RICHARD DAWKINS

THE BLIND WATCHMAKER

 

 

 

CHAPTER 3

ACCUMULATING

SMALL CHANGE



We have seen that living things are too improbable and too beautifully 'designed' to have come into existence by chance. How, then, did they come into existence? The answer, Darwin's answer, is by gradual, stepby- step transformations from simple beginnings, from primordial entities sufficiently simple to have come into existence by chance. Each
successive change in the gradual evolutionary process was simple enough,
relative to its predecessor, to have arisen by chance. But the whole sequence of cumulative steps constitutes anything but a chance process, when you consider the complexity of the final end-product relative to the original starting point. The cumulative process is directed by nonrandom survival. The purpose of this chapter is to demonstrate the power of this cumulative selection as a fundamentally nonrandom process.

If you walk up and down a pebbly beach, you will notice that the pebbles are not arranged at random. The smaller pebbles typically tend to be found in segregated zones running along the length of the beach, the larger ones in different zones or stripes. The pebbles have been sorted, arranged, selected. A tribe living near the shore might wonder at this evidence of sorting or arrangement in the world, and might develop a myth to account for it, perhaps attributing it to a Great Spirit in the sky with a tidy mind and a sense of order. We might give a superior smile at such a superstitious notion, and explain that the arranging was really done by the blind forces of physics, in this case the action of waves. The waves have no purposes and no intentions, no tidy mind, no mind at all. They just energetically throw the pebbles around, and big pebbles and small pebbles respond differently to this treatment so they end up at different levels of the beach. A small amount of order has come out of disorder, and no mind planned it.

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44 The Blind Watchmaker

The waves and the pebbles together constitute a simple example of a system that automatically generates non-randomness. The world is full of such systems. The simplest example I can think of is a hole. Only objects smaller than the hole can pass through it. This means that if you start with a random collection of objects above the hole, and some force shakes and jostles them about at random, after a while the objects above and below the hole will come to be nonrandomly sorted. The space below the hole will tend to contain objects smaller than the hole, and the space above will tend to contain objects larger than the hole. Mankind has, of course, long exploited this simple principle for generating non-randomness, in the useful device known as the sieve.

The Solar System is a stable arrangement of planets, comets and debris orbiting the sun, and it is presumably one of many such orbiting systems in the universe. The nearer a satellite is to its sun, the faster it has to travel if it is to counter the sun's gravity and remain in stable orbit. For any given orbit, there is only one speed at which a satellite can travel and remain in that orbit. If it were travelling at any other velocity, it would either move out into deep space, or crash into the Sun, or move into another orbit. And if we look at the planets of our solar system, lo and behold, every single one of them is travelling at exactly the right velocity to keep it in its stable orbit around the Sun. A blessed miracle of provident design? No, just another natural 'sieve'. Obviously all the planets that we see orbiting the sun must be travelling at exactly the right speed to keep them in their orbits, or we wouldn't see them there because they wouldn't be there! But equally obviously this is not evidence for conscious design. It is just another kind of sieve.

Sieving of this order of simplicity is not, on its own, enough to account for the massive amounts of nonrandom order that we see in living things. Nowhere near enough. Remember the analogy of the combination lock. The kind of non-randomness that can be generated by simple sieving is roughly equivalent to opening a combination lock with only one dial: it is easy to open it by sheer luck. The kind of nonrandomness that we see in living systems, on the other hand, is equivalent to a gigantic combination lock with an almost uncountable number of dials. To generate a biological molecule like haemoglobin, the red pigment in blood, by simple sieving would be equivalent to taking all the amino-acid building blocks of haemoglobin, jumbling them up at random, and hoping that the haemoglobin molecule would reconstitute itself by sheer luck. The amount of luck that would be required for this feat is unthinkable, and has been used as a telling mind-boggier by Isaac Asimov and others.

 



 

Accumulating small change 45

A haemoglobin molecule consists of four chains of amino acids twisted together. Let us think about just one of these four chains. It consists of 146 amino acids. There are 20 different kinds of amino acids commonly found in living things. The number of possible ways of arranging 20 kinds of thing in chains 146 links long is an inconceivably large number, which Asimov calls the 'haemoglobin number'. It is easy to calculate, but impossible to visualize the answer. The first link in the 146-long chain could be any one of the 20 possible amino acids. The second link could also be any one of the 20, so the number of possible 2-link chains is 20 x 10, or 400. The number of possible 3-link chains is 20 x 20 x 20, or 8,000. The number of possible 146-link chains is 20 times itself 146 times. This is a staggeringly large number. A million is a 1 with 6 noughts after it. A billion 11,000 million) is a 1 with 9 noughts after it. The number we seek, the 'haemoglobin number', is (near enough) a 1 with 190 noughts after it! This is the chance against happening to hit upon haemoglobin by luck. And a haemoglobin molecule has only a minute fraction of the complexity of a living body. Simple sieving, on its own, is obviously nowhere near capable of generating the amount of order in a living thing. Sieving is an essential ingredient in the generation of living order, but it is very far from being the whole story. Something else is needed. To explain the point, I shall need to make a distinction between 'single-step' selection and 'cumulative' selection. The simple sieves we have been considering so far in this chapter are all examples of single-step selection. Living organization is the product of cumulative selection.

The essential difference between single-step selection and cumulative selection is this. In single-step selection the entities selected or sorted, pebbles or whatever they are, are sorted once and for all. In cumulative selection, on the other hand, they 'reproduce'; or in some other way the results of one sieving process are fed into a subsequent sieving, which is fed into . . ., and so on. The entities are subjected to selection or sorting over many 'generations' in succession. The end-product of one generation of selection is the starting point for the next generation of selection, and so on for many generations. It is natural to borrow such words as 'reproduce' and 'generation', which have associations with living things, because living things are the main examples we know of things that participate in cumulative selection. They may in practice be the only things that do. But for the moment I don't want to beg that question by saying so outright.

Sometimes clouds, through the random kneading and carving of the winds, come to look like familiar objects. There is a much published photograph, taken by the pilot of a small aeroplane, of what looks a bit

 



 

46 The Blind Watchmaker

like the face of Jesus, staring out of the sky. We have all seen clouds that reminded us of something - a sea horse, say, or a smiling face. These resemblances come about by single-step selection, that is to say by a Single coincidence. They are, consequently, not very impressive. The resemblance of the signs of the zodiac to the animals after which they are named, Scorpio, Leo, and so on, is as unimpressive as the predictions of astrologers. We don't feel overwhelmed by the resemblance, as we are by biological adaptations - the products of cumulative selection. We describe as weird, uncanny or spectacular, the resemblance of, say, a leaf insect to a leaf or a praying mantis to a cluster of pink flowers. The resemblance of a cloud toaweaselisonly mildly diverting, barely worth calling to the attention of our companion. Moreover, we are quite likely to change our mind about exactly what the cloud most resembles.

Hamlet. Do you see yonder cloud that's almost in shape of a camel? Polonius. By the mass, and 'tis like a camel, indeed.

Hamlet. Methinks it is like a weasel. Polonius. It is backed like a weasel. Hamlet. Or like a whale?

Polonius. Very like a whale.

