Figure 6.10 Real shells with a range of cross-sectional shapes: (clockwise from bottom left): speckled whelk, Cominella aispersa; left-handed Neptune, Neptunia contraria; Japanese wonder shell, Thatcheria mirabilis; the Eloise, Acteon eloisae; Rapa snail, Rapa rapa; great scallop, Pecten maximus; graceful fig shell, Ficus gracilis. {213}
of shells which, as well as coming from different parts of the cubic museum, also have complicated, non-circular cross-sections of their basic tube.
My Blind Snailmaker program incorporates this extra variation by the rather crude expedient of providing a repertoire of predrawn cross-sectional outlines. Each of these outlines is then transformed (flattened vertically or horizontally) by the current (and mutable) value of the gene shape. The program then generates a tube of that transformed outline, sweeping it around and out just as if it were a circular tube. A better way to handle this problem — and one which I might attempt one day — would be to program the computer to simulate the actual growth process varying around the leading edge of the tube and thereby form ornate cross-sections. Nevertheless, for what it is worth, Figure 6.11 is a ‘zoo’ of computer shells produced by the existing program, through artificial selection using the human eye. They were bred for resemblance to known shells, some of them approximately similar to those of Figure 6.10, some of them similar to other shells that you might find on a beach or while diving.
The cross-sectional shape of the tube can be regarded as an additional dimension (or set of dimensions) in the Museum of All Shells. Setting that on one side and reverting to our simplifying assumption of a circular cross-section, one of the beauties of shells is that they are easy to fit into a Museum of All Possible Forms that we can actually draw in three dimensions. But this doesn't mean that all parts of the theoretical museum are tenanted in real life. In real life, as we have seen, most of the volume of the museum tower block is empty. Raup shaded the lived-in regions (Figure 6.9), and they constitute much less than half the volume of the cube. Stretching far to the north and west, gallery after gallery houses hypothetical shells that could exist according to the mathematical model but which actually have never been seen on this planet. Why not? And why, since we are asking such questions, are the shells that have really existed confined to this particular cuboidal building in the first place? {214}
Figure 6.11 ‘Zoo’ of computer shells of different cross-sectional shapes bred using the Blind Snailmalser program. They were bred by artificial selection, the eye choosing them for their resemblance to familiar real shells, including some members of the range depicted in Figure 6.10. {215}
What might a shell look like if it did not fit into the mathematical tower block? Figure 6.12a shows a computer-generated snail that doesn't. Instead of having a fixed spire value, its spire value changes as it grows older. More recent, wider, parts of the shell grow with a lower spire value than developmentally earlier, narrower, parts of the shell. This is why the whole shell has such an ‘unnaturally’, and presumably vulnerably, pointed top. This snail is hypothetical. It exists in the computer only. The computer ‘cone’ shell in Figure 6.12b also has an unnaturally pointed top. It too was drawn by the Blind Snailmaker program, but with the spire value programmed to decrease, rather than remain constant, as development proceeded.
The shells in Figure 6.13 are real, and I suspect that they too have a spire gradient, meaning that they begin life with a high spire value and gradually decrease it as they grow older. According to Raup, there were some real ammonites that changed their shell signature numbers as they grew older. You could say that as they grow older these odd shells move from one part of the museum to another and that they still stay within the museum. But it is also true to say that, since the juvenile body is included as part of the adult one, there is no one cabinet in the museum where the whole body can be housed. People could disagree over whether the animals in Figure 6.13 should be regarded as truly confined to the three dimensions of the box. Geerat Vermeij, one of today's leading experts
Figure 6.12 (a) computer snail and (b) computer cone-shell with pointy spires produced by a ‘gradient’ on the spire gene. {216}
Figure 6.13 Real shells whose resemblance to the computer shells of the previous figure suggests that they too develop with spire gradients. Left: tiger maurea, Maurea tigris; right: general cone, Conns generalis.
on the zoology of shelled animals, believes that a tendency to change signature numbers as the animals grow older may be the norm rather than the exception. He believes, in other words, that most molluscs shift their position in the mathematical museum, at least a little bit, as they grow up.
