Background The influence of linkage disequilibrium (LD), epistasis, and inbreeding on the genotypic variance continues to be an important area of investigation in genetics and evolution. Although the current knowledge about biological pathways and gene networks imply that epistasis is important in determining quantitative traits, the empirical evidence for a range of species and traits is that the genetic variance is most additive. This is confirmed by some recent theoretical studies. However, because these investigations have assumed linkage equilibrium, only additive effects, or simplified assumptions for the two- and high-order epistatic effects, the objective of this investigation was to provide additional information about the impact of LD and epistasis on the genetic variances in non-inbred and inbred populations, using a simulated data set.Results The epistatic variance in generation 0 corresponded to 1 to 10% of the genotypic variance, with 30% of epistatic genes, but it corresponded to 5 to 45% assuming 100% of epistatic genes. After 10 generations of random cross or selfing the ratio epistatic variance/genotypic variance increased in the range of 15 to 1,079%. The epistatic variances are maximized assuming dominant epistasis, duplicate genes with cumulative effects, and non-epistatic gene interaction. A minimization occurs with complementary, recessive, and dominant and recessive epistasis. In non-inbred populations, the genetic covariances have negligible magnitude compared with the genetic variances. In inbred populations, excepting for duplicate epistasis, the sum of the epistatic covariances was in general negative and with magnitude higher than the non-additive variances, especially under 100% of epistatic genes.Conclusions The LD level for genes, even under a relatively low gene density, has a significant effect on the genetic variances in non-inbred and inbred populations. Assuming digenic epistasis, the additive variance is in general the most important component of the genotypic variance in non-inbred and inbred populations. The ratio epistatic variance/genotypic variance is proportional to the percentage of interacting genes and increases with random cross and selfing. In general, the additive x additive variance is the most important component of the epistatic variance. The maximization of the epistatic variance depends on the allele frequency, LD level, and epistasis type.