Hamilton, William Donald

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(b. Cairo, Egypt, 1 August 1936; d. Oxford, United Kingdom, 7 March 2000)

life sciences, evolutionary biology, sociobiology, population genetics.

Hamilton, one of the most influential theoretical biologists of the twentieth century, worked in several areas of mathematical evolutionary biology. His theory of inclusive fitness, popularized as kin selection in The Selfish Gene by Richard Dawkins (1976), was integral to the foundation of the evolutionary subdiscipline of sociobiology in the 1960s and 1970s. Hamilton ranged widely over questions of evolutionary theory in his career, constellated more or less loosely around two central concerns: the evolution of social behavior, particularly of altruism; and the evolution and maintenance of sexual reproduction.

Early Years . Hamilton was born in Cairo to émigré New Zealand parents and raised largely in the Kent countryside in southern England. Interested in science and natural history from childhood, Hamilton was nearly killed as a boy while experimenting with chemical explosives; less dangerously, he was inspired by a great-aunt’s gift of her collection to take up insect collecting. A birthday gift of Edmund Briscoe Ford’s Butterflies (1945) introduced him to the theories of genetics and evolution, which interested him enough to request a copy of Charles Darwin’s On the Origin of Species as a school prize. After two years of national service (1955–1957), Hamilton entered St. John’s College, Cambridge University, in 1957 on a state scholarship to study natural sciences.

At the time Hamilton went up to Cambridge, molecular genetics, thanks to James D. Watson and Francis Crick, was the avant-garde of biology, but Hamilton made an early decision that his interests lay elsewhere and he would not try to keep up with the field. This independence of intellectual interests and stubbornness in pursuing them—which remained lifelong characteristics—meant that Hamilton’s university career, capped by a satisfactory but not outstanding upper second degree, was not evidently brilliant. This was due, Hamilton said in later years, to the time taken from his official studies by his discovery of the book that was to set the course of his scientific life, Ronald A. Fisher’s The Genetical Theory of Natural Selection (1930), a fundamental text of the so-called modern synthesis uniting Darwinian natural selection with Mendelian genetics. Although Hamilton was studying biology and genetics, none of his professors, who were biologists trained in the interwar period and were more interested in ecology than in questions about the action of natural selection and evolution, assigned Fisher’s book. In fact, Hamilton was given to understand by his instructors that Fisher, while sound as a statistician, was suspect as a biologist. Nevertheless, Fisher’s book came to the young Hamilton as a revelation. His enthusiasm was roused both by Fisher’s rigorous adherence to the principle of natural selection in evolutionary explanation, and by Fisher’s lengthy application of his mathematical population genetics to human affairs—the very day he discovered the book, Hamilton wrote to his sister Mary a postcard that was particularly enthusiastic about the final third of the book, devoted to Fisher’s analysis of the evolutionary problems facing the human species and his eugenic prescriptions for repair.

In his own autobiographical writings, Hamilton painted his younger student self as an isolated, Romantic hero, burdened with knowledge too great for ordinary minds to bear. Fisher’s work provided a focus for Hamilton’s lifelong scientific and personal preoccupations, which were the application of the principle of natural selection, as Hamilton strictly understood it, as the key to understanding evolution, and worries about the tenuousness of human society in view of human selfishness and aggression. Hamilton was accustomed from an early age “to believe.... that the quickest way to understand what puzzled me was to spend more time thinking about what I already knew, not necessarily collecting more data” (Narrow Roads of Gene Land, 1997, vol. 1, p. 12) and the data he had told him that human beings were young Werthers, fundamentally unhappy self-absorbed self-interested creatures—this was what he was himself, he believed, and why would other people be fundamentally different? From gloomy introspection Hamilton turned the tools of population genetics he had learned from Fisher on the problem of explaining why, if fundamental selfishness was the norm, communities could exist at all.

Biologists who had studied the origins of sociality (including of human society), from Darwin through the 1950s, had, in general, considered the evolution of societies to be a more elaborate manifestation of the cooperative tendencies necessarily inherent in all organized life, beginning with the cell and continuing through the organism and the family to societies. Just as the parts of a cell had to function together for life to continue, and as the cells of an individual organism must work together, and as sexual organisms must cooperate to at least a minimal degree to reproduce, so too were the individuals in a society parts of a greater whole whose cooperation was required to maintain life and their species. The questions biologists asked about social evolution, then, had less to do with how societies held together once evolved than with the mechanisms of their original evolution.

Hamilton’s principal achievement was to transform the question, “Why do societies exist?” into an individual question, “Why should I be part of society?” The first question took the species as the fundamental unit of interest, as had been usual in evolutionary biology until that time, while the second focused on the individual. The answer Hamilton developed lay not in the mechanisms of social interaction, but in the identification of a deeper-lying self-interest that caused societies to evolve under appropriate circumstances of individual advantage.

After university, Hamilton hoped to continue in graduate study of biology, but had a great deal of trouble finding an institution and advisor receptive to his proposed research question, the origins of altruism, and his proposed means of attacking it, mathematical population biology. Potential advisors and institutional homes were put off either by his mathematical bent, or by his interest in the question of altruism, with its clearly implied links to the explanation of human evolution and possible whiff of eugenics. He finally cobbled together a course of study, enrolling for an MSc in human demography at the London School of Economics (LSE), and then for a PhD jointly supervised by John Hajnal, a demographer at the LSE, and Cedric Smith, a geneticist at the Galton Laboratory, University College London. Slowly a mathematical treatment of the evolution of altruistic behavior, defined as behavior actively harmful to the personal reproductive possibilities of its performer, began to take shape.

