The Evolution of Altruism between Siblings

Hamilton's rule states that natural selection will cause an individual to value a sibling half as much as itself (50% altruism). The rule is normally justified on the grounds that siblings share half of their rare genes in common or that half of their genes are identical by descent. Neither of these arguments withstands close examination. This paper provides a more satisfactory justification for Hamilton's rule. Using a simple model of competition between altruistic alleles, it demonstrates mathematically how, under certain conditions, natural selection will lead to the 50% altruism between siblings predicted by this rule. Computer simulations are then used to explore what happens under more general conditions. In every case, the direction of evolution is towards 50% altruism. However, the pace of convergence is sometimes very slow, which suggests that in practice Hamilton's rule will be only a very rough approximation. These results are established without reference to the proportion of genes by descent or of rare genes that siblings share in common. The paper concludes by considering briefly some of the factors that might prevent the eventual victory of 50% altruism and allow alleles for more selfish and less selfish forms of behavior to coexist permanently.