by Oren Harman
Hamilton’s sensitive soul had recognized the shock to George’s sensibility, penetrating the short lines of a reprint request from a complete stranger directly to his gut. For, reading Hamilton’s 1964 paper on rB > C, George could not help but wonder: Was nepotistic altruism really the very best Nature could muster?13 If so, prospects for humanity seemed bleak. Worse, Hamilton, in his reply, was painting an even emptier picture of morality: The very feeling of repugnance from a limited kin-directed goodness may itself be a trick of the genes to bring about a favored behavior; broadening altruism beyond the family would have the salutary effect of increasing overall genetic diversity, a biological end that would place “pure” moral sentiment in a rather darker, functional light.
Was there no way to win? Was goodness either true but limited or broad but nothing but a sham? Or was Hamilton suggesting something even more sinister: that no matter what the level or scope, humans were ultimately slaves to their true genetic masters? “Your letter is exceedingly interesting,” George began in reply; he was a “as the twig is bent, the tree grows” man, but perhaps genes really were what controlled twig growth in the first place. It was extraordinary how much Fisher had pioneered and yet how much he had left after him. Still, had Hamilton recognized the flip side of kin selection: nepotism toward family meaning ill intention toward strangers? And would he be interested in a joint collaboration along the lines of “Natural Selection for Malevolence Toward Non-Relatives”?14
It was the end of March 1968, and Hamilton was already on his way to study multiqueen wasps in the jungles of Brazil; there was no address to which to post a reply.15 With the orphaned letter in hand and heart racing at its dire contents, George took a second look at Hamilton’s letter: “what sort of ‘game’ the genes are expected to be playing,” it read. Game? What was this about?
“I am sure that prisoner’s dilemma situations,” Hamilton had written, “are common and important in biological evolution.” Precisely what this meant, George was not yet sure, but the stranger whose paper he had found in the Senate House Library had provided a clue that he might follow. Perhaps a morsel of goodness could be found, after all, to help allay his greatest fears.
He kept toiling away in the libraries: half a dozen papers started and given up. “My big one,” he wrote to his daughter Kathleen back in America, “will be on the evolutionary origin of the human family,” explaining:
In many bird species, but only comparatively few mammals, the biological father contributes directly to the care of his off spring. In most mammalian species, the father just mates with the mother and she does all the child rearing herself. In a smaller number of mammalian species, there is some joint care by all the adult males in a group of all the young, but not individualized preferential care by fathers toward their own off spring. For example, dominant male baboons are intensely protective toward infant baboons, but do not differentiate between their own off spring and other infants. But in the human species, the dominant pattern in most or perhaps all cultures has involved preferential care by adult males toward their own children. Problem: why did our species evolve in this way…?16
He signed it, without a hint of irony, “With love, Daddy.”
George continued to sway here and there, still lacking focus and searching for some unknown intellectual breakthrough. Shortly afterward, in the Senate House Library once more, he came across a paper in Nature that grabbed his attention. Already in the Descent of Man Darwin had recognized the problem: Deer antlers are “expensive” designs and yet highly ineffective weapons for inflicting injury on an opponent.17 How then had they evolved? A certain G. Stonehouse now claimed to have the answer: Elaborate in form, often gigantic, antlers had evolved to dissipate heat by means of the flow of blood through the vascular covering of velvet during summer; they were the expensive but obligate result of the demands of thermoregulation. Males were usually the ones who grew them because males are larger and therefore more in need of dissipating heat. Stonehouse was confident that he had solved Darwin’s mystery: What looked like a burdensome decoration was actually a physiological necessity.18
George was not convinced. Antlers had been on his mind since the summer of 1967, and still he hadn’t cracked the mystery. He mulled it over in his head. He thought about Hamilton’s clue. He tossed and turned. And then, in a flash, it hit him. Games! Of course! He had already been there! Yellowing away in some drawer, No Easy Way was after all about the Cold War dynamic of American and Russian disarmament; the logic of détente based on the threat of deterrence. Suddenly it all connected: If deer really needed to cool off, skin flaps and large ears were surely a less expensive route to follow than seasonal renewal of antlers. Besides, roe deer were in velvet in spring and without velvet in summer, and lowland tropical species would have to dissipate all year round. No, deer antlers could not be a solution to the problem of thermoregulation. Rather, they were ingenious accessories to nature’s invention of limited combat. It was a classic von Neumann game.19
Here was its logic: If a group of male deer varied in both fighting ability (E signifying greater fighting ability than e) and ability to deescalate combat (D signifying greater ability to deescalate than d), one could go about calculating just how each deer (De, DE, de, and dE) might fare against another. Attaching probabilities to injury, survival, and victory, George discovered a fascinating result: Extended over four or five rutting seasons per generation and a hundred generations or so, limited combat strategies proved successful and should evolve. One obvious way to do this would be to grow ornate antlers: Since locking heads with such appendages is clearly less deadly than ramming one or two powerful sharp horns to the body, antlers would act as the biological analogy to a boxer pulling punches.
