Darwin’s Devices

Chapter 6 PREDATOR, PREY, AND VERTEBRAE

WE ALL KNOW WHY PREDATION IS SUCH A STRONG SELECTION force: dying sucks. Those about to die, here to salute you, are the Tadro4 prey, introduced in the last chapter as the feed-or-flee Evolvabots. Even though the Tadro4s bear the name Tadro, they are, compared to Tadro3, a different kettle of fish. The most important changes have to do with what Tadro4 and its whole new world seek to model: vertebrates in a prey-versus-predator world. Tadro4 has to be equipped with a new nervous system and a new body in order to eat and try not to be eaten. And, to pull this all off, we also needed to design and build a predator capable of tracking and chasing the Tadro4 prey.

When you are in the middle of a big, multiyear project like the Tadro3-athon, you have plenty of time to second-guess your no-turning-back decisions. We’d regularly convene our whole team of Vassar and Lafayette College researchers, give progress reports, teach one another about our different fields, and then try to find gentle ways to tell our colleagues and students that their work was a piece of sh …, sh …, shaving cream. That’s the charm and the curse of the academic: you are trained to criticize anything that moves. We are trained to be intellectual predators. As professorial types, we model this predatory behavior for our students, stalking not people but the ideas that they use and generate. We also model being the prey, the one presenting an argument to the circling sharks.

All students are prey. Sorry. When we are in student mode, we have to admit first to ourselves and then to others that we don’t know something. Talk about vulnerability! Who wants to be an openly vulnerable prey item? But ignorance or misunderstanding is a problem: no way around it. So anytime we want to get better at what we are doing, we have to admit that we have problems. As Jenny Ming, cofounder and past president of the clothing retailer Old Navy, said, “You can’t fix something if you don’t admit it’s wrong.”[105]

Okay. What’s wrong with Tadro3? I’ve already taken you through our acute crisis of confidence in Chapter 4. When the population of Tadro3s wasn’t evolving as we predicted, we switched our collective behavioral mode from conduct-experiments-and-analyze-data to stop-and-look-for-mistakes. We found the mistake that turned out to be a happy one: the wobble of Tadro3 was not a sign of energy inefficiency but rather a metric of enhanced maneuverability. That problem was tactical. On the strategic level chronic problems can’t be solved in the same way: they are a by-product of making plans. Once a particular set of strategic plans are set in motion, chronic problems persist unless you revise and start over or until you evaluate the strategically flawed experiment and design the next one.

On the strategic level, you can argue, as my colleague in biology did way back in Chapter 1, that modeling itself is a conceptually flawed process. You won’t be surprised, from everything I’ve said about modeling, that I disagree with the no-modeling critique.

At the same time, I agree with Barbara Webb (see Chapter 3): we need to justify carefully the specific modeling approach that we take. So now that you’ve been through our design process (Chapter 3), seen the Tadro3 model system in action (Chapter 4), and gotten a taste of the mechanisms that help us understand Tadro3’s behavior (Chapter 5), we can revisit Webb’s criteria for judging the value of our biorobotic model.

By Webb’s criteria, have we produced a good model? Recall that in addition to “relevance” (= able to test a hypothesis) and “medium” (= physical basis of robot), we selected “behavioral match” and “mechanistic accuracy” as two other figures of merit for our Evolvabot models. Do we see matched behaviors and accurate mechanisms within the hierarchy of skeleton individuals population? In terms of behavioral match, the complexity of the evolutionary patterns in the Tadro3 system is evidence that the system behaves realistically on the population level. Further, because we know that evolutionary mechanisms of selection and randomness cause those complex patterns, the accuracy of those mechanisms is also high.

But what about the mechanistic accuracy of the Tadro3 itself, the levels in our hierarchy of individual and skeleton? When we present our evolutionary biorobotic work at the Annual Meeting of the Society for Integrative and Comparative Biology, I let our students know that they can expect a visit from a constructive predator from the laboratory of Robert Full, professor and director of the Poly-pedal Laboratory at the University of California. Full is world famous for his careful experimental study of invertebrates, isolation of functional principles that unify seemingly different behaviors, and implementation of those principles in the design and operation of biomimetic robots.[106] So when Full or one of his colleagues arrives to critique, we are, as the Ferengi say, all ears.[107]

One of the most powerful critiques from Full’s lab is that our Tadros are too simple. Therefore, the argument goes, the Tadros are not accurate models of biological phenomena. Tadro3 fails as a model at the level of an individual agent. As with all useful critiques, it’s true, at least in part. So as prey items, eager to learn, we first try to admit that we have a problem. Then we try to figure out how—or if—to fix it. One defensive fix is to attempt to do a better job of explaining the different ways that you can judge biorobots as scientific models. That’s why I summarized Barbara Webb’s approach to biorobotic modeling in the first place.[108]

Another fix is to go back to the beginning and revisit the KISS principle. We used KISS to justify creating a simple model first. Now we were being criticized for the simplicity of Tadro3. So what’s next? What new elements do we add to the model, and why? Will those new features, which will certainly make our robots more complex, also be the right ones to make our models more accurate mechanistically and in terms of representing biological systems? To answer the what-next question is why I took the time in Chapter 5 to talk about embodied brains, neural circuits, and the subsumption approach to modeling the recticulospinal sensory-motor system of fish. We add biologically based complexity to the nervous system of Tadro3 to create Tadro4.

