In humans, IOUs and money are devices that permit delays in the transactions. The parties to the trade don't hand over the goods simultaneously but can hold a debt over to the future, or even trade the debt on to others. As far as I know, no non-human animals in the wild have any direct equivalent of money. But memory of individual identity plays the same role more informally. Vampire bats learn which other individuals of their social group can be relied upon to pay their debts (in regurgitated blood) and which individuals cheat. Natural selection favours genes that predispose individuals, in relationships of asymmetric need and opportunity, to give when they can, and to solicit giving when they can't. It also favours tendencies to remember obligations, bear grudges, police exchange relationships and punish cheats who take, but don't give when their turn comes.

For there will always be cheats, and stable solutions to the game-theoretic conundrums of reciprocal altruism always involve an element of punishment of cheats. Mathematical theory allows two broad classes of stable solution to 'games' of this kind. 'Always be nasty' is stable in that, if everybody else is doing it, a single nice individual cannot do better. But there is another strategy which is also stable. ('Stable' means that, once it exceeds a critical frequency in the population, no alternative does better.) This is the strategy, 'Start out being nice, and give others the benefit of the doubt. Then repay good deeds with good, but avenge bad deeds.' In game theory language, this strategy (or family of related strategies) goes under various names, including Tit-for-Tat, Retaliator and Reciprocator. It is evolutionarily stable under some conditions in the sense that, given a population dominated by reciprocators, no single nasty individual, and no single unconditionally nice individual, will do better. There are other, more complicated variants of Tit-for-Tat which can in some circumstances do better.

I have mentioned kinship and reciprocation as the twin pillars of altruism in a Darwinian world, but there are secondary structures which rest atop those main pillars. Especially in human society, with language and gossip, reputation is important. One individual may have a reputation for kindness and generosity. Another individual may have a reputation for unreliability, for cheating and reneging on deals. Another may have a reputation for generosity when trust has been built up, but for ruthless punishment of cheating. The unadorned theory of reciprocal altruism expects animals of any species to base their behaviour upon unconscious responsiveness to such traits in their fellows. In human societies we add the power of language to spread reputations, usually in the form of gossip. You don't need to have suffered personally from Xs failure to buy his round at the pub. You hear 'on the grapevine' that X is a tightwad, or — to add an ironic complication to the example — that Y is a terrible gossip. Reputation is important, and biologists can acknowledge a Darwinian survival value in not just being a good reciprocator but fostering a reputation as a good reciprocator too. Matt Ridley's The Origins of Virtue, as well as being a lucid account of the whole field of Darwinian morality, is especially good on reputation.*)

The Norwegian economist Thorstein Veblen and, in a rather different way, the Israeli zoologist Amotz Zahavi have added a further fascinating idea. Altruistic giving may be an advertisement of dominance or superiority. Anthropologists know it as the Potlatch Effect, named after the custom whereby rival chieftains of Pacific north-west tribes vie with each other in duels of ruinously generous feasts. In extreme cases, bouts of retaliatory entertaining continue until one side is reduced to penury, leaving the winner not much better off. Veblen's concept of 'conspicuous consumption' strikes a chord with many observers of the modern scene. Zahavi's contribution, unregarded by biologists for many years until vindicated by brilliant mathematical models from the theorist Alan Grafen, has been to provide an evolutionary version of the potlatch idea. Zahavi studies Arabian babblers, little brown birds who live in social groups and breed co-operatively. Like many small birds, babblers give warning cries, and they also donate food to each other. A standard Darwinian investigation of such altruistic acts would look, first, for reciprocation and kinship relationships among the birds. When a babbler feeds a companion, is it in the expectation of being fed at a later date? Or is the recipient of the favour a close genetic relative? Zahavi's interpretation is radically unexpected. Dominant babblers assert their dominance by feeding subordinates. To use the sort of anthropomorphic language Zahavi delights in, the dominant bird is saying the equivalent of, 'Look how superior I am to you, I can afford to give you food.' Or 'Look how superior I am, I can afford to make myself vulnerable to hawks by sitting on a high branch, acting as a sentinel to warn the rest of the flock feeding on the ground.' The observations of Zahavi and his colleagues suggest that babblers actively compete for the dangerous role of sentinel. And when a subordinate babbler attempts to offer food to a dominant individual, the apparent generosity is violently rebuffed. The essence of Zahavi's idea is that advertisements of superiority are authenticated by their cost. Only a genuinely superior individual can afford to advertise the fact by means of a costly gift. Individuals buy success, for example in attracting mates, through costly demonstrations of superiority, including ostentatious generosity and public-spirited risk-taking.

We now have four good Darwinian reasons for individuals to be altruistic, generous or 'moral' towards each other. First, there is the special case of genetic kinship. Second, there is reciprocation: the repayment of favours given, and the giving of favours in 'anticipation' of payback. Following on from this there is, third, the Darwinian benefit of acquiring a reputation for generosity and kindness. And fourth, if Zahavi is right, there is the particular additional benefit of conspicuous generosity as a way of buying unfakeably authentic advertising.

Through most of our prehistory, humans lived under conditions that would have strongly favoured the evolution of all four kinds of altruism. We lived in villages, or earlier in discrete roving bands like baboons, partially isolated from neighbouring bands or villages. Most of your fellow band members would have been kin, more closely related to you than members of other bands — plenty of opportunities for kin altruism to evolve. And, whether kin or not, you would tend to meet the same individuals again and again throughout your life — ideal conditions for the evolution of reciprocal altruism. Those are also the ideal conditions for building a reputation for altruism, and the very same ideal conditions for advertising conspicuous generosity. By any or all of the four routes, genetic tendencies towards altruism would have been favoured in early humans. It is easy to see why our prehistoric ancestors would have been good to their own in-group but bad — to the point of xenophobia — towards other groups. But why — now that most of us live in big cities where we are no longer surrounded by kin, and where every day we meet individuals whom we are never going to meet again — why are we still so good to each other, even sometimes to others who might be thought to belong to an out-group?

It is important not to mis-state the reach of natural selection. Selection does not favour the evolution of a cognitive awareness of what is good for your genes. That awareness had to wait for the twentieth century to reach a cognitive level, and even now full understanding is confined to a minority of scientific specialists. What natural selection favours is rules of thumb, which work in practice to promote the genes that built them. Rules of thumb, by their nature, sometimes misfire. In a bird's brain, the rule 'Look after small squawking things in your nest, and drop food into their red gapes' typically has the effect of preserving the genes that built the rule, because the squawking, gaping objects in an adult bird's nest are normally its own offspring. The rule misfires if another baby bird somehow gets into the nest, a circumstance that is positively engineered by cuckoos. Could it be that our Good Samaritan urges are misfirings, analogous to the misfiring of a reed warbler's parental instincts when it works itself to the bone for a young cuckoo? An even closer analogy is the human urge to adopt a child. I must rush to add that 'misfiring' is intended only in a strictly Darwinian sense. It carries no suggestion of the pejorative.