A Theory of Altruism . Hamilton’s theory of inclusive fitness synthesized several different elements and approaches. First were tools drawn from each of the three founding fathers of population genetics, Fisher, the British biologist John Burdon Sanderson Haldane, and the American biologist Sewall Wright. Fisher’s mathematical population genetics, with a particular emphasis on the universal applicability of Fisher’s “fundamental theorem of natural selection” (natural selection will result in the evolution of organisms equipped to produce a maximum number of offspring given their environmental and other constraints), combined with his concerns about human evolution, provided Hamilton’s foundation. Hamilton also drew on an animadversion of Haldane’s about the circumstances under which genetically directed self-sacrificial behavior could spread (Haldane had thought it rather unlikely). Finally, after a considerable period of cumbersome ad hoc calculation, Hamilton found and applied to the analysis of altruistic behavior Wright’s “coefficient of relatedness,” a mathematical expression of the probability that, at a given locus, the alleles present will be identical by descent.

To these three building blocks, Hamilton contributed two major novelties. The first was a rigorous insistence that selective costs and benefits had to be analyzed strictly from the perspective of the individual gene, rather than from the point of view of the species or even of the organism. In this, Hamilton was drawing on the perspectives and techniques of rational choice theory, a school of analysis using the tools of game theory and economic analysis, at first primarily applied in economics and political science. Rational choice theory developed in the years after World War II and aimed to turn decision making into a science and to analyze it according to the principles of economic and game-theoretic logic. Hamilton became interested in the possible applications of rational choice theory to his own biological preoccupations while pursuing his PhD; his coadvisor, Smith, a Quaker interested in applying scientific ideas to promoting world peace, maintained a small library on the subject and hosted a discussion group in peace and conflict studies, an area of rational choice theory associated with pacifist political responses to the Cold War. This mathematized, cost-benefit approach to problems of moral as well as scientific import suited Hamilton’s inclinations well. Using the tools of rational choice theory, altruistic behavior could be drained of the troublesomely subjective questions of the motivation of the altruist and the perception of the recipient, to be redefined solely as action conferring reproductive gain to the recipient at a reproductive cost to the altruist.

According to Fisher’s fundamental theorem, however, such behaviors could not possibly evolve, as organisms are constantly selected to maximize their own reproduction. The appearance of many such self-sacrifices in nature, then, became a paradox: if natural selection is all-powerful, and acts only to further the reproduction of the individual, no individual could evolve characters that would impede its own reproduction—and yet, examples abound of such characters in nature, including animals that give alarm calls to warn others of predators but thus drawing predators’ attention to themselves, and sterile worker castes among social insects. These had presented no problems when the evolution of species and groups had been the primary object of explanation, and when sociality had been a general given; Darwin, for example, had in chapter seven of the Origin of Species (1859) dismissed the evolution of sterility in social insects as a problem “of no very great difficulty” for natural selection, as long as it were “profitable to the community” that some individuals should be born “capable of work, but incapable of procreation” (p. 236). Under Fisher’s redefinition, however, such cases became problematic indeed.

Hamilton resolved this newly discovered paradox by extending the notion of offspring to cover not only those directly engendered by an organism, but also those related individuals whom the organism caused to exist by its structures, behaviors, or what-have-you. That is, to further the existence and reproduction of siblings, cousins, parents, nieces, or other kin was in a fundamental way the same as furthering the existence of offspring, as doing so perpetuated the share of the organism’s own genes that the relative carried, and thus in the organism’s own interest just as engendering offspring is. Relatives, however, are not all created equal. Some are genetically closer than others; a diploid organism’s children and parents, for example, share exactly one half of its genes, its siblings share one half on average (because of the shuffling of genes that takes place during the formation of sex cells in meiosis, this is an average rather than an exact coefficient), while half siblings and nieces share one quarter on average and first cousins an eighth. Hamilton asserted that the inducement to benefit a relative bearing one’s own genes, therefore, had to be discounted by the distance of the relationship (measured by Wright’s coefficient of relatedness); he formalized this inducement, denoted k, in what came to be known as Hamilton’s rule: k> 1/r, a gene causing an organism to benefit relatives at the expense of its own reproduction will be selected and increase in a population if the benefit to the “altruist” outweighs the discounted relationship. As Hamilton himself put it,

a gene causing altruistic behavior towards brothers and sisters will be selected only if the behavior and the circumstances are generally such that the gain is more than twice the loss; for half-brothers it must be more than four times the loss; and so on. To put the matter more vividly, an animal acting on this principle would sacrifice its life if it could thereby save more than two brothers, but not for less. (1963, p. 355)

An organism’s inclusive fitness consisted of all the copies of its own genes it caused to exist, whether by direct parenthood or by the preservation of relatives containing some fraction. The criterion of fitness was thus broadened from the individual to the family, while at the same time Hamilton shifted the focus of the analysis of natural selection from the organism to the gene, since, he asserted, “despite the principle of ‘survival of the fittest’ the ultimate criterion which determines whether G [a gene causing some theoretical, unspecified kind of altruistic behavior] will spread is not whether the behavior is to the benefit of the behaver but whether it is to the benefit of the gene G” (Hamilton, 1963; repr. in Narrow Roads, 1997, vol. 1, p. 7).