I don't know who it was first pointed out that, given enough time, a monkey bashing away at random on a typewriter could produce all the works of Shakespeare. The operative phrase is, of course, given enough time. Let us limit the task facing our monkey somewhat. Suppose that he has to produce, not the complete works of Shakespeare but just the short sentence 'Methinks it is like a weasel', and we shall make it relatively easy by giving him a typewriter with a restricted keyboard, one with just the 26 (capital) letters, and a space bar. How long will he take to write this one little sentence?

The sentence has 28 characters in it, so let us assume that the monkey has a series of discrete 'tries', each consisting of 28 bashes at the keyboard. If he types the phrase correctly, that is the end of the experiment. If not, we allow him another 'try' of 28 characters. I don't know any monkeys, but fortunately my 11-month old daughter is an experienced randomizing device, and she proved only too eager to step into the role of monkey typist. Here is what she typed on the computer:

UMMK JK CDZZ F ZD DSDSKSM S SS FMCV PU I DDRGLKDXRRDO RDTE QDWFDVIOY UDSKZWDCCVYT H CHVY NMGNBAYTDFCCVD D RCDFYYYRM N DFSKD LD K WDWK HKAUIZMZI UXDKIDISFUMDKUDXI

 





 

Accumulating small change 47

She has other important calls on her time, so I was obliged to program the computer to simulate a randomly typing baby or monkey:

WDLDMNLT DTJBKWIRZREZLMQCO P Y YVMQKZPGJXWVHGLAWFVCHQYOPY MWR SWTNUXMLCDLEUBXTQHNZVIQF FU OVAODVYKDGXDEKYVMOGGS VT HZQZDSFZIHIVPHZPETPWVOVPMZGF GEWRGZRPBCTPGQMCKHFDBGW ZCCF

And so on and on. It isn't difficult to calculate how long we should reasonably'expect to wait for the random computer (or baby or
monkey) to type METHINKS IT IS LIKE A WEASEL. Think about the total number of
possible phrases of the right length that the monkey or baby or random computer could type. It is the same kind of calculation as we did for haemoglobin, and it produces a similarly large result. There are 27 possible letters (counting 'space' as one letter) in the first position. The chance of the monkey happening to get the first letter-M -right is therefore 1 in 27. The chance of it getting the first two letters ME - right is the chance of it getting the second letter - E - right (1 in
27)
given that it has also got the first letter - M - right, therefore 1/27 x 1/27, which equals 1/729. The chance of it getting the first word - METHINKS - right is 1/27 for each of the 8 letters, therefore (1/27) X (1/27) x (1/27) x (1/27). .., etc. 8 times, or (1/27) to the power 8. The chance of it getting the entire phrase of 28 characters right is (1/27) to the power 28, i.e. (1/27) multiplied by itself 28 times. These are very small odds, about 1 in 10,000 million million million million million million. To put it mildly, the phrase we seek would be a long time coming, to say nothing of the complete works of Shakespeare.

So much for single-step selection of random variation. What about cumulative selection; how much more effective should this be? Very very much more effective, perhaps more so than we at first realize, although it is almost obvious when we reflect further. We again use our computer monkey, but with a crucial difference in its program. It again begins by choosing a random sequence of 28 letters, just as before:

WDLMNLT DTJBKWIRZREZLMQCO P

It now 'breeds from' this random phrase. It duplicates it repeatedly, but with a certain chance of random error - 'mutation' - in the copying. The computer examines the mutant nonsense phrases, the 'progeny' of the original phrase, and chooses the one which, however slightly, most resembles the target phrase, METHINKS IT IS LIKE A

 





 

48 The Blind Watchmaker

WEASEL. In this instance the winning phrase of the next 'generation' happened to be:

WDLTMNLT DTJBSWIRZREZLMQCO P

Not an obvious improvement! But the procedure is repeated, again mutant 'progeny' are 'bred from' the phrase, and a new 'winner' is chosen. This goes on, generation after generation. After 10 generations, the phrase chosen for 'breeding' was:

MDLDMNLS ITpSWHRZREZ MECS P

After 20 generations it was:

MELDINLS IT ISWPRKE Z WECSEL

By now, the eye of faith fancies that it can see a resemblance to the

target phrase. By 30 generations there can be no doubt:

METHINGS IT ISWLIKE B WECSEL

Generation 40 takes us to within one letter of the target:

METHINKS IT IS LIKE I WEASEL

And the target was finally reached in generation 43. A second run of the computer began with the phrase:

Y YVMQKZPFfXWVHGLAWFVCHQXYOPY,

passed through (again reporting only every tenth generation):

Y YVMQKSPFTXWSHLIKEFV HQYSPY YETHINKSPITXISHLIKEFA WQYSEY METHINKS IT ISSLIKE A WEFSEY METHINKS IT ISBLIKE A WEASES METHINKS IT ISJLIKE A WEASEO METHINKS IT IS LIKE A WEASEP

and reached the target phrase in generation 64. m a third run the computer started with:

GEWRGZRPBCTPGQMCKHFDBGW ZCCF

and reached METHINKS IT IS LIKE A WEASEL in 41 generations of selective 'breeding'.

The exact time taken by the computer to reach the target doesn't matter. If you want to know, it completed the whole exercise for me, the first time, while I was out to lunch. It took about half an hour. (Computer enthusiasts may think this unduly slow. The reason is that

 





 

Accumulating small change 49

the program was written in BASIC, a sort of computer baby-talk. When I rewrote it in Pascal, it took 11 seconds.) Computers are a bit faster at this kind of thing than monkeys, but the difference really isn't significant. What matters is the difference between the time taken by cumulative selection, and the time which the same computer,
working flat out at the same rate, would take to reach the target phrase if it were forced to use the other procedure of
single-step selection: about a million million million million million years. This is more than a million million million times as long as the universe has so far existed. Actually it would be fairer just to say that, in comparison with the time it would take either a monkey or a randomly programmed computer to type our target phrase, the total age of the universe so far is a negligibly small quantity, so small as to be well within the margin of error for this sort of back-of-an-envelope calculation. Whereas the time taken for a computer working randomly but with the constraint of cumulative selection to perform the same task is of the same order as humans ordinarily can understand, between 11 seconds and the time it takes to have lunch.

There is a big difference, then, between cumulative selection (in which each improvement, however slight, is used as a basis for future building), and single-step selection (in which each new 'try' is a fresh one). If evolutionary progress had had to rely on single-step selection, it would never have got anywhere. If, however, there was any way in which the necessary conditions for cumulative selection could have been set up by the blind forces of nature, strange and wonderful might have been the consequences. As a matter of fact that is exactly what happened on this planet, and we ourselves are among the most recent, if not the strangest and most wonderful, of those consequences.

It is amazing that you can still read calculations like my haemoglobin calculation, used as though they constituted arguments against Darwin's theory. The people who do this, often expert in their own field, astronomy or whatever it may be, seem sincerely to believe that Darwinism explains living organization in terms of chance - 'single- step selection' - alone. This belief, that Darwinian evolution is 'random', is not merely false. It is the exact opposite of the truth. Chance is a minor ingredient in the Darwinian recipe, but the most important ingredient is cumulative selection which is quintessentially nonrandom.