But what about testing a hypothesis? Is the Tadro3 system relevant? Yes. We set out to use our Evolvabots to test the hypothesis that selection for enhanced feeding behavior drove the evolution of vertebrae in early vertebrates. We substituted structural stiffness of the notochord for number of vertebrae in a vertebral column. Because the population of Tadro3 evolved reduced structural stiffness but better swimming behavior under selection, we disproved the hypothesis that selection for enhanced feeding behavior drove the evolution of vertebrae. However, we came to recognize that the hypothesis itself is probably overly simplistic, given that feeding behavior and structural stiffness of the notochord can become decoupled with a fitness function that rewards multiple sub-behaviors for feeding alone. This led us to add complexity to the selection environment of Tadro3, tossing in a predator to create the wild and crazy new world of Tadro4.

Another set of critiques of Tadro3 came from the predators within. Every time we got our multi-institutional research group together, Rob Root, professor of mathematics at Lafayette College and one of the team leaders on the evolutionary simulation project, was always itching to sink his teeth into the robotic Tadro3. One of the many great things about collaborating with Rob is that his bites are gentle and always meant to be constructive. It also helps that he is persistent when we want to deny that we’ve got any problems. As we slowly unrolled the methods and results from the Tadro3 experiments over many months, here’s the blood in the water that got Rob’s jaws clacking: (1) our fitness function was a composite of feeding-related behaviors rather than being, for example, the actual amount of food collected; (2) our fitness function was a sum of unscaled measures; (3) the composite feeding behavior did not include acceleration performance; (4) the population size was too small (remember in Chapter 2 that Rob had brought up the issue of the large effect that randomness can have with a small number of cases); (5) the number of generations was too few to show large evolutionary trends, and (6) vertebrae were missing in action.

I ran these recollections by Rob recently. He agreed that these had been his primary critiques. He had always found it fascinating, he added, that vertebrae evolved independently multiple times in vertebrates. That convergent evolution, he noted, appeared to be contingent upon the prior evolution of enhanced sensory systems, notably the paired nose, eyes, and ears that characterize vertebrates. This observation is part of the justification for the sophisticated nervous system and sensor systems that we talked about in the last chapter: Tadro4, to succeed as a potential prey in the prey-versus-predator world, needs to have the nervous and sensory-motor systems to give itself a fighting chance of survival.[109]

At the time of Rob’s critiques, all we could say, given that we couldn’t change our evolving Tadro3 system mid-stream, was, “Great points, Rob! Well taken. Next time.” Fortunately, at the same time that the robotic Tadro3 system was busy evolving, Rob and another one of our collaborators, Chun Wai Liew, associate professor of computer science at Lafayette College, were taking on the Tadro3 system and the biological hypothesis it tests using a different technique: digital simulation.

I’d done my own predatory critique back in Chapter 1, bringing up digital simulation only to dismiss it. The dismissal part was not entirely fair, I know, and it raised some hackles on my friends who gave me feedback on the early draft of that chapter. My point, which I still argue is valid, was that embodied robots have the advantage over digital ones because the embodied ’bots can’t violate the laws of physics. This is true. However, if you can build an accurate “physics engine”[110] and use it in your digital simulation, then you can avoid creating completely unrealistic models. You can even learn something too, as we’ll see.

To model a world that gives your actions predictability, you need the rules that a physics engine provides. Gravity, momentum transfer, and projectile motion are all implicit rules in role-playing video games like Grand Theft Auto. Entertainment, argues Tom Ellman, associate professor of computer science at Vassar, is just the tip of the iceberg for physics-based animation. Science, education, and engineering are other areas in which realistic world models are important. Although building situation-specific animations is difficult and time consuming, Tom has developed software that automatically, based on inputs from an interactive human user, unfolds the physics-based world.[111] Aeronautical and automotive engineers use real-time three-dimensional animation of rigid bodies to help speed the development of new airplanes and cars. When you can build and test a vehicle on the computer, then you can bend, twist, kill, crush, and destroy it with impunity. And you can do so over and over to explore the impact of changes in the vehicle’s design.

As part of their design process using a digitally simulated world, engineers also employ what they call “genetic algorithms” (GA). The GA approach is evolutionary, using randomness to create novel variants of a design. The performance of the variants is judged using a fitness function that seeks to maximize, usually, a single aspect of performance. The variants with the best fitness are selected to mutate and mate to create a next generation of novel designs for testing.

By searching for an engineering design that optimizes a single aspect of performance, such as fuel economy, the GA process is an example of a class of procedures called “hill climbing” routines. The hill, in this case, is the specific area in your design space that combines features in a way that gives you the best possible—the optimal—results.[112] Once your evolutionary simulation finds the top of a hill, you then stop and build the winning design as a physical entity. By the way, only if that physical embodiment of the digital simulation works as predicted can your digital simulation be said to have been “validated.” In many ways, we were validating backward, having started with a physical system, Tadro3, and creating the digital simulation of it.

In need of a physics engine for the Tadro3 world, Rob, Chun Wai, and their students Megan Cummins and Greg Rodebaugh took on the task. They had to simulate the force-coupled interactions of the elastic and flexible tail of Tadro3 with the water motion that the tail and body creates. No matter how simple “go build a physics engine for Tadro3” sounds, in practice the problem is a bear, for reasons mentioned in the last chapter when we were talking about using the body rather than the nervous system to “solve” all the hard computational problems. Here we actually had to grapple with all the mathematical complexity. Rob and Greg focused on a creating a tractable approach to the physics. They began by modifying the “immersed boundary layer” method created by Charles Peskin, professor of mathematics at New York University’s Courant Institute, to work for the particular situation of swimming fish.