Hamilton wrote up the theory of inclusive fitness in two versions. One was a lengthy, fully mathematical treatment that unified understanding of a considerable body of case studies of altruistic behaviors that Hamilton drew from the scientific literature, the fruit of his graduate research. The second was a short, mostly verbal abstract of the whole, containing only the mathematical relation of Hamilton’s rule and some general, theoretical remarks on its applicability. He met difficulty in publishing both. The first he submitted to the Journal of Theoretical Biology, where it spent considerable time in the reviewing process; ultimately the referee (John Maynard Smith, a mathematical biologist of similar interests) asked that it be split into two parts. The second he sent with perhaps naive optimism to Nature, which promptly rejected it, the editor suggesting that its specialized topic might be more appropriate to a “psychological or sociological journal.” Hamilton was stung by this rejection, which he attributed to his LSE affiliation, but the editor may well have seen that one of Hamilton’s objectives was to explain human society, even though his only allusion to the subject in the paper was an oblique concluding reference to Fisher’s work on man. On a second submission, to the American Naturalist, the paper was accepted and published in 1963.

After the revisions and splitting called for by the referee for the Journal of Theoretical Biology, that journal published “The Genetical Evolution of Social Behaviour,” parts 1 and 2, in 1964. The first part of the paper contained the mathematical arguments culminating in the derivation of Hamilton’s rule; its arguments were almost exclusively cast in the language and methodology of modern population genetics. The second part hearkened back in its methodology to Darwin's, as Hamilton used the theory of inclusive fitness to explain a diverse array of social traits recorded in the biological literature, including alarm calling, mutual grooming, the fusion of colony organisms, and postreproductive behavior in cryptic (camouflaged) moth species compared with that of aposematic species (bad-tasting with vivid warning colors). In each case, Hamilton argued that his theory of inclusive fitness could coherently explain the evolution of phenomena that had been disparate in the literature as aspects of a single principle at work, Fisher’s fundamental theorem of natural selection, mandating the maximization of favorable genes under selection.

Like Darwin, Hamilton also turned to the apparently problematic case of the social insects to provide a clinching argument. Where the crux of the problem for Darwin had been the difficulty of evolving castes of differentiated sterile workers that could not directly pass on their sometimes extravagant modifications from the reproductive forms, for Hamilton the difficulty lay in the evolution of sterility itself, for if every individual, and every gene, is, figuratively speaking, attempting to maximize its replication, then evolved sterility would be the ultimate Fisherian impossibility. What possible self-interest could make an organism forgo any chance of reproduction, when reproduction is the very definition of self-interest? Darwin, viewing the community as the object of natural selection in such cases, had, as noted, found no great difficulty in this point, but Hamilton, who did not see communities as meaningful entities, refused to accept Darwin’s argument (which had remained the general explanation of the evolution of social behavior since his time), insisting on an argument that acknowledged what he took to be genes’ fundamental selfishness. Hamilton pinned his argument on the peculiar genetics of the family Hymenoptera, comprising the wasps, ants, and bees.

Hymenopterans are characterized by an unusual sex-determination system, known as haplodiploidy. Female hymenopterans are, like members of most sexually reproducing species, diploid: they have two sets of chromosomes in each cell, one derived from their mother, one from their father. Males, however, are haploid: they have only one set of chromosomes, from their mother; males hatch from unfertilized eggs and thus, oddly, have no father at all. These facts have interesting consequences for Hamilton’s arguments concerning inclusive fitness. A female hymenopteran is related to her mother and to her father by one-half each, likewise to her own daughters and sons by one-half each. But because she shares all of the one-half of her genes derived from her father with all of her sisters (presuming her mother mated only once), she is related to each of her sisters by three-quarters on average (one-half identical in all cases, derived from the father; one-half of the remaining half, derived from the mother, shared on average). By the same calculation, she is related to her brothers by only one-quarter on average. A male is related to his brothers as well as to his sisters by one-quarter on average. Because sisters are more closely related to each other than to any other relatives, including their own parents or potential offspring, the conclusion Hamilton drew is that haplodiploidy, at least in cases where females mated only once, would predispose the Hymenoptera to the evolution of social systems in which sisters furthered each other’s success and in which males, relatively little related to their sisters or brothers, would have no incentive to take part. The argument applied only to the haplodiploid hymenoptera, and in its strongest form only to the case in which a fertile female had mated only once (multiple paternity would dilute sisters’ relatedness to one another), but it gained particular strength from the long-standing observation that complex social behavior and the evolution of sterile female castes had apparently evolved numerous times in the Hymenoptera from solitary lineages, while, in contrast, complex sociality and sterile castes were known to have evolved only one other time among insects, in the single lineage arising from the cockroaches and leading to the termites (which are fully diploid organisms, and so not subject to the same argument).

The power of inclusive fitness was to make every instance of apparent “altruism” evolutionarily explicable as an act of selfishness. This new view of altruism required a new definition: altruism consisted of promoting another organism’s genetic self-interest at the expense of the altruist’s own. That is, the individual cost to the altruist became a crucial component of the definition, and analysis of altruistic behavior had correspondingly to focus on the genetic self-interest of the individual, not the colony or the group or the species. In the second part of “The Genetical Evolution of Social Behaviour,” Hamilton’s rhetorical method also evoked Darwin’s in his confrontation of the apparent difficulties for his theory in the form of observations published in the literature that apparently contradicted the evolutionary action of kin selection. Hamilton admitted, for example, that in at least some species of hymenopterans (honeybees, for example) multiple matings by fertile females were well attested, lessening the force of the argument for inclusive fitness as the evolutionary glue holding colonies together. Recorded instances of adoption of unrelated orphan chicks in various bird species likewise provided an apparent counterinstance. Hamilton insisted, however, that in every case, either previous observations must have been misinterpreted, or the behavior in question represented a “biological error,” actively maladaptive and thus, by Fisher’s principle, doomed. This rigorous insistence on the necessity to analyze behavior as correlated to the genes that promoted it, then to analyze it in terms of the benefits to the reproduction of those genes, was Hamilton’s principal contribution in “The Genetical Evolution of Social Behaviour,” one that was to help to transform both the language and the theory of evolutionary biology.

