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THE GENETIC OF : A BRIEF HISTORY

H. Allen Orr Abstract | Theoretical studies of adaptation have exploded over the past decade. This work has been inspired by recent, surprising findings in the experimental study of adaptation. For example, morphological sometimes involves a modest number of genetic changes, with some individual changes having a large effect on the or . Here I survey the history of adaptation theory, focusing on the rise and fall of various views over the past century and the for the slow of a mature theory of adaptation. I also discuss the challenges that face contemporary of adaptation.

1 STANDING Adaptation is not . As Ronald A. Fisher These questions have two things in common. First, Allelic variation that is currently emphasized in 1930, adaptation is characterized by the they are important; indeed they are among the simplest segregating within a ; movement of a population towards a phenotype that and most obvious questions that can be asked about the as opposed to that appear best fits the environment. The result is an often changes underlying Darwinian evolution. Second, they by new events. astonishingly precise match between an and are not answered by traditional evolutionary theory. In

FITNESS the world in which it . But as Fisher also empha- , the deeper problem is that they are not even asked A quantity that is proportional sized, the steady increase in the frequency of an by traditional evolutionary theory. to the mean number of viable, under selection need not invariably result in “the adap- Despite this near theoretical void, experimental evo- fertile progeny produced by a tive modification of specific forms”. lutionary have begun to address several of the . among ‘selfish ’,for instance, can change a popula- above questions. These studies — and the sometimes tion’s ratio but we have no to expect any surprising answers that they have provided — have improved fit between an organism and its environment. reinvigorated attempts to elaborate a mathematical To an evolutionary , there is another, sim- theory of adaptation. Here I survey these attempts. My pler way of distinguishing between selection and adap- approach is historical, considering the rise and fall of tation: we know a lot about the former but little about various views on the genetic basis of adaptation, the rea- the latter. Many important questions about the genetic sons a mature theory has been slow to develop and the basis of adaptation remain unanswered. Do most prospects and problems facing current theory. involve new or STANDING GENETIC As we will see, recent models of adaptation seem to VARIATION? Do most adaptations involve single genes of successfully explain certain qualitative patterns that large phenotypic effect (‘major’ genes)? If so, can we say characterize morphological evolution in and anything about the expected effect of this major ? plants, as well as patterns that characterize fitness Can we describe the distribution of phenotypic effects increase in microbes. Although this is encourag- among the mutations that are substituted during a typi- ing — and long overdue — future work must deter- cal bout of adaptation? How does FITNESS change as a mine whether present theory can explain the genetic Department of , population approaches an optimum? For example, do data quantitatively. University of Rochester, evolve quickly at first and then more Rochester, New York 14627, slowly? Because random mutations are more likely to be Micromutationism: its rise and fall USA. e-mail: aorr@mail. deleterious in complex than in simple - The theory. The earliest view of the genetic basis of adap- rochester.edu isms, do complex organisms adapt more slowly than tation was pre-Mendelian. This view, which emphasized doi:10.1038/nrg1523 simple ones? the extreme gradualness of phenotypic evolution, began

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7–11 Box 1 | Experimental studies of adaptive evolution genetics ., for example — the brashest and most articulate of the Mendelians — Genetic analyses of phenotypic differences between or populations often argued that the popularity of micromutationism merely reveal major quantitative trait loci (QTL). A recent burst of work, for instance, has reflected the light demands it placed on naturalists.“By focused on the genetic basis of armour-plate reduction and pelvic reduction in suggesting that the steps through which an adaptive postglacial-lake forms of the threespine stickleback, Gasterosteus aculeatus. arises are indefinite and insensible, all fur- Although marine forms of this species are heavily armoured, lake populations ther trouble is spared. While it could be said that (which are recently derived from the marine form) are not. Instead, lake forms have repeatedly and independently evolved reduced armour-plate and pelvic species arise by an insensible and imperceptible process structures, leaving little doubt that these morphological changes are adaptive. of variation, there was clearly no use in tiring ourselves QTL and developmental genetic studies indicate that this adaptive evolution by trying to perceive that process. This labor-saving sometimes involves the same genes97–99.A strong , Pitx1, has been counsel found great favor”12. identified that has a major effect on pelvic reduction; the Pitx1 sequence is Despite such opposition — and despite the larger identical between marine and lake forms, indicating that this case of morphological victory of Mendelism — the micromutationist view change involved regulatory evolution99. won out among evolutionists by about 1930. To a con- Similarly, Sucena and Stern100 showed that a qualitative