But wouldn’t a deer with malicious intent and a sharp set of forward-pointing horns always stand to benefit? This is where the game came in, and the notion of an evolutionary stable strategy:
A sufficient condition for a genetic strategy to be stable against evolutionary perturbation is that no better strategy exists that is possible for the species without taking a major step in intelligence or physical endowment. Hence a fighting strategy can be tested for stability by introducing perturbations in the form of animals with deviant behaviour, and determining whether selection will automatically act against such animals.20
When George did this, he discovered that antlers were the winners, and besides that they entailed some simple rules: First, an animal should avoid battle with a stronger animal. Second, it should be aggressive against a weaker animal. And third, when fighting an equal opponent, it should try an occasional “probe”—an escalation of combat meant to judge the adversary’s reaction. Most important of all, however, was the principle of “getting even.”21
It was an unbeatable strategy. An animal deficient in retaliatory behavior would in iterated encounters lose to it, but so would a third animal with a reduced tendency to deescalate when the score is even, and a fourth with a reduced tendency to probe. Most important of all, it turned on the fundamental game-theoretic rule: One’s best strategy always depended on what the other player was doing. It would be to the advantage of an animal possessing a territory, for example, having more to lose, to fight longer if a challenger is likely to quit earlier; conversely, it would be to the territory seeker’s advantage to quit earlier (and occasionally perform a probe) if the territory possessor was likely to fight to the death. Of course it was an oversimplification: Nature might hold the possibility of a lightning-quick fatal blow, or more than two categories of aggressive behavior might be in practice. Still, in a species that did not form coalitions, the basic strategy couldn’t be bested. It was the very same strategy, George explained, that characterizes human “two-person game” conflict “at all levels from kindergarten children to nations.”22
Pushed to its logical end, the limited-combat model ultimately resulted in the sublimation of all-out battle into the harmless domain of symbolic threat at a distance. For even in spe
cies that could discern two distinct levels of physical combat, such as locking antlers versus attacking the body, not fighting at all would always be safer than fighting gently. Of course, everything depended on the ability to discern the character of your opponent: An evolutionary arms race had been put in place between signals for strength (and “wildness” and “unpredictability”) and the ability to judge their honesty. Still, the greater the variation in antlers in a population of males, the greater the chance that fighting will be avoided: A glance from afar (perhaps aided by some roaring and bellowing) would suffice to exclude most of the combat.
The flip side of kin selection, he had begun to write to Hamilton before learning that he was off in the jungle, was malevolence toward nonrelatives—a less-than-encouraging thought. But combat, too, was a Janus-like construction, and its flip side was the more hopeful promise of altruism. Kin selection could account for parental care and, perhaps, when the mechanisms responsible for discriminating degree of relationship were faulty, for “good deeds” to strangers. But George found it implausible that it could account for all cases in nature.
The literature he was reading was now beginning to finally settle in his head. George C. Williams, he now discovered, had made a suggestion on the matter in his 1966 book Adaptation and Natural Selection: Animals that live in stable social groups and that are intelligent enough to form personal friendships and animosities beyond the limits of family could evolve a system of cooperative behavior. But reciprocity, George now saw, actually demanded much less: In a species where cooperative behavior is important, the logic of games would suffice to ensure cooperation. There was really no need for the ability to form friendships and hates; the trick, rather, was for non-cooperative behavior to be retaliated against.
African hunting dogs were an example: Occasionally, it had been observed, a pack member is “mobbed,” tumbled and rolled to the ground by the multitude. To George this seemed like the perfect punishment (and background threat) to ensure the remarkable cooperative behavior the dogs usually exhibit as a group. The logic was simple: Since an individual would increase in fitness both by helping others and thereby avoiding attack, and by attacking deviants enough to cause them to help him, both the tendency to cooperate and the tendency to attack those who did not cooperate would be selected for in evolution. Policing and punishment were necessary requirements for cooperation.23
It was not only an original application of game theory to animal behavior; it was a startling reflection. George had yet to figure out the evolutionary origins of the human family, fatherhood, and love, but these game-theoretic evolutionary asides were a beginning. Tidying up the rather long paper, “Antlers, Intraspecific Combat, and Altruism,” he sent it off to Nature in August 1968.
That very week he got an address from Imperial College for Hamilton’s whereabouts in Brazil and decided to send his belated reply. He’d been positively surprised to learn that the prisoner’s dilemma had an application to genetics, Thank you. Now, though, he was working on “a more transparent (though less rigorous) derivation” of the 1964 kin-selection math. When the time came would Hamilton mind checking it? His approval would obviously be valuable.24
Shortly afterward George moved into a flat on the corner of Little Titchfield Street and Great Titchfield Street, just a five-minute walk north of Oxford Circus.
