John Long - Darwin’s Devices

FIGURE 4.1. (facing page) Evolution of a population of Tadro3s. Phenotypes and genes change over generational time. Both kinds of changes are how we measure evolutionary change. Because we know what’s happening in terms of selection and random genetic events, we know when selection is a factor. The square frames around some of the generation numbers indicate when selection was strong enough to create differences in the reproduction of individuals making offspring for the next generation. For example, the change in the population’s feeding behavior from generation 1 to 2 can be attributed to both selection and random genetic effects. In generations in which selection is not strong, any changes in the next generation are caused only by the random genetic effects. The population’s actual evolutionary path is indicated with a solid line; its simple and expected path is indicated with a dashed line. Points are averages; error bars are standard deviations.

Given that we know the Tadro3 world inside and out, we sure as heck-fire better be able to explain the unexpected directions in the evolution of the population Tadro3s.

Let’s jump-start the process of interpretation by revisiting the big picture. We were interested in creating Evolvabots that could test a hypothesis about the evolution of early vertebrates: natural selection for enhanced feeding behavior drove the evolution of vertebrae in early vertebrates. From this hypothesis we came up with a primary prediction: selection for enhanced feeding behavior will cause the population of Tadro3s to evolve stiffer tails. Implied in that prediction is another: the evolutionary change will be directional, moving the population from flexible to stiff tails in concert with ever-improving feeding behavior.

What’s clear is that these predictions are too simple. Take a close look at the reality of the hard data (Figure 4.1). The average score for feeding behavior [32] This single number that measures feeding behavior is a composite from the fitness function that we developed in Chapter 3. We defined better “relative fitness” for an individual in a given generation, relative to other individuals in that generation, as the sum of their scaled values for increased swimming speed, decreased time to the light target, reduced distance from the light target over the course of the whole experiment, and reduced wobble as they moved. These relative fitness values only make sense within a generation relative to other competing individuals at that time and place: they can’t be compared across generations. To make those cross-generation comparisons for Figure 4.1, we compared any individual’s performance to the average of all individuals over all ten generations scaled by the standard deviation of the particular sub-behaviors, speed, time, distance, and wobble. In statistical terms, we summed up the z-scores of each sub-behavior for each individual. increases greatly from generation 1 to 2 while the standard deviation, [33] In statistics one standard deviation, which changes in value depending on the situation, is a measure of how far away from the average most numbers in a group of numbers fall. A small standard deviation means that most numbers in the group are close to the average of the group. represented by the length of the bars emanating from the filled circles, decreases. This initial change sure looks like the direction we predicted: enhanced feeding behavior. The decrease in variance might be expected, too, because selection was just picking individuals with the highest feeding behavior to reproduce. But in the very next generation, 3, the average score for feeding behavior drops and then continues downward through generation 4. What’s up, Doc?

At first glance, this downward trend looks crazy-wrong: how can we select for improved feeding behavior and get just the opposite? The short answer is this: in generation 2 differences in feeding behavior among individuals were not large enough to cause differences in reproduction. All three individuals contributed the same number of gametes (egg and sperm)—two—to the mating pool of six gametes. Our mating algorithm assigned differences in reproductive output according to the differences in fitness between individuals. Even though the fitness function assigned slightly different numbers to each individual—based on their abilities to swim quickly, reach the light target quickly, stay and feed near the light target, and move around smoothly—in generation 2 those fitness differences were just too small to matter. [34] If you are interested in the mathematics of the mating that we used, you can find the details in our paper on the evolution of Tadro3: J. H. Long Jr., T. J. Koob, K. Irving, K. Combie, V. Engel, N. Livingston, A. Lammert, and J. Schumacher, “Biomimetic Evolutionary Analysis: Testing the Adaptive Value of Vertebrate Tail Stiffness in Autonomous Swimming Robots,” Journal of Experimental Biology 209, no. 23 (December 2006): 4732–4746.

When individuals contribute equally to the next generation, we have an evolutionary tie. This tie means that the parents are likely to make a generation of offspring that looks, on average, like themselves. In evolutionary terms, there was an absence of selection, or no selection pressure. Either phrase might sound a bit inaccurate, as we had selection judging individual Tadro3s in a given generation using our fitness-function scorecard. But keep in mind that ultimately it’s differential reproduction among individuals that makes evolution by natural selection work.

In the absence of selection, how, then, do we get evolutionary change? Recall Darwin’s lament from Chapter 2: “Great is the power of steady misinterpretation.” He was referring to the fact that many scientists overplayed the power of selection, to the extent that they ignored other evolutionary mechanisms and, as a result, saw adaptations in every cranial bulge and fingerprint, when sometimes randomness is what’s at work.

Darwin had little hard evidence to counter this misconception because he lacked our understanding of genetics, which, ironically, was developed by a contemporary of Darwin’s, Gregor Mendel, but languished in an obscure journal until the early twentieth century. With our current understanding of genetics, of course, we know that random genetic changes are always occurring, both in the germ-line and other cells. More randomness can come into play during mating. Although some mating is decidedly not random, for many organisms it is. We set up our Tadro3 population to engage in random mating. After each gamete was given a certain probability of mutating or not, we took all six of the gametes the parents produced, and combined the gametes into pairs randomly. Those pairs of haploid gametes combined to give us the new diploid genome for each new baby Tadro3.

At this point, my colleague Rob Root, a mathematician and central collaborator on many of our Tadro projects, would want me to remind you that we have a problem with our randomness because we are operating in the realm of “the mathematics of small numbers.” Our population size of three is simply too small for the statistical assumptions of flip-a-coin randomness to hold. The result, if you were flipping coins, is that you could easily hit heads, heads, and heads, three in a row. You’d say that you were “on a roll,” and it sure would not look like a random process until you flipped the coin about twenty more times. Geneticists call this mathematical description of what happens in populations of small size “genetic drift.” [35] In John Gillespie’s Population Genetics: A Concise Guide, 2nd ed. (Baltimore: Johns Hopkins University Press, 2004), he speaks of “demographic stochasticity” as this source of small-number randomness. He also points out a second such source, the segregation of the different parental alleles into separate gametes. Both sources together he calls genetic drift. In our robotic simulation segregation is not a factor because our quantitative characters are, by design, split evenly between chromosomes.