Kin selection: A classical approach and a general solution.

The necessary conditions for the spread of genes that determine social behaviors and the rate of spread of these genes are derived for a simple model (single locus, two alleles, random mating, discrete generations) by using the classical population genetics approach pioneered by Haldane and the linear fitness function used previously by D. S. Wilson. These results are derived for social behaviors that are manifested by individuals within families, within pairs of families, or within groups of k families, for both diploid and haplodiploid organisms. I show that, when the groups of socially interacting individuals consist of the members of more than one family, severe restrictions are placed on the evolution of altruistic and social behaviors. Specifically, in these instances, the necessary conditions for the evolution of social behaviors are more stringent and the rate of evolution is greatly reduced.