Population genetic theory of kin selection: Multiple alleles at one locus.

Exact population genetic models of one-locus sib-to-sib kin selection with an arbitrary number of alleles are studied. First, a natural additive scaling is established for the genotypic value associated with probabilities of performance of altruism. Two classes of polymorphic equilibria are possible, one corresponding to the usual one-locus viability equilibria and the other reflecting the kin-selection assumptions of the model. At both, the covariance between additive genotypic value and genotypic fitness vanish. Further, the sign of this covariance determines the fate of rare alleles introduced near the first class of equilibria. In addition, the covariance explains the differences between Hamilton's rule, which results from Hardy-Weinberg assumptions, and exact initial increase conditions.