The causal meaning of Hamilton's rule

Hamilton's original derivation of his rule for the spread of an altruistic gene (rb>c) assumed additivity of costs and benefits. Recently, it has been argued that an exact version of the rule holds under non-additive pay-offs, so long as the cost and benefit terms are suitably defined, as partial regression coefficients. However, critics have questioned both the biological significance and the causal meaning of the resulting rule. This paper examines the causal meaning of the generalized Hamilton's rule in a simple model, by computing the effect of a hypothetical experiment to assess the cost of a social action and comparing it to the partial regression definition. The two do not agree. A possible way of salvaging the causal meaning of Hamilton's rule is explored, by appeal to R. A. Fisher's 'average effect of a gene substitution'.