Clouds are not capable of entering into cumulative selection. There is no mechanism whereby clouds of particular shapes can spawn daughter clouds resembling themselves. If there were such a mechanism, if a cloud resembling a weasel or a camel could give rise to

 



 

50 The Blind Watchmaker

a lineage of othel clouds of roughly the same shape, cumulative selection would have the opportunity to get going. Of course, clouds do break up and form 'daughter' clouds sometimes, but this isn't enough for cumulative selection. It is also necessary that the 'progeny' of any given cloud should resemble its 'parent' more than it resembles any old 'parent' in the 'population'. This vitally important point is apparently misunderstood by some of the philosophers who have, in recent years, taken an interest in the theory of natural selection. It is further
necessary that the chances of a given cloud's surviving and spawning copies should depend upon its shape. Maybe in some distant galaxy these conditions did arise, and the result, if enough millions of years have gone by, is an ethereal, wispy form of life. This might make a good science fiction story -
The White Cloud, it could be called - but for our purposes a computer model like the monkey/Shakespeare model is easier to grasp.

Although the monkey/Shakespeare model is useful for explaining the distinction between single-step selection and cumulative selection, it is misleading in important ways. One of these is that, in each generation of selective 'breeding', the mutant 'progeny' phrases were judged according to the criterion of resemblance to a distant ideal target, the phrase METHINKS IT IS LIKE A WEASEL. Life isn't like that. Evolution has no long-term goal. There is no long-distance target, no final perfection to serve as a criterion for selection, although human vanity cherishes the absurd notion that our species is the final goal of evolution. In real life, the criterion for selection is always short-term, either simple survival or, more generally, reproductive success. If, after the aeons, what looks like progress towards some distant goal seems, with hindsight, to have been achieved, this is always an incidental consequence of many generations of short-term selection. The 'watchmaker' that is cumulative natural selection is blind to the future and has no long-term goal.

We can change our computer model to take account of this point. We can also make it more realistic in other respects. Letters and words are peculiarly human manifestations, so let's make the computer draw pictures instead. Maybe we shall even see animal-like shapes evolving in the computer, by cumulative selection of mutant forms. We shan't prejudge the issue by building-in specific animal pictures to start with. We want them to emerge solely as a result of cumulative selection of random mutations.

In real life, the form of each individual animal is produced by embryonic development. Evolution occurs because, in successive generations, there are slight differences in embryonic development.

 



 

Accumulating small change 51

These differences come about because of changes (mutations - this is the small random element in the process that I spoke of) in the genes controlling development. In our computer model, therefore, we must have something equivalent to embryonic development, and something equivalent to genes that can mutate. There are many ways in which we could meet these specifications in a computer model. I chose one and wrote a program that embodied it. I shall now describe this computer model, because I think it is revealing. If you don't know anything about computers, just remember that they are machines that do exactly what you tell them but often surprise you in the result. A list of instructions for a computer is called a program (this is standard American spelling, and it is also recommended by the Oxford Dictionary: the alternative, 'programme', commonly used in Britain, appears to be a Frenchified affectation).

Embryonic development is far too elaborate a process to simulate realistically on a small computer. We must represent it by some simplified analogue. We must find a simple picture-drawing rule that the computer can easily obey, and which can then be made to vary under the influence of 'genes'. What drawing rule shall we choose? Textbooks of computer science often illustrate the power of what they call 'recursive' programming with a simple tree-growing procedure. The computer starts by drawing a single vertical line. Then the line branches into two. Then each of the branches splits into two subbranches. Then each of the sub-branches splits into sub-sub-branches, and so on. It is 'recursive' because the same rule (in this case a branching rule) is applied locally all over the growing tree. No matter how big the tree may grow, the same branching rule goes on being applied at the tips of all its twigs.

The 'depth' of recursion, means the number of sub-sub-. .. branches that are allowed to grow, before the process is brought to a halt. Figure 2 shows what happens when you tell the computer to obey exactly the same drawing rule, but going on to various depths of recursion. At high levels of recursion the pattern becomes quite elaborate, but you can easily see in Figure 2 that it is still produced by the same very simple branching rule. This is, of course, just what happens in a real tree. The branching pattern of an oak tree or an apple free looks complex, but it really isn't. The basic branching rule is very simple. It is because it is applied recursively at the growing tips all over the tree - branches make sub-branches, then each sub-branch makes sub-sub-branches, and so on - that the whole tree ends up large and bushy.

Recursive branching is also a good metaphor for the embryonic development of plants and animals generally. I don't mean that animal

 



 

52 The Blind Watchmaker

 


image


Figure 2

embryos look like branching trees. They don't. But all embryos grow by cell division. Cells always split into two daughter cells. And genes always exert their final effects on bodies by means of local influences on cells, and on the two-way branching patterns of cell division. An animal's genes are never a grand design, a blueprint for the whole body. The genes, as we shall see, are more like a recipe than like a blueprint; and a recipe, moreover, that is obeyed not by the developing embryo as

 



 

Accumulating small change 53

a whole, but by each cell or each local cluster of dividing cells. I'm not denying that the embryo, and later the adult, has a large-scale form. But this large-scale form emerges because of lots of little local cellular effects all over the developing body, and these local effects consist primarily of two-way branchings, in the form of two-way cell splittings. It is by influencing these local events that genes ultimately exert influences on the adult body.

The simple branching rule for drawing trees, then, looks like a promising analogue for embryonic development. Accordingly, we wrap it up in a little computer procedure, label it DEVELOPMENT, and prepare to embed it in a larger program labelled EVOLUTION. As a first step towards writing this larger program, we now turn our attention to genes. How shall we represent 'genes' in our computer model? Genes in real life do two things. They influence development, and they get passed on to future generations. In real animals and plants there are tens of thousands of genes, but we shall modestly limit our computer model to nine. Each of the nine genes is simply represented by a number in the computer, which will be called its value. The value of a particular gene might be, say 4, or -7.

How shall we make these genes influence development? There are lots of things they could do. The basic idea is that they should exert some minor quantitative influence on the drawing rule that is DEVELOPMENT. For instance, one gene might influence the angle of branching, another might influence the length of some particular branch. Another obvious thing for a gene to do is to influence the depth of the recursion, the number of successive branchings. I made Gene 9 have this effect. You can regard Figure 2, therefore, as a picture of seven related organisms, identical to each other except with respect to Gene
9. I shan't spell out in detail what each one of the other eight genes does. You can get a general idea of the
kinds of things they do by studying Figure 3. In the middle of the picture is the basic tree, one of the ones from Figure 2. Encircling this central tree are eight others. All are the same as the central tree, except that one gene, a different gene in each of the eight, has been changed - 'mutated'. For instance, the picture to the right of the central tree shows what happens when Gene 5 mutates by having +1 added to its value. If there'd been room, I'd have liked to print a ring of 18 mutants around the central tree. The reason for wanting 18 is that there are nine genes, and each one can mutate in an 'upward' direction (1 is added to its value) or in a ' downward' direction (1 is subtracted from its value). So a ring of 18 trees would be enough to represent all possible single-step mutants that you can derive from the one central tree.

 



 

54 The Blind Watchmaker

 


image


Figure 3

Each of these trees has its own, unique 'genetic formula', the numerical values of its nine genes. I haven't written the genetic formulae down, because they wouldn't mean anything to you, in themselves. That is true of real genes too. Genes only start to mean
something when they are translated, via protein synthesis, into
growingrules for a developing embryo. And in the computer model too, the numerical values of the nine genes only mean something when they are translated into growing rules for the branching tree pattern. But you can get an idea of what each gene does by
comparing the bodies of two organisms known to differ with respect to a certain gene. Compare, for instance, the basic tree in the middle of the picture with the two trees on either side, and you'll get some idea of what Gene 5 does.

