Does Hamilton's rule describe the evolution of reciprocal altruism?

Abstract

On intuitive grounds, many have felt that Hamilton's Rule, br greater than c, should describe the evolution of reciprocal altruism and "green beard" genes. However, difficulties have been encountered in applying the rule to situations in which the benefits an individual receives are a function of his own phenotype as well as that of his partner. These difficulties are resolved by recognising that there are two important coefficients of genetic relatedness: r1 is the coefficient already familiar to sociobiologists from the applications of Hamilton's Rule to kin selection; r2 is the coefficient of genetic relatedness between individuals who express the same phenotype. It is shown that the r in Hamilton's Rule is a weighted average of these two coefficients. The weights, along with r1 and r2, are intuitively meaningful. A remarkable fact is that r2 = 1, regardless of how genotype determines phenotype.