difference in larval siderable extent, this victory reflected the efforts of (the presence or absence of a lawn of fine ) between two species of Drosophila Fisher, a founding father of and a (Drosophila simulans and Drosophila sechellia) is due to a single gene. Through tireless champion of Darwinian . Fisher suc- DEFICIENCY MAPPING and COMPLEMENTATION TESTS,they showed that the relevant gene is cessfully fused micromutationism with Mendelism13, ovo/shaven-baby,which resides on the X . producing a mathematical framework known as the Evidence for major genes is not limited to animals. Work in the 1990s showed, . Response to selection, he argued, for example, that the evolution of maize from its wild teosinte involved the substitution of a QTL that had large effects on morphology (for example, tb1, could be analysed through a kind of statistical mechan- which affects lateral-branching pattern101,102 and tga1,which affects kernel ics: instead of following the effects of individual genes architecture101,103). Although the evolution of maize involved intervention, on a selected phenotype, one could calculate their aggre- QTL studies of two wild species of Mimulus yielded qualitatively similar results. gate effects under the assumption that a character is Mimulus lewisii is primarily -pollinated, whereas Mimulus cardinalis is underlaid by an infinite number of genes, each unlinked primarily pollinated by ; not surprisingly, the flowers of the two to all others, each having no EPISTATIC INTERACTIONS with species differ markedly. In a QTL analysis of a suite of floral characters that the others, and each having an infinitesimally small distinguish these species, Bradshaw et al.104,105 found that one to six QTL underlie effect on the character3,14.Although modern evolutionists each of the 12 floral traits analysed. For 9 of these 12 traits, at least one QTL treat the infinitesimal model as little more than a math- explains 25% or more of the species difference. Indeed, a single QTL at the ematical convenience15 (the model has many attractive yup qualitatively affects carotenoid concentration between the species. properties, including constant ADDITIVE GENETIC VARIANCE Recent work further shows that replacement of chromosomal material at the yup under selection), there is some evidence that Fisher region from one species with that from the other has a large effect on went further and considered the infinitesimal view a visitation106. 16 Despite these findings, there can be no doubt that many QTL of small effect also reasonable approximation to biological (see contribute to adaptation. As experimental sample sizes and therefore statistical power especially Fisher’s role in the debate over the genetic 11 increase, more of these small-effect QTL will surely be found. basis of ).

The data. Early empiricists, including Theodosius Dobzhansky17,Hermann J. Muller18–20,Kenneth with Charles himself, who argued that “natural Mather21,22 and Julian Huxley23,24,claimed that there selection can act only by taking advantage of slight suc- was considerable empirical support for micromutation- cessive variations; she can never take a leap, but must ism. For example, Huxley argued that “selective advan- 2 DEFICIENCY MAPPING advance by the shortest and slowest steps” .Although tages so small as to be undetectable in any one , A type of genetic mapping that Darwin had no clear understanding of the nature of are capable … of producing all the observed phenomena uses chromosomal deletions to inheritance (or more exactly, had an incorrect under- of biological evolution….Evolutionary change is almost ‘uncover’ recessive alleles that 3 23 affect a trait. standing of it ), he concluded that the heritable basis of always gradual” .Despite such confident statements, adaptive evolution was extremely fine-grained. After all, the case studies to which these early workers pointed COMPLEMENTATION TESTS precise adaptation is possible only if organisms can were uniformly (and in retrospect, appallingly) The use of genetically defined come to fit their environments by many minute adjust- weak11,25.Rigorous data bearing on micromutation- knockout mutations to identify ments (see also REF.4). This ‘micromutational’ view of ism did not appear until remarkably recently, in the loci that affect a trait. adaptation proved extraordinarily influential, laying the 1980s. Although this delay partly reflected certain tech- BIOMETRIC foundation for the British BIOMETRIC school of evolution nical difficulties — such as the development of dense An approach to the study of led by and Walter Weldon. The biometri- linkage maps — part of the problem was inherent in that emphasizes cians used newly invented statistical tools, such as regres- the micromutational view itself. Although all scientific quantitative measurements (such as of body size) and sion, to analyse the inheritance of CONTINUOUS CHARACTERS, views are simplifications of nature, the micromuta- 5,6 statistical analysis. as well as the evolutionary response to selection .(See tional view had the unfortunate effect of excluding William B. Provine’s7 classic history of this period, entire classes of questions from empirical study. There CONTINUOUS CHARACTER including the formation of the influential Royal is little reason, after all, to ask non-trivial questions A trait (such as body size) that Committee on Biometrics.) about the genes that underlie adaptation if one assumes varies smoothly (continuously) in magnitude; as opposed to This micromutational view of adaptation was vig- that there are thousands of them, each with small and discrete characters. orously challenged by the rising Mendelian school of interchangeable effects on the phenotype.