Meanwhile, Chun Wai, an expert in evolutionary computing, wisely proposed that while Rob and Greg were building the better physics engine, he and Megan make progress on the digital evolution front by using a less accurate but computationally straightforward mathematical model, developed by the late Sir James Lighthill, called the elongated-body theory (EBT). With help from Rob, they used EBT to calculate the thrust that the digital Tadro3 would generate. Once digital Tadro3s could wiggle their tails, generate thrust, swim, and turn, Chun Wai and Megan created an evolutionary world, one in which the digital Tadro3s (let’s call them digi-Tad3s) attempted to detect light, swim toward it, and then orbit it (Figure 6.1).

Sound familiar? It should: the digi-Tad3 world modeled the physical world of the robotic Tadro3. Released from the time-and-person constraints of experiments in the real robotic world, we could test thousands of individual digi-Tad3s in each generation and, furthermore, test thousands of generations. Best of all, the digi-Tad3s gave us the ability to rerun the experiment hundreds of times, each time varying the tail stiffness with which the population started.[113] It’s true: you just can’t do that with embodied robots.

The most interesting result from all of the digi-Tad3 runs was this: no matter where a population of digi-Tad3s started in terms of average tail stiffness, the population evolved toward the same value of stiffness, what looks like an equilibrium (Figure 6.1, lower graph). We’ve called this equilibrium value the “optimal hill of tail stiffness” because it appears to balance the mechanical demand of rapid propulsion, on the one hand, and maneuverability, on the other. Although a very stiff vertebral column allows the digi-Tad3 to swim quickly, that same stiff-tailed digi-Tad3 can’t orbit tightly around the light source. The balance between speed and maneuverability is enforced by the fitness function, which rewards increased speed and, at the same time, a decreased orbital radius.

What we’ve learned about the apparently optimal tail stiffness in Digi-Tad3 helps us understand good ol’ embodied Tadro3. If you remember, two of the four times that selection was present in the population of Tadro3s, the tail stiffness increased. Tail stiffness of the population decreased the other two times that selection was present. We highlighted this pattern in Chapter 4 by pointing out this surprise: the same selection pressure generated two different directional trends. What Digi-Tad3 suggests about this oscillation is that the stiffness of Tadro3’s tail was moving back and forth in order to keep climbing the hill and finding the equilibrium. In other words, we didn’t see tail stiffness evolve in a single direction because we happened, by chance, to have started the population of Tadro3s next to the hill of optimal stiffness. Tadro3 was “born on the side of a hill.”[114]

In both digital and embodied worlds the fitness function computes the selection pressure in each generation. The fitness function is the algorithm that we use to judge the players in the game of life. Differences in the performance of the players, coupled with the random influences of mating, mutation, and genetic drift, change the composition of the population of players generation by generation.

Given selection’s central role in the evolutionary game, Rob’s point about how we implemented the fitness function in Tadro3 was a great one. He suggested that we simply measure the energy that each Tadro3 harvested. Nick Livingston, working as the assistant director of the Interdisciplinary Robotics Research Laboratory at Vassar, hit upon the same idea. To measure the amount of energy harvested, Nick suggested that we mount a small solar panel on top of each Tadro and let the Evolvabots use the energy that they collect as a direct fitness function. Just let the Tadros go: “Fly! Be Free!”[115] The Tadro with the highest fitness would be the last Evolvabot standing, figuratively, or swimming, literally.

A solar-powered Tadro4 is a great idea for both strategic and tactical reasons. Strategically, we’d be using actual energy harvesting as a behavior linked directly to survival, just like organic agents do. Direct energy harvesting would eliminate the criticism that we were “just” simulating selection with the fitness function calculated from numbers assigned to a host of arbitrary behaviors. Tactically, direct energy harvesting would make our experiments run much faster. When we analyze video frame by frame and manually select the points of all our robots, we end up needing tens of person-hours of earnest effort to make it happen. Because we need the data from the video to calculate fitness and we need fitness to create the genomes of our next generation of Tadro3s, the video analysis is a bottleneck. Perhaps more importantly, we all go mad, mad, mad from the excruciating boredom of the manual process.[116] I’m always surprised that video analysis is not a stronger selection pressure on our students; they are really tough (some even claim, when pressed, to “not mind it”—these students are the Zen masters among us).

Direct energy harvesting for locomotion should work, no problem. Solar-powered cars race across the Australian Outback in the World Solar Challenge.[117] We took a page from their playbook and added a solar panel to a Tadro3. We wired the panel to provide electrical power to a battery. However, we ran, or swam, into an immediate problem: we didn’t have enough solar power. Tadro3’s water world, unlike the desert, has a limited supply of light, a concentrated source that is surrounded by near-dark conditions. We tried increasing the overall level of light, but then we quickly overwhelmed the light sensors, and they couldn’t detect any differences. We added sunglasses (I’m not joking), but still no luck. Then we took a different tack. We gave the Tadros a small electrical charge to get going in the dark. However, in practice, each Tadro gets a slightly different amount of energy. This unfairness comes about because all batteries are slightly different in terms of their power densities and other electrical properties that govern how much energy they store and how easily it flows. We could never be certain that the charge given was the same, even when we meant it to be. Also, batteries with only a little bit of charge tend to discharge erratically. Stymied by these physical realities in our water world, we abandoned the solar ship.

This left us with our old indirect fitness nemesis: calculate a host of performance metrics and put them together to yield a single number, the individual’s evolutionary fitness. With the addition of predator-avoidance to the mix, we obviously needed to shake things up a bit. Based on what we’d learned about Tadro3 in Chapter 4, we reasoned that feeding behavior was measured well by two sub-behaviors: (1) average speed throughout the trial and (2) average distance from the light.[118] We took Rob’s point about acceleration to heart and added three additional sub-behaviors we thought were critical for avoiding predators: (3) peak acceleration during an escape, (4) number of escapes, and (5) average distance from the predator.

