A selection of biomorphs bred by the Blind Watchmaker program
Dan Dennett later fruitfully elaborated the idea under the name ‘Library of Mendel’ and I too carried it further in Climbing Mount Improbable in my fanciful Museum of All Possible Animals:
Imagine a museum with galleries stretching towards the horizon in every direction . . . preserved in the museum is every kind of animal form that has ever existed, and every kind that could be imagined. Each animal is housed next door to those that it most resembles. Each dimension in the museum – that is each direction along which a gallery extends – corresponds to one dimension in which the animals vary . . . the galleries criss-cross one another in multidimensional space, not just the ordinary three-dimensional space that we, with our limited minds, are capable of visualizing.
In Climbing Mount Improbable, I introduced this ‘Museum’ using the rather special example of mollusc shells. It had been understood for a while that a shell is a (logarithmically) expanding tube, growing at the margin. If we ignore the cross-sectional shape of the tube (for example, by assuming it’s a circle), the form of every shell is determined by only three numbers which, in Climbing Mount Improbable, I dubbed flare, verm and spire. Flare determines the rate of expansion of the tube as it grows; spire determines the departure from the plane. Spire is zero in a typical ammonite (all in one plane) but has a high value in, say, Turritella. Flare is high in a cockle (indeed, the ‘tube’ expands so rapidly it runs out before it reaches the point of looking like a tube at all), low in Turritella. Verm takes longer to explain in words, but high verm is epitomized by Spirula in the picture. As the American palaeontologist David Raup realized, if there are only three numbers governing variation in shape of a set of animals, all those animals can be accommodated in a simple mathematical space – a three-dimensional cube. We don’t need a hypercube: an actual cube will do. And by the same token I realized that I could write a snail version of my biomorph program, with only three genes instead of nine. Instead of choosing which of a set of tree-like biomorphs to breed from, I could present snailomorphs or – let’s not mix our languages – conchomorphs. By choosing the favoured breeder, generation after generation, it should be possible to evolve from any shell to any other. Evolution would be a step-by-step trajectory through the cube of all possible shells.
To write the program, I had only to substitute a new three-gene snail embryology module in place of the original nine-gene biomorphs embryology. All the rest was the same. And it did, indeed, prove very easy to breed any shell starting from any other shell, simply by choosing, in every generation, the shell that most resembled the target. 3-D printers hadn’t been invented in those days. If I’d had one, I would have ‘printed’ the entire cube. As it was, I had to be content with printing the six edges of the cube on flat squares of paper, which I glued to the outside of a cardboard box. There’s a photo in the picture section of Lalla holding the ‘snail box’.
Shells to illustrate flare, verm and spire: (a) high flare: Liconcha castrensis, a bivalve mollusc; (b) high verm: Spirula; (c) high spire: Turritella terebra.
Presumably real-life evolution is free to wander anywhere in the cube – the virtual Museum of All Possible Shells. However, as Raup had earlier noted, there are some sizeable ‘no go’ areas (volumes, rather) in which, although the mathematics would permit it, no shells have ever actually survived. This is because these forms would be functionally inviable. Mutants that strayed into these ‘Here Be Dragons’ zones simply died. Below are four mathematically possible denizens of an untenanted region of the cube. They don’t exist as shells although, interestingly, they do exist as horns of antelopes and other bovids.
But it isn’t strictly true that the Museum of All Possible Shells is a three-dimensional cube. It’s this only if we ignore the cross-sectional shape of the growing tube and assume that it is, for example, a perfect circle. I tried making it a variable ellipse instead of a circle, by adding a fourth gene to the original three. But real life isn’t as geometrically perfect as that. For many shells, the cross-sectional shape is not easy to specify mathematically (though it is of course in principle possible), so I resorted to entering it into the program freehand. Apart from this modification to the embryology module, the program remained the same, with only three genes, and I was able to breed an encouragingly realistic menagerie of shells on my computer screen (see below).
In addition to the original tree embryology and the snail embryology, were there yet more embryology modules that could be imported into my evolution program? I had long been fascinated by D’Arcy Thompson’s ‘transformations’. That great Scottish zoologist (see pages 90–1) had been one of those who inspired Raup and later me in our shell work. But he was best known for his demonstration that a biological form could be transformed into a related form by a mathematical transformation. You can visualize it by drawing an animal form, say the crab Geryon, on a sheet of stretched rubber. Then you find that you can transform the shape into a variety of related crabs by stretching the rubber in mathematically specified ways. Here is D’Arcy Thompson’s representation of this process. Geryon is drawn on squared graph paper (‘rubber’) at top left. The (alas only approximate) form of five other crabs is obtained by distorting the graph coordinates (stretching the ‘rubber’) in five different mathematically elegant ways.
