A single locus model of the interaction between natural selection and artificial selection for a quantitative character in a finite population, assuming heterozygote superiority in natural fitness but additive action on the character, has been studied using transition probability matrices.If natural selection is strong enough to create a selection plateau in which genetic variance declines relatively slowly, then the total response to artificial selection prior to the plateau will be much less than that expected in the absence of natural selection, and the half-life of response will be shorter. Such a plateau is likely to have a large proportion, if not all, of the original genetic variance still present. In selection programmes using laboratory animals, it seems likely that the homozygote favoured by artificial selection must be very unfit before such a plateau will occur. A significant decrease in population fitness as a result of artificial selection does not necessarily imply that the metric character is an important adaptive character.These implications of this model of natural selection are very similar to those derived by James (1962) for the optimum model of natural selection. In fact, there seems to be no aspect of the observable response to artificial selection that would enable anyone to distinguish between these two models of natural selection.