The Geometry of Adaptation London from Cambridge Expressly to Walk About the Streets to Study Crystals, Prisms Nick Barton and the Like in the Optician’S Windows

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or almost 50 years, exploration of Io, during the Voyager space mission1; and the large Galilean moons of Jupiter in 1996 the Galileo spacecraft revealed that Fhas delivered a continuing stream of Ganymede has a strong magnetic field2, surprises. The four moons — Io, Europa, probably stemming from an internal Ganymede and Callisto — have increasingly dynamo. come to appear as an exotic and remarkably Now, in the paper on page 777 of this diverse planetary system in their own right. issue3, comes strong evidence for the exis- 100 YEARS AGO In 1979 we had the discovery of the most tence of oceans not very far below the sur- What was the condition of England in dramatic volcanism known in the Solar faces of Europa and Callisto. This evidence 1845? Her universities had degenerated System, on the innermost Galilean satellite results from the observation of electromag- into hauts lycées. With regard to the 8 University teaching, I may state that even Evolutionary biology as late as the late fifties a senior wrangler — I had the story from himself — came to The geometry of adaptation London from Cambridge expressly to walk about the streets to study crystals, prisms Nick Barton and the like in the optician’s windows. Of laboratories in the universities there were arwin1 explained the evolution of most likely to increase fitness, they are also none; of science teaching in the schools complex adaptations, such as the most likely to be lost by chance. Even in a large there was none; there was no Dvertebrate eye, through the gradual population, a single mutation that increases organisation for training science teachers. “accumulation of innumerable slight varia- relative fitness by s has a chance of only If an artisan wished to improve his tions, each good for the individual possessor”. around 2s of being established4. Kimura knowledge he had only the moribund In contrast, the early geneticists emphasized showed that if the selective advantage of a Mechanics’ Institutes to fall back upon. ... the role of major mutations, and disregarded mutation is proportional to its effective We lacked then everything which Germany natural selection2. The mathematical theory size, x, then the chance that the mutant had equipped herself with in the matter of of Fisher, Haldane and Wright reconciled is favourable and becomes common is scientific industries. Did this matter? Was Mendelian genetics with Darwinian gradual- 2x(1ǁȆ(x)). The expected effective size of it more than a mere abstract question of a ism by showing that genetic variants that successful mutations is E[x] =4(Ꭷ2/Ț)/3 = want of perfection? It mattered very slightly enhanced reproductive success 1.06. Thus, mutations of intermediate effect much! ... At this time we had, fortunately would quickly replace their competitors. are most likely to contribute. For example, for us, in England, in very high place, a Nevertheless, the conflict over the magnitude with nǃ50 dimensions, the first adaptive German fully educated by all that could be of the genetic changes responsible for step will average 30% of the distance to the learned at one of the best equipped adaptation continues to this day3. Although optimum, d/2. However, because its direc- modern German Universities, where he classical population genetics can find the tion is random, it will take the population studied both science and the fine arts. I consequences of a given pattern of selection, only about 4% further towards the optimum. refer to the Prince Consort. From that it says nothing about the causes of such Orr5 now goes beyond these arguments year to his death he was the foundation of selection. Indeed, theoretical support for by considering the whole evolutionary our English educational renaissance ... gradualism rests mainly on a geometrical sequence by which a population approaches From Nature 20 October 1898. analogy, proposed by Fisher4 in 1930, which the optimum. The distribution of sizes of suggests that large changes to a complex the first step is given by Kimura’s formula. 