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In the 1980s, two new experimental approaches and theory. Evolutionary geneticists find themselves in a were developed that finally allowed the collection of rig- decidedly awkward position. On the one , we can orous data on the genetics of adaptation — QUANTITATIVE point to a rich and formidable body of mathematical TRAIT LOCUS (QTL) analysis and MICROBIAL EXPERIMENTAL theory on phenotypic evolution, built largely on an EVOLUTION.In QTL analysis, the genetic basis of pheno- infinitesimal foundation. On the other hand, we can typic differences between populations or species can be point to a large and growing body of data on the genetic analysed using a large suite of mapped molecular mark- basis of adaptation. The problem, of course, is that the ers. In microbial evolution work, microbes are intro- formidable theory says little or nothing about the formi- duced into a new environment and their adaptation to dable data. To ask what might seem an obvious ques- this environment is allowed; genetic and molecular tools tion, where is the theory that tells us what we should then allow the identification of some or all of the genetic find in QTL or microbial evolution experiments? changes that underlie this adaptation. The results of More precisely, recent empirical findings force us to both approaches were surprising: evolution often confront two questions. Can we a theory of involved genetic changes of relatively large effect and, at adaptive evolution that speaks in the same terms as the least in some cases, the total number of changes seemed data; that is, in terms of individual mutations that have to be modest. As this empirical literature has been well individual effects? And if so, can this theory account for reviewed26–30,I devote little space to it here. However, the observed phenomena? BOX 1 describes several classical studies, including Several attempts to construct such a theory have those that analyse the evolution of reduced body been made throughout the history of evolutionary armour or pelvic structure in lake stickleback, the loss genetics. Although my survey of these attempts is far of larval trichomes (fine ‘hairs’) in Drosophila species, from exhaustive, I consider each of the two main classes and the evolution of new morphologies in maize and of adaptation model — those that are phenotype-based the monkeyflower Mimulus spp. Microbial studies fur- and those that are DNA-sequence based. ther revealed that genetic changes occurring early in adaptation often have larger fitness effects than those Phenotypic evolution that occur later31, and that parallel adaptive evolution Given his role as father of the infinitesimal model, it is is surprisingly common32–35. surprising to learn that Fisher also presented the first These experimental findings posed — and continue model of adaptation that allowed individual mutations to to pose — a considerable challenge to evolutionary have different-sized phenotypic effects. In The Genetical geneticists: to bridge the gap between adaptation data Theory of Natural Selection, Fisher offered his so-called EPISTATIC INTERACTION Any non-additive interaction between two or more mutations at different loci, such that their combined effect on a phenotype Box 2 | Fisher’s geometric model of adaptation deviates from the sum of their Ronald A. Fisher argued that his geometric model 0.5 individual effects. captures the statistical essence of adaptation — the

ADDITIVE GENETIC VARIANCE fact that “one thing [the organism] is made to 0.4 The part of the total genetic conform to another [the environment] in a large variation that is due to the main number of different respects”1.Fisher represented (or additive) effects of alleles on each character of an organism as an axis in a Cartesian 0.3 a phenotype; as opposed to the ) x coordinate system. The optimal combination of trait ( and epistatic a P variances. The additive variance values is represented by of this coordinate 0.2 determines the degree of system (see FIG. 1). Because of a recent environmental resemblance between relatives change, the population no longer resides at the 0.1 and therefore the response to optimum.As in actual Darwinian evolution, Fisher’s selection. model has three features. First, that populations must adapt by using mutations that are random with 0 respect to the needs of organisms (that is, that are 0 0.5 1 1.5 2 2.5 3 (QTL). A mapped chromosomal x region that has a detectable effect random in phenotypic direction, pointing away from on a phenotypic difference the optimum at least as often as towards). Second, that mutations have different phenotypic ‘sizes’ (that is, some mutations between two populations or are vectors of large magnitude and others are vectors of small magnitude). Third, that populations must adapt in the face of species. A QTL does not (that is, a mutation affects many characters and, although improving one character, might worsen many others). necessarily correspond to a Fisher showed that the probability, Pa (x), that a random mutation of a given phenotypic size, r, is favourable is single gene, but can reflect Φ Φ several linked genes. 1 – (x), where is the cumulative distribution of a standard normal random variable and x is a standardized mutational size, x = r √n /(2z), where n is the number of characters and z is the distance to the optimum. This MICROBIAL EXPERIMENTAL probability, which is plotted in the figure, falls rapidly with mutational size. This famous plot from Fisher’s The Genetical EVOLUTION Theory of Natural Selection1 shows that infinitesimally small mutations enjoy a 50% chance of being favourable but that An experimental approach that this probability falls rapidly for progressively larger mutations. Although Fisher presented no derivation of his famous involves the ‘real ’ probability, it has since been re-derived by Leigh107,and Hartl and Taubes44. adaptation of microbes (typically , phage or Essentially all studies of adaptation in Fisher’s geometric model assume that adaptation involves the appearance and yeast) to defined laboratory substitution of new mutations (not standing genetic variation) and that the optimum does not move during the bout of conditions. adaptation that is studied (but see REF.108). Results might well differ under other scenarios92.

