John Long - Darwin’s Devices

To allow for the likely possibility that selection might target the length of the tail for a variety of reasons, some of which may have to do with structural stiffness and some not, we created a genome that coded for L and E separately. By not coding for the variable I , we were holding that part of the geometry—and everything else about Tadro3 for that matter—constant. In the language of a geneticist, both L and E were quantitative characters, polygenes, multiple loci capable of producing smooth gradations in the phenotypes for which they code. All loci for L were located on a chromosome separate from the loci for E in order to allow for independent assortment. In other words, having quantitative traits means that the genome does not contain the simple on-off, wrinkled pea or smooth, kind of genes that we call “Mendelian.” Each set of genes is, instead, a continuous number scale, capable, within a given window, of producing a range of E values different from a range of L values.

You can see the independent changes in the proportion of E and L genes in the bottom panel of Figure 4.1. Notice that as the proportion of L genes increases from generation 7 onward, the structural stiffness, k , in the middle panel, plunges. This is exactly what we’d expect from our equation for k , on previous page. That L 3term in the denominator is increasing dramatically, and it is lowering k at the same time that the E term in the numerator is decreasing and also lowering k . Faced with this kind of genetic evolution, poor old structural stiffness doesn’t stand a chance.

Over the course of ten generations, the population’s average value of the structural stiffness of the tail, k , plummets from above 5 to below 1 Nm -1. We’ve seen what was happening genetically to cause the decreased value of structural stiffness. But these genetic changes don’t speak to how selection—which judges individuals by their behavior, not by their genetics—was interacting with randomness and history. We still have two bothersome itches to scratch: (1) Why did the structural stiffness decrease under selection for enhanced feeding behavior when we predicted that it would increase? (2) Why does feeding behavior seem at times to be unrelated to the structural stiffness of the notochord?

I want to warn you right now about a tempting siren who begins singing on the rocks at about this point in a study. When, as was the case with Tadro3, your experiment produces a result that appears to be the exact opposite of what you predicted, the immediate emotional response is to be disappointed and self-flagellating. My students and I certainly were. When we graphed the data in Figure 4.1, we had to have a group counseling session immediately to air concerns and responses. In the lightning reaction round, we heard: What went wrong? Our experiment didn’t work! These data suck! We stink as scientists! My line then, and I’m sticking to it now, is that if you design an experiment carefully, execute it well by tracking down mistakes as they occur and running controls, your data will always be great. Data just are. No matter what those data say about your predictions, they and the experiment that generated them stand on their own, with their total value determined by how well you measured what you set out to measure.

The negative emotional response, I reckon, comes from the fact that we all secretly think that we understand our experimental system well enough to know exactly how it will turn out. We are, from an emotional point of view, just running through the experiment to show other people what we’ve already figured out in our heads. [38] You can find a great introduction to the evidence for our mental modeling in the following book: Read Montague, Your Brain Is (Almost) Perfect: How We Make Decisions (New York: Plume, 2006). By the time we’ve made our prediction, a process that is really like running our own internal model cognitively, we have committed emotionally to a particular outcome. We aim to “prove” our point through demonstration.

Although disappointment and disillusionment in the face of unexpected results may be natural emotional responses—and ones that I share with my students—they run counter to the way that many but not all of us reason scientifically. Strictly speaking, we demonstrate that some testable concept is true through our repeated failure to show it to be false. [39] The philosopher of science, Karl Popper, has formalized the “hypothetical-deductive” methodology in order to avoid what other philosophers have called the “problem of induction,” or generalizing from a few observations to the world in general. Most of our statistical hypothesis testing in science is structured around the idea of falsification or rejection of the “null” hypothesis. The danger with this approach is that if you reject the null hypothesis, you are tempted to treat the alternative as “true,” when in fact it becomes the new null to be tested. An excellent place to start with this kind of careful inference is with Popper himself: Karl R. Popper, The Logic of Scientific Discovery (New York: Basic Books, 1959). Although we can certainly demonstrate that something predictable happens every time we release our coffee mug from a height of two meters, no one has seen gravity. [40] For that matter (ahem …), no one has seen energy. In fact, physicists don’t even know what energy is. Richard Feynman, the Nobel Laureate in Physics, and his coauthors Robert Leighton and Matthew Sands point this out eloquently in The Feynman Lectures on Physics , vol. 1 (Reading, MA: Addison-Wesley, 1964), 4-2. Gravity is a concept for a kind of energy related to the masses of objects. The relationships that we see between objects on planets and between planets and stars in space is observable and consistent with our concept of gravity; hence, having failed repeatedly to disprove those consistent relationships between objects, most of us think that gravity is a fact. Because the failure to reject gives us confidence in the truth that we infer about gravity, we employ gravity, in turn, as an inferential tool to create new scenarios. We use the fact of gravity to infer the presence of the universe’s unseen dark matter. If dark matter were shown to be nonexistent, that observation would indirectly refute the gravitational paradigm. In sum, to prove, we attempt to refute. [41] I’ve given short shrift here to an interesting philosophical debate: logical positivism versus Popper’s hypothetico-deductivism. One distillation of the difference is modus ponens versus modus tollens logic, respectively.

Following our therapy session, which included a harnessed descent into the cave of refutational negativism, our Tadro team decided to look deeper into the data. We needed to figure out if, in fact, our data sucked (which is always a real possibility) or if the results were screaming in our faces about something really interesting that we just hadn’t anticipated. I’ll spare you the tedium involved in figuring out if your data suck: it’s all the usual kinds of things about checking your transcriptions, lab notebooks, mathematical formulae, control experiments, and calibrations of instruments. [42] In case you are interested in what we did to try to find our flaws, here’s an example. We were very concerned that our initial measurements of structural stiffness were somehow flawed. We had created a standard curve that gave us a value of material stiffness, E , for a given amount of gelatin and cross-linking time. We retested that formula to make sure it was accurate. Moreover, if our method for making and measuring the biomimetic notochords was highly variable, that would be an additional source of random variation and noise. To test this we split up into three different groups and completely remade all of our tails, and then we tested them for structural stiffness using a materials testing device. We compared the three groups for inter-rater reliability, the level of agreement between us. In the worst case the correlation of our stiffness measurements between groups was 0.91 out of 1.0. We came to the conclusion that we couldn’t explain our results away with the reflexive “bad data by bad scientists.” Something much more interesting was afoot.