W. D. Hamilton
Hamilton's rule

Hamilton enrolled in an MSc course in demography at the London School of Economics (LSE), under Norman Carrier, who helped secure grants for his studies. Later, when his work became more mathematical and genetical, he had his supervision transferred to John Hajnal of the LSE and Cedric Smith of University College London (UCL).

Both Fisher and J. B. S. Haldane had seen a problem in how organisms could increase the fitness of their own genes by aiding their close relatives, but not recognised its significance or properly formulated it. Hamilton worked through several examples, and eventually realised that the number that kept falling out of his calculations was Sewall Wright 's coefficient of relationship. This became Hamilton's rule: in each behaviour-evoking situation, the individual assesses his neighbour's fitness against his own according to the coefficients of relationship appropriate to the situation. Algebraically, the rule posits that a costly action should be performed if:

where C is the cost in fitness to the actor, r the genetic relatedness between the actor and the recipient, and B is the fitness benefit to the recipient. Fitness costs and benefits are measured in fecundity. r is a number between 0 and 1. His two 1964 papers entitled The Genetical Evolution of Social Behaviour are now widely referenced.

The proof and discussion of its consequences, however, involved detailed mathematics, and two reviewers passed over the paper. The third, John Maynard Smith, did not completely understand it either, but recognised its significance. Having his work passed over later led to friction between Hamilton and Maynard Smith, as Hamilton thought Maynard Smith had held his work back to claim credit for the idea (during the review period Maynard Smith published a paper that referred briefly to similar ideas). The Hamilton paper was printed in the Journal of Theoretical Biology and, when first published, was largely ignored. Recognition of its significance gradually increased to the point that it is now routinely cited in biology books.

Much of the discussion relates to the evolution of eusociality in insects of the order Hymenoptera (ants, bees and wasps) based on their unusual haplodiploid sex-determination system. This system means that females are more closely related to their sisters than to their own (potential) offspring. Thus, Hamilton reasoned, a "costly action" would be better spent in helping to raise their sisters, rather than reproducing themselves.

The supergenes notion (sometimes called the Green-beard effect) - that organisms may evolve genes that are able to identify identical copies in others and preferentially direct social behaviours towards them - was theoretically clarified and withdrawn by Hamilton in 1987.
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