Reception of Inclusive Fitness and Further Work on the Evolution of Sociality . Hamilton’s papers on inclusive fitness did not at first make much splash. In a letter to Nature published in 1964, before the publication of Hamilton’s paper in the Journal of Theoretical Biology, Maynard Smith, a referee of “The Genetical Evolution of Social Behaviour,” coined the phrase kin selection to apply to Hamilton’s theory, but rather disingenuously equally credited Hamilton’s American Naturalist article and Haldane’s brief remarks of 1951 with the concept (this quasi-breach of the ethics of peer review came between the two men, and Smith came to regret it). The first sustained attention to Hamilton’s paper came from students of the Hymenoptera, who specialized in Hamilton’s chief case study. Edward O. Wilson, who was at this time emerging as the world’s preeminent specialist on ants, read Hamilton’s paper in 1965, not expecting to find much of interest in it. By his own account, Wilson was at first hostile to the idea that an unknown graduate student could have “cut the Gordian knot. Anyway, there was no Gordian knot in the first place, was there? I had thought there was probably just a lot of accidental evolution and wonderful natural history.... [But finally] I gave up. I was a convert, and put myself in Hamilton’s hands” (Wilson, 1994, p. 320). Wilson contacted Hamilton, and in the fall of 1965 the two men attended a meeting of the Royal Entomological Society of London, where Wilson strongly advocated Hamilton’s theory in an invited lecture on the social behavior of insects. Wilson also devoted substantial space to inclusive fitness in his book The Insect Societies (1971), the first major synthetic work on the social insects to appear in forty years. However, Wilson, though he played an integral role in publicizing Hamilton’s work on inclusive fitness, was never an entire convert to the all-sufficiency of kin selection in explaining the origin of sociality in the social insects. Indeed, although the argument about haplodiploidy provided the catchiest component of Hamilton’s 1964 paper, and the only illustration of inclusive fitness that nonbiologists tend to remember, the arguments pro and con as to whether haplodiploidy accounts for the evolution of sociality in the Hymenoptera have never ceased among students of social insects, with no final consensus in sight. Hamilton’s work also received favorable mention in George Christopher Williams’s Adaptation and Natural Selection (1966), an influential manifesto against the arguments for group selection made by Vero Copner Wynne-Edwards and in favor of a rigorously individual-level approach to natural selection.

Hamilton’s influence began to grow among evolutionary biologists as the few who had read and understood the import of his papers worked to bring him from his initial scientific and social isolation into the networks of scientists interested in evolution and behavior. Wilson, for example, invited Hamilton to lecture at Harvard University in 1969, en route to a Smithsonian Institution conference on “Man and Beast” that brought together specialists from various fields to discuss the impact of recent biological work on understandings of human nature; it was on this visit to Harvard that Hamilton met Robert Trivers, then a graduate student there and later an important collaborator and ally in explaining the evolution of altruistic behavior. The two works that brought Hamilton’s name and theory before a wider audience of both scientists and the general public, however, were Wilson’s Sociobiology(1975) and Dawkins’s The Selfish Gene (1976). While Wilson in Sociobiology treated inclusive fitness as just one of a number of motors of social evolution (albeit an extremely important one), Dawkins seized on Hamilton’s fundamental vision of the gene as the central locus of natural selection to redefine Darwinism around the idea of the “selfish gene” and to establish a program for biology that made Hamilton’s gene-centered cost-benefit theoretical language and apparatus central to the analysis of all evolutionary problems. From about 1974, citations of Hamilton’s 1964 papers in the scientific literature began an exponential rise, reaching some four thousand total in the Institute for Scientific Information (ISI) Web of Science database by 2007, making “The Genetical Evolution of Social Behaviour” the most-cited paper ever published in the Journal of Theoretical Biology. In concert with Williams, Maynard Smith, Wilson, Dawkins, Trivers, and others, Hamilton’s principal achievement was so thoroughly to revise the language of evolutionary biology that it has become nearly impossible to speak in evolutionary explanations except in terms of the self-interest of the organism or gene.

Over the twenty or so years following “The Genetical Evolution of Social Behaviour,” Hamilton continued to work on problems connected to the evolution of sociality in both animals and humans. In 1963–1964 he spent time in Brazil at the laboratory of Warwick Kerr, making observations and testing theories of evolution in social insects. After returning to Britain, he was offered a lectureship in genetics at Imperial College, University of London (Hamilton later learned that he had been one of only two applicants for the post, the first of whom had turned it down). This position gave him excellent facilities for observation and natural historical experiment in Sil-wood Park at the university’s field station, an “entomological Mecca.” The teaching duties were not especially onerous, fortunately for all concerned: Hamilton began at this period to build a solid lifelong reputation as a dreadful teacher and lecturer (Imperial College students regularly petitioned that marks in Hamilton’s courses not be counted toward their degrees, “in view of the nature of the teaching”). Moreover, as Hamilton’s professional isolation began to ease in the late 1960s, so too did his personal isolation. In 1966 he married Christine Friess, a student in dentistry; the couple had three daughters.

