Kinship and covariance

Price's (1970) covariance theorem can be used to derive an expression for gene frequency change in kin selection models in which the fitness effect of an act is independent of the genotype of the recipient. This expression defines a coefficient of relatedness which subsumes r(Wright, 1922), b(Hamilton, 1972), ρ (Orlove &; Wood, 1978), and R(Michod &; Hamilton, 1980). The new coefficient extends the domain of Hamilton's rule to models in which the average gene frequency of actors differs from that of recipients.