Where the original Watt governor makes use of negative feedback, our hypothetical doctored governor exemplifies the opposite process of positive feedback. Positive-feedback processes have an unstable, runaway quality. Slight initial perturbations are increased, and they run away in an ever-increasing spiral, which culminates either in disaster or in an eventual throttling down at some higher level due to other processes. Engineers have found it fruitful to unite a wide variety of processes under the single heading of negative feedback, and another wide variety under the heading of positive feedback. The analogies are fruitful not just in some vague qualitative sense, but because all the processes share the same underlying mathematics. Biologists studying such phenomena as temperature control in the body, and the satiation mechanisms that prevent overeating, have found it helpful to borrow the mathematics of negative feedback from engineers. Positive-feedback systems are used less than negative feedback, both by engineers and by living bodies, but nevertheless it is positive feedbacks that are the subject of this chapter.
The reason engineers and living bodies make more use of negative than positive-feedback systems is, of course, that controlled regulation near an optimum is useful. Unstable runaway processes, far from being useful, can be downright dangerous. In chemistry, the typical positive-feedback process is an explosion, and we commonly use the word explosive as a description of any runaway process. For instance, we may refer to somebody as having an explosive temper. One of my schoolmasters was a cultured, courteous and usually gentle man, but he had occasional explosions of temper, as he himself was aware. When extremely provoked in class he would say nothing at first, but his face showed that something unusual was going on inside. Then, beginning in a quiet and reasonable tone he would say: ‘Oh dear. I can’t hold it. I’m going to lose my temper. Get down below your desks. I’m warning you. It’s coming.’ All the time his voice was rising, and at the crescendo he would seize everything within reach, books, wooden-backed blackboard erasers, paperweights, inkpots, and hurl them in quick succession, with the utmost force and ferocity but with wild aim, in the general direction of the boy who had provoked him. His temper then gradually subsided, and next day he would offer the most gracious apology to the same boy. He was aware that he had gone out of control, he had witnessed himself becoming the victim of a positive-feedback loop.
But positive feedbacks don’t only lead to runaway increases; they can lead to runaway decreases. I recently attended a debate in Congregation, Oxford University’s ‘parliament’, on whether to offer an honorary degree to somebody. Unusually, the decision was a controversial one. After the vote, during the 15 minutes that it took to count the ballot papers, there was a general hubbub of conversation from those waiting to hear the result. At one point the conversation strangely died away, and there was total silence. The reason was a particular kind of positive feedback. It worked as follows. In any general buzz of conversation there are bound to be chance fluctuations in noise level, both up and down, which we normally don’t notice. One of these chance fluctuations, in the direction of quietness, happened to be slightly more marked than usual, with the result that some people noticed it. Since everybody was anxiously waiting for the result of the vote to be announced, those that heard the random decrease in noise level looked up and ceased their conversation. This caused the general noise level to go down a little more, with the result that more people noticed it and stopped their conversation. A positive feedback had been initiated and it continued rather rapidly until there was total silence in the hall. Then, when we realized that it was a false alarm, there was a laugh followed by a slow escalation in noise back up to its former level.
The most noticeable and spectacular positive feedbacks are those that result, not in a decrease, but in a runaway increase in something: a nuclear explosion, a schoolmaster losing his temper, a brawl in a pub, escalating invective at the United Nations (the reader may heed the warning with which I began this chapter). The importance of positive feedbacks in international affairs is implicitly recognized in the jargon word ‘escalation’: when we say that the Middle East is a ‘powder keg’, and when we identify ‘flashpoints’. One of the best-known expressions of the idea of positive feedback is in St Matthew’s Gospel: ‘Unto everyone that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.’ This chapter is about positive feedbacks in evolution. There are some features of living organisms that look as though they are the end-products of something like an explosive, positive-feedback-driven, runaway process of evolution. In a mild way the arms races of the previous chapter are examples of this, but the really spectacular examples are to be found in organs of sexual advertisement.
Try to persuade yourself, as they tried to persuade me when I was an undergraduate, that the peacock’s fan is a mundanely functional organ like a tooth or a kidney, fashioned by natural selection to do no more than the utilitarian job of labelling the bird, unambiguously as a member of this species and not that. They never persuaded me, and I doubt if you can be persuaded either. For me the peacock’s fan has the unmistakable stamp of positive feedback. It is clearly the product of some kind of uncontrolled, unstable explosion that took place in evolutionary time. So thought Darwin in his theory of sexual selection and so, explicitly and in so many words, thought the greatest of his successors, R. A. Fisher. After a short piece of reasoning he concluded (in his book The Genetical Theory of Natural Selection):
plumage development in the male, and sexual preference for such developments in the female, must thus advance together, and so long as the process is unchecked by severe counterselection, will advance with ever-increasing speed. In the total absence of such checks, it is easy to see that the speed of development will be proportional to the development already attained, which will therefore increase with time exponentially, or in geometric progression.