Hamilton continued in this period to work out problems connected with his thinking on inclusive fitness. The paper that Hamilton claimed to be proudest of in his career, “Extraordinary Sex Ratios,” published in Science in 1967, treated the evolution in various species of sex ratios deviating from the 50–50 female-male ratio that Fisher had mathematically established to be the evolutionary default in cases of panmixia (where every female has an equal chance of mating with every male). Hamilton took on several different sorts of evolutionary forces that could disturb the force driving the ratio back to 50–50: viscous populations, for example, in which males mated only with the females immediately surrounding them (cases occur often in nature, frequently with sibling mating, as when newly hatched brothers fertilize their sisters from a batch of eggs laid by a parasitic wasp on an insect host). In these cases, Hamilton demonstrated that natural selection would produce a bias toward the production of females, since the return on the investment on sons (which can fertilize many females each) would diminish as they competed among themselves to fertilize females (which would mate only once). Hamilton’s paper, however, had larger ends in view than the peculiarities of parasitic insect reproduction. He considered the selective outcomes of the various possibilities that a gene determining sex ratio in a diploid species might be found on either the X (female) chromosome, the Y (male) chromosome, or on an auto-some (a chromosome common to both sexes). Again using the gene's-eye perspective, Hamilton argued that different chromosomes would then “want” different sex ratios, because the arguments for inclusive fitness that covered the interactions of one organism with another would equally apply to the interaction of one chromosome with another (given that a diploid organism contains two sets of chromosomes from two different individuals, who may be more or less related to one another). Drawing on the apparatus of mathematical game theory, Hamilton further predicted that sex ratios in populations would, under specified conditions of inheritance and environment, settle at fractions that he called “unbeatable.” This idea, viewing organisms as though they were rational, strategic agents seeking to maximize their own inclusive fitness, drew on the same underlying use of game theory and prefigured the more generalized version of the “evolutionarily stable strategy,” or ESS, that was proposed in 1973 by Maynard Smith and George Price, whose collaboration was a strong link between Hamilton’s and Smith’s thinking. Price, a self-taught mathematical population geneticist, had contacted Hamilton in the wake of his papers on inclusive fitness, having subsequently devised an independent mathematical formulation that elegantly covered Hamilton’s case. Hamilton and Price subsequently collaborated on a pair of papers published in Nature in 1970 covering the evolution of selfish and spiteful behaviors, complementary to the evolution of altruism.

From the very beginning of his systematic thinking on altruism as a Cambridge undergraduate, Hamilton had been motivated to explain the puzzle, as he saw it, of the existence of altruistic behavior not only in the animal world but in human beings as well. In common with Darwin and virtually all evolutionary biologists of the late nineteenth and early twentieth centuries (including, importantly, his idol Fisher), Hamilton believed that evolutionary biology pursued two intertwined aims: the first to explain the history of life on earth, and the second to explain human nature, to explain us to ourselves. While biologizing explanations of human nature, particularly those advancing evolutionary explanations for human racial or individual differences, had fallen out of favor among professional evolutionary biologists in the wake of eugenics and German National Socialist abuses, and as evolutionary biology established itself as an institutional scientific discipline distinct from sociology and anthropology, a number of younger evolutionary biologists in the 1960s, including Hamilton and Wilson, were deeply interested in such questions and preparing to address them directly in their scientific work. Hamilton’s first published paper in 1963 had already obliquely alluded to this theme, and in a paper published in 1975 as part of the proceedings of a conference organized by the anthropologist Robin Fox and the primatologist Irven DeVore, “Innate Social Aptitudes of Man: An Approach from Evolutionary Genetics,” Hamilton addressed the question of human nature and its evolution directly (in a paper he viewed as an homage to Price, who had died by suicide earlier that year). Hamilton here extended the notion of inclusive fitness, drawing on Price’s work, to account for the differential evolution of altruistic behavior among groups. His remarks on the selective advantages of warfare, despite its “gross inefficiency ....[as] an alternative to birth control and infanticide,” and his speculations about the evolution of intragroup altruism combined with warlike aggressiveness among “barbaric pastoralists” such as the Bantu, drew some heated criticism (including from the anthropologist Sherwood Washburn, one of the volume’s dedicatees and coauthor of Hamilton’s article’s epigraph), criticism that prefigured the storm that was to break out over Wilson’s Sociobiology and Dawkins’s Selfish Gene over the next year; Trivers teasingly called it Hamilton’s “fascist paper.”

In 1978, invited by fellow sociobiologist Richard D. Alexander, Hamilton moved from Britain to the United States, taking up a professorship in the biology department at the University of Michigan, Ann Arbor, where he was to remain until 1984. While at Michigan, Hamilton’s longstanding interest in game theory came to the fore in his collaboration with Robert Axelrod, a political scientist who was a colleague at Ann Arbor in the Institute of Public Policy Studies (now the Gerald R. Ford School of Public Policy). Hamilton and Axelrod’s collaboration, “The Evolution of Cooperation,” published in Science in 1981 played, like Maynard Smith and Price’s evolutionarily stable strategies, an important role in the reunion of the political and economic roots of rational choice theory with its offshoot in biology. Hamilton had become interested in game theory in general, and in the particular instance known as the Prisoner’s Dilemma, in the early 1960s on reading an article in Scientific American on John von Neumann’s work written by the Russian-American rational choice theorist Anatol Rapoport. The Prisoner’s Dilemma is a non-zero-sum game, conventionally described with the following scenario and matrix: two accomplices in a crime, A and B, arrested by the police, are separately interrogated and offered a plea deal to offer state’s evidence against the other. If A and B both decline this deal, they will each serve six months. If A takes it, while B remains silent, according to the terms of the deal A will go free while B will serve five years. The reverse will happen if B rats out A. And if each each testifies against the other, both will serve two years.

