Hamilton’s rule

Hamilton’s rule, in ecology and sociobiology, mathematical formula devised by British naturalist and population geneticist W.D. Hamilton that supports the notion that natural selection favours genetic success, not reproductive success per se. It recognizes that individuals can pass copies of their genes on to future generations through direct parentage (the rearing of offspring and grand-offspring) as well as indirectly by assisting the reproduction of close relatives (such as nieces and nephews) through altruistic behaviour (behaviour that benefits other individuals at the expense of the one performing the action).

Hamilton’s rule underlies the theory of inclusive fitness (in which an organism’s genetic success is believed to be derived from cooperation and altruistic behaviour. Inclusive fitness suggests that altruism occurring among organisms who share a given percentage of genes enables those genes to be passed on to subsequent generations. Inclusive fitness applying only to relatives is called kin selection.

Hamilton’s rule (r × B > ℂ) specifies the conditions under which reproductive altruism evolves. B is the benefit (in number of offspring equivalents) gained by the recipient of the altruism, ℂ is the cost (in number of offspring equivalents) suffered by the donor while undertaking the altruistic behaviour, and r is the genetic relatedness of the altruist to the beneficiary. Relatedness is the probability that a gene in the potential altruist is shared by the potential recipient of the altruistic behaviour.

Altruism can evolve in a population if a potential donor of assistance can more than make up for losing ℂ offspring by adding to the population B offspring bearing a fraction r of its genes. For example, a female lion with a well-nourished cub gains inclusive fitness by nursing a starving cub of a full sister because the benefit to her sister (B = one offspring that would otherwise die) more than compensates for the loss to herself (ℂ = approximately one quarter of an offspring), since the survival probability of her own non-starving cub is only slightly reduced. Given that the average genetic relatedness (that is, r) between two full sisters is 0.5, then according to Hamilton’s rule (0.5 × 1) > 0.25. In essence, the genes for altruism spread by promoting aid to copies of themselves.