Hamilton's missing link

Hamilton's famous rule was presented in 1964 in a paper called “The genetical theory of social behaviour (I and II)”, Journal of Theoretical Biology 7, 1–16, 17–32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper's central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton's rule does follow from his central result.