Let us turn to the opposite question of why large areas of the museum are empty of real shells. Figure 6.14 shows a sample of computer-generated shells from deep in the ‘no-go1 regions of the museum. Some of them might look fine on the head of an antelope or bison, but as mollusc shells they have never seen the light of day. With the question of why there are no shells like this, we come right back to the controversy with which we began. Is evolution limited by lack of available variation, or is it that natural selection doesn't even ‘want’ to visit certain areas of the museum? Raup himself interpreted the empty areas — the unshaded zones of his cube — in selectionist terms. There is no selection pressure on shellfish to move into the areas represented by the gaps. Or, to put it another way, shells with those theoretically possible shapes would, in practice, have been bad shells in which to live: perhaps weak and easily crushed; or otherwise vulnerable, or uneconomical of shell material. {217}
Figure 6.14 Theoretical ‘shells’ that don't exist — except perhaps as antelope horns.
Other biologists think that the mutations that were needed to move into these areas of the museum were just never available. Another way of putting this view is to say that the tower block of conceivable shells that we have drawn is not, in fact, a true representation of the space of all possible shells. According to this view large areas of the tower block would not be possible even if they were desirable from a survival point of view. My own instinct favours Raup's selectionist interpretation but I don't want to pursue the matter for the moment because, in any case, I only introduced shells as an illustration of what we mean by mathematical spaces of possible animals.
I cannot leave the ‘no-go’ areas without briefly looking at some oddities that really do exist in the world. Spirula is a small, swimming cephalopod mollusc (the group that includes squids and ammonites) related to Nautilus. The opened-out shape of the shell betokens a high verm (larger than 1/flare), and we have already met Spirula in this capacity in Figure 6.4. If it is suggested that high verm shells like this normally don't survive because they are structurally weak, Spirula fits the suggestion rather well. It doesn't live inside its shell but uses it as {218}
Figure 6.15 Real shells that are out on a limb, in unfrequented parts of the Museum of All Shells. Common spirula, Spirula spirula, and West Indian tube shell, Vermicularia spirata.
an internal flotation organ. Since the shell doesn't serve for protection, nature allowed it to follow an evolutionary trajectory into what is normally a no-go region of the Museum of All Possible Shells. It is still firmly within the cube of the museum. This may be true of the West Indian tube shell drawn in Figure 6.15. which has taken up the way of life — and the shape — of a tube worm. Go to the bottom right of Figure 6.8 and you'll at least be in the general area of the museum where the West Indian tube shell is housed. On the other hand, close relatives of this creature (and also some extinct ammonites) have a much odder, less regular shape and they certainly cannot be housed in any one part of the museum.
Not only does our three-dimensional museum ignore the fact that tube cross-sections are not necessarily circles. It also ignores the rich patterns on the surface of shells: the tiger stripes and leopard spots of Figure 6.10, the V-form calligraphy of Figure 6.4a and the whole repertoire of flutings and ridgings to be found sculpted and painted on other shells. Some of these patterns could be accom
modated in our model by an instruction to the computer, as {219} follows: as you sweep round and round, building up the expanding tube as a series of rings, make every nth ring thicker than the rest. Depending upon the value of n this rule could show itself as vertical stripes at a particular spacing on the surface of the shell. More complicated rules for the computer can generate more elaborate patterns. A German scientist called Hans Meinhardt has made a special study of such rules. Figure 6.16 shows the surface patterns on two real shells, an olive shell and a volute, on the left. On the right are the strikingly similar patterns generated by computer rules implemented by Meinhardt's computer program. You can see that his rules produce results akin to those that grow tree-like biomorphs, but he thinks of them in terms not of twigs growing {220}
Figure 6.16 Shell surface patterns and computer-generated equivalents.
but of waves of pigment-secreting and inhibiting activity sweeping over cells. The details are found in his book, The Algorithmic Beauty of Sea Shells, but I must leave this subject and return to my main theme of the Museum of All Shells.