I had long been fascinated to dream of ‘What might D’Arcy Thompson have done with a computer?’ Indeed, I once set it as an exam question in the final honour school of zoology at Oxford. I don’t think anybody answered it – perhaps, sadly, because none of their lectures had equipped them to do so, and (I suppose it’s understandable) nervous exam candidates like to play it safe. Now I wanted to try to answer my own question by modifying my biomorph program. The genes, instead of controlling the development of a tree, would mathematically control the stretching of virtual ‘rubber’ in the computer. As with the conchomorphs, it would be necessary to rewrite only the kernel embryology routine of the original biomorphs program. All the rest could remain the same. It should be possible to ‘evolve’ from Geryon to, say, Corystes through step-by-step selection. Following D’Arcy Thompson himself, I was prepared to overlook the fact that these crabs are all modern species, none descended from any other. I was captivated by the idea that related animals can be seen as stretched, twisted, distorted versions of each other, distorted versions of their neighbours in the great Mathematical Museum of All Animals.
The mathematical and computer skills required were beyond me even if I’d had the time to exercise them, so I joined a consortium at Oxford to bid for a grant to hire two programmers. One was to work on my ‘D’Arcy Thompson’ project and the other on an unconnected project concerned with agriculture. The programmer who came to work on ‘my’ project was Will Atkinson, and he proved to be everything I could have wished for.
The ‘genes’ in Will’s ‘D’Arcy’ program did a variety of things. Some changed the ‘stretched rubber’ from rectangle to trapezium, the magnitude of the distortion determined by the numerical value of the gene. Some changed one or both ‘axes’ to logarithmic, or did various other mathematical transformations. The biological shape drawn on the rubber changed progressively as the observer chose favoured ‘progeny’ for ‘breeding’, just as in my original biomorphs program.
Elegantly written as Will’s program was, the forms that it ‘evolved’ seemed to get less and less ‘biological’ as the generations went by. The evolving animals increasingly looked like degenerate versions of their ancestors, rather than newly viable transformations; not like real evolutionary descendants, as my original evolving biomorphs did. Will and I worked out the reason for this, and it is an informative one. The ‘D’Arcymorphs’ don’t have an embryology. What evolves from one generation to the next is not the animal forms themselves but the ‘rubber’ on which they are drawn.
And D’Arcy Thompson’s original transformations, after all, were never really evolutionary, since the animals he drew
were both adult and modern. Adult animals don’t change into other adult animals. Embryonic processes evolve from the embryonic processes of ancestors. Julian Huxley (my sometime predecessor as tutor in zoology at New College) modified D’Arcy Thompson’s method to transform embryos into adults, and this, as Peter Medawar pointed out, is a more biologically realistic usage. The reason my original biomorphs were ‘fertile’, even ‘creative’, in generating biological form is that they had an embryology: a recursive, branching tree, which had a kind of built-in propensity to keep evolving in freshly interesting directions. The ‘conchomorphs’, too, had their own (very different but still biologically interesting) embryology, capable of generating a rich variety of biologically realistic forms. Isn’t real-life embryology ‘creative’ like that? Do embryologies even evolve to become better at generating evolution? Could there be a kind of higher-level selection of embryologies, choosing those that are evolutionarily fecund? This was the germ of my idea of the ‘evolution of evolvability’, and I’ll return to it in a moment.
My original biomorphs in The Blind Watchmaker, with their nine genes, meandered their evolutionary way within the confines of a nine-dimensional hypercube. Evolutionary trends consisted of an inch-by-inch walk through this particular hypercube, this nine-dimensional Museum of All Biomorphs. I was interested in possible ways of escaping from the hypercube altogether, out into a larger hypercube. One way of doing this was by substituting a completely different embryology, for example replacing tree embryology with snail embryology, and I pursued it. But before I did that I was interested in exploring the consequences of increasing the number of genes affecting my existing embryology, the embryology of the original tree biomorphs. This would be equivalent to expanding, to more than nine, the number of dimensions of mathematical space available for evolution, and I hoped it would give me insight into real biological evolution. I did it in two stages. The second stage introduced genes for colour, and made its debut in Climbing Mount Improbable. The first stage – still monochrome – appeared in an appendix added to the 1991 reprint of The Blind Watchmaker. There I upped the number of genes from nine to sixteen. The branching tree embryology remained at the core, and the new genes (once again, genes were just numbers) implemented various ways of drawing this basic biomorph. ‘Segmentation’ genes drew a series of biomorphs, in line astern, mimicking the segments of an earthworm or a centipede. One gene determined how many segments were drawn, another controlled the distance between segments, another implemented ‘gradients’ of progressive change as you went from front to back. Segmented biomorphs (see opposite) resembled arthropods even more than my ‘Zarathustra’ insects. They look ‘biological’, don’t they, even if you can’t pin them down to particular, real-life species? Another suite of genes ‘mirrored’ biomorphs in various planes of symmetry.
The sixteen-dimensional hypercube, with its new symmetry genes and segmentation genes, permitted the evolution of a much wider repertoire of biomorphs than were permitted in the original nine-dimensional space. It was even possible to breed a rather imperfect alphabet, with which I ineptly attempted to sign my name (see below). It would have been completely impossible to breed an alphabet with the original nine genes, and the imperfections of the letters discoverable in the sixteen-dimensional hypercube suggest that further genes would be needed to increase the flexibility of biomorph evolution.
