A computer program models the same oscillation as demonstrated in the lab.
Some days you have to learn a new word. If the word comes with a new concept, well and good. If I need to invoke the concept, I am armed. One imposition on my patience was the word “tsunami.” The proper expression is “tidal wave,” a wave so big that even in mid ocean it interacts physically with the ocean floor, just the same as the tide – the only difference being the source of the energy, astronomical or geological; a secondary meaning is that it is newsworthy, (That’s an odd expression; it is frequently the most unworthy decisions that are considered newsworthy.) news meaning “tidings,” rather clever I should say. In Japanese, the word tsunami means “wave of the tide.” When I pointed this out to a tenured professor in Japanese issues, he replied, “Yes, literally that is the meaning, but in fact it just means a very big wave.” And in fact, tidal wave means the same thing, only a bit more specific.
Then there is “sea star.” I used to do volunteer work at what used to be called the Clearwater Marine Science Center. I was looking forward to hobnobbing with working scientists, but when the captain of the excursion boat realized I was a competent deck hand, that was my permanent assignment. Then one fateful day the marine biologist who was adding color to the excursion held up an animal and announced that it was a sea star. With my best effort at patience, I waited until the visitors had left and inquired, “Am I to infer that the word starfish has been canceled?” “Yes, because it isn’t a fish,” in a tone of voice that suggested she didn’t think I knew that. I was in the same category as the children, and accordingly insulted. If you are going to go into a word and pull out some letters and criticize them, you have to deal with the fact that it is not the patron saint of yapping dogs nor does is resemble a starf. It certainly is not a star, nor does it live in the sea but on the bottom. What was wrong with saying, “It’s not a true fish, meaning a spinal cord and gills,” going on to say that living in the water is not constant, since there is the walking catfish, nor symmetry since we have flounders. I think that would be more helpful than just, “No, Johnny, you’re stupid.” Johnny knows perfectly well it is not a true fish. Give me a new word without a new concept, and I shall not be happy.
Very well, then, “zygote.” We have spoken of it before. But it’s important, and we’re going to go over it again and again until … you know the drill.
Three most important kinds of things in society are relationships, tools and words. I kind of like the old ones and understand if you don’t want to learn one, but grit your teeth. The word is “zygote” and we’ll be using in in two forms. It means “yoke” as in a yoke of oxen. But in histology (no you don’t need to learn that one) the word means a cell that has been formed by a sperm entering an egg (ovum):
SPERM + OVUM
ZYGOTEEgg and sperm combine to form a zygote; an absurdly oversimplified explanation of sex.
Fig. 29
When we speak of the mechanism of infertility, the first logical step is to distinguish “pre-zygotic infertility” from “post-zygotic infertility.” Those are the two forms of the word zygote we must know. Pre-zygotic is what happens before the zygote forms and post-zygotic happens afterwards. Since there is clearly a mechanism, as Sibly pointed out, for relative infertility brought on by lack of closer kinship, is it pre-zygotic, post-zygotic or both?
The Icelandic data we looked at earlier showed lower kinship reduced the number of children and the number of grandchildren; to a first approximation, this suggest both pre-zygotic and post-zygotic mechanisms in action.
I had written a computer program in C++ language. The program modeled only a post-zygotic mechanism using an epigenetic process. Eager to spread what I knew I had copies made on CDs. I was not so eager but what I had the compiled code locked onto the CD. I sent the master off to a place in Israel, the only service that offered to make protected discs of anything but music. I got a prompt message saying that some of the things in included were in folders, and the disc could not be properly secured unless everything was out in the open. If I had been feeling paranoid before, that went over the top. There could be no explanation but they were copying everything they were “protecting.” No problem. If they wanted to try to steal it, the source code was copyrighted. And any attention was welcome.
I still have a couple hundred copies. If you want one, I’ll send it to you for a souvenir. Your current operating system may not work on it, and your security system may judge it dangerous. With an old computer and no security, you might be able to make it work, but since it has been out of my hands, I can’t swear there is no virus … although I have never had evidence for one. If the discs prove so popular that the time and cost are significant, I may start asking you send a prepaid envelope. But you don’t need it. I’ll give it to you later. The version that is coming includes a pre-zygotic process model. Don’t turn that on, and you’ll have essentially the post-zygotic version.
I tweaked the parameters (if you take interest, you may do a lot of that) until I got this:
Time course of a highly tweaked computer model of a population under the control of a straight post-zygotic mechanism.
Fig. 30 10
Does it look like damped oscillation to you? Rapid rise and slow fall of fertility? It does to me. It seems beyond doubt that we are hot on the spoor of the mechanism.
