Abstract.Recent attempts to apply selective breeding strategies in fish populations have focused on the genetic effects of selection. The basic mechanisms of long‐term response to selection are discussed with reference to experience from laboratory and farm animal populations. A simplified polygenic model is presented, and it is shown that considerable response may be obtained for polygenic traits without essential changes in allele frequencies and genetic variability, and that the probability of fixation of alleles or genotypes because of selection will be low when the trait is affected by a larger number of loci. The span between the extreme fixed genotypes for such traits may easily become wider than that which may be realized under normal biological conditions. This is illustrated with some examples from Atlantic salmon.Salmo salarL. The effects of divergent fitness selection of populations on genetic differentiation and allele frequencies are also considered, and some examples from experiments with Norwegian river strains of Atlantic salmon are discussed. It is shown that the river strains are not expected to differ much in frequencies of fitness alleles if the number of loci affecting the fitness trait is large, and that considerable overlapping of genetic values for fitness between strains may be expecte