophyses will allow, their heads end up as far as six feet underground.
Stevens and Parrish have been scratching their heads over this finding. Why would an animal maintain flexibility for an impossible movement? It’s conceivable that these species needed to be so oddly limber while they were still embryos, to curl their necks up in the egg. If that were the case, however, you might expect that other sauropods would be as flexible. Perhaps the nineteenth century paleontologists were right after all, up to a point: perhaps the dinosaurs did in fact sometimes feed on underwater vegetation but did so by standing on dry land and plunging their heads deep into a lake or swamp.
Or perhaps it’s Bakker who is right. Stevens’s work does indeed suggest that sauropods might have reared up on their hind legs without doing much harm to their backs, but Parrish wonders if they’d really want to bother trying to reach the treetops that way. “The tall part of the flora is dominated by conifers,” he explains. “Everything in the biologist in me goes against specializing on conifers, because the nutrition is so low. If you think of picking the pinecones off a pine tree–think of how much work that would have to be. Sauropods had to be going after something that was abundant and easy to procure.” Parrish thinks the sauropods would have to stick to the lush understory instead to eat efficiently. The computer-generated necks of Diplodocus and Apatosaurus might make sense for this kind of browsing if they reared up into a tripod position. Rather than reach the treetops, their oddly flexible necks would have let them feed down the length of a tree.
A bizarre picture, to be sure, but no more bizarre than sauropod bulls confronting each other with cracks of 40-foot-long whips. And no more bizarre, for that matter, than cyberpaleontology itself, and the thought that the secrets of the very big might someday be revealed by the technology of the very small.
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