 Prisoner B remains silentPrisoner B testifies
Prisoner A remains silentEach serves six monthsPrisoner B goes free; Prisoner A serves five years
Prisoner A testifiesPrisoner A goes free; Prisoner B serves five years)Each serves two years

The source of the game’s titular dilemma is that although each prisoner’s best strategy is to testify against his accomplice, he knows that this is his accomplice’s best strategy too. A rational prisoner would always choose to testify, although this precludes the possibility of a lighter sentence for both, because the penalty for loyalty in the event of his accomplice’s treachery is so severe. In its generalized form, the Prisoner’s Dilemma stipulates that mutual cooperation has a better outcome than mutual defection, which both have a better outcome than the loser’s penalty (the “sucker’s payoff”) in a situation where one player cooperates and the other defects. Hamilton’s initial formulation of “altruism” and its opposite number, “spite,” as two choices in a matrix of alternative behaviors (help others at cost to one’s own reproduction, hurt others at cost to one’s own reproduction) had owed its form to the Prisoner’s Dilemma, as Hamilton noted in his paper for the “Man and Beast” colloquium. And in the conclusion to “Innate Social Aptitudes of Man” Hamilton explicitly asserted the relevance of the Prisoner’s Dilemma to the evolutionary explication of human evolution and behavior:

“One hears that game theorists, trying to persuade people to play even two-person games like ‘Prisoner’s Dilemma,’ often encounter exasperated remarks like: ‘There ought to be a law against such games!’ Some of the main points of this paper can be summarized as an answer to this comment: that often, in real life, there is a law, and we can see why, and that sadly we also see the protean nature of this Dilemma, which, when suppressed at one level, gathers its strength at another.” (reprinted in Narrow Roads, 2001, vol. 2, pp. 347–349)

Axelrod contacted Hamilton, on recommendation from Dawkins, because he was interested in the literature on evolutionarily stable strategies. Hamilton had presumed, as most game theorists did, that continued defection (all-defect or ALL-D) was always the core winning strategy for players of the Prisoner’s Dilemma, as it was easily demonstrated to be in the case of a fixed number of games; this perhaps accounted for the melancholy of his conclusion to “Innate Social Aptitudes of Man.” Axelrod, however, had run a tournament, open to all comers (fourteen strategies in all, submitted by economists, sociologists, political scientists, and mathematicians, were played against each other in a round-robin), to discover the best strategy for playing an open-ended number of rounds of the game. This tournament was won by Rapoport (Hamilton’s first guide in game theory, by happy chance), who submitted the simplest strategy, called TIT FOR TAT: begin by cooperating, then do whatever the opponent has done in the move before, whether cooperate or defect. On a second round of the tournament (sixty-two entries, including evolutionary biologists, physicists, and computer scientists in addition to the earlier entrants), Rapoport’s TIT FOR TAT won again. Axelrod and Hamilton argued that Hamilton’s kin selection provided a key to understanding how TIT FOR TAT strategies could have won out evolutionarily in the history of life over ALL-D to permit the evolution of sociality, since inclusive fitness gave organisms a genetic incentive to cooperate over defection, even at reproductive cost to themselves. Effectively, this meant that the game’s payoff matrix was recalculated, so that apparent losses might in fact conceal a player’s part interest in its opponent’s gain. In his usual style, Hamilton adduced a number of previously puzzling examples from the published biological literature that might serve as illustrations of the new principle. Axelrod and Hamilton’s paper, like Hamilton’s original papers on inclusive fitness, gave rise to a veritable industry or subdiscipline within biology, testing examples and attempting to expand or refute the principle; unlike inclusive fitness, however, this work was immediately widely recognized as important, not only published in Science but also honored as that prestigious journal’s most important paper for the year 1981.

From the late 1970s, Hamilton also began to receive international honors and recognition for his scientific work; among other honors, he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1978 and a Fellow of the Royal Society of London in 1980; in 1988 he received the Darwin Medal of the Royal Society, and in 1993 received both the Crafoord Prize of the Swedish Academy of Sciences and the Kyoto Prize of the Inamori Foundation.

Evolution of Sex . In the late 1970s, Hamilton began investigating the subject that provided the second major focus of his interests in evolutionary theory: the evolution and maintenance of sexual reproduction. Unlike altruism when Hamilton began thinking about it, the evolution of sex was a topic that had since the mid-1960s already been treated by other biologists in his circle (like Williams and Maynard Smith), although Hamilton, in his iconoclastic way, had failed to be convinced by any of them. Although the purpose of sex seems obvious—surely it is for reproduction and to maintain the variability necessary for natural selection to work on to keep a species from going extinct?—from the gene's-eye view it is not. Sexual reproduction not only shuffles an organism’s genes, but also eliminates half of them in every offspring, which receives another complementary set from the other parent. In selfish-gene terms, sex inflicts considerable damage on a gene’s potential reproduction, unlike asexual reproduction (as by budding or cloning), which replicates all genes. How then could sex have been evolved over this heavy short-term disadvantage, and why should natural selection continue to maintain it?

