Kin selection is the theory put forward by the biologist W.D. Hamilton to explain the problem of altruism. The theory is as follows:
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 Mendelian 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.
• 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. The theory of kin selection 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).
The high levels of altruistic behavior found in the social insects like these ants opposite conforms to the theory of kin selection because they are genetically much closer related than most species.