This, too, is exactly what real-life geneticists do. Geneticists normally don't know how genes exert their effects on embryos. Nor do they know the complete genetic formula of any animal. But by

 



 

Accumulating small change 55

comparing the bodies of two adult animals that are known to differ according to a single gene, they can see what effects that single gene has. It is more complicated than that, because the effects of genes interact with each other in ways that are more complicated than simple addition. Exactly the same is true of the computer trees. Very much so, as later pictures will show.

You will notice that all the shapes are symmetrical about a left/right axis. This is a constraint that I imposed on the DEVELOPMENT procedure. I did it partly for aesthetic reasons; partly to economize on the number of genes necessary (if genes didn't exert mirror-image effects on the two sides of the tree, we'd need separate genes for the left and the right sides); and partly because I was hoping to evolve animal-like shapes, and most animal bodies are pretty symmetrical. For the same reason, from now on I shall stop calling these creatures 'trees', and shall call them 'bodies' or 'biomorphs'. Biomorph is the name coined by Desmond Morris for the vaguely animal-like shapes in his surrealist paintings. These paintings have a special place in my affections, because one of them was reproduced on the cover of my first book. Desmond Morris claims that his biomorphs 'evolve' in his mind, and that their evolution can be traced through successive paintings.

Back to the computer biomorphs, and the ring of 18 possible mutants, of which a representative eight are drawn in Figure 3. Since each member of the ring is only one mutational step away from the central biomorph, it is easy for us to see them as children of the central parent. We have our analogue of REPRODUCTION, which, like DEVELOPMENT, we can wrap up in another small computer program, ready to embed in our big program called EVOLUTION. Note two things about REPRODUCTION. First, there is no sex; reproduction is asexual. I think of the biomorphs as female, therefore, because asexual animals like greenfly are nearly always basically female in form.

Second, my mutations are all constrained to occur one at a time. A child differs from its parent at only one of the nine genes; moreover, all mutation occurs by +1 or 1 being added to the value of the corresponding parental gene. These are just arbitrary conventions: they could have been different and still remained biologically realistic.

The same is not true of the following feature of the model, which embodies a fundamental principle of biology. The shape of each child is not derived directly from the shape of the parent. Each child gets its shape from the values of its own nine genes (influencing angles, distances, and so on). And each child gets its nine genes from its parent's nine genes. This is just what happens in real life. Bodies don't get passed down the generations; genes do. Genes influence embryonic

 



 

56 The Blind Watchmaker

development of the body in which they are sitting. Then those same genes either get passed on to the next generation or they don't. The nature of the genes is unaffected by their participation in bodily development, but their likelihood of being passed on may be affected by the success of the body that they helped to create. This is why, in the computer model, it is important that the two procedures called DEVELOPMENTandREPRODUCTIONarewrittenastwowatertight compartments. They are watertight except that REPRODUCTION passes gene values across to DEVELOPMENT, where they influence the growing rules. DEVELOPMENT most emphatically does not pass gene values back to REPRODUCTION - that would be tantamount to 'Lamarckism' (see Chapter 11).

We have assembled our two program modules, then, labelled DEVELOPMENT and REPRODUCTION. REPRODUCTION passes genes down the generations, with the possibility of mutation. DEVELOPMENT takes the genes provided by REPRODUCTION in any given generation, and translates those genes into drawing action, and hence into a picture of a body on the computer screen. The time has come to bring the two modules together in the big program called EVOLUTION.

EVOLUTION basically consists of endless repetition of REPRODUCTION. In every generation, REPRODUCTION takes the genes that are supplied to it by the previous generation, and hands them on to the next generation but with minor random errors - mutations. A mutation simply consists in +1 or 1 being added to the value of a randomly chosen gene. This means that, as the generations go by, the total amount of genetic difference from the original ancestor can become very large, cumulatively, one small step at a time. But although the mutations are random, the cumulative change over the generations is not random. The progeny in any one generation are different from their parent in random directions. But which of those progeny is selected to go forward into the next generation is not random. This is where Darwinian selection comes in. The criterion for selection is not the genes themselves, but the bodies whose shape the genes influence through DEVELOPMENT.

In addition to being REPRODUCED, the genes in each generation are also handed to DEVELOPMENT, which grows the appropriate body on the screen, following its own strictly laid-down rules. In every generation, a whole 'litter' of 'children' (i.e. individuals of the next generation) is displayed. All these children are mutant children of the same parent, differing from their parent with respect to one gene each. This very high mutation rate is a distinctly unbiological feature of the

 



 

Accumulating small change 57

computer model. In real life, the probability that a gene will mutate is often less than one in a million. The reason for building a high mutation rate into the model is that the whole performance on the computer screen is for the benefit of human eyes, and humans haven't the patience to wait a million generations for a mutation!

The human eye has an active role to play in the story. It is the selecting agent. It surveys the litter of progeny and chooses one for breeding. The chosen one then becomes the parent of the next generation, and a litter of its mutant children are displayed simultaneously on the screen. The human eye is here doing exactly what it does in the breeding of pedigree dogs or prize roses. Our model, in other words, is strictly a model of artificial selection, not natural selection. The criterion for 'success' is not the direct criterion of survival, as it is in true natural selection. In true natural selection, if a body has what it takes to survive, its genes automatically survive because they are inside it. So the genes that survive tend to be, automatically, those genes that confer on bodies the qualities that assist them to survive. In the computer model, on the other hand, the selection criterion is not survival, but the ability to appeal to human whim. Not necessarily idle, casual whim, for we can resolve to select consistently for some quality such as 'resemblance to a weeping willow'. In my experience, however, the human selector is more often capricious and opportunistic. This, too, is not unlike certain kinds of natural selection.

The human tells the computer which one of the current litter of progeny to breed from. The genes of the chosen one are passed across to REPRODUCTION, and a new generation begins. This process, like real-life evolution, goes on indefinitely. Each generation of biomorphs is only a single mutational step away from its predecessor and its successor. But after 100 generations of EVOLUTION, the biomorphs can be anything up to 100 mutational steps away from their original ancestor. And in 100 mutational steps, much can happen.

I never dreamed how much, when I first started to play with my newly written EVOLUTION program. The main thing that surprised me was that the biomorphs can pretty quickly cease to look like trees. The basic two-way branching structure is always there, but it is easily smothered as lines cross and recross one another, making solid masses of colour (only black and white in the printed pictures). Figure 4 shows one particular evolutionary history consisting of no more than 29 generations. The ancestor is a tiny creature, a single dot. Although the ancestor's body is a dot, like a bacterium in the primeval slime, hidden inside'it is the potential for branching in exactly the pattern of the

 




 

The Blind Watchmaker

 


image



 

Accumulating small change 59

central tree of Figure 3: it is just that its Gene 9 tells it to branch zero times! All the creatures pictured on the page are descended from the dot but, in order to avoid cluttering the page, I haven't printed all the descendants that I actually saw. I've printed only the successful child of each generation (i.e. the parent of the next generation) and one or two of its unsuccessful sisters. So, the picture basically shows just the one main line of evolution, guided by my aesthetic selection. All the stages in the main line are shown.