In a series of papers from 1980 through the mid-1990s, in cooperation with a series of coauthors, including Axelrod, Jon Seger, and Marlene Zuk, Hamilton combined the approaches he had developed since the beginning of his career to tackle this question. The theory he and they developed drew on Hamilton’s gene's-eye view, interest in game theory, and broad interests in ecology and natural history. Hamilton believed that it was improbable that inanimate selective forces could maintain sex, because directional selection would not retain variation: eventually alleles would either be fixed in the population or eliminated entirely, but the continued production of variation itself would not be selected. Ecologists, however, had observed that continuous change was fostered in nature in two common situations: predator-prey cycles and host-parasite relations. Ecologists studied the continually varying densities of species rather than of their genes, but Hamilton believed that analogous principles might well apply to foster the continued selection of variability of genotypes within a species, that is, to provide a selective advantage to the continual reshuffling that sexual reproduction provides, over the short-term advantages of asexual reproduction. He focused on parasite-host interactions, because they were universal (every species, even the very smallest bacteria, falls prey at least to viruses) and generally fairly species-specific, which seemed from ecological models to foster the emergence of cycling phenomena. Hosts and parasites would thus be locked in a continuous war of innovation and defense, in which a combination of genes advantageous in one generation might become positively disadvantageous in the next, as parasites and disease organisms evolved to circumvent it. A perverse outcome was the prediction that sexual selection, as studied since Darwin, would prove to have multiple and sometimes conflicting purposes—to distinguish and mate with the healthiest possible individual might make adaptive sense in the short run, but it might also, given that diseases and parasites were always in hot pursuit, make sense to distinguish and mate with the sickest possible individual, whose currently disadvantageous genes might nevertheless be just what was required at the next turn of the cycle.

While straightforward in outline, the working out of such a picture was enormously complicated. Mathematical population genetics models handled well only stable states in simple models, whereas Hamilton needed to create a model in which two or more species were simultaneously accounted for, and in which each species varied at multiple loci, each of which might cycle independently. Eventually, in what Hamilton regarded as his culminating work on the subject, he and his collaborators (Axelrod and Reiko Tanese) proposed a series of individual-based models that argued that under various complex and realistic scenarios, sexual reproduction would be positively selected. This concluding paper and its theory, which Hamilton found satisfyingly in accordance with his finely-honed intuitions about how the natural world worked, contrast strongly in methodology and application with his earlier work on the evolution of sociality. The latter gave rise to two fully generalizable, universal, mathematized predictive theories (inclusive fitness and the TIT FOR TAT resolution of the Prisoner’s Dilemma as motors of the evolution of sociality), whereas the former depended for its rhetorical force on the particularity of individual, contingent natural relationships, frequently evoking Hamilton’s encyclopedic command of biological and ecological observations, both his own and others’.

Teaching and Research Style . Although the importance of inclusive fitness to the development of the new “neo-Darwinism” of the late 1960s and 1970s brought Hamilton, as observed above, into much greater contact with other scholars (his first coauthored paper, with Robert M. May, was published in 1977), he nevertheless retained throughout his career much of the isolated, contrarian, loner persona of his early, overlooked, graduate-student odyssey through institutions and advisors. To a great degree this was a matter of personal style and choice. Hamilton had little inclination for the kind of institutional empire-building that would have established him in an influential chair, funded by lavish grants, and surrounded by graduate students and postdocs who would further disseminate his power. Moreover, he never ceased to be riven by the deep self-doubts and insecurities that fueled his interest in the origins of sociality and sexual reproduction and his anxieties about where his answers might lead him personally or human society in general. He also positively relished his self-image as a contrarian, who dared to say what few other biologists would (although he never wrote a book accessible to a wider audience than his fellow biologists, and so did not, like Wilson and Dawkins, of whose courage in thus doing he wrote admiringly, put himself in the public line of fire). And he was greatly (self-) handicapped by his inability to communicate with a large audience (whether of students or colleagues). His teaching was notoriously poor, and his colloquia and presentations little better—the technique of using a handheld microphone as a slide pointer, thus rendering his arguments beyond, “Here, as you can see ....” inaudible, while his mouth continued visibly to move, was only one of a repertoire that kept him incomprehensible. Hamilton wryly admitted that, on the basis of his lectures, students would have good reason to doubt that he understood even his own ideas.

In 1984 Hamilton left the University of Michigan for a Royal Society Research Professorship at Oxford University, where he remained for the rest of his life. The requirements of the job were tailor-made for Hamilton: it required him to give only one lecture to students per year (which he often forgot to do). Hamilton’s contrarian streak also contributed to his decision to leave Ann Arbor, driven out by what he considered the rising tide of insidious (and evolutionarily contraindicated) American political correctness. He was incomprehendingly irate, for example, at the strongly negative reception given (by an acid “lady academic” search committee chair and the student herself) to a letter of recommendation (the strongest, he believed, he had ever written) for a student, in which he praised her mathematical ability as “especially remarkable in view of her sex.” Women, in his view, being demonstrably, and almost certainly innately, weaker in mathematics, he had in fact meant the phrase as singling her out for higher regard rather than lower, and could “hardly credit that what [he] wrote could be interpreted in any other way” (Narrow Roads, 2001, vol. 2, pp. 307–308).

