Natural selection, acting directly on fitness or through stabilizing selection for other traits, has always been present in natural populations. In principle, this force will reduce the genetic variability, which is required for artificial selection programs. The genetic improvement of a trait with economic interest by selection programs depends on the amount of genetic diversity for that trait in a particular population. Most studies on the development of breeding programs account only for the genetic variation for the target trait itself. The objective in this work is determining, through computer simulations, the consequences for the evolution of selection programs, considering not only the variability for the trait of interest but also for fitness under different mutational models. Additionally, a scenario where the trait was subjected to stabilizing selection was also studied. Different parameters as effective population size, phenotypic mean, phenotypic variance and heterozygosity were used to monitor the performance in the different scenarios. In conclusion, considering the action of direct natural selection does not lead to lower levels of genetic variability for neutral traits, and thus it does not reduce the ability of populations to respond to artificial selection regardless of the mutational model used. On the other hand, stabilizing selection penalizes individuals with an extreme phenotype (which is the major objective in the artificial selection), reducing their fitness. Therefore, the artificial selection was ineffective in improving traits subjected to stabilizing selection. © 2017 Elsevier B.V.