Let's briefly go through the first few generations of the main line of evolution in Figure 4. The dot becomes a Y in generation 2. In the next two generations, the Y becomes larger. Then the branches become slightly curved, like a well-made catapult. In generation 7, the curve is accentuated, so that the two branches almost meet. The curved branches get bigger, and each acquires a couple of small appendages in generation 8. In generation 9 these appendages are lost again, and the stem of the catapult becomes longer. Generation 10 looks like a section through a flower; the curved side-branches resemble petals cupping a central appendage or 'stigma'. In generation 11, the same 'flower' shape has become bigger and slightly more complicated.

I won't pursue the narrative. The picture speaks for itself, on through the 29 generations. Notice how each generation is just a little different from its parent and from its sisters. Since each is a little different from its parent, it is only to be expected that each will be slightly more different from its grandparents (and its grandchildren), and even more different still from its great grandparents (and great grandchildren). This is what cumulative evolution is all about, although, because of our high mutation rate, we have speeded it up here to unrealistic rates. Because of this. Figure 4 looks more like a pedigree of species than a pedigree of individuals, but the principle is the same.

When I wrote the program, I never thought that it would evolve anything more than a variety of tree-like shapes. I had hoped for weeping willows, cedars of Lebanon, Lombardy poplars, seaweeds, perhaps deer antlers. Nothing in my biologist's intuition, nothing in my 20 years' experience of programming computers, and nothing in my wildest dreams, prepared me for what actually emerged on the screen. I can't remember exactly when in the sequence it first began to dawn on me that an evolved resemblance to something like an insect was possible. With a wild surmise, I began to breed, generation after generation, from whichever child looked most like an insect. My incredulity grew in parallel with the evolving resemblance. You see the eventual results at the bottom of Figure 4. Admittedly they have

 



 

The Blind Watchmaker

eight legs like a spider, instead of six like an insect, but even so! I still cannot conceal from you my feeling of exultation as I first watched these exquisite creatures emerging before my eyes. I distinctly heard the triumphal opening chords of Also spiach Zaiathustia (the '2001 theme') in my mind. I couldn't eat, and that night 'my' insects' swarmed behind my eyelids as I tried to sleep.

There are computer games on the market in which the player has the illusion that he is wandering about in an underground labyrinth, which has a definite if complex geography and in which he encounters dragons, minotaurs or other mythic adversaries. In these games the monsters are rather few in number. They are all designed by a human programmer, and so is the geography of the labyrinth. In the evolution game, whether the computer version or the real thing, the player (or observer) obtains the same feeling of wandering metaphorically through a labyrinth of branching passages, but the number of possible pathways is all but infinite, and the monsters that one encounters are undesigned and unpredictable. On my wanderings through the backwaters of Biomorph Land, I have encountered fairy shrimps, Aztec temples, Gothic church windows, aboriginal drawings of kangaroos, and, on one memorable but unrecapturable occasion, a passable caricature of the Wykeham Professor of Logic. Figure 5 is another little collection from my trophy room, all of which developed in the same kind of way. I want to emphasize that these shapes are not artists' impressions. They have not been touched-up or doctored in any way whatever. They are exactly as the computer drew them when they evolved inside it. The role of the human eye was limited to selecting, among randomly mutated progeny over many generations of cumulative evolution.

We now have a much more realistic model of evolution than the monkeys typing Shakespeare gave us. But the biomorph model is still deficient. It shows us the power of cumulative selection to generate an almost endless variety of quasi-biological form, but it uses artificial selection, not natural selection. The human eye does the selecting. Could we dispense with the human eye, and make the computer itself do the selecting, on the basis of some biologically realistic criterion? This is more difficult than it may seem. It is worth spending a little time explaining why.

It is trivially easy to select for a particular genetic formula, so long as you can read the genes of all the animals. But natural selection doesn't choose genes directly, it chooses the effects that genes have on bodies, technically called phenotypic effects. The human eye is good at choosing phenotypic effects, as is shown by the numerous breeds of

 




 

Accumulating small change 61

 


image


dogs, cattle and pigeons, and also, if I may say so, as is shown by Figure
5. To make the computer choose phenotypic effects directly, we should have to write a very sophisticated pattern-recognition program. Pattern-recognizing programs exist. They are used to read print and even handwriting. But they are difficult, 'state of the art' programs, needing very large and fast computers. Even if such a patternrecognition program were not beyond my programming capabilities, and beyond the capacity of my little 64-kilobyte computer, I wouldn't bother with it. This is a task that is better done by the human eye, together with - and this is more to the point - the 10-giganeurone computer inside the skull.

It wouldn't be too difficult to make the computer select for vague general features like, say, tall-thinness, short-fatness, perhaps curvaceousness, spikiness, even rococo ornamentation. One method would be to program the computer to remember the kinds of qualities that humans have favoured in the past, and to exert continued selection of the same general kind in the future. But this isn't getting

 



 

62 The Blind Watchmaker

us any closer to simulating natural selection. The important point is that nature doesn't need computing power in order to select, except in special cases like peahens choosing peacocks. In nature, the usual selecting agent is direct, stark and simple. It is the grim reaper. Of course, the reasons for survival are anything but simple - that is why natural selection can build up animals and plants of such formidable complexity. But there is something very crude and simple about death itself. And nonrandom death is all it takes to select phenotypes, and hence the genes that they contain, in nature.

To simulate natural selection in an interesting way in the computer, we should forget about rococo ornamentation and all other visually defined qualities. We should concentrate, instead, upon simulating nonrandom death. Biomorphs should interact, in the computer, with a simulation of a hostile environment. Something about their shape should determine whether or not they survive in that environment. Ideally, the hostile environment should include other evolving biomorphs: 'predators', 'prey', 'parasites', 'competitors'. The particular shape of a prey biomorph should determine its vulnerability to being caught, for example, by particular shapes of predator biomorphs. Such criteria of vulnerability should not be built in by the programmer. They should emerge, in the same kind of way as the shapes themselves emerge. Evolution in the computer would then really take off, for the conditions would be met for a self-reinforcing 'arms race' (see Chapter
7), and I dare not speculate where it would all end. Unfortunately, I think it may be beyond my powers as a programmer to set up such a counterfeit world.

If anybody is clever enough to do it, it would be the programmers who develop those noisy and vulgar arcade games - Space Invaders' derivatives. In these programs a counterfeit world is simulated. It has a geography, often in three dimensions, and it has a fast-moving time dimension. Entities zoom around in simulated three-dimensional space, colliding with each other, shooting each other down, swallowing each other amid revolting noises. So good can the simulation be that the player handling the joystick receives a powerful illusion that he himself is part of the counterfeit world. I imagine that the summit of this kind of programming is achieved in the chambers used to train aeroplane and spacecraft pilots. But even these programs are small-fry compared to the program that would have to be written to simulate an emerging arms race between predators and prey, embedded in a complete, counterfeit ecosystem. It certainly could be done,
however. If there is a professional programmer out there who feels like collaborating on the challenge, I should like to hear from him or her.

