Kin Selection - Hamilton's Rule

Hamilton's Rule

Formally, such genes should increase in frequency when

where

r = the genetic relatedness of the recipient to the actor, often defined as the probability that a gene picked randomly from each at the same locus is identical by descent.

B = the additional reproductive benefit gained by the recipient of the altruistic act,

C = the reproductive cost to the individual of performing the act.

This inequality is known as Hamilton's rule after W. D. Hamilton who published, in 1964, the first formal quantitative treatment of kin selection to deal with the evolution of apparently altruistic acts.

Originally, the definition for relatedness (r) in Hamilton's rule was explicitly given as Sewall Wright's coefficient of relationship: the probability that at a random locus, the alleles there will be identical by descent (Hamilton 1963, American Naturalist, p. 355). Subsequent authors, including Hamilton, sometimes reformulate this with a regression, which, unlike probabilities, can be negative. Regression analysis producing statistically significant negative relationships indicates that two individuals can be less genetically alike than two random ones on average (Hamilton 1970, Nature & Grafen 1985 Oxford Surveys in Evolutionary Biology). This has been invoked to explain the evolution of spiteful behaviours. Spiteful behavior defines an act (or acts) that results in harm, or loss of fitness, to both the actor and the recipient.

In the 1930s J.B.S. Haldane had full grasp of the basic quantities and considerations that play a role in kin selection. He famously said that, "I would lay down my life for two brothers or eight cousins". Kin altruism is the term for altruistic behaviour whose evolution is supposed to have been driven by kin selection.

Haldane's remark alluded to the fact that if an individual loses its life to save two siblings, four nephews, or eight cousins, it is a "fair deal" in evolutionary terms, as siblings are on average 50% identical by descent, nephews 25%, and cousins 12.5% (in a diploid population that is randomly mating and previously outbred). But Haldane also joked that he would truly die only to save more than a single identical twin of his or more than two full siblings.

In 2011, experimentalists found empirically that Hamilton's rule describes very accurately the conditions under which altruism emerged in simulated populations of foraging robots. The accuracy of this first quantitative corroboration of Hamilton's rule is all the more impressive given that Hamilton's model made several simplifications that did not apply to the foraging robots.