Significance of linkage disequilibrium and epistasis on the genetic variances and covariance between relatives in non-inbred and inbred populations

Because no feasible theoretical model can depict the complexity of phenotype development from a genotype, the joint significance of linkage disequilibrium (LD), epistasis, and inbreeding on the genetic variances remains unclear. The objective of this investigation was to assess the impact of LD and epistasis on the genetic variances and covariances between relatives in non-inbred and inbred populations using simulated data. We provided the theoretical background and simulated grain yield assuming 400 genes in 10 chromosomes of 200 and 50 cM. We generated five populations with low to high LD levels, assuming 10 generations of random cross and selfing. The analysis of the parametric LD in the populations shows that the LD level depends mainly on the gene density. The significance of the LD level is impressive on the magnitude of the genotypic and additive variances, which is the most important component of the genotypic variance, regardless of the LD level and the degree of inbreeding. Regardless of the type of epistasis, the ratio epistatic variance/genotypic variance is proportional to the percentage of the epistatic genes. For the epistatic variances, except for duplicate epistasis and dominant and recessive epistasis, with 100% of epistatic genes, their magnitudes are much lower than the magnitude of the additive variance. The additive x additive variance is the most important epistatic variance. Our results explain why LD for genes and relationship information are key factors affecting the genomic prediction accuracy of complex traits and the efficacy of association studies.