Hamilton's rule and conditionality

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Abstract
Hamilton's rule is that an altruistic act shoud be performed when r times the benefit to a recipient is greater than the cost to the donor, where r is a measure of the extent of genetic similarity at the locus determining the action. This rule applies when the action is conditional upon role. Roles X and Y are defined in terms of an asymmetry between the pair of interacting relatives; e.g. X and Y may be older/ younger, stronger/weaker, etc. To obey Hamilton's rule, roles must be assigned randomly with respect to the genotype of the pair of relatives, and a gene must be expressed in one role only; i.e. its expression must be conditional upon role. If gene action is unconditional so that a gene is expressed in both roles, the rule (at least in its simplest form) may not apply. Simple models of conditional and unconditional gene action are compared for the case of dyadic interactions between full sibs in sexually reproducing diploids. In many cases it will be desirable to determine the optimal behaviour to be shown in each of the two phenotypic roles, X and Y. The obvious way to model this is to assume conditionality (one locus determines what to do in X and another determines what to do in Y). However, an unconditional version is possible in which one locus controls the general magnitude of the action and another controls the relative probability of action in the two roles. These two quite different genetic mechanisms can yield the same pair of optima, but only if special conditions are satisfied for the unconditional version.

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