Kin selection

Suppose that a rare gene for altruism is present in an individual. Let r denote likelihood that it is also in another individual, given as a probability between 0 and 1. This can be deduced from Mendel’s rules. If the new mutation is in a parent, there is a 1/2 chance it will be in its offspring; and there is likewise a 1/2 chance that a gene in an individual is also in its brother or sister. Provided that

• the recipient is an altruist, and that

• the recipient's benefit exceeds the altruist’s cost,

then there is a net increase in the average fitness of the altruistic types as a whole. These two provisos are embedded in Hamilton's rule, named after W.D. Hamilton, who mainly invented the theory of kin selection. It states that an individual is selected to behave altruistically provided that

rb > c

The altruist still pays a cost of c for performing the act; the recipient receives a benefit b . However, the chance that the altruistic gene is in the recipient is r . When rb exceeds c there will be a net increase in the average fitness of the altruists. The number of copies of the gene for altruism will increase because the loss of copies from the excess death of the individuals who actually perform acts of altruism is more than made up for by the excess survival of the individuals who receive it (and contain the gene for altruism). This is the theory of kin selection.