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geometric model as an explicit attempt to capture the “statistical requirements of the situation”of adaptation1. In this model, an organism is represented as a of phenotypic characters, each measured on a Cartesian axis and each having an optimal value in the present environment (BOX 2; FIG. 1).Because of a recent environ- mental change, the population has fallen off the opti- mum; the problem for adaptation is to return to the optimum. The essence of Darwinian evolution is that populations must attempt this return by producing mutations that are random with respect to the organ- ism’s need, that is those that have random direction in phenotypic space. Crucially, some of these mutations might be larger than others. Fisher used his geometric model to ask a simple ques- tion — what is the probability that a random mutation of a given phenotypic size will be beneficial? He showed Figure. 1 | Adaptation in Fisher’s geometric model. A bout that, although infinitesimally small mutations enjoy a of adaptation in Ronald A. Fisher’s geometric model is shown. 50% chance of being beneficial, this probability falls to For simplicity, the organism that is considered comprises only three characters. The population begins on the surface of the “exceedingly small values”with increasing mutational size sphere and, by substituting beneficial mutations (red vectors), (see figure in BOX 1). Fisher therefore concluded that very evolves towards the phenotypic optimum at the centre of the small mutations are the genetic basis of adaptation — a sphere. The mutations that are substituted become smaller on conclusion that was extraordinarily influential and that average as the population nears the optimum. Modified, with was cited by nearly all the founders of the modern syn- permission, from REF.41  (2002) Macmillan Magazines Ltd. thesis (reviewed in REF.25). Interestingly, although Fisher published his calculations only in 1930, brief comments in previous publications36 reveal that he had arrived at his for subsequent substitutions, fall off by an almost con- micromutational conclusion far earlier and for essentially stant proportion; that is, as an approximate geometric the same reasons as he emphasized in 1930. sequence. Adaptation is therefore characterized by a pat- Ironically, although Fisher offered the first sensible of diminishing returns — larger-effect mutations are model of adaptation, the sole question he asked of it typically substituted early on and smaller-effect ones suppressed all further interest in the model. His answer, later38–41.These results appear to be reasonably robust to after all, suggested that micromutationism is plausible assumptions about the precise shape of the fitness func- and that one could, therefore, study adaptation through tion and the distribution of mutational sizes provided to infinitesimally based . To make it natural selection38,39. doubly ironic, Fisher erred here and his conclusion Although Fisher’s model has recently been used to (although not his calculation) was flawed. Unfortunately, study the evolution of sex 42, the evolution of develop- his was only detected half a century later, by Motoo ment43, COMPENSATORY EVOLUTION44, the distribution of Kimura37.Kimura pointed out that to contribute to adap- phenotypes under mutation–selection-drift balance45, tation, mutations must do more than be beneficial — they MUTATION LOAD in finite populations46 and the effects of must escape accidental loss when rare — and mutations species hybridization47,some of the most surprising of larger effect are more likely to escape such loss. Taking findings concern the so-called cost of complexity. both factors into account, Kimura concluded that muta- Analysis of Fisher’s model shows that complex species tions of intermediate size are the most likely to contribute (those having many characters) typically show slower to adaptation, a conclusion that did curiously little to increases in fitness during adaptation than do simple 48 COMPENSATORY EVOLUTION curb enthusiasm for micromutationism. species .Part of the reason is that the distance travelled Evolution in which a second In the late 1990s, however, it became clear that to the optimum by a beneficial mutation is smaller in a substitution compensates for the Kimura’s conclusion was also not what it first seemed. complex than a simple species (this distance decreases deleterious effects of an earlier Although Kimura derived the distribution of sizes among with the square root of the number of characters)48. substitution. mutations that are used at a particular step in adaptation Recent work by Welch and Waxman49 indicates that this

MUTATION LOAD this is not the same as the distribution of mutations that cost of complexity might be a general feature of adapta- The decrease in population are substituted throughout an entire bout of adaptation, a tion; indeed, this cost may be little affected by the degree fitness below its value bout that might involve many steps (FIG. 1).Using a com- of organismal . owing to recurrent deleterious bination of analytical theory and computer simulation, it mutation. has been shown38,39 that the size distribution of mutations Sequence evolution MODULARITY that are substituted over entire bouts of adaptation is Maynard Smith and sequence spaces. Although Fisher’s The that organisms are nearly exponential. Adaptation in Fisher’s model there- model takes into account the Mendelian nature of muta- broken developmentally into fore involves a few mutations of relatively large pheno- tion, it does not reflect the molecular basis of inheritance; roughly independent modules, typic effect and many of relatively small effect. This work that is, the fact that DNA is a linear sequence of such that mutations affecting traits in one module do not further showed that the mean sizes of mutations substi- that, among other things, encodes a linear affect traits in other modules. tuted at the first versus the second substitution, and so on sequence of amino acids. In the early 1960s, however,