We see evidence for a post-zygotic mechanism, but in the lab, we don’t see a pre-zygotic process. If there is one, it can only have limited power. When the Spanish learned that Cortez had murdered Montezuma, they were shocked. Giving the treasures of Mexico and the land back to the rightful owners was out of the question, but the Spanish court brought Montezuma’s children to Spain and made them part of the royal line. They continue to this day. Earlier contact between those who originally left Africa and went north and those who went east must have been quite limited. How long had Spaniards and Mexicans been separated? A thousand generations or so? It seems clear that, post-zygotic fertility in both parents permitting, pre-zygotic infertility cannot be absolute.
The amount of noise, or rather the signal noise ratio in the experimental case and in the virtual case, are not terribly different. Also, if you count the cycles, before the damped oscillation ceases being obvious, you’ll get four cycles for the lab study and only three in the model. It would be tempting to say that they are in the same ballpark. However, and more of this later, the computer program establishes a number of sites, the number of sites being chosen by the user, that are subject to epigenetic change, which occurs to random sites at a rate established by the user and makes changes in a random direction. Each generation, the pattern – the virtual epigenome – of each pair of mating partners is compared and the number of offspring is reduced by an amount set by the user depending on how much the two are different. It may be tempting to say that the number of sites in the computer might be close to the number in real life. Resist any such temptation. Once pre-zygotic infertility is thrown into the mix, things change a lot.
The peaks come down in an orderly fashion with the exception of the initial peak, which is anomalously high. That is no surprise. The way the program is set up, epigenomes are compared and differences reduce fertility accordingly. But when the program starts to run, every site of virtual epigenetic change is, as it is created, set to zero, so there is no difference at all in the first generation, and fertility is through the roof.
Well and good for the peaks, but the valleys are getting lower as well. If you examine the behavior of a Foucault pendulum, a simple, swinging ball hanging from a wire and nicely prepared to exclude extraneous forces other than air resistance and the rotation of the earth, it will – provided the arc of swing is small – give a pretty good approximation of a simple, damped harmonic motion. Both ends of the arc move toward the center. This kind of behavior is so common that the term damped oscillation needs no further explanation. But if the effect is an oscillation with increasing amplitude, there is no phrase antonymical with “damped oscillation,” so one is obliged to resort to circumlocution. None of the errors possible in the construction of a Foucault pendulum will result in oscillation with increasing amplitude. To get this, you must include a power source such as a wet hen, if you are unkind enough or on good enough terms with the chicken so she enjoys the game, or else an electromagnetic drive.
We observe good old damped oscillation all right, but if the peaks and valleys are both dropping, then the center to which the system is attracted is moving slightly. If you go back to the Sibly curve shown in chapter 3, there is a vertical arrow indicating the point of attraction. Do not blame that one on Sibly; I drew it in myself, suggesting it was too obvious for demur. And yet, in the event that arrow appears to edge very slightly toward the right.
Therefore, a computer program using only virtual post-zygotic infertility can simulate a recognizably similar pattern of population change as is found in the lab. That is the gist of this chapter. You may skip the remainder as it offers no new data.
A recurring theme we have is that it is a jolly good idea, given a large amount of data, to graph the data out and look for a pattern to emerge. I have mentioned that when I was younger I much preferred to look at raw data to looking at a graph. I did not begin to grasp the value of graphs until I embarked of this project. I have found that a graph can give intuitive insight not obvious in the data. For instance, after working with the flies daily for years the emergence of the damped oscillation took me totally by surprise. The sight of it is intuitively obvious, although even then I didn’t really grasp it until a friend encouraged me.
But when it comes to the descending values of the valleys, intuition fails. If the computer and the lab disagreed, I was quite prepared to shrug it off with an “It could go either way.” And indeed, maybe it could, but if so, what variable would dictate that? It is worse than the Danish data that was baffling before. That involved people making choices even though the lack of influence of education or income on those choices suggests they are not real. But here, there is no question of choice for the computer.
I have not tried this, but my understanding is that when a computer launches its pseudorandom number program it notes the date, down to the second, and then goes to its table of “random” numbers and counts down to the current second and starts pulling numbers from that point. Give it a program with random elements and launch it the same second of the next year and the result should be exactly the same. There is no ambiguity.
So, the computer result is totally fixed from the get go. Intuitively that means to me that the output should be intuitively obvious. The fact that it is not is something I earnestly wish I could understand. Maybe some day a better mind than mine will work it out.