Individual and group selection with competition.

The response of a randomly mating population which is expected to follow selection of phenotypic units, comprising individuals or groups whose members have an arbitrary degree of relatedness, was formulated using a model which included additive and dominance competition effects. The derivation involved three steps. Twenty-two quadratic components were defined, six describing individual (direct) and neighbor (associate) effects, and 16 describing direct by associate interactions for different loci, for single loci with different alleles, and for identical alleles. Six covariances between pairs of individual phenotypes and three of individuals with their offspring were defined according to whether or not their direct or associate genotypes are common, and expressed in terms of the quadratic components. Finally, variances of selection units of different types and their covariance with their offspring were expressed as compounds of these individual covariances. Explicit formulations for mass, clonal and full-sib selection show that without constraints on the quadratic components, and hence on the magnitude and type of competition operative, no predictions as to the relative efficiencies of these three methods can be made.