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theorists began to develop models of adaptation that Their approach emphasized the idea that different were sequence-based. As with so many innovative in sequence spaces might feature different numbers of late twentieth-century evolutionary genetics, the key local optima. This is most easily seen by picturing a ‘fit- insight was that of John Maynard Smith50.Maynard ness landscape’.Fitness, or adaptive landscapes were Smith50,51 emphasized what would become a dominant introduced by Sewall Wright70,71 in his studies of the theme in the theory of adaptation — real adaptation SHIFTING BALANCE THEORY of evolution (for an excellent occurs in a sequence space that, unlike the phenotypic review of landscape types and theory, see REF. 72). space considered above, is discrete. He also emphasized Wright’s landscapes typically plotted the fitnesses of dif- that this discreteness imposes certain constraints on ferent combinations of across multiple loci adaptation. For example, the number of possible sequ- (Wright spoke of a “field of possible gene combina- ences at a gene is limited — given a gene that is L base- tions”). The fitness landscapes considered by NK theo- pairs long, only 4L different sequences are possible. The rists were similar, except that each ‘locus’ was typically constraints on adaptation are, however, far more severe taken to represent a particular site in a DNA sequence. than this number implies. Because the per site mutation To see this, imagine all possible DNA sequences at a rate is low (~10–9 per ), Maynard Smith argued gene as points on a grid (FIG. 2);sequences that differ that multiple (for example, double or triple) mutations slightly from each other reside near each other on this are “probably too rare to be important in evolution”51. grid, whereas sequences that differ more substantially Instead, natural selection is constrained to surveying reside farther apart; the fitness of each sequence is then sequences that differ from the wild type at a single site. plotted as its height above this grid. The resulting pic- There are only 3L such one-mutational step sequences; a ture of hills and valleys represents a . finite number indeed. The key point is that fitness landscapes can differ in Maynard Smith also emphasized that adaptation their ruggedness. The smoothest possible landscape fea- involves what came to be called ‘adaptive walks’ through tures a single optimum and all adaptation necessarily sequence space:“if evolution by natural selection is to involves walks up this single peak; the most rugged occur, functional [or DNA sequences] must landscape possible features many local optima and adap- form a continuous network which can be traversed by tation involves walks up the nearest optimum. The NK unit mutational steps without passing through non- model allows one to ‘tune’ the ruggedness of fitness land- functional intermediates”51.In particular, if a wild-type scapes between these extremes by varying two mathe- sequence can mutate to one or more fitter sequences, matical parameters (N and K), allowing the analysis of natural selection will ultimately substitute one of these adaptation for many of landscapes. beneficial alleles; this new wild-type sequence will in turn produce its own suite of one-mutational step sequences and, if any is fitter than the current wild-type, Global optimum selection will again substitute one of these beneficial alleles. This adaptive walk ends only when the popula- tion arrives at a wild-type sequence that is fitter than all of its 3L one-mutational-step neighbours. At that point, the population has arrived at a local optimum. Although Maynard Smith’s work appeared early in the molecular revolution, his ideas on adaptive walks Local optimum were almost entirely ignored for two decades. The cause of this neglect seems clear: the rise of the neutral theory of . Throughout the 1960s and 1970s, W evolutionary geneticists grew increasingly convinced that much, if not most, molecular evolution reflects the substitution of neutral52,53 or nearly neutral37,54–56 mutations, not beneficial ones. Throughout much of this period, the study of adaptation itself grew intellec- tually suspect57 and the theoretical study of molecular adaptation essentially ceased. Figure 2 | A fitness landscape. The underlying grid represents a DNA sequence space. Although such a space cannot actually SHIFTING BALANCE THEORY Kauffman and NK models. In the 1980s, theoretical be represented in two dimensions (and instead must be A largely verbal theory of study of adaptation at the sequence level finally depicted as a high dimensional hypercube), we can loosely evolution which maintains that resumed. One of the best known of these new efforts imagine that alleles that are similar in sequence sit near each the interaction between natural other on the grid shown, whereas alleles that are different in selection, and involved so-called NK models. This work, launched by 58 sequence sit farther apart. Allelic fitnesses (W) are plotted above migration is more important Kauffman and Levin , ultimately grew into a large and that the action of any single sophisticated body of mathematical and computational the grid. Adaptation in a large population will involve adaptive force. argued that 59–69 walks up the nearest fitness peak. Because natural selection will literature .Arguing that evolutionary geneticists not allow a population to descend into an adaptive valley, this theory helped to explain possess “essentially no theory of adaptation”,Kauffman how species could effectively adaptation drives a population to a local optimum, which might 58 search for the global, and not and colleagues set out to discover the laws, if any, that or might not correspond to the global optimum. Modified, with merely local, optimum. describe adaptation through sequence space. permission, from REF.111  (2004) Sinauer Associates Inc.