Such thoughts led me back to biology and to propose the idea of the evolution of evolvability.
The evolution of evolvability
The year after The Blind Watchmaker was published, I was invited by Christopher Langton, visionary inventor of the science of artificial life, to the inaugural conference of his new discipline at the Los Alamos National Laboratory in New Mexico. It was sobering to see where the original atomic bomb was developed and recall, in the midst of the long peace, the dark oracular words of Robert Oppenheimer after the first atom bomb test in the desert:
We knew the world would not be the same. Few people laughed, few people cried, most people were silent. I remembered the line from the Hindu scripture, the Bhagavad-Gita . . . . ‘Now I am become Death, the destroyer of worlds.’ I suppose we all thought that, one way or another.
The people who gathered for the first Artificial Life conference were very different from Oppenheimer’s colleagues, but I could imagine that the atmosphere was a little bit similar: pioneers coming together to work on a completely new and strange enterprise, albeit ours was constructive and theirs as destructive as can readily be imagined. In addition to Chris Langton himself, I was pleased to meet various luminaries of the nearby Santa Fé Institute, including Stuart Kauffman, Doyne Farmer and Norman Packard. The latter two had been comrades-in-arms in an adventurous – indeed perilous – attempt to break the bank at Las Vegas, using principles of Newtonian physics with miniature computers concealed in their shoes and operated by their toes. The whole story is entertainingly told by Thomas Bass, in yet another of those books whose title I decline to mention because it was gratuitously changed as it crossed the Atlantic.
Something of the same risky spirit, together with the dreamlike atmosphere of the New Mexico desert, seemed to be embodied in a charming young woman whom I also met at the conference, and who drove me to her home in the desert outside Santa Fé. She tried to persuade me to take Ecstasy. I hadn’t heard of it before (this was 1987), and I now think I was right to decline her offer although it felt cowardly at the time. But something about her soft beauty, her strange adobe house, the ‘New Age’ music she played for me, the ghostly silence of the desert and the crisp clarity of the air which, as in a dream, shrank the distance to the mountains, gave me a high with no need for the drug. Somehow that little interlude in her company, especially the hundred-mile view of the mountains almost psychedelically magnified on the south-western horizon, sums up for me the atmosphere at that remarkable conference.
I entitled my talk ‘The evolution of evolvability’ and, so far as I am aware, my lecture, followed by my paper in the published proceedings of the conference, represents the debut of that now much used phrase. I used a Mac to demonstrate the extra freedom to evolve in the expanded ‘biomorph space’ granted by the increase from nine to sixteen genes, and I then went on to expound the biological moral.
It’s too easy for an arch-adaptationist like me to think that natural selection can achieve anything, without limit. But selection can work only on the mutations that embryology throws up (this was one of the ‘constraints on perfection’ that I had listed in The Extended Phenotype, five years earlier). Evolutionary change is a crawl through the multidimensional corridors of the Museum of All Possible Animals. But some of the corridors, if not totally blocked, are harder to negotiate than others, and evolution, like water trickling down a hill, will seek the path of least resistance. The point about the evolution of evolvability is this. Maybe some previously blocked, or quantitatively impeded, corridors in the museum can be suddenly unblocked by the evolutionary invention of an innovation in embryology. The first segmented individual, back in Precambrian antiquity, may or may not have been better at surviving than its unsegmented parents. But the embryological revolution that birthed it triggered a new burst of evolution, as if floodgates had been suddenly opened. Could there then be a kind of higher-level natural selection, choosing whole lineages by virtue of the evolutionary ‘fertility’ of their embryologies? To me, as a committed Darwinian adaptationist back in the 1980s, this was verging on a heretical idea, but it was one that excited me.
The first segmented animal must have had unsegmented parents. And it must have had at least two segments. The essence of segments is that they are like one another in complex respects. A centipede is a train with a long series of identical leg-bearing trucks in the middle, a sensory engine at the front and a genital caboose at the back. The segments of the human spine are not identical, but all have the same pattern of a vertebra, dorsal and ventral nerves, muscle blocks, repeated blood vessels and so on. Snakes have hundreds o
f vertebrae and some species have hugely more vertebrae than others, most of them identical to their neighbours in the ‘train’. Since all snake species are cousins of one another, individual snakes must from time to time be born with more (or fewer) vertebrae than their parents, and always a whole number more (or fewer). You can’t have half a segment. You can go from 150 segments to 151, or to 155, but not to 150.5 or 149.5 segments. Segments are all or none. We now understand pretty well how this comes about – by what are called homeotic mutations. Amazingly – a stunning discovery that long post-dates my undergraduate days reading zoology – it is the same homeotic mutations that mediate segmentation in both vertebrates and arthropods, and genes can even be transplanted from mice to fruit flies and have something tantalizingly like the same effect.
Brief Candle in the Dark Page 36