Rob had also made the point that we needed to scale each of these sub-behaviors by how much they varied among the individuals we were testing. For those of you who know and care about statistics, he suggested we use what’s called a z-score. In our case, we start by taking the difference between, say, individual 5’s peak acceleration and the average peak acceleration of all six of the Tadro4 individuals in that generation. That difference is then scaled by dividing by the standard deviation of the peak acceleration for all individuals in that population. For the predator-prey world, then, an individual’s evolutionary fitness is the sum of the z-scores from the five sub-behaviors.

In that explanation of z-scores you can see that we also addressed another of Rob’s criticisms of Tadro3: we expanded the population size from three to six for Tadro4. When we told this to Rob, he burst out laughing: “Wow! Six individuals. That’s a really big population, John.” Where would we be without friends to point out sarcastically the ridiculous? But here, again, the ugly anterior extremity of actually running the experiment rears up. When we double the population size, we double the amount of tail building and video analysis that we have to do. We thought we’d give six a try and see if we could survive. We did, and as you’ll see, we’re darn proud of all of that work!

The work that we do is also multiplied by the number of generations that we run. Rob wanted more generations because he knew that evolutionary change is usually slow and gradual. Also, he had seen that our populations of digi-Tad3s needed, at a minimum, one hundred generations to find the equilibrium of optimal stiffness. But given that we were already doubling the work by doubling the population size, the best we could promise here was to try to make it to ten generations.

The final criticism—no vertebrae—was one that we all knew from the start of the whole Evolvabot project. When Joe Schumacher had made Tadro2 he had used a long eraser as the notochord and snapped tube clamps around it to simulate rigid vertebrae. This was a great solution at the time. When we designed Tadro3 we had focused on building a biomimetic axial skeleton, in part to deal with the kind of criticism that Bob Full had about our mechanistic accuracy at the level of the skeleton. Because the notochord of the biomimetic skeleton was built from molecular collagen, the stuff of real animal connective tissues, we were pleased as punch on the accuracy side of things. However, as soon as we tried to put Joe’s tube clamps on the biomimetic notochord, we destroyed it. The gelatin just was too brittle to withstand much in the way of squeezing or clamping; it would form small cracks that would then propagate into wholesale and catastrophic notochordal failure during swimming.

“Damn the torpedoes—full speed ahead!”[119] We had to have vertebrae. In Chapter 3 we talked about why building a vertebral column was a challenge: we have to attach dry and rigid structures, the vertebrae, to wet and flexible ones, the intervertebral joints. The composite assembly of alternating vertebrae and joints needs to be mechanically robust enough to be used as the propulsive tail of a Tadro. In addition, the joints, where the bending occurs, have to be of a biologically realistic stiffness. At the time of Tadro3 we’d been unable to meet this design specification, so we compromised by building the continuous hydrogels of different material stiffnesses.

Our failures with Tadro3 taught us that we needed to come up with some new tricks for Tadro4. Because we knew that working in isolation can sometimes produce creative and unexpected results, we decided to split our multi-institutional team in two.[120] Our first marine platoon was led by Tom Koob at the Shriners Hospital for Children in Tampa, Florida. Working with Adam Summers, associate professor and associate director of the Friday Harbor Laboratories at the University of Washington, and Adam’s PhD student, Justin Schaefer, Tom’s team took the high road. First, they created beautiful double cup–shaped vertebrae, just like the kinds you find in sharks, in a software program engineers use called SolidWorks. They then used a rapid prototyping machine to convert the three-dimensional software objects into 3-D physical objects (Figure 6.2).

A single vertebra is composed of a number of structures: a vertebral centrum, the cylinders shown in Figure 6.2 that form a chain of bones separated by the intervertebral joints; a neural arch, a rigid structure running along the top of the centra that forms a c-shaped covering over the nervous system’s spinal cord (note: the spinal cord does not run through the intracentral canal, the hole that runs through the centrum shown in Figure 6.2); sometimes a neural spine, a spike of bone that shoots up off the top of the neural arch; a hemal arch, the mirror opposite of the neural spine, covering the major veins and arteries that run under the centra posterior to the anus; sometimes a hemal spine, a spike of bone that shoots down from the bottom of the hemal arch.

The exact structure of a vertebra depends on which species you are looking at and where along the vertebral column you happen to be looking. Because we were using the caudal vertebrae of sharks as our biological target (Figures 6.2 and 6.3), let me describe them.[121] Compared to those of bony fishes, the vertebrae of sharks are relatively simple, lacking neural and hemal spines (Figure 6.4). The neural and hemal arches are not fused to the centra, and those arches form their own small-diameter columns that span the intervertebral joints.

To make a vertebral column Justin and Tom figured out how to sew the vertebrae together using long horse hairs glued to the perimeter of each element. Because the hairs serve the same function as the intervertebral ligaments of real vertebral columns, we called this model 1 the ligament-linked artificial vertebral column (Figure 6.3). Between the vertebrae they injected gelatin, like the marshmallow in the middle of a camper’s s’more. Once the gelatin firmed up, the whole column was bathed in a chemical fixative. This fixative cross-linked the gelatin, making the molecular collagen into a lattice that was both stiffer than the raw gelatin and resistant to degradation. This may sound familiar: the hydrogels that we made from gelatin and cross-linked were our artificial notochords that functioned as the axial skeleton in Tadro3.