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Gillespie and the mutational landscape. How many sequences at a gene should be highly fit and how many lethal? Just what does the distribution of fitnesses look like on a fitness landscape? Unfortunately, we have almost no data relating to these questions. Given this 54 55 ) situation, Ohta and Kimura suggested that we con- W ( f sider fitnesses as randomly drawn from a probability distribution. The question is, of course, which distribu- tion? In the early 1980s, John Gillespie75,76 surprisingly argued that it might not matter much. The reason unexpectedly follows from the point noted above — that adaptation typically begins from a high fitness W sequence. Figure 3 | The distribution of fitnesses at a locus. An Gillespie’s insight was that, although we do not arbitrary distribution of fitnesses among alleles at some gene is know the detailed distribution of fitnesses at any gene, shown (W, fitness value; f(W), frequency of a certain fitness we do know two things: that the wild-type represents a value). Although the precise shape of this distribution will, in draw from the right tail of the fitness distribution; and 75–77 reality, almost always be unknown, John Gillespie that beneficial mutations represent even more extreme emphasized that, in most cases, the wild-type allele will be draws from this tail (see FIG. 3). And this, Gillespie75–77 highly fit; that is, drawn from the right-hand tail of the distribution (black arrow). Consequently, beneficial mutations argued, means that we can import extreme value represent even more extreme draws (green arrows). This theory (EVT) into the study of adaptation. EVT is a implies that (EVT) can be used to study body of probability theory that is concerned with the adaptation (see also BOX 3). properties of draws from the tails of distributions78,79. Remarkably, EVT shows that these draws have certain properties that are asymptotically independent of the NK theorists derived several approximate results that (usually unknown) details of the distribution, a robust- characterize such landscapes. These included the proba- ness that is reminiscent of the central limit theorem79. bility that a sequence is a local optimum, the number of Although EVT is important in modern mathematical local optima, the proportion of local optima that can be finance and risk analysis (extreme swings in security reached from a given sequence and the average length of prices and insurance claims can have devastating effects adaptive walks on landscapes of varying ruggedness on portfolios and insurance firms, respectively80), it (reviewed in REFS 60,69). NK and related models (such as had, until Gillespie’s work, little role in evolutionary the Block model73) were also applied to the study of genetics. But Gillespie saw that, as most adaptation AFFINITY MATURATION during immune response58–60,64, occurs in the right tail of fitness distributions, EVT genetic regulatory networks58,60 and RNA folding67. might tell us a good deal about the adaptation of Although NK models successfully explained certain DNA sequences (BOX 3). features of affinity maturation60 and received consider- Gillespie75–77 used EVT to study adaptation over what able attention in computer and in physics (in he called the “mutational landscape”.He was primarily which problems in SPIN GLASSES are similar74), it seems fair concerned with evolution under strong selection–weak to say that these models ultimately had a lesser impact on mutation (SSWM) conditions. His weak mutation evolutionary genetics where they began. In retrospect, assumption was essentially equivalent to that of Maynard two features of many NK studies were unbiological. The Smith: mutation rates per site are sufficiently low for us to first involves the ‘move rule’ used to decide which of sev- ignore double ; his strong selection assumption eral beneficial sequences a population will sub- meant roughly that mutations are either definitely bene- stitute at the next step in adaptation. The NK literature ficial or deleterious (neutral mutations are not allowed). focused on two such rules: random, in which a beneficial Under SSWM assumptions, a population is essentially sequence is randomly chosen from those avail- fixed for a single wild-type sequence at any moment in able58,61,63–67 and gradient, in which the fittest of available time and this wild-type sequence recurrently mutates to beneficial sequences is always chosen58,63,67,68.The prob- 3L neighbouring sequences. Because the wild-type lem is that natural selection uses neither of these rules sequence enjoys high fitness, it is assumed that few, if (the correct move rule is described in the next section). any, of these 3L mutant sequences are beneficial. Each AFFINITY MATURATION Second, the NK literature typically considered adapta- beneficial allele is likely to be lost accidentally each time it An increase in the affinity of an tion from a random starting sequence or even from the appears but, because mutation is recurrent, one will for an antigen which is worst possible sequence58,62–64,66,67,69.Real adaptation, eventually be substituted; this completes one step in seen as an immune response improves. however, often begins from a wild-type sequence of high an adaptive walk. The new wild-type sequence now fitness. The wild-type allele, after all, produces a func- produces it own set of 3L mutants and the process is SPIN GLASSES tional protein and was, until a recent environmental repeated. Gillespie assumed that mutant fitnesses are Magnetic objects that are change, the fittest sequence that was locally available. As drawn from the same distribution throughout a disordered and in which we will see (and as Kauffman later acknowledged60), the (brief) adaptive walk; adaptation is therefore charac- adjacent dipoles can either ‘point’ in the same direction or simple fact that the wild-type allele is highly fit turns out terized by the movement of a population out along a in opposite directions. to be of considerable importance. tail of fitnesses.