The neighborhood had the feel of a Sherlock Holmes locale. There was the butcher shop just below, owned by a German Jew, and Frank’s Coffee House serving espresso across the way. Down the street on the corner of Mortimer and Great Portland was the local pub, the George, established in 1799 and still sporting its alabaster ceiling lamps, creaking wooden floors, and regulars slouched over ales and half-true yarns. Great Titchfield housed the unwealthy but comfortable—physicians, solicitors, journalists and the occasional eccentric bachelorette writer. It was a narrow and sleepy road flanked by red-and-brown four-story white-windowsill-painted Victorians, strangely providing the illusion of colluding to crowd out the sky at their crowns. Just a hundred yards to the west, Regent Street ran majestically north up to All Souls Church in Langham Place, before curling around the massive white stone BBC Broadcasting House into broad Portland Place with its Jaguars and Rolls-Royces and posh Royal Institutes of Physics and British Architects. It was a far cry from New York City’s Greenwich Village.
Tucked away behind Regent Street, the flat on Little Titchfield was a spacious three-bedroom on the second floor of a landmark four-story redbrick with an attic and black thatched roof. George would be paying the last two of a seven-year lease that had been made during a down market.25 It was a find.
Still, as peaceful as the environs were, there was a distinct but unexplained feeling he simply could not shake off. Whether walking home from Oxford Circus on the main, winding through a narrow back alley, or sipping a coffee at Frank’s, the ever-present stone spire of All Souls was watching him, forbidding and portentous, like a hawk its unsuspecting prey.
Meanwhile, sweating beneath the August sun at the Royal Society/Royal Geographical Society Expedition Base Camp in Mato Grosso, Hamilton sat down to pen his reply. George was a faceless correspondent, but Bill always tried to get back to those who wrote to him. Besides, he was one of the few who seemed excited by the notion of the genetic origins of altruism. Sure, he’d be very interested in the intended paper, but if George owned only a single copy he shouldn’t dare send it to Brazil. The post was very unreliable, but he could try a relatively safe address at their next stop in Belén. Otherwise, he and Christine and Romilda and Godofredo would be back in England toward December or January. Posting the letter, he returned to his wasps and soon forgot about George.26
Back in England, with the chilly winds of fall blowing, George hunkered down in the libraries. The idea of kin selection just wouldn’t let go of his mind. Even in the terms of his own mathematics, could Hamilton really be right: “altruistic” genes able to spread only via family? If that was true, would the opposite of altruism—malevolence and war—be the fate of the unrelated? The bleakness of it depressed him.
He began to wonder: Was relatedness really the sine qua non? What if shared genes for altruism sufficed? Clearly relatedness could be one way to share such genes, but it needn’t be the only way. In that case Hamilton’s rule would be just an instance of a wider phenomenon. This had been the essence of the question about genes recognizing themselves in other bodies that he had written to him in early March. If altruists could somehow find one another, they needn’t necessarily be related to help propagate their kind.27
He thought it through carefully. The problem was one of tracking the change in a character over time: What was the most transparent way to do this? Say there is a group of ten people with different heights, and a second group is formed, with the same number of people but a different sample of heights. To do this you are allowed to take only the heights that existed in the first group, but in a different proportion. Say the average height of the first group is 5.5 feet. How best to predict the average height of the second group? The answer was intuitively simple: The average height of the new group would be determined by the relationship between the height of each individual and the number of “copies” made of that individual in the second group, divided by the average number of copies. Scientifically speaking, that relationship was called a “covariance.” So if half of the members of the first group are 5 feet tall and half are 6 feet tall, but the new group contains many more 6 footers than 5 footers, the new population will now have an average height much closer to 6 feet. A covariance equation
captures this relationship by explaining how the number of copies made (w) of the different heights (z) determine the average height of the new group ().
This was a general-selection equation: It would hold true for everything from a child choosing radio channels to the earth preserving fossils to the culling of chemical crystals in far-off galaxies. But it could also be applied to biological traits like baldness and strength and crook
ed teeth, and, most profitably, to the evolution of social behaviors like altruism. All one needed to do was have z stand for the trait and w for its fitness (“copies” of traits simply mean their fitness), and, like a rabbit pulled out of a conjurer’s hat, the covariance equation told you how it would evolve from one generation to the next. George hadn’t done all the work yet, but already saw that his was a more abstract approach than using coefficients of kinship and could be made to work just the same: The spread of altruism could be tracked via statistical covariance of the character with fitness rather than calculations of the pathways of relatedness. Hamilton’s rB > C notwithstanding, altruism depended on association, not family.28
The reason was immediately clear to George: Natural selection is indifferent to why individuals end up together in groups; whether it’s due to common descent, or similarity in traits, or any other pretext doesn’t matter. On the other hand, since covariance could be made to treat relatedness as a statistical association rather than a measure of common ancestry, relatedness could actually be negative. What this meant mathematically was that while under conditions of a particular association altruism could evolve, under the conditions of another association spite could evolve: Everything depended on the environment. Spitefulness wasn’t just the selfish harming of others to help oneself; it was doing harm to oneself in order to harm one’s enemy even more. Explaining its evolution was therefore a similar problem to explaining the evolution of altruism: Both behaviors reduced fitness but existed nonetheless. It was a possibility Hamilton had entirely overlooked.