in the 1960s (Hamilton, 1964a,b). Taking a gene’s-eye view, Hamilton reasoned that a gene could spread in future generations not only by contributing to the production of offspring, but also by aiding reproduction of other relatives who might share the gene. Genetic relatedness specifies the comparative values of different kin. Hamilton’s rule predicts what behaviors will be favored by selection. A particularly useful form of Hamilton’s rule, for behaviors that exert a fitness cost, c, on some relatives and give a fitness benefit, b, to others, is rbb > rcc. The two fitness effects are scaled by the relatedness of the actor to those benefited, rb, and to those harmed, rc. Crucially, individuals can be selected to give up their own offspring (rc = 1/2) to help other relatives, provided the benefit b is sufficiently higher than the cost c. Genetic relatedness among individuals is essential, for without it no value of b, the benefit to cooperation, will favor giving up reproducing oneself.
Hamilton (1964b) also noticed a special feature of social ants, bees, and wasps: they share a haplodiploid sex determination mechanism in which haploid males arise from unfertilized eggs and diploid females arise from normal fertilized eggs (Normark, 2003). This is an ancestral trait in Hymenoptera that arose long before sociality (Hamilton, 1967), but it affects relatednesses in ways that could favor sociality. What makes it significant for sociality is that sisters are related by 3/4 because they share all their genes from their haploid father. Other things being equal, a sister would therefore pass on more genes by rearing sisters (r = 3/4) than by rearing her own progeny (r = 1/2), favoring daughters who remain with their mothers to rear additional sisters. Hamilton noted that this observation could potentially explain at a stroke at least two salient feature of social insects (Hamilton, 1964b). First, there have been many origins of sociality in the haplodiploid Hymenoptera and few elsewhere, termites being the most notable exception. Second, only females work in the Hymenoptera, whereas both sexes work in diploid termites.
However, this haplodiploid hypothesis is debatable, for a variety of reasons (Alexander et al., 1991; Queller and Strassmann, 1998). First, most haplodiploids have not evolved sociality, whereas a few diploids have. Another issue is that relatedness is elevated only to full sisters and is lowered to brothers (r = 1/4) (Crozier, 1970). Thus, if a female helps to rear an equal mixture of sisters and brothers, the average relatedness (1/2) is exactly the same as to her own offspring and exactly the same as full siblings in diploids. Haplodiploidy can still help if workers can concentrate on rearing sisters (Hamilton, 1972), but the advantage is transitory and disappears at sex ratio equilibrium (Crozier and Pamilo, 1996).