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75–77 Gillespie described several results that character- two to five. Molecular evolution at a gene therefore The empirical finding that a ize adaptation over the mutational landscape. Perhaps occurs in small bursts of substitutions. Put differently, particular type of protein or most importantly, he calculated the ‘move rule’ that is molecular evolution by natural selection a signa- DNA sequence evolves at a used by positive natural selection. He showed that, when ture that differs from that left by neutrality — whereas nearly constant rate through time. several beneficial mutations are available to a wild-type neutral evolution yields a simple MOLECULAR CLOCK (with sequence, the probability that a population jumps to a substitutions that occur as a POISSON PROCESS), natural POISSON PROCESS beneficial allele j at the next step in evolution is, under selection does not (the molecular clock is instead A simple statistical process in SSWM conditions, s /Σs,wheres is the selective advan- ‘overdispersed’). Gillespie77,85,86 argued that adaptation which there is a small and j constant probability of change tage of an allele, and the summation involves all avail- explained the existing molecular evolutionary data better during each short interval of able beneficial alleles. Explained in words, this formula than neutrality did (see also REF.87). time. means that the chance that a particular beneficial allele Much of the recent work on adaptation theory has is the next substituted is proportional to the selective focused on Gillespie’s mutational landscape model. advantage of that allele. Beneficial mutations of greater Several results have been described over the past several effect are therefore more likely, although not guaran- years. Perhaps most surprising, two studies88,89 showed teed, to be the next substituted. This move rule differs that beneficial mutations should have exponentially dis- from those used in NK studies (despite REF.81). tributed fitness effects that are independent of many bio- Most of Gillespie’s work focused on entire adaptive logical details. Most recent analyses of the mutational walks. He noted two key . First, because the fitness landscape model, however, have focused on the unit of wild-type sequences increases during adaptation, event in adaptation — the substitution of a beneficial beneficial mutations become increasingly difficult to mutation. It has been shown90 that, if the current wild- come by. The theory of records82,83 shows that the type sequence is the ith fittest allele (that is, i – 1 benefi- cumulative number of alleles that break the previous cial mutations are available), the population will jump to ‘fitness record’ (that is, that are beneficial) only a beneficial allele that has mean fitness rank (i + 2)/4 at increases logarithmically during adaptive walks84. the next substitution. Adaptation is, therefore, character- Second, Gillespie77 showed that the mean number of ized by surprisingly large jumps in fitness rank. If thir- steps taken during adaptive walks is small — typically teen beneficial mutations are available to a wild-type sequence, populations will typically jump to the fourth best allele at the next step in adaptation. Adaptation therefore leap-frogs many moderately beneficial muta- Box 3 | Adaptation and extreme value theory tions, arriving at a strongly beneficial one. Recent work Classical extreme value theory (EVT) emerged from early work by the Ronald A. also shows that at the DNA sequence Fisher and the probabilists Richard von Mises and Boris V.Gnedenko, among others level is more common under natural selection than (reviewed in REFS 78,79,109). EVT is concerned with the asymptotic properties of the largest under neutrality. In fact, the probability of parallel evolu- draws from a probability distribution, as the number of draws becomes large. The most tion approximately doubles under positive selection91. fundamental, and best known result from EVT concerns the distribution of maxima. If Computer simulations of entire adaptive walks further many values from a given ‘parent’ distribution are drawn, the largest value saved, and show that at least half the total gain in fitness that occurs then this process is repeated many , the distribution of these maxima approaches during adaptation is due to a single substitution90. Once the so-called extreme value distribution. There are in fact three extreme value again, therefore, adaptation features relatively large distributions — one for ‘ordinary’ parent distributions (the Gumbel type), another for jumps. Indeed, adaptation seems to be characterized by a many parent distributions that are truncated on the right (the Weibull type) and a last ‘Pareto principle’, in which the majority of an effect for parent distributions that lack all or higher moments (the Fréchet type). The Gumbel (increased fitness) is due to a minority of causes (one type includes most ordinary distributions — for example, the normal, lognormal, gamma, exponential,Weibull and logistic — and was the focus of classical EVT.The Gumbel substitution). Finally, recent theory shows that, condi- extreme value distribution is often referred to as ‘the’extreme value distribution. The tional on the substitutions occurring, the mean selection biologically important point is that extreme draws from a surprisingly wide array of coefficient, s, among mutations that are fixed at subse- parent distributions all converge to the same extreme value distribution. EVT is generally quent steps in adaptation decreases as an approximate characterized by such to distributional details, allowing conclusions to be made geometric sequence — again revealing a pattern of about adaptation that depend only weakly on the (generally unknown) distribution of diminishing returns — and that the