 



 

Accumulating small change 63

Meanwhile, there is something else that is much easier, and which I intend trying when summer comes. I shall put the computer in a shady place in the garden. The screen can display in colour. I already have a version of the program which uses a few more 'genes' to control colour, in the same kind of way as the other nine genes control shape. I shall begin with any more-or-less compact and brightly coloured biomorph. The computer will simultaneously display a range of mutant progeny of the biomorph, differing from it in shape and/or colour pattern. I believe that bees, butterflies and other insects will visit the screen, and 'choose' by bumping into a particular spot on the screen. When a certain number of choices have been logged, the computer will wipe the screen clean, 'breed' from the preferred biomorph, and display the next generation of mutant progeny.

I have high hopes that, over a large number of generations, the wild insects will actually cause the evolution, in the computer, of flowers. If they do, the computer flowers will have evolved under exactly the same selection pressure as caused real flowers to evolve in the wild. I am encouraged in my hope by the fact that insects frequently visit bright blobs of colour on women's dresses (and also by more systematic experiments that have been published). An alternative possibility, which I would find even more exciting, is that the wild insects might cause the evolution of insect-like shapes. The precedent for this - and hence the reason for hope - is that bees in the past caused the evolution of bee-orchids. Male bees, over many generations of cumulative orchid evolution, have built up the bee-like shape through trying to copulate with flowers, and hence carrying pollen. Imagine the 'bee-flower' of Figure 5 in colour. Wouldn't you fancy it if you were a bee?

My main reason for pessimism is that insect vision works in a very different way from ours. Video-screens are designed for human eyes not bee eyes. This could easily mean that, although both we and bees see bee-orchids, in our very different ways, as bee-like, bees might not see video-screen images at all. Bees might see nothing but 625 scanning lines! Still, it is worth a try. By the time this book is published, I shall know the answer.

There is a popular cliche, usually uttered in the tones Stephen Potter would have called 'plonking', which says that you cannot get out of computers any more than you put in. Other versions are that computers only do exactly what you tell them to, and that therefore computers are never creative. The cliche is true only in a crashingly trivial sense, the same sense in which Shakespeare never wrote anything except what his first schoolteacher taught him to write words. I

 



 

64 The Blind Watchmaker

programmed EVOLUTION into the computer, but I did not plan 'my' insects, nor the scorpion, nor the spitfire, nor the lunar lander. I had not the slightest inkling that they would emerge, which is why 'emerge' is the right word. True, my eyes did the selecting that guided their evolution, but at every stage I was limited to a small clutch of progeny offered up by random mutation, and my selection 'strategy', such as it was, was opportunistic, capricious and short-term. I was not aiming for any distant target, and nor does natural selection.

I can dramatize this by discussing the one time when I did try to aim for a distant target. First I must make a confession. You will have guessed it anyway. The evolutionary history of Figure 4 is a reconstruction. It was not the first time I had seen 'my' insects. When they originally emerged to the sound of trumpets, I had no means of recording their genes. There they were, sitting on the computer screen, and I couldn't get at them, couldn't decipher their genes. I delayed switching the computer off while I racked my brain trying to think of some way of saving them, but there was none. The genes were too deeply buried, just as they are in real life. I could print out pictures of the insects' bodies, but I had lost their genes. I immediately modified the program so that in future it would keep accessible records of genetic formulae, but it was too late. I had lost my insects.

I set about trying to 'find' them again. They had evolved once, so it seemed that it must be possible to evolve them again. Like the lost chord, they haunted me. I wandered through Biomorph Land, moving through an endless landscape of strange creatures and things, but I couldn't find my insects. I knew that they must be lurking there somewhere. I knew the genes from which the original evolution had started. I had a picture of my insects' bodies. I even had a picture of the evolutionary sequence of bodies leading up to my insects by slow degrees from a dot ancestor. But I didn't know their genetic formula.

You might think that it would have been easy enough to reconstruct the evolutionary pathway, but it wasn't. The reason, which I shall come back to, is the astronomical number of possible biomorphs that a sufficiently long evolutionary pathway can offer, even when there are only nine genes varying. Several times on my pilgrimage through Biomorph Land I seemed to come close to a precursor of my insects, but, then, in spite of my best efforts as a selecting agent, evolution went off on what proved to be a false trail. Eventually, during my evolutionary wanderings through Biomorph Land - the sense of triumph was scarcely less than on the first occasion -1 finally cornered them again. I didn't know (still don't) if these insects were exactly the same as my original, 'lost chords of Zarathustra' insects, or whether

 



 

Accumulating small change 65

they were superficially 'convergent' (see next chapter), but it was good enough. This time there was no mistake: I wrote down the genetic formula, and now I can 'evolve' insects whenever I want.

Yes I am piling on the drama a bit, but there is a serious point being made. The point of the story is that even though it was I that programmed the computer, telling it in great detail what to do, nevertheless I didn't plan the animals that evolved, and I was totally surprised by them when I first saw their precursors. So powerless was I to control the evolution that, even when I very much wanted to retrace a particular evolutionary pathway it proved all but impossible to do so. I don't believe I would ever have found my insects again if I hadn't had a printed picture of the complete set of their evolutionary precursors, and even then it was difficult and tedious. Does the powerlessness of the programmer to control or predict the course of evolution in the computer seem paradoxical? Does it mean that something mysterious, even mystical was going on inside the computer? Of course not. Nor is there anything mystical going on in the evolution of real animals and plants. We can use the computer model to resolve the paradox, and learn something about real evolution in the process.

To anticipate, the basis of the resolution of the paradox will turn out to be as follows. There is a definite set of biomorphs, each permanently sitting in its own unique place in a mathematical space. It is permanently sitting there in the sense that, if only you knew its genetic formula, you could instantly find it; moreover, its neighbours in this special kind of space are the biomorphs that differ from it by only one gene. Now that I know the genetic formula of my insects, I can reproduce them at will, and I can tell the computer to 'evolve' towards them from any arbitrary starting point. When you first evolve a new creature by artificial selection in the computer model, it feels like a creative process. So it is, indeed. But what you are really doing is finding the creature, for it is, in a mathematical sense, already sitting in its own place in the genetic space of Biomorph Land. The reason it is a truly creative process is that finding any particular creature is
extremely difficult, simply and purely because
Biomorph Land is very very large, and the total number of creatures sitting there is all but infinite. It isn't feasible just to search aimlessly and at random. You have to adopt some more efficient - creative - searching procedure.

Some people fondly believe that chess-playing computers work by internally trying out all possible combinations of chess moves. They find this belief comforting when a computer beats them, but their belief is utterly false. There are far too many possible chess moves: the search-space is billions of times too large to allow blind stumbling to

 



 

66 The Blind Watchmaker

succeed. The art of writing a good chess program is thinking of efficient short cuts through the search-space. Cumulative selection, whether artificial selection as in the computer model or natural selection out there in the real world, is an efficient searching procedure, and its consequences look very like creative intelligence. That, after all, is what William Paley's Argument from Design was all about. Technically, all that we are doing, when we play the computer biomorph game, is finding animals that, in a mathematical sense, are waiting to be found. What it feels like is a process of artistic creation. Searching a small space, with only a few entities in it, doesn't ordinarily feel like a creative process. A child's game of hunt the thimble doesn't feel creative. Turning things over at random and hoping to stumble on the sought object usually works when the space to be searched is small. As the search-space gets larger, more and more sophisticated searching procedures become necessary. Effective searching procedures become, when the search-space is sufficiently large, indistinguishable from true creativity.

