Population growth rate (fertility) on the vertical axis and population size on the horizontal.
Fig. 20
Chapter 3
Richard Sibly demonstrates a general principle dictating faster growth with smaller animal populations.
We are in pursuit of whatever makes inbreeding kill babies, because it does not stop there. We have seen that the mechanism is inherited but not genetic, and it stabilizes a population at some moderate size, neither too small to survive nor too large. It is time for some data.
A man named Richard Sibly led a team that wrote an article2. They collected every paper published before 2005 that was about serial field counts of wild animals. If you went into a field periodically and counted rabbits and published your results your paper was analyzed.
In all they found 1,700 studies they thought suitable and discussed what was found. If a study ran for 5 or 10 years. That would be something like ten thousand years of data collected by professionals. That is a lot of work, longer than recorded history I should say. The result is not going to go away. Sibly did not publish an overall result, but he looked at the collection and gave a typical example. I have made bold to do a sketch of it.
Population growth rate (fertility) on the vertical axis and population size on the horizontal.
Fig. 20
Feast your mind for a moment on the idea that holds it together. The horizontal axis is easy. It’s just the animals counted. The vertical axis is the population growth rate. You might be able to contrive an explanation based on predators or disease, but over the next few talks that will not hold up. The cause is a difference in fertility.
The line is incomplete. There is no evidence for inbreeding depression. The line should be falling to the left of the arrow peak. We agree that inbreeding depression happens. Sibly says he did not observe it in the wild, but he excluded from analysis populations that went extinct. So, I think it more than fair to say that there is an undemonstrated falloff in fertility at very low population sizes.
The important point is indicated with an arrow. Here there is neither positive nor negative growth. For humans that is ideal. Opinions may vary on just how many people we want on the planet, but there can be no disagreement on the right growth rate. Negative growth eventually leads to extinction. Positive growth eventually leads to the kind of environmental and resource exhaustion that we have been warned of so much. Zero growth is best. Population size would have to be decided and cooperated on.
Crucially, at smaller population sizes than the zero-growth point but close to the zero-growth point, the fertility rises rapidly. At larger sizes the fertility falls slowly. This is what we needed to see. The curve stabilizes the population size at some moderate value. So long as the displacement from the zero point is not too great the population will return to that point. If the displacement is too extreme, extinction beckons.
Suppose the population is so small that inbreeding depression reduces fertility to below replacement. From then on, each subsequent generation is smaller and more inbred that the last, and the population will collapse. This happens in animal husbandry even though Sibly’s amazing compilation of wild studies does not show it.
But if the population is allowed to become extremely large, it will eventually run into the speciation-linked problem described in chapter 2. (You know,
“Again and again.”)
If it were possible to divide human kind into a number of mutually exclusive societies, each the size of the population at this point of zero growth, and if kinship were such that they were to reach equilibrium then, we would have a stable world population. Just what each local population size should be is not known to me. It might be possible to work it out from the Icelandic genealogies such as we shall be looking at next. How it could be set up in a way that left everybody happy or even whether there will ever be the will to try are questions that are as baffling as they are important. I cannot imagine another route to a stable world population that would not require unacceptable intrusion by some state-like regime that would inescapably attempt to warp the whole system to its own benefit.
That, so far, is the heart of this chapter. Once again, we shall expand, and in so doing stray from strict support by data. And again, you should feel free to skip or skim.
Sibly’s data are iron clad beyond beseeching, but do not let the clarity, the brevity and the importance of his work obscure how tremendous an accomplishment we are looking at. This is abstract reasoning at its finest. This particular pattern is going to be a recurrent theme, but first let us look at abstract reasoning as a thing.
During WW II there was a brilliant man, Alan Turing, who worked with the British government cracking German code. There is much drama associated with his life, but I shall remark on his contributions. For one thing, he suggested a way to tell if a computer was conscious. The idea was to have a computer connected to a teletype console and in parallel two more consoles connected by teletype. A subject would sit at one console and not know whether he or she was interfacing with a human or a computer. If the subject could not tell, then the computer was conscious. A lot of us think that it would just mean the computer programmer was smarter than the test subject or a human teletype was hosting a person pretending to be a computer.
A second idea Turing had was to design an imaginary computer based on part of the architecture of the computers he was using to attack the German codes. He demonstrated that his computer could solve any problem that any computer that could ever be built could solve. Massively parallel, deep memory, deep learning, quantum computer based, enormous memory would be of no avail. Sooner or later his imaginary machine could do the same thing. This idea has never been seriously challenged.
