On the evolution of altruism by kin selection.

A general model for the evolution of altruism is formulated. Central to the model is a pair of local fitness functions, which prescribe the fitness of the altruist and selfish phenotypes as functions of the composition of local groups into which prereproductives are subdivided. When the local groups are sibships or other kin groups, the model is one for kin selection. Functions for cost and benefit of altruism are derived from the fitness functions. Conditions for evolution of altruism are then determined in terms of cost and benefit. It is shown that the Hamilton rule has quantitative validity only in the special case of linear fitness functions. Sufficient conditions are found for qualitative validity of the Hamilton rule. Qualitative violation of the rule is also possible.