50 YEARS AGO system are unlikely to be favourable. Now, The population is then, on average, a factor Co-operation between the Standard Oil reporting in Evolution, H. Allen Orr5 shows (1–2E[x]/n) closer to the optimum. The Co. and its subsidiaries of America and that adaptation may be based on larger process is then repeated from this new the I.G. Farben-industrie of Germany led factors than previously supposed. starting point. Orr shows that, to a close to the formation in 1929 of a joint Fisher’s argument is simple. Suppose that approximation, substitutions continue with company ... . The final result of this co- an organism is described by n traits, and that a distribution that retains the same form, but operation brought to America the its fitness increases towards some optimal has a continually shrinking scale (Fig. 1). technique of the preparation of Buna S, value. If a population lies away from the opti- Remarkably, the overall distribution of sizes an all-purpose synthetic rubber ... . mum, then a random change that takes it of factors fixed over this adaptive ‘walk’ to Howard tells with what sense of urgency inside an n-dimensional sphere centred on the optimum is exponential, ~exp(–ȕx), he and his colleagues regarded the the optimum will increase its fitness, and may with ȕ = 2.9. This result is independent of necessity for the setting up of a synthetic be established by natural selection (Fig. 1, the dimension n, but does assume a uniform rubber industry, and how, in the face of a overleaf). A small change is as likely to be distribution of mutational effects. general apathy, his Company decided to favourable as unfavourable, whereas a change Orr shows that for a variety of mutational erect the necessary plant for the larger than the diameter, d, of the sphere must distributions, biased either to smaller or manufacture of Buna S on a small scale. be disadvantageous. Fisher showed that, for larger effects, the distribution of factors fixed Even after Pearl Harbour, all their efforts large n, the chance that a change of magni- remains close to exponential (although with to get this vital material made on a large tude r (a sum over all traits) increases fitness larger or smaller ȕ). Evolution by a series of scale came to nothing ... until the setting is (1ǁȆ(x)), where Ȇ is the cumulative gradually diminishing random draws means up of the Baruch Committee in August ǃ Ꭷߍ normal distribution, and x r n/d is a that the largest step, xmax, is probably larger 1942; and the resulting appointment of a measure of the effective size of the change. So, than the first, and increases logarithmically rubber director with absolute power as the complexity of the organism (represent- with n; for example, with n = 50 dimensions, cleared away all the difficulties, with the ed by n) increases, a change of absolute mag- E[xmax] = 1.68, corresponding to a magni- result that in a very short time the nitude r is less likely to be an improvement. tude 48% of the original distance to the opti- American synthetic rubber industry was But a fundamental flaw in Fisher’s argu- mum. Thus, large changes are established in among the largest in the country. ment was found, half a century later. Kimura6 the early stages of adaptation towards a fixed From Nature 23 October 1948. pointed out that although small changes are optimum, mainly because alleles with the

Figure 1 Approach of a population Daedalus towards an optimum through selection of a series of random Dead metallic silence mutations, through a space of ten dimensions. The population begins Noise, that curse of modern living, is at a point on the outer sphere, at a spread in many ways. The racket of a diesel distance d/2 from the central engine, for example, is greatly amplified optimum (where d is the diameter of by vibrating sheet-metal surfaces such as the sphere). The first successful the rocker cover, the sump-case and the mutation has magnitude r = 0.137d, body panels of the vehicle housing it. 8 and takes the population 8.7% of the Workplace machines, domestic gadgets, way to the optimum (first line, and even clattering pots and pans, also leading to the second sphere). The owe much of their characteristic noise to third successful mutation has the the undamped vibration of metal surfaces. largest magnitude, 0.271d; it is If all our products could be made (say) of followed by smaller steps which, on wood, life would be much more peaceful. average, follow a geometric series. So Daedalus wants to load engineering metals with vibration-damping inclusions. Cast iron, for example, one of the quietest largest effect on fitness are most likely to be Fisher’s geometrical analogy is an of metals, contains many tiny graphite picked up by natural selection. Later, small extreme abstraction of organismic complex- inclusions which absorb vibration. Sadly, changes do contribute, but they are not ity. One problem is that it is hard to know they also act as crack-initiating sites, and responsible for much of the improvement in what is meant by the number of dimensions, make it brittle. Daedalus recalls that fitness. n. The morphology, development and polystyrene (which has rather a metallic The prediction that the effects of the behaviour of an organism can be described ring itself) is damped by certain organo- genes responsible for adaptation should by an indefinite number of phenotypic metallic ring compounds. The organic ring follow an exponential distribution roughly dimensions that may all be influenced by in these molecules can rotate stepwise applies to individual traits, as well as to the many genes. The number of degrees of free- around the bond joining it to the metal. sum over