overall distribu- fitnesses at a gene. tion of s among mutations that are substituted during Gillespie75–77 assumed that the distribution of fitnesses (see FIG. 3) belongs to the adaptation is roughly exponential90. Gumbel type and subsequent work on the mutational landscape has followed suit. Recent These results are obviously reminiscent of those work provides some support for this assumption. It can be shown, for example, that the from Fisher’s geometric model — a similarity that is distribution of mutational effects in Fisher’s geometric model is of the Gumbel type surprising given the fundamental differences between (A.O., unpublished data). EVT describes not only the distribution of largest values from a the older phenotypic and newer DNA sequence-based parent distribution, but the distribution of the second, third, and so on, largest values79. models92.This congruence represents one of the most EVT also describes the asymptotic distributions of the ‘extreme spacings’ between the tantalizing results to emerge from recent adaptation largest and next-largest (and so on) draws — given a Gumbel-type parent distribution, theory, indicating (although certainly not proving) that these spacings are independent exponential random variables with averages that behave adaptation to a fixed optimum by new mutations may 110 in a certain simple way .This result has a fundamental role in recent theory of be characterized by certain robust patterns. Future work adaptation, as fitness differences among beneficial mutations represent extreme spacings. could of course show that different biological scenarios Recent work has begun to explore the consequences of non-Gumbel fitness distributions (for example, adaptation from the standing genetic on adaptation over the mutational landscape (A.O., unpublished data). variation) are characterized by different patterns.

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Limitations and conclusions the data. There are in fact two problems. The first is The history of evolutionary genetics indicates that two that current theory is limited in several ways — all the main factors slowed the development of a mature theory models that have been mentioned rest on important of adaptation. The micromutational view of quantitative assumptions and idealizations. Fisher himself noted genetics and the neutral theory of population genetics. such limitations in correspondence about his geo- We cannot, after all, construct a meaningful theory of metric model96,92.And the mutational landscape adaptation if we assume away the existence of muta- model assumes that adaptation occurs at a single gene tions that have different-sized phenotypic effects or if we (or small ), that fitness distributions show cer- assume that substitutions at the DNA-sequence level tain tail behaviour, and that mutant fitnesses are taken have no effect on fitness. The fact that we possess little from the same distribution throughout adaptation. theory of adaptation went largely unnoticed until the Although they are reasonable starting points for theory, 1980s, when QTL and microbial evolution approaches none of these assumptions is necessarily correct and yielded abundant data that revealed a finite (and often changing any might well change our predictions modest) number of substitutions that have definite (and (however, see BOX 3). often different) effects on the phenotype or fitness. The second problem concerns testability. Although In this article, I have emphasized that the appearance adaptation models have become more concrete and per- of such data forced evolutionary geneticists to confront haps more realistic, it is not clear that they have become two questions. First, can we construct a theory of adapta- more testable. The difficulty is practical, not principled. tion that speaks in the same terms as the data? And, if so, Whereas current theory does make testable predictions, can this theory actually account for the empirical phe- the effort required to perform these tests is often enor- nomena observed? The answer to the first question is mous (particularly as the theory is probabilistic, making clearly yes. Evolutionists can and have built models of predictions over many realizations of adaptation). Given, adaptation that speak in terms of individual mutations for example, the inevitable and often severe limits on that have individual effects (whether phenotypic or fit- replication in microbial evolution work, we can usually ness). The answer to the second question is less clear. do no more than test qualitative predictions. Present theory appears to adequately explain certain Despite such limitations, experiments to test the more qualitative patterns that characterize genetic data on tractable predictions of present theory (for example, those adaptation. Four such patterns are: that there are more that focus on a single step in adaptation, where greater beneficial mutations of small than large effect89,93,94; that replication is possible) are important. The main reason is QTL studies reveal more substitutions of small than large that the two problems noted above are related; only by effect26,28,95;that microbial studies show that early substi- testing present predictions can we determine which, if tutions have larger fitness effects than later ones (that is, any, of the assumptions that underlie current theory are there is pattern of diminishing returns)31; and that parallel inappropriate. Only then will theorists know which evolution is common at the DNA sequence level32–35. assumptions to change, deriving new — and perhaps However, it is unclear whether current theory accom- different — predictions and ultimately allowing the plishes much more than qualitative agreement with elaboration of a more realistic theory of adaptation.

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