I introduced the idea of the museum because of the singular fact that — setting aside the complications of tube cross-section, ornament and variable signatures — most known variants among shells can be approximated using a mere three numbers plugged into a drawing rule. To accommodate animal forms other than shells, we shall usually {221} have to imagine a museum built in a larger number of dimensions than we can draw. Difficult as it is to visualize the myriad-dimensioned Museum of All Possible Animals, it is easy to keep in our heads the simple idea that animals are housed near those that they most closely resemble, and that it is possible to move in any direction, not just straight along corridors. An evolutionary history is a snaking trajectory through some part of the museum. Since evolution is going on independently in all parts of the richly diverse animal and plant kingdoms, we can think of thousands of trajectories, tunnelling in different directions through different regions of the multi-dimensional museum (notice how far we have come from the very different metaphor of Mount Improbable).
Now the controversy with which we began can be re-expressed as follows. Some biologists feel that as you walk the long corridors of the museum what you will find is smooth gradations in all directions. Large portions of the museum are never, as a matter of fact, visited by living flesh and bone but, according to this view, they would be visited if only natural selection ‘wanted’ to nose its way into those portions. A different set of biologists, with whom I am less in sympathy but who may be right, feel that large portions of the museum are forever barred to natural selection; that natural selection might batter eagerly on the doors of a particular corridor but never be admitted, because the necessary mutations simply cannot arise. Other parts of the museum, according to an imaginative variant of this view, far from being barred to natural selection, act like magnets or sinks, sucking animals towards them, almost regardless of natural selections best efforts. According to this view of life, the Museum of Possible Animal Forms is not an evenly laid-out mansion of long galleries and stately corridors with smoothly changing qualities, but a set of well-separated magnets, each one bristling with iron filings. The iron filings represent animals, and the empty spaces between the magnets represent intermediate forms which might or might not survive if they came into existence, but couldn't exist in the first place. Another, and probably better, way to express this view is to say that our perception of what constitutes an ‘intermediate’ or a ‘neighbour’ in animal space is wrong. True neighbours are those forms which, as a {222} matter of fact, can be reached in a single mutational step. These may or may not look, to our eyes, like neighbours.
I have an open mind about this controversy although I lean in one direction. On one point, though, I insist. This is that wherever in nature there is a sufficiently powerful illusion of good design for some purpose, natural selection is the only known mechanism that can account for it. I do not insist that natural selection has the keys to every corridor of the Museum of All Possible Animals, and I certainly don't think that all parts of the museum can be reached from all other parts. Natural selection is very probably not free to wander where it will. It may be that some of my colleagues are right, and natural selections freedom of access as it snakes, or even hops, around the museum is severely limited. But if an engineer looks at an animal or organ and sees that it is well designed to perform some task, then I will stand up and assert that natural selection is responsible for the goodness of apparent design. ‘Magnets’ or ‘attractors’ in Animal Space cannot, unaided by selection, achieve good functional design. But now, let me soften my position just a little by introducing the idea of ‘kaleidoscopic’ embryologies. {223}
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CHAPTER 7
BODIES ARE BUILT BY THE PROCESSES OF GROWTH — mostly in the embryo — so a mutation, if it is to change the shape of a body, will normally do it by adjusting the processes of embryonic growth. A mutation might, for instance, speed up the growth of a particular piece of tissue in the embryonic head, resulting eventually in a lantern-jawed adult. Changes that occur early in foetal development can lead to dramatic knock-on effects later — two heads, perhaps, or an extra pair of wings. Such drastic mutations, for reasons that we saw in Chapter 3, are unlikely to be favoured by natural selection. In this chapter I am making a different point. This is that the kind of mutations that are available for natural selection to work on will depend upon the kind of embryology that the species possesses. Mammal embryology works in a very different way from insect embryology. There may be analogous, though smaller, differences in the types of embryology adopted by different orders of mammals. And the point I want to come on to is that some types of embryology may, in some sense, be ‘better’ at evolving than others. I don't mean more likely to mutate, which is another matter altogether. I mean that the kinds of variations thrown up by some types of embryology may be more evolutionarily promising than the kinds of variations thrown up by other types of embryology. Moreover, a form of higher-level selection — what I have previously dubbed ‘the evolution of evolvability’ — may lead to the world becoming peopled {224} by types of creatures whose embryologies made them good at evolving.
