A simple mathematical model of genic directional selection is developed to study frequency changes of genetic marker alleles that are partially linked to a quantitative trait locus (QTL) under artificial selection. The effects of population size, number of generations of artificial selection, recombination between marker locus and QTL, and the strength of selection on the change in allele frequency are analysed by the diffusion equation approach and by stimulation. Using these results, we investigate the power of statistical tests for the detection of QTLs based on the observation of significant marker allele frequency changes in selection experiments. The probability of inferring the correct location of a QTL is also obtained.