A third idea was that a computer can never do abstract reasoning. It cannot predict whether a computer program will reach a conclusion or run on indefinitely. For instance, have the computer take the number ten and subtract twos. If it ever comes up with three, stop. Obviously, it will never reach three. But, unless you teach it, the computer can only run the program not pick up on what is obvious to us. I have looked over Turing’s reasoning, and although I cannot claim to follow it all, I saw no glaring errors.
Now science, as we know it, tends to reduce everything to a form a computer can deal with. In short, if it is known to science, it can be recorded and manipulated by a suitable computer. But the computer is incapable of abstract reasoning. So, abstract reasoning is scientifically impossible. Yet we know that we can do it all the time. There will be a number of occasions as we proceed when we shall call upon it.
The first thing, then, we must hold as a caution in abstract reasoning is that it shouldn’t exist at all. Yet we shall, as I promised, try to remain within the bounds of science and still employ abstract reasoning.
A second caution is that abstract reasoning can be quite treacherous. It can lead to a false conclusion. For instance, a Russian named Pavlov famously taught some dogs that they would get, or at least see, food shortly after a bell was rung or a buzzer sounded. Eventually a dog would start salivating at the sound even though no food was in evidence. Pavlov concluded that he had “conditioned” the dog. Adjusted its behavior as one might set a clock or (years later) program a computer. The dog was thus a sort of robot.
But it seems equally valid to conclude that the dog has an imagination. The sound of the bell got the dog to thinking about food and thus starting to drool. Thus, the dog had an inner life, had situational awareness, something denied to a clock or a computer. Well the two conclusions drawn from the same line of evidence cannot both be true. Abstract reasoning, however prudently done, can lead straight into error. Back in the days of Medieval scholastic debates, a friar named William of Ockham came up with the principle of parsimony, now called Occam’s razor. It suggested one must always adopt the simplest explanation to cover the evidence. Very well and good, but new evidence keeps piling up, new explanations are needed so the principle or parsimony is usually, if not always, flat wrong. So, abstract reasoning must be judged with great caution. The best way I know is to insist on many independent lines of reasoning that all come to the same end, and I shall be providing this.
We do abstract reasoning. Can Pavlov’s maligned dogs do it? There is some evidence I rather wish somebody would gather. Imagine a computer screen upon which nice obvious red circles can be placed in random but not overlapping or contiguous places. Arrange two buttons. The one on the left will give a dog a treat if the dog sees 1, or 5 circles. The dog gets the treat by pressing the right button for 2, 4 or 6 circles. Train the dog until it is pulling perfect scores.
Now, with no fanfare, give the dog 3 circles. You, of course, will instantly say it is an odd number so it should mean take the left button. But how about a dog? It has a fifty-fifty chance from the get go, so a single trial would mean nothing. But run through the whole rigamarole with a hundred dogs, and you can draw a conclusion. If the dogs split it right down the middle, half would be right and half wrong, so we take a perfect negative result to be fifty right. (Or wrong, but we’ll go with right.) Now my own rather self-taught statistics guestimate is that the square root of 100 dogs is 10. So, a standard deviation is about, oh, something like around 10. So, if the dogs together beat 80 correct choices, then that’s maybe, sort of 3 standard deviations. The chance now is not 50-50. They’ll do it by chance once in a thousand times. You can be pretty sure that most of them have met the challenge and done the requisite reasoning. That should be good enough to tell people, to publish, but if something of monumental importance hung on the conclusion, I for one would insist on bigger numbers and more standard deviations before making a policy decision.
Of course, if fewer than 20 dogs got it right, you would have to wonder if somehow or other they’d got together to jerk your chain.
Now would be the time to say a tearful farewell two a hundred dogs that by now have fallen in love with you. I could not bear it.
In real life, of course you’d get a professional statistician to do the numbers, and he’d use tables to work it out to a bunch of decimal points.
The dogs, given the attention of an interested person, would really, really try. You might think chimpanzees would be a better choice, but chimps available for scientific experimentation are rare and highly prized. It’s probably not viable. Corvid birds are very clever and, so far as I know, are not excessively affectionate. They might be worth a try. If one were to get totally enamored by such things, I’d say trying it out on squid or octopus (https://www.merriam-webster.com/words-at-play/the-many-plurals-of-octopus-octopi-octopuses-octopodes ) would be cute. They have no anatomical central nervous system and might be capable of parallel processing, if that helped.
There is work being done so see whether an animal can be surprised by a “magic” trick.3 If so, maybe that would constitute abstract reasoning so we might find out some day.
I can think of three formal ways this perfidious mode of thought can be classed:
Sibly piled up his mass of information, and given that much to work with, he properly drew a conclusion by inductive logic. He looked for a pattern and found one. This will be a recurrent theme in this book.