  Though this argument was hinted at by Haldane in the 1930s, and to a lesser extent by Darwin in his discussion of sterile insect castes in  The Origin of Species, it was first made explicit by William Hamilton (1964) in a pair of seminal papers. Hamilton demonstrated rigorously that an altruistic gene will be favoured by natural selection when a certain condition, known as Hamilton's rule, is satisfied. In its simplest version, the rule states that b &gt; c/r, where c is the cost incurred by the altruist (the donor), b is the benefit received by the recipients of the altruism, and r is the co-efficient of relationship between donor and recipient. The costs and benefits are measured in terms of reproductive fitness. The co-efficient of relationship depends on the genealogical relation between donor and recipient—it is defined as the probability that donor and recipient share genes at a given locus that are ‘identical by descent’. (Two genes are identical by descent if they are copies of a single gene in a shared ancestor.) In a sexually reproducing diploid species, the value of r for full siblings is ½, for parents and offspring ½, for grandparents and grandoffspring ¼, for full cousins 1/8,  and so-on. The higher the value of r, the greater the probability that the recipient of the altruistic behaviour will also possess the gene for altruism. So what Hamilton's rule tells us is that a gene for altruism can spread by natural selection, so long as the cost incurred by the altruist is offset by a sufficient amount of benefit to sufficiently closed related relatives. The proof of Hamilton's rule relies on certain non-trivial assumptions; see Frank 1998, Grafen 1985, 2006, Queller 1992a, 1992b, Boyd and McIlreath 2006 and Birch forthcoming for details.