Our second marine platoon worked at Vassar and was led by Kira Irving, a major in our neuroscience and behavior program at the time. Kira had been part of the Tadro3 team, along with Keon Combie, a major in biochemistry, and Virginia Engel and Gianna McArthur, both majors in biology. This group also got help from Kurt Bantilan, another major in neuroscience and behavior, and Carl Bertsche, Vassar’s resident expert in machining.

In response to the problem of holding together a chain of rigid and flexible elements, Kira’s team came up with a solution quite different from that of Tom’s (Figure 6.5). Instead of using horse hairs as ligaments, they used thin plastic coffee stirrers as neural and hemal arches running along the top and bottom of the column, spanning each joint and preventing dislocation. This was a shark-like solution (see Figure 6.4), and it gave us the ability to explore something unusual: having very long intervertebral joints. We call this model 2 the arch-linked artificial vertebral column.

Both model 1 and model 2 gave us three structures to evolve: (1) the length of the centrum, (2) the angle of the concave joint surface on the centrum, and (3) the length of the intervertebral joint. In this respect, they were equivalent models. Where they differed dramatically, however, was in how they operated mechanically when we bent them. Model 1, the ligament-linked vertebral column, appeared to be dominated by the mechanical properties of the horse hairs. Doug Pringle, a gifted mechanical engineer in Tom’s lab, helped Justin perform bending tests on the biomimetic vertebral columns. Instead of stretching the horse hairs on one side (the convex side) and squishing the joint material on the other side (concave side) during bending, they noticed that the horse hairs were stiff enough that they weren’t allowing much stretching. As a result, the model 1 column bent by compressing one side, buckling locally at each joint. If you can picture this geometry in your head, then if one side of the column compresses while the other stays the same length, then the whole structure bends and shortens.

Shortening of the column didn’t happen in model 2, the arch-linked vertebral column, because it used the coffee stirrers to hold the length of the column constant along its midline. During bending we saw compression of the concave side of the joint and elongation of the convex side. This looked good—at first. However, on the elongated side of the bend, we could sometimes see a separation of the hydrogel material from the face of the rigid vertebra. When this occurred it meant that the bending properties of the joint were being controlled only by the hydrogel on the compression side and the neural and hemal spines along the midline. To keep the joint attached to the vertebra, we found that we could put in a little bit of cyanoacrylate glue.

Both models of the vertebral column are beautiful examples of biomimetic design (not that I’m biased or anything). They capture the composite nature of real vertebral columns, creating a serial column of rigid and flexible material.[122] They both use a collagen-derived hydrogel for the viscoelastic intervertebral joint. They both have vertebral centra with the cup-shaped joint surfaces that we see in sharks. In addition, even though the two kinds of columns bend in different ways, their stiffness is in the same range as the stiffness we find in the vertebral columns of sharks. In order to fine-tune our biomimetic designs, we continue to explore the mechanical behavior of both the biomimetic vertebral columns and the shark vertebral columns under the expert guidance of Dr. Marianne Porter, a postdoctoral researcher in my laboratory.

The biomimetic design from Tom’s lab was the preliminary winner. We thought we could solve the problem of the too-stiff horse hairs by using either fewer hairs or a different kind of material for a ligament. In addition, the arch-linked design, by virtue of its arches, had bending stiffness even when no joint was present. As with the horse hairs, we could solve that problem by reducing the stiffness of the arches. With the arch design we were also having some problems making the vertebrae and, as mentioned, keeping the joint attached to the vertebrae. The rapid prototyping, because it was computer controlled, made centra more repeatably than our hand-milled process. In addition, the horse hairs, by enforcing bending by buckling, never let the vertebrae unleash the joint material.

Thus, we began with the ligament-linked model 1. Because we were performing the robotic experiments at Vassar, we needed to train our students how to make the model 1 biomimetic vertebral columns. Because Tom and I had been meeting for research every fall at the Mount Desert Island Biological Laboratory in Salisbury Cove, Maine, we decided to use our time there to transfer the production technology. Keon and Virginia came with me to learn the task. Keon, always very keen on new techniques, volunteered to be the first trainee. Despite Tom’s patience and Keon’s prowess as an experimentalist, the manufacturing of the ligament-linked columns was proving to be slow at best, and a mess at worst. Imagine having to align seven small objects, keep them equally spaced, and then glue long fibers to their outsides. We built little rigs to help align and hold all the parts, but still, on most days we found that Keon soon became one with the vertebral column. Virginia and I were even worse. Our collective failure made us appreciate the abilities of Justin, who made the series of original model 1 vertebral columns down in Tom’s lab in Florida. However, Justin, working on his own PhD project, was unavailable for full-time work in our vertebral column factory at Vassar.

When we returned to Vassar bearing the bad news about model 1, Kira resolved to find a better way to build model 2. Rather than linking with the stiff coffee stirrers, she designed a method to hang the vertebrae, like a string of pearls, into a mold and pour gelatin around the whole construct. The gelatin encased the vertebral column, forming a sort of pig-in-a-blanket. I loved this idea because the blanket encasement was the beginning of a body, a structure that we had blithely ignored in our previous attempts to build a vertebrated tail. With a bit more work, we thought that this new vertebral column + body design would work.

When Kira, Keon, Kurt, Gianna, Virginia, and I contemplated honing the new pig-in-a-blanket design, we had an epiphany: stop! We were spending all of our time making biomimetic vertebral columns and none of it evolving robots. The lack of a working Tadro4 system was particularly poignant because we had just welcomed into the lab a talented robot engineer, Nicole Doorly, a major in cognitive science. In order not to lose her and to move our research program along, we had to settle quickly on a vertebral column design that, in our unsteady hands, we could scale up in order to produce reliable and custom columns at the rate that we needed.

