Inclusive Fitness - Hamilton's Rule

Hamilton's Rule

In the context of sociobiology, which holds that some behavior can be influenced by genes and therefore can evolve by natural selection, Hamilton proposed that inclusive fitness offers a mechanism for the evolution of altruism. He claimed that this leads natural selection to favor organisms that would behave in ways that maximize their inclusive fitness.

Hamilton's rule describes mathematically whether or not a gene for altruistic behavior will spread in a population:

where

• is the probability, above the population average, of the individuals sharing an altruistic gene – commonly viewed as "degree of relatedness".
• is the reproductive benefit to the recipient of the altruistic behavior, and
• is the reproductive cost to the altruist,

In a recent paper, Gardner et al. suggest that Hamilton's rule can be applied to multi-locus models, but that it should be done at the point of interpreting theory, rather than the starting point of enquiry. They suggest that one should “use standard population genetics, game theory, or other methodologies to derive a condition for when the social trait of interest is favored by selection and then use Hamilton’s rule as an aid for conceptualizing this result". A recent paper by Nowak et al. suggested that standard natural selection theory is superior to inclusive fitness theory, stating that the interactions between cost and benefit can not be explained only in terms of relatedness. This, Nowak said, makes Hamilton's rule at worst superfluous and at best ad hoc. Gardner in turn was critical of the paper, describing it as "a really terrible article", and along with other co-authors has written a reply, submitted to Nature. In work prior to Nowak various authors derived different versions of a formula for r, all designed to preserve Hamilton's rule. Orlove noted that if a formula for r is defined so as to ensure that Hamilton's Rule is preserved then the approach is by definition ad hoc. However, he published an unrelated derivation of the same formula for – a derivation designed to preserve two statements about the rate of selection – which on its own was similarly ad hoc. Orlove argued that the existence of two unrelated derivations of the formula for reduces or eliminates the ad hoc nature of the formula, and of inclusive fitness theory as well. The derivations were demonstrated to be unrelated by the fact that corresponding parts of the two identical formulae for are derived from the genotypes of different individuals. The parts that were derived from the genotypes of different individuals were terms to the right of the minus sign in the covariances in the two versions of the formula for . By contrast, the terms left of the minus sign in both derivations come from the same source.