Significance of Linkage Disequilibrium and Epistasis on the Genetic Variances in Non- Inbred and Inbred Populations

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.

Significance of Linkage Disequilibrium and Epistasis on the Genetic Variances in Non-Inbred and Inbred Populations

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.

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.

Estimation of non-additive genetic variance in human complex traits from a large sample of unrelated individuals

Non-additive genetic variance for complex traits is traditionally estimated from data on relatives. It is notoriously difficult to estimate without bias in non-laboratory species, including humans, because of possible confounding with environmental covariance among relatives. In principle, non-additive variance attributable to common DNA variants can be estimated from a random sample of unrelated individuals with genome-wide SNP data. Here, we jointly estimate the proportion of variance explained by additive , dominance and additive-by-additive genetic variance in a single analysis model. We first show by simulations that our model leads to unbiased estimates and provide new theory to predict standard errors estimated using either least squares or maximum likelihood. We then apply the model to 70 complex traits using 254,679 unrelated individuals from the UK Biobank and 1.1M genotyped and imputed SNPs. We found strong evidence for additive variance (average across traits . In contrast, the average estimate of across traits was 0.001, implying negligible dominance variance at causal variants tagged by common SNPs. The average epistatic variance across the traits was 0.058, not significantly different from zero because of the large sampling variance. Our results provide new evidence that genetic variance for complex traits is predominantly additive, and that sample sizes of many millions of unrelated individuals are needed to estimate epistatic variance with sufficient precision.

Genomic heritability estimates in sweet cherry reveal non-additive genetic variance is relevant for industry-prioritized traits

ABSTRACTBackgroundSweet cherry is consumed widely across the world and provides substantial economic benefits in regions where it is grown. While cherry breeding has been conducted in the Pacific Northwest for over half a century, little is known about the genetic architecture of important traits. We used a genome-enabled mixed model to predict the genetic performance of 505 individuals for 32 phenological, disease response and fruit quality traits evaluated in the RosBREED sweet cherry crop data set. Genome-wide predictions were estimated using a repeated measures model for phenotypic data across 3 years, incorporating additive, dominance and epistatic variance components. Genomic relationship matrices were constructed with high-density SNP data and were used to estimate relatedness and account for incomplete replication across years.ResultsHigh broad-sense heritabilities of 0.83, 0.77, and 0.75 were observed for days to maturity, firmness, and fruit weight, respectively. Epistatic variance exceeded 40% of the total genetic variance for maturing timing, firmness and powdery mildew response. Dominance variance was the largest for fruit weight and fruit size at 34% and 27%, respectively. Omission of non-additive sources of genetic variance from the genetic mode resulted in inflation of narrow-sense heritability but minimally influenced prediction accuracy of genetic values in validation. Predicted genetic rankings of individuals from single-year models were inconsistent across years, likely due to incomplete sampling of the population genetic variance.ConclusionsPredicted breeding values and genetic values a measure revealed many high-performing individuals for use as parents and the most promising selections to advance for cultivar release consideration, respectively. This study highlights the importance of using the appropriate genetic model for calculating breeding values to avoid inflation of expected parental contribution to genetic gain. The genomic predictions obtained will enable breeders to efficiently leverage the genetic potential of North American sweet cherry germplasm by identifying high quality individuals more rapidly than with phenotypic data alone.

Should gene interactions be included in genomic evaluation in animal breeding?

The genetic comparison of animals is based on their own performance and that of animals sharing genetic factors with them. Their expected genetic similarity is deduced from pedigree information and also now directly using a large number of molecular genetic markers over the genome (genomic breeding values). Quantitative trait analyses may also include gene interaction or epistatic effects. Additive x additive interaction effects have been found, particularly in crosses of inbred and widely diverse selected lines. These and gene functional studies have generated much interest in including the interaction effects in genome-wide analyses within populations, including animal breeding stocks. Several issues need consideration before incorporating them in genetic models: influence of gene interaction on the genetic evaluation and on the gains produced by selection, proportion of epistatic variance with multiple genes, expectations with common allele frequency distributions, and probability of finding interaction effects with the genomic tools. - The average effect of an allele already includes interaction effects with other loci, but with magnitude dependent on their frequencies. If a major epistatic effect is favourable, selection may fix the respective allele quickly. With milder effects the frequencies of interacting favourable alleles at both loci of pair will increase. - Even with additive effects in an underlying genotype, the relationship between phenotypes and genotypes may be non-linear and there is epistasis on the observed scale. An example is a categorical trait (diseased or not), where the analysis on the observed scale using an approximating model can be transformed to the underlying additive scale. In the multiplicative model the amount of epistasis increases with the coefficient of variation (CV), but the proportion never exceeds 1- ln(1+CV2)/CV2, and most of the epistatic variance is due to two-locus interactions. - The additive variance is directly proportional to heterozygosity (H), with a maximum at allele frequency ½ in a biallelic case. Additive x additive variance requires segregation in both the interacting loci A and B and is proportional to HAHB, and correspondingly for more loci. Hence epistatic variance can reach high values only when allele frequencies near ½. - As the number of loci (n) is increased, average effects at individual loci decline with 1/√n (i.e. variance as 1/n). Similarly additive x additive effects must decline as 1/n. In genome-wide analyses, the number of effects to be estimated is the square of that for individual loci. With many thousands of markers very stringent test criteria have to be used so the power is very low. It has become obvious that the genomic tools cannot harvest all the existing genetic variation. In particular the variation due to rare alleles is often undetected. Such problems are even more likely in considering interaction effects. In summary, gene interaction effects are automatically utilized in selection using additive models while most epistatic effects are expected to be very small and difficult to detect in genome-wide analyses.

On epistasis: why it is unimportant in polygenic directional selection

There is a difference in viewpoint of developmental and evo-devo geneticists versus breeders and students of quantitative evolution. The former are interested in understanding the developmental process; the emphasis is on identifying genes and studying their action and interaction. Typically, the genes have individually large effects and usually show substantial dominance and epistasis. The latter group are interested in quantitative phenotypes rather than individual genes. Quantitative traits are typically determined by many genes, usually with little dominance or epistasis. Furthermore, epistatic variance has minimum effect, since the selected population soon arrives at a state in which the rate of change is given by the additive variance or covariance. Thus, the breeder's custom of ignoring epistasis usually gives a more accurate prediction than if epistatic variance were included in the formulae.

The struggle to exploit non-additive variation

Whereas animal breeders largely focus on improvement using additive genetic variance, inbreeding and asexual reproduction allow plant breeders to at least partially exploit non-additive genetic variance as well. We briefly review various approaches used by breeders to exploit dominance and epistatic variance, discuss their constraints and limitations, and examine what (if anything) can be done to improve our ability to further use often untapped genetic variation.

Use of inbred sires to exploit epistatic variance (short communication)

The genetic variance of inbred sires is increased and variance due to additive x additive effects proportionately more than that due to additive ones. In case of inbreeding by mating sire to daughters the time interval elite sire – son needs not to be elongated so that the genetic progress could be increased by this procedure. This pertains even more to the procedure. where inbred sires are produced from sib mating. Use of such sires should increase the genetic gain via the sire son path by about 10 %.