Should gene interactions be included in genomic evaluation in animal breeding?
Authors: Mäki-Tanila Asko , Hill William G. 
Published: April 2019

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.