A theory of natural selection incorporating interaction among individuals. II. Use of related groups

The present series of studies attempts to accommodate interaction among individuals in evolutionary theory. The interaction phenomenon is characterized by two dimensions (direct and associate) of gene activity. For optimal selection results, a balance between the two dimensions must occur. In the first paper of the series, it was shown that random interactions resulted in an unbalanced selection response. The expression for gene frequency change involved direct, but not associate, effects. The next three papers of the series (II, III and IV) are designed to explore the possibility that restricting interactions to certain non-random patterns may ameliorate the problem of selection balance.In the present study the interactions are restricted to related individuals in a population that is in Hardy-Weinberg equilibrium. A preliminary analysis in which interactions are restricted to full-sibs is made. This analysis is extended to the more general case in which interactions occur among related individuals of any class whose coefficient of relationship is measured by ‘r’. The classical pairwise interaction results of Hamilton are verified and extended to include interactions among individuals in groups of arbitrary size, n.Restricting interactions to related individuals tends to improve the condition of selection balance. It does this by introducing associate effects into the expression for gene frequency change. The extent to which this is accomplished is a function of the coefficient of relationship (r), and the number of interacting genotypes.