Compromise. Everybody hates that word. A compromise, it is rumored, is guaranteed to satisfy no one. No one on Team Tadro was going to be satisfied with a compromise because we’d put so much time into the design and prototyping of the fancy models 1 and 2. We were scared of the bête noire of compromise under the bed, knowing all the work that we were about to discard. Enter sandman: “Take my hand. We’re off to Never-Never Land.”[123]

In the new predator-prey land of Tadro4, the biomimetic-vertebral-column compromise consists of an artificial notochord, borrowed from Tadro3, outfitted with a series of rings forming vertebrae (Figure 6.6). This model 3, which we call, surprisingly, the ring centra vertebral column, has a number of advantages, he says bravely, over the previous vertebral column models: (1) it doesn’t need to be held together by ligaments or neural arches, (2) it has fewer parts than either model 1 or 2, and (3) it can be assembled more quickly, in about five minutes (compared to thirty minutes) once all of the parts are present.

What we lose with model 3, though, is the ability to evolve the shape of the centra because the ring centra have no cup-like joint faces.[124] With that simplification, we also lose the close approximation of shape to the vertebral columns of sharks. And we’re not done yet. We further simplified manufacturing, keeping the overall length of the vertebral column constant.

Simplification begets simplification. A constant column length plus unchanging centra meant that only the length of the vertebral joint could change as the number of vertebrae did. Simple! Increase the number of vertebra, and the amount of intervertebral joint available for bending decreases, thereby stiffening the vertebral column.

The full manufacturing process for model 3 involved making a slew of hydrogels, cross-linking them all in the same way so as to produce artificial notochords of similar material properties, and then gluing ring centra to each notochord to create an artificial vertebral column (Figure 6.6). This process was scaled up to production level for the game of life with Tadro4, under Gianna’s supervision, with Hannah Rosenblum, Hassan Sakhtah, Elise Stickles, and Andres Gutierrez operating our assembly line.

Because we distilled the evolution of the vertebral column down to a single trait—number of vertebrae—we had a system that allowed us to test our next biological hypothesis: selection for enhanced feeding behavior and predator avoidance drove the evolution of vertebrae. Testing this hypothesis also relies on the design of the stuff attached to the vertebral column, which I haven’t told you about yet. We need the body with sensors to track light and predators, a microcontroller to compute the two-layer subsumption neural system, and motors to flap and turn the tail. All of this comes together in Tadro4 (Figure 6.7).

Tadro4 is really two different kinds of robot: an Evolvabot that we call “PreyRo” (Prey and Robot) and a nonevolving robot predator, “Tadiator” (Tadpole and Gladiator). When PreyRo and Tadiator interact in a water world with a light source, this is the Tadro4 predator-prey world (Figure 6.8). The fact that Tadiator doesn’t evolve doesn’t worry us, by the way. In biological predator-prey systems, predators are often much longer lived than their prey. Not that an evolving predator wouldn’t be interesting! But we’ve got to leave something to do in the Tadro5 world.

PreyRo is modeled after a species of Paleozoic fish called Drepanaspis gemeundenensis (Figure 6.7). Drepanaspis, a jawless marine fish living 400 million years ago, swam using a short flexible tail and a rigid, flattened disk of a body, which lacked paired fins of any sort. Preserved in the bones that form its rigid body disk is the evidence of its sensory systems: a pair of small and widely spaced eyes and a lateral line system.[125] The flattened shape of the body of Drepanaspis is similar to that of living skates, stingrays, and electric rays, most of whom spend time on and in the ocean floor, feeding, burrowing, and resting. As Marianne pointed out, electric rays may be the most similar living species to Drepanaspis in terms of locomotor function if not ancestry because neither has or had the ability to use its body disk for propulsion. They generate thrust with a short tail that makes the whole animal look like a pancake propelled by a headless fish pushing, tugboat-like, from the rear. What we know about electric rays is that they are able to swim up in the water column. We suspect that Drepanaspis had the same ability.

Critters with hard shells, like Drepanaspis or any number of mollusks during those ancient times, appear to have been under intense selection pressure from predators, evolving tough armor and sea bottom–loving habits in response.[126] But even shells and armor could be crushed by the giant jawed fishes of the day, like Dunkleosteus, who had the prerequisite size, skeletal structure, and muscle strength to do the job, as shown by Mark Westneat, curator of zoology at the Field Museum of Natural History and director of the Biodiversity Synthesis Center.[127] So if you were smart, in an evolutionary sense, you, as a jawless fish and potential meal, couldn’t rely on armor alone. Best not even to test your armor in the first place. Run!

Cowards get a bad rap. But dying sucks, remember? Cowards survive, for the moment, by running away. Running or swimming or flying away turns out to be the nearly universal response of animals to danger. Only those glued to a rock, hiding in a burrow, blessed with camouflage, or hormone-crazed in mating season don’t flee to escape from danger. As we’ve seen, fish rely on the lateral line to detect dangers, and we built one using an infrared (IR) proximity detector, a small device that emits an IR pulse and uses the time it takes for the pulse to bounce back off an object to calculate the distance to the object. The mechanism is quite different, but the function is the same.[128]

Nicole, our chief engineer on the Tadro4 project, put an IR sensor on each side of PreyRo along with the two photoresistors serving as eyespots (Figure 6.7). The onboard microcontroller continuously samples both kinds of paired sense organs. If you remember the subsumption architecture we described in Chapter 5, then you can probably see the solution. At the default, or lowest level, PreyRo forages and feeds, using the difference in light intensity between the two photoresistors to calculate the direction to the light source. PreyRo is constantly making adjustments in its heading to make that difference zero, where a difference of zero means that it’s headed straight up the light-intensity gradient. And so PreyRo forages to feed on the light. Until, that is, the escape behavior overrides the forage-and-feed behavioral module.

