This all changed in the hands of a lonely London student, called Bill Hamilton, who dedicated himself to the first formal evolutionary analysis of altruism. His results are summarized with the following simple rule: altruistic behaviors will be favored by natural selection when rb > c 
where b is the reproductive benefit to the recipient, c is the cost in terms of lifetime reproduction for the actor, and r is the genetic relatedness between actor and recipient (Figure 3 a). For example, selection can favor helping a sister (r = 0.5) to raise her offspring when one can raise more than twice as many of her offspring (indirect fitness), than one's own (direct fitness), because this will increase the overall propagation of copies of the actor's genes. The sum of fitness effects through indirect effects and direct effects is the 'inclusive fitness effect' of a behavior (see Kin Selection).
Hamilton's definition of altruism requires the action to carry a cost to lifetime reproduction; a position solidified by E. O. Wilson who used this altruism as a center piece for his highly influential book Sociobiology. Hamilton's work also emphasizes the clarity that can come with gene-level thinking, which was later popularized by Dawkin's The Selfish Gene.
The social insects are among the best and most discussed examples of Hamilton's altruism in behavioral ecology (Figure 2d). Not only are they social, they are eusocial, with their division of work and reproduction among colony members. Comparable altruism occurs in other insects including some gall-forming aphids and thrips, which have a defensive soldier caste (Figure 2c). In social vertebrates, sibling care is common that is no doubt often formally altruistic (Figure 2a). However, individuals can
Figure 3 Four nonmutually exclusive processes that generate altruism or altruism-like behaviors. Altruists are smiling and same-color individuals are genetically related. (a) Strong altruism can be selected when individuals are genetically related (left-hand side) but not when they are unrelated (right-hand side). (b) Weak altruism (gray, left-hand side) can be selected when helping the group feeds back on the actor, even though this increases the fitness of other group members more (white, left-hand side), because it increases reproduction relative to the population as a whole (right-hand side). (c) Reciprocal altruism can increase personal reproduction. (d) Enforcement: one individual forces altruism-like behavior from another individual that may or may not obtain a fitness benefit from their action. Note that the behaviors in (b) and (c) increase the personal reproduction of the actor, and are therefore not altruism in the original strict sense of Hamilton, which required a decrease in the personal reproductive fitness of the actor. Also, actions that arise purely through enforcement (d) are better viewed as adaptations of the enforcer, rather than altruistic adaptations of the helping individual.
(a) Inclusive fitness + group selection High relatedness
(b) Group selection
(c) Reciprocal altruism
©©y usually reproduce later on, making it difficult to distinguish between true altruism, and behaviors with a delayed reproductive benefit. An interesting potential exception, however, is human menopause, which appears to reduce personal reproduction in order to help raise grand-offspring and under some definitions would constitute altruism. Altruism is also found in microbes (Figure 2b). For example, individual cells often pay a growth cost to release a shared product, like digestive enzymes, which benefit other cells. There are good data to support the idea that relatedness drives altruism in the social insects (Figure 4) and vertebrates (see Kin Selection), and the altruistic release of shared products in microbes has been shown to require genetic related-ness among cells.
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