Hamilton’s lifelong determination to follow his evolutionary reasoning out to the logical end, no matter how bitter or pessimistic, led him into other such social fixes. From his earliest thinking about altruism and sociality, under Fisher’s tutelage, Hamilton was convinced of the logical imperative underpinning the practice of negative eugenics. In a review of a book on “human diversity” published in 1965, Hamilton asserted that the prevention of the reproduction of unfit people bearing deleterious genes at some stage of their life cycles was necessary, if the “genetic trust built for us by our ancestors” was not to be squandered; he claimed that the most efficient and most merciful means of doing so would be the practice of “humane eugenic infanticide” (Hamilton, 1965, pp. 203–205). Similarly, at a meeting of a Royal Society group for the study of population constituted in the mid-1960s, Hamilton (still a graduate student) advocated that the group should study the biological underpinnings of differential propensities among different human populations, to be met with stony rebuke from the chairman. In the autobiographical essays that Hamilton wrote to accompany the first two volumes of his collected papers, Narrow Roads of Gene Land (1997 and 2001), Hamilton enlarged greatly on these related themes, painting a bleak picture of a human future in which individual people, kept alive only by the most pervasive, invasive medical technologies because so many deleterious genes and gene combinations have remained in the pool by the relaxing of human and natural selection, have been reduced by their relationship to technology to mere components in a giant human superorganism, in a dead-end social devolution like that of the social insects.

Hamilton’s self-portrait as a disillusioned “crank,” doomed to follow the lone Romantic’s path, hopelessly out of touch with current social norms and pieties thanks to his rigorous insistence on following evolutionary principles wherever they led him, was, however, at odds with the persona he enjoyed among friends and colleagues. He was greatly revered by colleagues and former students (many of them female), who held him in the highest affection and who attested, particularly after his death, to his great personal kindness and practice of unstinting cooperation, whatever the self-doubts that underlay his practice of them might have been.

Controversies over AIDS; Hamilton’s Death . The same contrarian, deeply held intellectual principles that led Hamilton into social and professional difficulties led him to his premature death. In the late 1990s, Hamilton became intrigued by the iatrogenic theory proposed by Edward Hooper of the origin of AIDS: that the virus had been introduced from chimpanzees into human beings by way of polio virus tested by Western doctors on black Africans. Were this to be the case, it would have been the greatest catastrophe in the history of medicine, and Western scientists and pharmaceutical companies would be morally, and possibly legally, liable. Hamilton found the theory plausible, and did his best to help publicize it against what he saw as enormous, scientifically improper suppression of debate by vested interests; he was also worried about the implications for current medicine, as, for example, of xenotransplantation (the transplantation of tissues or organs from other species into humans). He made two expeditions to the Congo to collect samples of chimpanzee feces for analysis; on the second, he contracted a virulent strain of malaria, collapsed soon after returning to Britain, and died a few weeks later at the age of sixty-three. He was interred in Wytham Woods, Oxfordshire, to be given, as he had wished, to burying beetles and fungi and thus returned to the world of living things that had been his life’s study.


Only the principal articles and those quoted in the entry are listed. Hamilton’s complete articles have also been collected into three volumes under the title Narrow Roads of Gene Land; the first two volumes contain original autobiographical essays introducing each article, while the third was published posthumously and includes essays by colleagues and collaborators as well as bibliographical information. Hamilton’s personal and professional papers are held by the Manuscripts Division of the British Library, London. Since he died without warning, his papers and other materials remained as he had left them still in mid-career, and his family offered the library the rare opportunity of archiving a working scientist’s office, preserving Hamilton’s own order and relation among materials.


“The Evolution of Altruistic Behavior.” American Naturalist 97 (1963): 354–356.

“The Genetical Evolution of Social Behaviour, I and II.” Journal of Theoretical Biology 7 (1964): 1–16, 17–52.

“Human Diversity.” Population Studies 19, no. 2 (1965): 203–205.

“Extraordinary Sex Ratios.” Science 156 (1967): 477–488.

“Geometry for the Selfish Herd.” Journal of Theoretical Biology 31 (1971): 295–311.

“Selection of Selfish and Altruistic Behaviour in Some Extreme Models.” In Man and Beast: Comparative Social Behavior, edited by J. F. Eisenberg and Wilton S. Dillon. Washington, DC: Smithsonian Institution Press, 1971.

“Altruism and Related Phenomena, Mainly in Social Insects.” Annual Review of Ecology and Systematics 3 (1972): 193–232.

“Innate Social Aptitudes of Man: An Approach from Evolutionary Genetics.” In Biosocial Anthropology, edited by Robin Fox, ASA Studies 1. London: Malaby, 1975.

“Sex versus Non-Sex versus Parasites.” Oikos 35 (1980): 282–290.

With R. Axelrod. “The Evolution of Cooperation.” Science 211 (1981): 1390–1396.

With Marlene Zuk. “Heritable True Fitness and Bright Birds: A Role for Parasites?” Science 218 (1982): 384–387.

With Jon Seger. “Parasites and Sex.” In The Evolution of Sex: An Examination of Current Ideas, edited by Richard E. Michod and Bruce R. Levin. Sunderland, MA: Sinauer Associates, 1988.

With Robert Axelrod and Reiko Tanese. “Sexual Reproduction as an Adaptation to Resist Parasites (a Review).” Proceedings of the National Academy of Sciences of the United States of America 87 (1990): 3566–3573.

Narrow Roads of Gene Land: The Collected Papers of W. D. Hamilton. 3 vols. Oxford: Oxford University Press, 1997–2005.


Darwin, Charles. On the Origin of Species, a Facsimile of the First Edition. Cambridge, MA: Harvard University Press, 1964 [1859].

Grafen, Alan. “William Donald Hamilton.” Biographical Memoirs of the Royal Society 50 (2004): 109–132.

Wilson, Edward O. Naturalist. Washington, DC: Island Press, 1994.

Abigail Lustig

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