The computer biomorph models make these points well, and they constitute an instructive bridge between human creative processes, such as planning a winning strategy at chess, and the evolutionary creativity of natural selection, the blind watchmaker. To see this, we must develop the idea of Biomorph Land as a mathematical 'space', an endless but orderly vista of morphological variety, but one in which every creature is sitting in its correct place, waiting to be discovered. The 17 creatures of Figure 5 are arranged in no special order on the page. But in Biomorph Land itself each occupies its own unique position, determined by its genetic formula, surrounded by its own
particular neighbours. All the creatures in
Biomorph Land have a definite spatial relationship one to another. What does that mean? What meaning can we attach to spatial position?

The space we are talking about is genetic space. Each animal has its own position in genetic space. Near neighbours in genetic space are animals that differ from one another by only a single mutation. In Figure 3, the basic tree in the centre is surrounded by 8 of its 18 immediate neighbours in genetic space. The 18 neighbours of an animal are the 18 different kinds of children that it can give rise to, and the 18 different kinds of parent from which it could have come, given the rules of our computer model. At one remove, each animal has 324 (18 x 18, ignoring back-mutations for simplicity) neighbours, the set of its possible grandchildren, grandparents, aunts or nieces. At one remove again, each animal has 5,832 (18 x 18 x 18) neighbours, the set of possible great grandchildren, great grandparents, first cousins, etc.

 



 

Accumulating small change 67

What is the point of thinking in terms of genetic space? Where does it get us? The answer is that it provides us with a way to understand evolution as a gradual, cumulative process. In any one generation, according to the rules of the computer model, it is possible to move only a single step through genetic space. In 29 generations it isn't possible to move farther than 29 steps, in genetic space, away from the starting ancestor. Every evolutionary history consists of a particular pathway, or trajectory, through genetic space. For instance, the evolutionary history recorded in Figure 4 is a particular winding trajectory through genetic space, connecting a dot to an insect, and passing through 28 intermediate stages. It is this that I mean when I talk metaphorically about 'wandering' through Biomorph Land.

I wanted to try to represent this genetic space in the form of a picture. The trouble is, pictures are two-dimensional. The genetic space in which the biomorphs sit is not two-dimensional space. It isn't even three-dimensional space. It is nine-dimensional space! (The important thing to remember about mathematics is not to be frightened. It isn't as difficult as the mathematical priesthood sometimes pretends. Whenever I feel intimidated, I always remember Silvanus Thompson's dictum in Calculus Made Easy: 'What one fool can do, another can'.) If only we could draw in nine dimensions we could make each dimension correspond to one of the nine genes. The position of a particular animal, say the scorpion or the bat or the insect, is fixed in genetic space by the numerical value of its nine genes. Evolutionary change consists of a step by step walk through nine-dimensional space. The amount of genetic difference between one animal and another, and hence the time taken to evolve, and the difficulty of evolving from one to the other, is measured as the distance in ninedimensional space from one to the other.

Alas, we can't draw in nine dimensions. I sought a way of fudging it, of drawing a two-dimensional picture that conveyed something of what it feels like to move from point to point in the nine-dimensional genetic space of Biomorph Land. There are various possible ways in which this could be done, and I chose one that I call the triangle trick. Look at Figure 6. At the three corners of the triangle are three arbitrarily chosen biomorphs. The one at the top is the basic tree, the one on the left is one of 'my' insects, and the one on the right has no name but I thought it looked pretty. Like all biomorphs, each of these three has its own genetic formula, which determines its unique position in nine-dimensional genetic space.

The triangle lies on a flat two-dimensional 'plane' that cuts through the nine-dimensional hypervolume (what one fool can do, another .

 




 

68 The Blind Watchmaker

 


image


can). The plane is like a flat piece of glass stuck through a jelly. On the glass is drawn the triangle, and also some of the biomorphs whose genetic formulae entitle them to sit on that particular flat plane. What is it that entitles them? This is where the three biomorphs at the corners of the triangle come in. They are called the anchor biomorphs.

Remember that the whole idea of 'distance' in genetic 'space' is that genetically similar biomorphs are near neighbours, genetically different biomorphs are distant neighbours. On this particular plane, the distances are all calculated with reference to the three anchor biomorphs. For any given point on the sheet of glass, whether inside the triangle or outside it, the appropriate genetic formula for that point is calculated as a 'weighted average' of the genetic formulae of the three anchor biomorphs. You will already have guessed how the weighting is done. It is done by the distances on the page, more precisely the nearnesses, from the point in question to the three anchor biomorphs. So, the nearer you are to the insect on the plane, the more insect-like are the local biomorphs. As you move along the glass towards the tree, the 'insects' gradually become less insect-like and more tree-like. If you walk into the centre of the triangle the animals that you find there, for instance the spider with a Jewish seven-branched candelabra on its head, will be various 'genetic compromises' between the three anchor biomorphs.

But this account gives altogether too much prominence to the three anchor biomorphs. Admittedly the computer did use them to calculate

 




 

Accumulating small change 69

the appropriate genetic formula for every point on the picture. But actually any three anchor points on the plane would have done the trick just as well, and would have given identical results. For this reason, in Figure 7 I haven't actually drawn the triangle. Figure 7 is exactly the same kind of picture as Figure 6. It just shows a different plane. The same insect is one of the three anchor points, this time the right-hand one. The other anchor points, in this case, are the spitfire and the bee-flower, both as seen in Figure 5. On this plane, too, you will notice that neighbouring biomorphs resemble each other more than distant biomorphs. The spitfire, for instance, is part of a squadron of similar aircraft, flying in formation. Because the insect is on both sheets of glass, you can think of the two sheets as passing, at an angle, through each other. Relative to Figure 6, the plane of Figure 7 is said to be 'rotated about' the insect.

 


image


The elimination of the triangle is an improvement to our method, because it was a distraction. It gave undue prominence to three particular points in the plane. We still have one further improvement to make. In Figures 6 and 7, spatial distance represents genetic distance, but the scaling is all distorted. One inch upwards is not necessarily equivalent to one inch across. To remedy this, we must choose our three anchor biomorphs carefully, so that their genetic distances, one from the other, are all the same. Figure 8 does just this. Again the triangle is not actually drawn. The three anchors are the scorpion from Figure 5, the insect again (we have yet another 'rotation about' the

 



 

70 The Blind Watchmaker

insect), and the rather nondescript biomorph at the top. These three biomorphs are all 30 mutations distant from each other. This means that it is equally easy to evolve from any one to any other one. In all three cases, a minimum of 30 genetic steps must be taken. The little blips along the lower margin of Figure 8 represent units of distance measured in genes. You can think of it as a genetic ruler. The ruler doesn't only work in the horizontal direction. You can tilt it in any direction, and measure the genetic distance, and hence the minimum evolution time, between any point on the plane and any other (annoy - ingly, that is not quite true on the page, because the computer's printer distorts proportions, but this effect is too trivial to make a fuss about, although it does mean that you will get slightly the wrong answer if you simply count blips on the scale).

