Evolutionary conditions change drastically from generation 3 to 4. The compass of selection has backed from the south to northeast. This change means that instead of finding a peak by reducing the span of the caudal fin, the population ascends a different peak now by increasing both the span and the number of vertebrae. Traversing to generation 5, the population overshoots the summit, and selection points back from whence the population came.
Mapping the adaptive N-b landscape shows dramatically how a steady selection pressure—rewarding enhanced feeding and predator avoidance—can produce a tortuous evolutionary trajectory. What we still don’t know, however, is what the whole landscape looks like. How extensive is the range of adaptive peaks? Are they peaks or ridges? Do other adaptive peaks exist?
We could overcome our evolutionary ignorance using a modified directed-evolution approach. We could plop down populations of Evolvabots somewhere, run evolutionary trials, and let selection map the local terrain. This beam-me-down-Scotty procedure would be instructive, but it would be hit or miss with respect to the whole map. We’d run the risk of doing all that time-intensive evolutionary work only to find ourselves in the middle of an extensive fitness valley.
Given enough time and money, though, you could absolutely use directed evolution to expand your map. Populations of Evolvabots placed evenly and densely throughout the entire N-b landscape would enable you to accomplish what my colleague Chun Wai Liew calls an exhaustive search of the parameter space. This is not realistic with physical models, but it does work fine in digital simulation, assuming your landscape has only a couple dimensions, such as number of vertebrae and tail span, and covers just a little territory. But what if you add in predator-detection threshold, shape of the vertebrae, length of the tail, activity patterns of the muscles, and all of the various neural control mechanisms? By the explosive mathematics of combinatorics, each added dimension, k, expands the possible number of combinations, n, which in our case are different kinds of genotypes or phenotypes, by the following relationship with the number of possible values or conditions, j, within each dimension:
n=j k
Don’t let this cute little equation fool you. It hides a tactical hurricane. Before the storm, the wind is fair. Let’s say that we have only two dimensions—the number of vertebrae, N, and the span of the caudal fin, b—so that k = 2. If we allow both dimensions to have four conditions, j = 4, then the number of different phenotypes would be n =42, or 16. No problem.
But your lumbago should be telling you that a storm is approaching. Hold on tight. Let’s stay with our two dimensions, k = 2, but now make the number of conditions within each dimension a bit more realistic, say j = 14, which is how many vertebral states are possible in PreyRo (zero to thirteen vertebrae). Even though more conditions are possible for the span of the caudal fin (zero to fifty millimeters, in one-millimeter increments), we’ll just say that both have the same j value for the moment. For just our b-N adaptive landscape, that gives us a low-end estimate of n = 142 = 196 different phenotypes. The wind is pickin’ up. Reef the sails!
In PreyRo we have three dimensions, so k = 3. We’ll stay with our conservative estimate of fourteen possible conditions in each dimension. By adding a third dimension, we now have the possibility of n = 143 = 2,744 different phenotypes. But that figure underestimates the number of conditions, because the span of the caudal fin has fifty and the predator-detection threshold has fifty (10 to 60 centimeters in 1-centimeter increments). Let’s choose j = 25 and see what happens: n = 253 = 15,625 different phenotypes. Gale force winds! Batten down the hatches and man the bilge pumps! We are taking on water, matey.
This little exercise makes several things crystal clear. One: nautical metaphors are extremely annoying. Two: it is practically impossible, in the true sense of both words, to build and test all types of even a simple Evolvabot like PreyRo. Three: map makers wanting extensive or exhaustive maps of the adaptive landscape must resort to digital simulation because that is the only way to approach the number of trials needed in hill-searching and hill-climbing experiments. It’s also worth noting that there are ways to avoid having to do an exhaustive brute-force search of an entire landscape; Chun Wai uses different kinds of evolutionary algorithms to balance the demands of finding all of the peaks and doing so in a reasonable amount of time—like weeks instead of years. He has developed a meta-algorithm that decides when to use an exploring routine to search broadly and when to switch to a focusing routine that finds local hills.[143]
Seduced by the phenomenal cosmic power[144] of digital simulations and their handlers, I can’t help but wonder what in the world I was thinking. Using physically embodied robots? Evolving their biomimetic body parts? Enslaving students to work in the robot factory? Believing in autonomous behavior and situated-and-embodied intelligence? John, you dummy! Think of all the time and goodwill that you’ve wasted. Like it or not, digital simulation, clearly, is the way to go.
Then, a voice. I hear the Ghost of Christmas Past: “You see, John,” he whispers, “if you had not become obsessed with physically embodied robots, your life and the lives of those around you would have been much different. It would’ve been better.”[145]
Yes, I think, it would’ve been different … better. I could’ve explored the entire adaptive landscape of early vertebrates in the wink of an eye using digital simulation. My students and I could’ve moved beyond vertebrae. We might even have explored why fish evolved paired appendages, swim bladders, different body shapes, and the ability to live on land.
“John,” says the ghost, this time louder, “You must change your methodology. There is still time. Join your friends in the land of digital simulation, and you will come to understand why computational biology is de rigueur.” At the unexpected use of French, I turn, expecting to see my Gallic tormenter, hoping to plead for the opportunity to retool, perhaps in a year-long sabbatical at a stylish Parisian university or, if that’s not possible, in an intensive summer course at a marine laboratory on the Mediterranean. But I see no one.
Without meaning to, I say aloud, “I guess you’re right.” Now I hear the ghost smile, as if that’s possible, and I see him, or at least his face, beaming. “Yes, John, I am right. And you are right to change your ways while you still can, for the sake of yourself and for those around you. Now that you have seen what has been and what might be, I take my leave.”
A chilly breeze rustles the Post-its on my bulletin board as I hear the ghost ask a parting question, tossed casually, as if by a long-lost colleague walking away down the halclass="underline" “One last thing, John, that always puzzled me: what do robots have to do with biology?” At last recognizing the trick well played, I freeze, caught between my self-loathing for willfully betraying embodied robots and my embarrassment for falling prey to the old Ghost-of-Christmas-Past ploy. Cue Marlon Brando as the voice-over narrator: “Horror … Horror has a face … and you must make a friend of horror.”[146] Never!
143
C. W. Liew and M. Lahiri, “Exploration or Convergence? Another Meta-Control Mechanism for GAs,” in
144
“Phenomenal cosmic power! Itty-bitty living space!” said the genie in