It is typical of Fisher that what he found ‘easy to see’ was not fully understood by others until half a century later. He did not bother to spell out his assertion that the evolution of sexually attractive plumage might advance with ever-increasing speed, exponentially, explosively. It took the rest of the biological world some 50 years to catch up and finally reconstruct in full the kind of mathematical argument that Fisher must have used, either on paper or in his head, to prove the point to himself. I am going to try to explain, purely in nonmathematical prose, these mathematical ideas which, in their modern form, have largely been worked out by the young American mathematical biologist Russell Lande. While I would not be so pessimistic as Fisher himself who, in the Preface to his 1930 book, said ‘No efforts of mine could avail to make the book easy reading’, nevertheless, in the words of a kind reviewer of my own first book, ‘The reader is warned that he must put on his mental running shoes’. My own understanding of these difficult ideas has been a hard struggle. Here, despite his protests, I must acknowledge my colleague and former student Alan Grafen, whose own mental winged sandals are notoriously in a class of their own, but who has the even rarer ability to take them off and think of the right way to explain things to others. Without his teaching, I simply couldn’t have written the middle part of this chapter, which is why I refuse to relegate my acknowledgment to the Preface.
Before we come to these difficult matters, I must back-track and say a little about the origin of the idea of sexual selection. It began, like so much else in this field, with Charles Darwin. Darwin, although he laid his main stress on survival and the struggle for existence, recognized that existence and survival were only means to an end. That end was reproduction. A pheasant may live to a ripe old age, but if it does not reproduce it will not pass its attributes on. Selection will favour qualities that make an animal successful at reproducing, and survival is only part of the battle to reproduce. In other parts of the battle, success goes to those that are most attractive to the opposite sex. Darwin saw that, if a male pheasant or peacock or bird of paradise buys sexual attractiveness
, even at the cost of its own life, it may still pass on its sexually attractive qualities through highly successful procreation before its death. He realized that the fan of a peacock must be a handicap to its possessor as far as survival is concerned, and he suggested that this was more than outweighed by the increased sexual attractiveness that it gave the male. With his fondness for the analogy with domestication, Darwin compared the hen to a human breeder directing the course of evolution of domestic animals along the lines of aesthetic whims. We might compare her to the person selecting computer biomorphs in directions of aesthetic appeal.
Darwin simply accepted female whims as given. Their existence was an axiom of his theory of sexual selection, a prior assumption rather than something to be explained in its own right. Partly for this reason his theory of sexual selection fell into disrepute, until it was rescued by Fisher in 1930. Unfortunately, many biologists either ignored or misunderstood Fisher. The objection raised by Julian Huxley and others was that female whims were not legitimate foundations for a truly scientific theory. But Fisher rescued the theory of sexual selection, by treating female preference as a legitimate object of natural selection in its own right, no less than male tails. Female preference is a manifestation of the female nervous system. The female nervous system develops under the influence of her genes, and its attributes are therefore likely to have been influenced by selection over past generations. Where others had thought of male ornaments evolving under the influence of static female preference, Fisher thought in terms of female preference evolving dynamically in step with male ornament. Perhaps you can already begin to see how this is going to link up with the idea of explosive positive feedback.
When we are discussing difficult theoretical ideas, it is often a good idea to keep in mind a particular example from the real world. I shall use the tail of the African long-tailed widow bird as an example. Any sexually selected ornament would have done, and I had a whim to ring the changes and avoid the ubiquitous (in discussions of sexual selection) peacock. The male long-tailed widow bird is a slender black bird with orange shoulder flashes, about the size of an English sparrow except that the main tail feathers, in the breeding season, can be 18 inches long. It is often to be seen performing its spectacular display flight over the grasslands of Africa, wheeling and looping the loop, like an aeroplane with a long advertising streamer. Not surprisingly it can be grounded in wet weather. Even a dry tail that long must be a burdensome load to carry around. We are interested in explaining the evolution of the long tail, which we conjecture has been an explosive evolutionary process. Our starting point, therefore, is an ancestral bird without a long tail. Think of the ancestral tail as about 3 inches long, about a sixth the length of the modern breeding male’s tail. The evolutionary change that we are trying to explain is a sixfold increase in tail length.
It is an obvious fact that, when we measure almost anything about animals, although most members of a species are fairly close to the average, some individuals are a little above average, while others are below average. We can be sure that there was a range of tail lengths in the ancestral widow bird, some being longer and some being shorter than the average of 3 inches. It is safe to assume that tail length would have been governed by a large number of genes, each one of small effect, their effects adding up, together with the effects of diet and other environmental variables, to make the actual tail length of an individual. Large numbers of genes whose effects add up are called polygenes. Most measures of ourselves, for instance our height and weight, are affected by large numbers of polygenes. The mathematical model of sexual selection that I am following most closely, that of Russell Lande, is a model of polygenes.
