W.D. Hamilton

The genetic evolution of social behavior: bibliographical excerpts

"In brief outline, the theory points out that for a gene to receive positive selection it is not necessarily enough that it should increase the fitness of its bearer above the average if this tends to be done at the heavy expense of related individuals, because relatives, on account of their common ancestry, tend to carry replicas of the same gene: and conversely that a gene may receive positive selection even though disadvantageous to its bearers if it causes them to confer sufficiently large advantages on relatives. Relationships alone never gives grounds for certainty that a person carries a gene which a relative is known to carry except when the relationship is "clonal" or "mitotic" (e.g. the two are monozygotic twins) --- and even then, strictly, the possibility of an intervening mutation should be admitted. In general, it has been shown that Wright's Coefficient of Relationship r approximates closely to the chance that a replica will be carried. Thus it an altruistic trait is in question more than 1/r units of reproductive potential or "fitness" must be endowed on a relative or degree r for every one unit lost by the altruist if the population is to gain on average more replicas than it loses. Similarly, if a selfish trait is in question, the individual must receive and use at least a fraction r of the quantity of "fitness" deprived form his relative if the causative gene is to be selected." (Hamilton, W. D. (1964) The genetic evolution of social behavior. J Theoretical Biology 7: pp. 17-18)

"The social behavior of a species evolves in such a way that in each distinct behavior-evoking situation the individual will seem to value his neighbors' fitness against his own according to the coefficients of relationship appropriate to that situation." (Hamilton, W. D. (1964) The genetic evolution of social behavior. J Theoretical Biology 7: pp. 18)

"This means [see equation] that for a hereditary tendency to perform an action of this kind to evolve the benefit to a sib must average at least twice the loss to the individual, the benefit to a half-sib must be at least four times the loss, to a cousin eight times and so on. To express the matter more vividly, in the world of our model organisms, whose behavior is determined strictly by genotype, we expect to find that no one is prepared to sacrifice his life for any single person but that everyone will sacrifice it when he can thereby save more than two brothers, or four half-brothers, or eight first cousins...." (Hamilton, W. D. (1964) The genetic evolution of social behavior. J Theoretical Biology 7: pp. 16)