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Hamilton's Rule is a mathematical formula used to describe the conditions where altruistic behavior is likely to occur in a population and when it can be expected to evolve.

Versions of the Formula[]


r:  relatedness. The proportion of alleles shared between the altruist and the recipient. (Parents share roughly 50% of an organism's alleles, siblings share roughly 50% of an organism's alleles, first cousins share roughly 12.5% of an organism's alleles.)

B:  Benefit to the recipient. The additional number of offspring produced by the recipient as a result of the altruist's behavior.

C:  Cost to the altruist. The number of offspring the altruist was unable to produce as a result of the altruistic behavior.


r B > C          or          r B - C >0



Hardwick, S. (2012). Hamilton’s Rule and the Evolution of Altruism. Retrieved from http://www.youtube.com/watch?v=unUG0BPMaIw .

Gardner, A., West, S.A. & Wild, G. (2011) The genetical theory of kin selection. Journal of Evolutionary Biology, 1020-1043.