The Blind Watchmaker (13 page)

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 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 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 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.

As we saw in Chapter 2, many people find it hard to believe that something like the eye, Paley’s favourite example, so complex and well designed, with so many interlocking working parts, could have arisen from small beginnings by a gradual series of step-by-step changes. Let’s return to the problem in the light of such new intuitions as the biomorphs may have given us. Answer the following two questions:

1. Could the human eye have arisen directly from no eye at all, in a single step?

2. Could the human eye have arisen directly from something slightly different from itself, something that we may call X?

The answer to Question 1 is clearly a decisive no. The odds against a ‘yes’ answer for questions like Question 1 are many billions of times greater than the number of atoms in the universe. It would need a gigantic and vanishingly improbable leap across genetic hyperspace. The answer to Question 2 is equally clearly
yes
, provided only that the difference between the modern eye and its immediate predecessor X is sufficiently small. Provided, in other words, that they are sufficiently close to one another in the space of all possible structures. If the answer to Question 2 for any particular degree of difference is no, all we have to do is repeat the question for a smaller degree of difference. Carry on doing this until we find a degree of difference sufficiently small to give us a ‘yes’ answer to Question 2.

X is
defined
as something very like a human eye, sufficiently similar that the human eye could plausibly have arisen by a single alteration in X. If you have a mental picture of X and you find it implausible that the human eye could have arisen directly from it, this simply means that you have chosen the wrong X. Make your mental picture of X progressively more like a human eye, until you find an X that you
do
find plausible as an immediate predecessor to the human eye. There has to be one for you, even if your idea of what is plausible may be more, or less, cautious than mine!

Now, having found an X such that the answer to Question 2 is yes, we apply the same question to X itself. By the same reasoning we must conclude that X could plausibly have arisen, directly by a single change, from something slightly different again, which we may call X’. Obviously we can then trace X’ back to something else slightly different from it, X”, and so on. By interposing a large enough series of Xs, we can derive the human eye from something not slightly different from itself but
very
different from itself. We can ‘walk’ a large distance across ‘animal space’, and our move will be plausible provided we take small-enough steps. We are now in a position to answer a third question.

3. Is there a continuous series of Xs connecting the modem human eye to a state with no eye at all?

It seems to me clear that the answer has to be yes, provided only that we allow ourselves a
sufficiently large
series of Xs. You might feel that 1,000 Xs is ample, but if you need more steps to make the total transition plausible in your mind, simply allow yourself to assume 10,000 Xs. And if 10,000 is not enough for you, allow yourself 100,000, and so on. Obviously the available time imposes an upper ceiling on this game, for there can be only one X per generation. In practice the question therefore resolves itself into: Has there been enough time for enough successive generations? We can’t give a precise answer to the number of generations that would be necessary. What we do know is that geological time is awfully long. Just to give you an idea of the order of magnitude we are talking about, the number of generations that separate us from our earliest ancestors is certainly measured in the thousands of millions. Given, say, a hundred million Xs, we should be able to construct a plausible series of tiny gradations linking a human eye to just about anything!

So far, by a process of more-or-less abstract reasoning, we have concluded that there is a series of imaginable Xs, each sufficiently similar to its neighbours that it could plausibly turn into one of its neighbours, the whole series linking the human eye back to no eye at alL But we still haven’t demonstrated that it is plausible that this series of Xs actually existed. We have two more questions to answer.

4. Considering each member of the series of hypothetical Xs connecting the human eye to no eye at all, is it plausible that every one of them was made available by random mutation of its predecessor?

This is really a question about embryology, not genetics; and it is an entirely separate question from the one that worried the Bishop of Birmingham and others. Mutation has to work by modifying the existing processes of embryonic development. It is arguable that certain kinds of embryonic process are highly amenable to variation in certain directions, recalcitrant to variation in others. I shall return to this matter in Chapter 11, so here I’ll just stress again the difference between small change and large. The smaller the change you postulate, the smaller the difference between X” and X’, the more embryologically plausible is the mutation concerned. In the previous chapter we saw, on purely statistical grounds, that any
particular
large mutation is inherently less probable than any particular small mutation. Whatever problems may be raised by Question 4, then, we can at least see that the smaller we make the difference between any given X’ and X”, the smaller will be the problems. My feeling is that, provided the difference between neighbouring intermediates in our series leading to the eye is
sufficiently small
, the necessary mutations are almost bound to be forthcoming. We are, after all, always talking about minor quantitative changes in an existing embryonic process. Remember that, however complicated the embryological status quo may be in any given generation, each mutational
change
in the status quo can be very small and simple.

We have one final question to answer:

5. Considering each member of the series of Xs connecting the human eye to no eye at all, is it plausible that every one of them worked sufficiently well that it assisted the survival and reproduction of the animals concerned?