Coming from a dyed-in-the-wool Darwinist like me, this might sound like the rankest heresy. Natural selection is not supposed, in nice neo-Darwinian circles, to choose among large groupings. And didn't we agree in Chapter 3 that natural selection favours a zero mutation rate (which, fortunately for the future of life, it never reaches)? How can we now claim that a particular kind of embryology might be ‘good’ at mutating? Well, perhaps in the following sense. Certain kinds of embryology may be prone to vary in certain ways; other kinds of embryology tend to vary in other ways. And some of these ways may be, in some sense, more evolutionarily fruitful than others, perhaps more likely to throw up a great radiation of new forms, as the mammals did after the dinosaurs went extinct. It is this that I meant when I made that rather odd suggestion about some embryologies being ‘better at evolving’ than others.
A fair analogy is the kaleidoscope, except that kaleidoscopes are concerned with visual beauty, not utilitarian design. The coloured chips in a kaleidoscope settle into a random heap. But, because of the cunningly angled mirrors inside the instrument, what we see through the eyepiece is an ornately symmetrical shape like a snowflake. Random taps (‘mutations’) on the barrel cause slight movements in the heap of chips. But we, looking through the eyepiece, see these as changes that are repeated symmetrically at all points of the snowflake. We tap the barrel over and over, and seem to wander through a minor Aladdin's cave of gaudily jewelled shapes.
The essence of the kaleidoscope is spatial repetition. Random changes are repeated at all four points of the compass. Or it may be not four but some other number of points depending on the number of mirrors. Mutations too, although they are single changes in themselves, can have their effects repeated in different part
s of the body. We can regard this as another kind of non-randomness of mutation to add to the ones we dealt with in Chapter 3. The number of repetitions depends upon the type of embryology. I shall talk about various kinds of kaleidoscopic embryology. It was the experience of breeding biomorphs, and particularly the experience of putting software {225} ‘mirrors’ (see below) into the Blind Watchmaker program, that led me to accept the importance of kaleidoscopic embryology. It is therefore not accidental that for purposes of illustration in this chapter I shall rely heavily on biomorphs and other computer animals.
First symmetry, and we'll begin with the lack of it. We're pretty symmetrical ourselves (though not totally so) and so are most other animals that we meet, so were apt to forget that symmetry is not an obvious quality that every creature must have. Some groups of Protozoa (single-celled animals) are asymmetrical: cut them any way you wish, and the two bits won't be identical or mirror images of each other. What will be the impact of mutation on a purely asymmetrical animal? To explain this, it is easiest to switch to computer biomorphs.
The nine biomorphs of Figure 7.1a are all mutant variants of the same form, and all are produced by an embryology that has no constraints of symmetry. Symmetrical shapes are not forbidden but there is no particular eagerness to produce them. Mutations just change the shape, and that is all there is to it: no ‘kaleidoscopic’ effects or ‘mirrors’ are in evidence. But look at some more biomorphs (Figure 7.1b). These are again mutant forms of one another, but their embryology has a built-in symmetry rule: the program has been modified to include a ‘software mirror’ down the midline. Mutations can alter all sorts of things, just as they could for the asymmetrical biomorphs, but any random change to the left side will be mirrored on the right side as well. These forms look more ‘biological’ than the asymmetrical forms of the previous picture.