 


image


These two-dimensional planes cutting through nine-dimensional genetic space give some feeling for what it means to walk through Biomorph Land. To improve that feeling, you have to remember that evolution is not restricted to one flat plane. On a true evolutionary walk you could 'drop through', at any time, to another plane, for instance from the plane of Figure 6 to the plane of Figure 7 (in the vicinity of the insect, where the two planes come close to each other).

I said that the 'genetic ruler' of Figure 8 enables us to calculate the

 



 

Accumulating small change 71

minimum time it would take to evolve from one point to another. So it does, given the restrictions of the original model, but the emphasis is on the word minimum. Since the insect and the scorpion are 30 genetic units distant from one another, it takes only 30 generations to evolve from one to the other if you never take a wrong turning, if, that is, you know exactly what genetic formula you are heading towards, and how to steer towards it. In real-life evolution there is nothing that corresponds to steering towards some distant genetic target.

Let's now use the biomorphs to return to the point made by the monkeys typing Hamlet, the importance of gradual, step-by-step change in evolution, as opposed to pure chance. Begin by relabelling the graticules along the bottom of Figure 8, but in different units. Instead of measuring distance as 'number of genes that have to change in evolution', we are going to measure distance as 'odds of happening to jump the distance, by sheer luck, in a single hop'. To think about this, we now have to relax one of the restrictions that I built into the computer game: we shall end by seeing why I built that restriction in in the first place. The restriction was that children were only 'allowed' to be one mutation distant from their parents. In other words, only one gene was allowed to mutate at a time, and that gene was allowed to change its 'value' only by +1 or -1. By relaxing the restriction, we are now allowing any number of genes to mutate simultaneously, and they can add any number, positive or negative, to their current value. Actually, that is too great a relaxation, since it allows genetic values to range from minus infinity to plus infinity. The point is adequately made if we restrict gene values to single figures, that is if we allow them to range from -9 to +9.

So, within these wide limits, we are theoretically allowing mutation, at a stroke, in a single generation, to change any combination of the nine genes. Moreover, the value of each gene can change any amount, so long as it doesn't stray into double figures. What does this mean? It means that, theoretically, evolution can jump, in a single generation, from any point in Biomorph Land to any other. Not just any point on one plane, but any point in the entire ninedimensional hypervolume. If, for instance, you should want to jump in one fell swoop from the insect to the fox in Figure 5, here is the recipe. Add the following numbers to the values of Genes 1 to 9, respectively: -2,2,2,-2,2,0,-4,-1,1. But since we are talking about random jumps, all points in Biomorph Land are equally likely as destinations for one of these jumps. So, the odds against jumping to any particular destination, say the fox, by sheer luck, are easy to calculate. They are simply the total number of biomorphs in the space. As you can see, we

 



 

72 The Blind Watchmaker

are embarking on another of those astronomical calculations. There are nine genes, and each of them can take any of 19 values. So the total number of biomorphs that we could jump to in a single step is 19 times itself 9 times over: 19 to the power 9. This works out as about half a trillion biomorphs. Paltry compared with Asimov's 'haemoglobin number', but still what I would call a large number. If you started from the insect, and jumped like a demented flea half a trillion times, you could expect to arrive at the fox once.

What is all this telling us about real evolution? Once again, it is ramming home the importance of gradual, step-by-step change. There have been evolutionists who have denied that gradualism of this kind is necessary in evolution. Our biomorph calculation shows us exactly one reason why gradual, step-by-step change is important. When I say that you can expect evolution to jump from the insect to one of its immediate neighbours, but not to jump from the insect directly to the fox or the scorpion, what I exactly mean is the following. If genuinely random jumps really occurred, then a jump from insect to scorpion would be perfectly possible. Indeed it would be just as probable as a jump from insect to one of its immediate neighbours. But it would also be just as probable as a jump to any other biomorph in the land. And there's the rub. For the number of biomorphs in the land is half a trillion, and if no one of them is any more probable as a destination than any other, the odds of jumping to any particular one are small enough to ignore.

Notice that it doesn't help us to assume that there is a powerful nonrandom 'selection pressure'. It wouldn't matter if you'd been
promised a king's ransom if you achieved a lucky jump to the scorpion. The odds against your doing so are still half a trillion to one. But if, instead of jumping you
walked, one step at a time, and were given one small coin as a reward every time you happened to take a step in the right direction, you would reach the scorpion in a very short time. Not necessarily in the fastest possible time of 30 generations, but very fast, nevertheless. Jumping could theoretically get you the prize faster - in a single hop. But because of the astronomical odds against success, a series of small steps, each one building on the accumulated success of previous steps, is the only feasible way.

The tone of my previous paragraphs is open to a misunderstanding which I must dispel. It sounds, once again, as though evolution deals in distant targets, homing in on things like scorpions. As we have seen, it never does. But if we think of our target as anything that would improve survival chances, the argument still works. If an animal is a parent, it must be good enough to survive at least to adulthood. It is

 




 

Accumulating small change 73

possible that a mutant child of that parent might be even better at surviving. But if a child mutates in a big way, so that it has moved a long distance away from its parent in genetic space, what are the odds of its being better than its parent? The answer is that the odds against are very large indeed. And the reason is the one we have just seen with our biomorph model. If the mutational jump we are considering is a very large one, the number of possible destinations of that jump is astronomically large. And because, as we saw in Chapter 1, the number of different ways of being dead is so much greater than the number of different ways of being alive, the chances are very high that a big random jump in genetic space will end in death. Even a small random jump in genetic space is pretty likely to end in death. But the smaller the jump the less likely death is, and the more likely is it that the jump will result in improvement. We shall return to this theme in a later chapter.

That is as far as I want to go in drawing morals from Biomorph Land. I hope that you didn't find it too abstract. There is another mathematical space filled, not with nine-gened biomorphs but with flesh and blood animals made of billions of cells, each containing tens of thousands of genes. This is not biomorph space but real genetic space. The actual animals that have ever lived on Earth are a tiny subset of the theoretical animals that could exist. These real animals are the products of a very small number of evolutionary trajectories through genetic space. The vast majority of theoretical trajectories through animal space give rise to impossible monsters. Real animals are dotted around here and there among the hypothetical monsters, each perched in its own unique place in genetic hyperspace. Each real animal is surrounded by a little cluster of neighbours, most of whom have never existed, but a few of whom are its ancestors, its descendants and its cousins.

Sitting somewhere in this huge mathematical space are humans and hyenas, amoebas and aardvarks, flatworms and squids, dodos and dinosaurs. In theory, if we were skilled enough at genetic engineering, we could move from any point in animal space to any other point. From any starting point we could move through the maze in such a way as to recreate the dodo, the tyrannosaur and trilobites. If only we knew which genes to tinker with, which bits of chromosome to duplicate, invert or delete. I doubt if we shall ever know enough to do it, but these dear dead creatures are lurking there forever in their private corners of that huge genetic hypervolume, waiting to be found if we but had the knowledge to navigate the right course through the maze. We might even be able to evolve an exact reconstruction of a

 



 

74 The Blind Watchmaker

dodo by selectively breeding pigeons, though we'd have to live a million years in order to complete the experiment. But when we are prevented from making a journey in reality, the imagination is not a bad substitute. For those, like me, who are not mathematicians, the computer can be a powerful friend to the imagination. Like mathematics, it doesn't only stretch the imagination. It also disciplines and controls it.