Ignoring genotype by environment interaction in the genetic evaluation of dairy cattle reduces accuracy but may increase selection intensity.

Genotype by environment interaction (G×E) may exist for traits that are expressed in different environments. The G×E is often ignored in the genetic evaluation of selection candidates. We hypothesized that genetic gain in 2 environments is always higher when the true value of the genetic correlation (rg) between traits expressed in different environments is considered in the genetic evaluation. We tested this hypothesis by stochastic simulation of dairy cattle breeding programs in a mainstream and a niche environment. The rg was varied from 0 to 1 in steps of 0.1. We simulated the following 3 scenarios: 1Trait_1Index, 2Traits_1Index, and 2Traits_2Indices. The G×E was ignored in the genetic evaluation in the scenario with 1Trait and included in scenarios with 2Traits. Selection was based on the mainstream selection index in both environments in scenarios with 1Index. Selection in the mainstream environment was based on the mainstream selection index and selection in the niche environment was based on the niche selection index in the scenario with 2Indices. With moderate G×E (rg between 0.6 and 0.9), the highest genetic gain was achieved in the niche environment by selecting for the mainstream selection index and ignoring G×E. At lower rg, the highest genetic gain was achieved when considering G×E and selecting for the niche selection index. For the mainstream environment, it was never an advantage to ignore G×E. Therefore, although our hypothesis was confirmed in most cases, there were cases where ignoring G×E was the better option, and using the correct evaluation led to inferior genetic gain. The results of the current study can be used in animal breeding programs that encompass multiple environments.

Pedigree relationships to control inbreeding in optimum-contribution selection realise more genetic gain than genomic relationships.

BACKGROUND: We tested the premise that optimum-contribution selection with pedigree relationships to control inbreeding (POCS) realises at least as much true genetic gain as optimum-contribution selection with genomic relationships (GOCS) at the same rate of true inbreeding. METHODS: We used stochastic simulation to estimate rates of true genetic gain realised by POCS and GOCS at a 0.01 rate of true inbreeding in three breeding schemes with best linear unbiased predictions of breeding values based on pedigree (PBLUP) and genomic (GBLUP) information. The three breeding schemes differed in number of matings and litter size. Selection was for a single trait with a heritability of 0.2. The trait was controlled by 7702 biallelic quantitative-trait loci (QTL) that were distributed across a 30-M genome. The genome contained 54,218 biallelic markers that were used in GOCS and GBLUP. A total of 6012 identity-by-descent loci were placed across the genome in base populations. Unique alleles at these loci were used to calculate rates of true inbreeding. Breeding schemes were run for 10 discrete generations. Selection candidates were genotyped and phenotyped before selection. RESULTS: POCS realised more true genetic gain than GOCS at a 0.01 rate of true inbreeding in all combinations of breeding scheme and prediction method. POCS realised 14 to 33% more true genetic gain than GOCS with PBLUP in the three breeding schemes. It realised 1.5 to 5.7% more true genetic gain than GOCS with GBLUP. CONCLUSIONS: POCS realised more true genetic gain than GOCS because it managed expected genetic drift without restricting selection at QTL. By contrast, GOCS penalised changes in allele frequencies at markers that were generated by genetic drift and selection. Because these marker alleles were in linkage disequilibrium with QTL alleles, GOCS restricted changes in allele frequencies at QTL. This provides little incentive to use GOCS and highlights that we have more to learn before we can control inbreeding using genomic relationships in selective-breeding schemes. Until we can do so, POCS remains a worthy method of optimum-contribution selection because it realises more true genetic gain than GOCS at the same rate of true inbreeding.

Understanding the potential bias of variance components estimators when using genomic models.

BACKGROUND: Genomic models that link phenotypes to dense genotype information are increasingly being used for infering variance parameters in genetics studies. The variance parameters of these models can be inferred using restricted maximum likelihood, which produces consistent, asymptotically normal estimates of variance components under the true model. These properties are not guaranteed to hold when the covariance structure of the data specified by the genomic model differs substantially from the covariance structure specified by the true model, and in this case, the likelihood of the model is said to be misspecified. If the covariance structure specified by the genomic model provides a poor description of that specified by the true model, the likelihood misspecification may lead to incorrect inferences. RESULTS: This work provides a theoretical analysis of the genomic models based on splitting the misspecified likelihood equations into components, which isolate those that contribute to incorrect inferences, providing an informative measure, defined as [Formula: see text], to compare the covariance structure of the data specified by the genomic and the true models. This comparison of the covariance structures allows us to determine whether or not bias in the variance components estimates is expected to occur. CONCLUSIONS: The theory presented can be used to provide an explanation for the success of a number of recently reported approaches that are suggested to remove sources of bias of heritability estimates. Furthermore, however complex is the quantification of this bias, we can determine that, in genomic models that consider a single genomic component to estimate heritability (assuming SNP effects are all i.i.d.), the bias of the estimator tends to be downward, when it exists.