Frank, S. A. 1986. Hierarchical selection theory and sex ratios. I. General solutions for structured populations. Theoretical Population Biology 29:312-342.
Models of sex-ratio evolution in structured populations are derived with G. R. Price's covariance form for the hierarchical analysis of natural selection (1970, Nature 227, 520-521). Previous work on competition among related males for mates (local mate competition), competition among related females for a limiting resource (local resource competition), inbreeding, group selection, and asymmetry of genetic inheritance between males and females, are subsumed under a general formulation for sex-ratio biases in structured populations. I found that the evolutionarily stable strategy sex ratio (males:females) for diploids is 1 - Pm : 1 + Pf, where Pm is the regression coefficient of relatedness of the controlling genotypes on males competing for mates, Pf is the regression of controlling genotypes on females that compete for a fixed, limiting resource, and there is no inbreeding. For inbreeding and no competition among females, the evolutionarily stable strategy is 1 - Pm : 1 + Pmf, where Pmf is the regression of controlling genotypes on females' mates.