Now we must turn our attention to females, and how they choose their mates. It may seem rather sexist to assume that it is the females that would choose their mates, rather than the other way round. Actually, there are good theoretical reasons for expecting it to be this way round (see The Selfish Gene), and as a matter of fact it normally is in practice. Certainly modern long-tailed widow bird males attract harems of half a dozen or so females. This means that there is a surplus of males in the population who do not reproduce. This, in turn, means that females have no difficulty in finding mates, and are in a position to be choosy. A male has a great deal to gain by being attractive to females. A female has little to gain by being attractive to males, since she is bound to be in demand anyway.
So, having accepted the assumption that females do the choosing, we next take the crucial step that Fisher took in confounding Darwin’s critics. Instead of simply agreeing that females have whims, we regard female preference as a genetically influenced variable just like any other. Female preference is a quantitative variable, and we can assume that it is under the control of polygenes in just the same kind of way as male tail length itself. These polygenes may act on any of a wide variety of parts of the female’s brain, or even on her eyes; on anything that has the effect of altering the female’s preference. Female preference doubtless takes account of many parts of a male, the colour of his shoulder patch, the shape of his beak, and so on; but we happen to be interested, here, in the evolution of male tail length, and hence we are interested in female preferences for male tails of different length. We can therefore measure female preference in exactly the same units as we measure male tail length — inches. Polygenes will see to it that there are some females with a liking for longer than average male tails, others with a liking for shorter than average male tails, and others with a liking for tails of about average length.
Now comes one of the key insights in the whole theory. Although genes for female preference only express themselves in female behaviour, nevertheless they are present in the bodies of males too. And by the same token, genes for male tail length are present in the bodies of females, whether or not they express themselves in females. The idea of genes failing to express themselves is not a difficult one. If a man has genes for a long penis, he is just as likely to pass those genes on to his daughter as to his son. His son may express those genes whereas his daughter, of course, will not, because she doesn’t have a penis at all. But if the man eventually gets grandsons, the sons of his daughter may be just as likely to inherit his long penis as the sons of his son. Genes may be carried in a body but not expressed. In the same way, Fisher and Lande assume that genes for female preference are carried in male bodies, even though they are only expressed in female bodies. And genes for male tails are carried in female bodies, even if they are not expressed in females.
Suppose we had a special microscope, which enabled us to look inside any bird’s cells and inspect its genes. Take a male who happens to have a longer than average tail, and look inside his cells at his genes. Looking first at the genes for tail length itself, it comes as no surprise to discover that he has genes that make a long tail: this is obvious, since he has a long tail. But now look at his genes for tail preference. Here we have no clue from the outside, since such genes only express themselves in females. We have to look with our microscope. What would we see? We’d see genes for making females prefer long tails. Conversely, if we looked inside a male who actually has a short tail, we should see genes for making females prefer short tails. This is really a key point in the argument. The rationale for it is as follows.
If I am a male with a long tail, my father is more likely than not to have had a long tail too. This is just ordinary heredity. But also, since my father was chosen as a mate by my mother, my mother is more likely than not to have preferred long-tailed males. Therefore, if I have inherited genes for a long tail from my father, I am also likely to have inherited genes for preferring long tails from my mother. By the same reasoning, if you have inherited the genes for a short tail, the chances are that you have also inherited the genes for making females prefer a short tail.
We can follow the same kind of reasoning for females. If I am a female who prefers long-tailed males, the chances are that my mother also preferred long-tailed males. Therefore the chances
are that my father had a long tail, since he was chosen by my mother. Therefore if I have inherited genes for preferring long tails, the chances are that I have also inherited genes for having a long tail, whether or not those genes are actually expressed in my female body. And if I have inherited genes for preferring short tails, the chances are that I have also inherited genes for having a short tail. The general conclusion is this. Any individual, of either sex, is likely to contain both genes for making males have a certain quality, and genes for making females prefer that selfsame quality, whatever that quality might be.
So, the genes for male qualities, and the genes for making females prefer those qualities, will not be randomly shuffled around the population, but will tend to be shuffled around together. This ‘togetherness’, which goes under the daunting technical name of linkage disequilibrium, plays curious tricks with the equations of mathematical geneticists. It has strange and wonderful consequences, not the least of which in practice, if Fisher and Lande are right, is the explosive evolution of peacocks’ and widow birds’ tails, and a host of other organs of attraction. These consequences can only be proved mathematically, but it is possible to say in words what they are, and we can try to gain some flavour of the mathematical argument in non-mathematical language. We still need our mental running shoes, although actually climbing boots is a better analogy. Each step in the argument is simple enough, but there is a long series of steps up the mountain of understanding, and if you miss any of the earlier steps you unfortunately can’t take the later ones.
The Blind Watchmaker Page 27