The escape behavior is triggered when either the left or right IR proximity sensor detects an object within a preset threshold distance. If the left sensor triggers, then PreyRo interrupts the forage-and-flee behavior and initiates a fixed turning maneuver to move quickly to the right. The opposite is true if the right sensor triggers. Because this “predator detection threshold” can be altered in the programming of the microcontroller, we could evolve it.

This sensory character gives us a crude way to test Rob’s prediction that the evolution of the vertebrate nervous system—characterized in part by its paired sensory systems—has to evolve first in order to permit vertebrae to evolve. In other words, we predict that the evolution of vertebrae is contingent upon the prior evolution of, in this specific case, the sensitivity of the predator-detection system. This makes functional sense: why would the enhanced propulsion that vertebrae bring ever evolve without some means of detecting when it’s time to use it? The only way you know is to have a sensory system capable of detecting the predators. And although the eyes you use for foraging and feeding give you some predator-detection capabilities, you can’t see at night or in the dark of the deep. A lateral line, however, works anytime and anywhere. But just because a pattern makes functional sense to us doesn’t have any bearing on how and why that pattern actually occurred.

If the proposed functional codependence were true, I’d be sorely tempted to call the pattern “contingent-sequential evolution.” Sorry for the mouth-full phrase, but one can’t be too careful when speaking of evolutionary phenomena. The contingency refers specifically to an identified causal interaction of the characters. Without a causal mechanism, we just have a correlation. Correlations may occur by accident, for no other reason than two unrelated things happen to share a pattern. However, we never want to ignore correlations because functionally codependent systems are always, in some way, correlated.

When the pattern of the evolution of two or more characters are correlated, then that pattern is called—you guessed it—“correlated evolution.” When the correlation has a causal basis, it is called—you’ll never guess it—“concerted evolution.” Maybe you can see why, for a specific sequenced pattern of concerted evolution, I’ve proposed the phrase “contingent-sequential evolution.” Whatever the pattern of concerted evolution, to claim that you have one requires that you show the specific functional codependence between or among the characters. Categories of potential functional mechanism include genetic, developmental, and physiological.

Whereas concerted evolution means that two or more characters evolved because of their interactions, when no interactions are present we call that a pattern of “mosaic evolution.” Mosaic evolution was introduced in Chapter 2 so that we could make the important point that species are not “primitive” or “derived” but are, instead, mosaics of both ancestral and derived characters. Mosaic evolution is a fact of life, but it’s not the only fact of life. Concerted evolution is also a fact. If we look at enough characters, we will see both kinds of character evolution in any species: mosaic and concerted.[129]

In addition to our predicted lateral-line vertebrae pattern of sequential-contingent evolution, we also expect concerted evolution within the propulsion system itself. A character of all fishes, extinct and living, that varies like crazy is the shape of the caudal fin. The earliest known vertebrate, Haikouichthys,[130] has a caudal fin that tapers to a point, like an eel. Yet our Tadro4 target, Drepanaspis, has a twolobed caudal fin that splays apart, forming a sharp vertical trailing edge, or “Kutta condition,” to use the hydrodynamic lingo.[131] These two kinds of tails, tapered and splayed, are just some of the kinds that we see. In terms of propulsion, what matters is the length of that trailing edge, measured as the “span” of the caudal fin. The trailing edge is where the body sheds so-called bound vorticity into the water. If we were to revisit Lighthill’s Elongated Body Theory (EBT), which we used earlier to propel our digi-Tad3s, then we’d see that propulsive power generated by the fish is proportional to the square of the tail’s span. That square term is huge: a slightly larger tail span should help produce much more power.

Because both the tail’s span and the vertebral column are involved in generating propulsion, we predict that the two characters will show concerted evolution. Here’s why, specifically. In order for the square-of-the-span magic to work, what I told you above assumes that everything else about the motion of the fish’s body stays the same, including how far it moves its caudal fin side to side, what we measure as the lateral amplitude of the caudal fin. But that caudal fin amplitude will decrease when you put a bigger caudal fin on the body—it has to. It’s like when you, ignoring the better judgment of your parents, used to stick your hand out the window when speeding down the highway. Palm down, hand parallel to the road? No problem. Rotate your hand ninety degrees. Boom! Your hand flies backward and you ram your arm into the window frame. Ouch. The difference is drag, which is low in the first position and high in the second position.

A tail with a larger span has more drag when it moves laterally than does a tail with a smaller span. When the small span is increased to the large, the only way to keep the amplitude of the caudal fin constant in the face of the increased drag is to generate more power internally, in the machinery that is driving the tail. Guess what? That internal machinery includes the vertebral column, which we know stores and releases elastic energy as it bends. So here’s the basis of our concerted-evolution prediction: a stiffer vertebral column could compensate for the increased drag that accompanies the increased span of the caudal fin.

We set out to test the hypothesis that selection for enhanced feeding performance and predator avoidance would increase the number of vertebrae. Next thing you know, we are yammering on about two other characters that we are going to evolve: the predator-detection threshold and the span of the caudal fin. We predicted that both of these other traits would evolve in concert with the number of vertebrae, with predation-detection evolving before vertebrae (the sequential-contingent pattern of concerted evolution) and the span of the caudal fin evolving at the same time (just plain old concerted evolution). The alternative hypotheses are that predation-detection may evolve at the same time as number of vertebrae (concerted evolution) or may not be correlated with the number of vertebrae (mosaic evolution). Span of the caudal fin, too, may not be correlated with the number of vertebrate (mosaic evolution).

