Frank, S. A. 1997. Multivariate analysis of correlated selection and kin selection, with an ess maximization method. Journal of Theoretical Biology 189:307-316.
Kin selection coefficients are used in two distinct ways. First, these coefficients measure phenotypic correlations that affect the marginal costs and benefits of behaviors. For example, the phenotypic correlation in sex ratio produced by two females in an isolated patch influences the favored sex ratio. Second, kin selection coefficients describe genotypic correlations that measure fidelity of transmission. For example, a female values daughters versus nieces according to genotypic correlations.
It is widely known that kin selection coefficients may be interpreted as phenotypic or genotypic correlations in different contexts. However, these different interpretations have never been fully separated, and their different roles have not been clearly explained.
I provide proofs of a generic analytical approach. The technique automatically separates phenotypic correlations among social partners from genotypic components of transmission. The result is a general method that can be derived from first principles and applied to multivariate problems in social evolution. I emphasize a simple, practical maximization method that can be used to calculate equilibrium conditions for complex social interactions.