all traits. Orr argues that studies7 of dom, n, is presumably limited by the number The polymer is strongly damped in the the quantitative trait loci (QTL), which dis- of genetic loci (~105 genes and ~3ǂ109 base acoustic range of frequencies tinguish close taxa, are consistent with this pairs in man). However, once one thinks in corresponding to the stepping rate of the prediction. But it is not clear what would be terms of gene sequences rather than continu- ring. predicted by other models of evolution, or ous traits, a different geometry is required. So DREADCO chemists are whether these could be distinguished. Exist- Although many sequences are possible (4k synthesizing organic ring molecules ing methods for detecting QTL are biased with kbases), only a few (~3k) can be reached capable of binding to iron and other towards finding genes of spuriously large by a single mutation. It may be possible to do engineering metals, and are using powder effect7. More convincing evidence for the an analysis similar to Orr’s for this tightly sintering to disperse the most likely importance of major genes comes from stud- restricted geometry13, although this might candidates into bulk metals. Cunningly, ies of ‘candidate loci’, which often contribute come to different conclusions. The issues they are seeking molecules that are the to divergence and standing variation8,9. raised by Orr’s work are relevant to the opti- stablest combination of that set of atoms. However, such examples hardly fit with Fish- mization of any complex structure — be it Trapped in its metallic cage at the sintering er’s model, whereby mutations are drawn computer software or a mechanical device. temperature, such a molecule might well randomly from any of the many genes that But the universal genetic code, together with decompose; but it would re-form again might influence a trait. simple mathematics of natural selection, when the metal cooled. The resulting Some functions may necessarily be com- may allow population genetics to provide a metals will be acoustically dead yet still posed of many minor changes. For example, more general understanding of adaptation tough and ductile — single molecules are the efficiency and accuracy of translation can than is possible in other contexts. far too small to act as crack initiators. be improved by using triplet codons that Nick Barton is in the Institute of Cell, Animal and When perfected, DREADCO’s ‘Dead match the most abundant transfer RNAs. Population Biology, King’s Buildings, University of Metal’ range of alloys should sweep Each such change could have only a tiny Edinburgh, Edinburgh EH9 3JT, UK. through society. The big noises, such as effect on fitness10, so, for codon-usage bias, e-mail: [email protected] diesel engines, are the obvious targets. But adaptation is based on minute variations. 1. Darwin, C. On the Origin of Species by Means of Natural Daedalus attributes much of the edginess Nevertheless, such examples are hard to find Selection (Murray, London, 1859). of modern living to the quieter but ever- 2. Provine, W. The Origins of Theoretical Population Genetics and there are many limits to the success of (Univ. Chicago Press, 1971). present background noise from central- weakly selected variants, beyond the low fix- 3. Orr, H. A. & Coyne, J. A. Am. Nat. 140, 725–742 (1992). heating systems, air-conditioning units, ation probability identified by Kimura6 and 4. Fisher, R. A. The Genetical Theory of Natural Selection (Oxford office equipment, refrigerators, cookers, Orr5. In a large, asexual population, a Univ. Press, 1930). washing machines and so on. The formless, 5. Orr, H. A. Evolution 52, 935–949 (1998). favourable allele can fix only if it confers an 6. Kimura, M. The Neutral Theory of Molecular Evolution ever-changing insistence of this endless advantage that outweighs the loss in fitness (Cambridge Univ. Press, 1983). accompaniment to life gets on our nerves owing to the deleterious alleles with which it 7. Lynch, M. & Walsh, J. B. Genetics and Analysis of Quantitative in some very subtle way. He recalls the arises4. Even with sexual reproduction, link- Traits (Sinauer, Sunderland, MA, 1998). story of a housewife in a modern kitchen 8. McKenzie, J. A. & Batterham, P. Trends Ecol. Evol. 9, 166–170 age reduces the effectiveness of natural selec- (1994). who, hearing a sudden change in its tion, and can greatly reduce the fixation 9. Long, A. D., Mullaney, S. L., Mackay, T. F. C. & Langley, C. H. complex background racket, asked in probability of a weakly favoured allele11. Genetics 144, 1497–1510 (1997). bewilderment, “What’s just stopped?”. 10.Bulmer, M. Genetics 129, 897–907 (1991). Indeed, bias in codon usage is weaker in 11.Barton, N. H. Genetics 140, 821–841 (1995). With Dead Metal, they will all stop. regions of reduced recombination in 12.Kliman, R. M. & Hey, J. Genetics 137, 1049–1056 (1994). David Jones Drosophila12. 13.Gillespie, J. H. Evolution 38, 1116–1129 (1984).