The results of our evolutionary experiments in the predator-prey world of Tadro4 are fascinating (Figure 6.9). Our amazing Tadro4 teams met and exceeded all expectations. Led by Gianna in the summer of 2007, Hannah, Elise, Andres, and Hassan perfected the biomimetic-vertebral-column production line and conducted the first evolutionary run, which lasted for five generations before we had season-ending injuries to the robots.[132] Led by Hannah and Andres in the summer of 2008, Sonia Roberts and Jonathan Hirokawa conducted the second evolutionary run, which went for eleven generations. Because we started the two populations with the same average values for their evolving characters, the two runs are independent replications of the same experiment. It turns out that comparing the runs is critical for testing our hypotheses.

First and foremost, in both runs of the predator-prey world, the population of PreyRos quickly evolves more vertebrae, moving from the starting average of 4.5 to an average of 5.5 by the third generation. In the second run an equilibrium average of 5.7 vertebrae appears to have been reached. These early directional and positive increases, even though they are modest, provide tentative support for our big-picture hypothesis that the number of vertebrae increase when the population is under selection for enhanced performance in feeding and fleeing.

I can only say “tentatively support” because, as we talked about in Chapter 4, strictly speaking you can only falsify a hypothesis—you can’t prove it. So the phrase “tentatively support” is meant to recognize (1) that we have failed to falsify and (2) that over time repeated failures to falsify will eventually lead us to conclude that the hypothesis is probably true. Caution and consideration are required.

But it’s really, really hard not to get totally stoked when you see this pattern of evolutionary change. Emotionally, we—okay, I—want to yell, “Kick ass! We’ve proven that this specific type of selection on these fish-like autonomous agents works as we predicted!” But we mustn’t do that. And we mustn’t holler, “And we did it twice, you cynical bastards, and it worked both times! Evolvabots rock!” So we don’t. And we won’t. Ahem. What was I saying?

Right. “Dignity, always dignity.”[133] Please take the time to notice in Figure 6.9 that by reaching an apparent equilibrium, the population of PreyRos creates an evolutionary pattern with their average number of vertebrae that resembles the evolution pattern that we saw in the Digi-Tad3s and their average tail stiffness (see Figure 6.1). Is this coincidence? I think not. Once again we see evidence that is consistent with the hypothesis that the stiffness of the vertebrate axial skeleton has evolved to balance the mechanical demands of maneuverability, wherein a flexible axis works best, with those of speed, whereby a stiff axis outperforms.

Because we were evolving three characters—(1) number of vertebrae, (2) predator-detection threshold, and (3) span of the caudal fin—at the same time, the patterns of evolutionary change shared or not shared between them also inform. For example, in both runs of the predator-prey world, the PreyRo population’s changes in the predator-detection threshold are positively and strongly correlated with the changes in the number of vertebrae, at least over the first five generations (Figure 6.9, middle graph). This strong correlation tentatively supports the hypothesis of concerted evolution between these two characters. What we don’t see is a threshold-first-then-vertebrae-next pattern—with vertebrae lagging in time—that would support the sequential-contingent pattern.

This in-phase pattern of apparent concerted evolution is evidence that a functional codependence exists between sensing a predator and moving away from it.[134] Are we surprised? No. But that’s why you run the experiments. We aren’t surprised because we knew, from Chapter 5, that tightly linked perception-action feedback loops (PAFL) create behavioral modules. What’s new here is that we’ve shown that this particular PAFL—Escape!—is well characterized by the ability to detect predators and then flee from them. What’s also very interesting is that we’ve connected the Escape! PAFL to the evolution of vertebrae. This connection, measured here as a strong and positive correlation between predator-detection threshold and the number of vertebrae, allows us to understand how selection acting on behavior changes a feature of the skeleton.

We had also predicted an in-phase pattern of concerted evolution for the character pairing of number of vertebrae and the span of the caudal fin. Here, though (Figure 6.9, bottom graph), the direction of the correlation reverses from one run to the next, at least over the first five generations. Because we don’t see the same pattern in the two runs, this seems like a clear case in which we have refuted the hypothesis of concerted evolution. The default or “null” hypothesis is that the two characters show mosaic evolution, at least with respect to each other.

Mosaic evolution was a surprise. We thought for sure that these two characters, number of vertebrae and the span of the caudal fin, would show a functional connection because they are tightly connected in terms of anatomy and physiology. Again, this is why you run the experiments! This result highlights the fact that we always have to test our assumptions. I want to point out, though, that you could imagine different situations in which you might see a tight and consistent correlation between the two characters. For example, if we were just looking at swimming speed alone, devoid of any evolutionary environment, I’d predict that we’d see a relationship. So there!

It’s time to put our Tadros to bed. Tadro3, Digi-Tad3, and PreyRo (Tadro4) have done their jobs. They have evolved. Their characters—tail stiffness and the number of vertebrae—evolved and, in so doing, tested our hypotheses about what kinds of selection pressures may have driven the evolution of early vertebrates. We’ve learned that whereas selection for improved feeding behavior seems unlikely to have been the sole driver of increased number of vertebrae, when coupled with fleeing from predators, it becomes a much more powerful selective pressure.

With Tadros, we’ve seen how to start with the simplest autonomous agents you can imagine and then add in only the smallest bit of complexity needed to make a new and/or improved model of your biological system. Moreover, the simplicity of Tadros as embodied brains gave us an opportunity to understand the physical basis of the intelligence and behavior of feeding and fleeing. Finally, Tadros serve as working examples of this special category of robots that we’ve come to call Evolvabots.

As the Tadros sink into slumber, we still have much to explore.