Combined genomic evaluation of Merino and Dohne Merino Australian sheep populations.

BACKGROUND: The Dohne Merino sheep was introduced to Australia from South Africa in the 1990s. It was primarily used in crosses with the Merino breed sheep to improve on attributes such as reproduction and carcass composition. Since then, this breed has continued to expand in Australia but the number of genotyped and phenotyped purebred individuals remains low, calling into question the accuracy of genomic selection. The Australian Merino, on the other hand, has a substantial reference population in a separate genomic evaluation (MERINOSELECT). Combining these resources could fast track the impact of genomic selection on the smaller breed, but the efficacy of this needs to be investigated. This study was based on a dataset of 53,663 genotypes and more than 2 million phenotypes. Its main objectives were (1) to characterize the genetic structure of Merino and Dohne Merino breeds, (2) to investigate the utility of combining their evaluations in terms of quality of predictions, and (3) to compare several methods of genetic grouping. We used the 'LR-method' (Linear Regression) for these assessments. RESULTS: We found very low Fst values (below 0.048) between the different Merino lines and Dohne breed considered in our study, indicating very low genetic differentiation. Principal component analysis revealed three distinct groups, identified as purebred Merino, purebred Dohne, and crossbred animals. Considering the whole population in the reference led to the best quality of predictions and the largest increase in accuracy (from 'LR-method') from pedigree to genomic-based evaluations: 0.18, 0.14 and 0.16 for yearling fibre diameter (YFD), yearling greasy fleece weight (YGFW) and yearling liveweight (YWT), respectively. Combined genomic evaluations showed higher accuracies than the evaluation based on the Dohne reference only (accuracies increased by 0.16, 0.06 and 0.07 for YFD, YGFW, and YWT, respectively). For the combined genomic evaluations, metafounder models were more accurate than Unknown Parent Groups models (accuracies increased by 0.04, 0.04 and 0.06 for YFD, YGFW and YWT, respectively). CONCLUSIONS: We found promising results for the future transition of the Dohne breed from pedigree to genomic selection. A combined genomic evaluation, with the MERINOSELECT evaluation in addition to using metafounders, is expected to enhance the quality of genomic predictions for the Dohne Merino breed.

Estimating genomic relationships of metafounders across and within breeds using maximum likelihood, pseudo-expectation-maximization maximum likelihood and increase of relationships.

BACKGROUND: The theory of "metafounders" proposes a unified framework for relationships across base populations within breeds (e.g. unknown parent groups), and base populations across breeds (crosses) together with a sensible compatibility with genomic relationships. Considering metafounders might be advantageous in pedigree best linear unbiased prediction (BLUP) or single-step genomic BLUP. Existing methods to estimate relationships across metafounders Γ are not well adapted to highly unbalanced data, genotyped individuals far from base populations, or many unknown parent groups (within breed per year of birth). METHODS: We derive likelihood methods to estimate Γ . For a single metafounder, summary statistics of pedigree and genomic relationships allow deriving a cubic equation with the real root being the maximum likelihood (ML) estimate of Γ . This equation is tested with Lacaune sheep data. For several metafounders, we split the first derivative of the complete likelihood in a term related to Γ , and a second term related to Mendelian sampling variances. Approximating the first derivative by its first term results in a pseudo-EM algorithm that iteratively updates the estimate of Γ by the corresponding block of the H-matrix. The method extends to complex situations with groups defined by year of birth, modelling the increase of Γ using estimates of the rate of increase of inbreeding ( Δ F ), resulting in an expanded Γ and in a pseudo-EM+ Δ F algorithm. We compare these methods with the generalized least squares (GLS) method using simulated data: complex crosses of two breeds in equal or unsymmetrical proportions; and in two breeds, with 10 groups per year of birth within breed. We simulate genotyping in all generations or in the last ones. RESULTS: For a single metafounder, the ML estimates of the Lacaune data corresponded to the maximum. For simulated data, when genotypes were spread across all generations, both GLS and pseudo-EM(+ Δ F ) methods were accurate. With genotypes only available in the most recent generations, the GLS method was biased, whereas the pseudo-EM(+ Δ F ) approach yielded more accurate and unbiased estimates. CONCLUSIONS: We derived ML, pseudo-EM and pseudo-EM+ Δ F methods to estimate Γ in many realistic settings. Estimates are accurate in real and simulated data and have a low computational cost.

Redefining and interpreting genomic relationships of metafounders.

Metafounders are a useful concept to characterize relationships within and across populations, and to help genetic evaluations because they help modelling the means and variances of unknown base population animals. Current definitions of metafounder relationships are sensitive to the choice of reference alleles and have not been compared to their counterparts in population genetics-namely, heterozygosities, FST coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy-Weinberg equilibrium. Then, the relationship between or within populations is a cross-product of the form Γ b , b ' = 2 n 2 p b - 1 2 p b ' - 1 ' with p being vectors of allele frequencies at n markers in populations b and b ' . This is simply the genomic relationship of two pseudo-individuals whose genotypes are equal to twice the allele frequencies. We also show that this coding is invariant to the choice of reference alleles. In addition, standard population genetics metrics (inbreeding coefficients of various forms; FST differentiation coefficients; segregation variance; and Nei's genetic distance) can be obtained from elements of matrix Γ .

Confidence intervals for validation statistics with data truncation in genomic prediction.

BACKGROUND: Validation by data truncation is a common practice in genetic evaluations because of the interest in predicting the genetic merit of a set of young selection candidates. Two of the most used validation methods in genetic evaluations use a single data partition: predictivity or predictive ability (correlation between pre-adjusted phenotypes and estimated breeding values (EBV) divided by the square root of the heritability) and the linear regression (LR) method (comparison of "early" and "late" EBV). Both methods compare predictions with the whole dataset and a partial dataset that is obtained by removing the information related to a set of validation individuals. EBV obtained with the partial dataset are compared against adjusted phenotypes for the predictivity or EBV obtained with the whole dataset in the LR method. Confidence intervals for predictivity and the LR method can be obtained by replicating the validation for different samples (or folds), or bootstrapping. Analytical confidence intervals would be beneficial to avoid running several validations and to test the quality of the bootstrap intervals. However, analytical confidence intervals are unavailable for predictivity and the LR method. RESULTS: We derived standard errors and Wald confidence intervals for the predictivity and statistics included in the LR method (bias, dispersion, ratio of accuracies, and reliability). The confidence intervals for the bias, dispersion, and reliability depend on the relationships and prediction error variances and covariances across the individuals in the validation set. We developed approximations for large datasets that only need the reliabilities of the individuals in the validation set. The confidence intervals for the ratio of accuracies and predictivity were obtained through the Fisher transformation. We show the adequacy of both the analytical and approximated analytical confidence intervals and compare them versus bootstrap confidence intervals using two simulated examples. The analytical confidence intervals were closer to the simulated ones for both examples. Bootstrap confidence intervals tend to be narrower than the simulated ones. The approximated analytical confidence intervals were similar to those obtained by bootstrapping. CONCLUSIONS: Estimating the sampling variation of predictivity and the statistics in the LR method without replication or bootstrap is possible for any dataset with the formulas presented in this study.

Boundaries for genotype, phenotype, and pedigree truncation in genomic evaluations in pigs.

Historical data collection for genetic evaluation purposes is a common practice in animal populations; however, the larger the dataset, the higher the computing power needed to perform the analyses. Also, fitting the same model to historical and recent data may be inappropriate. Data truncation can reduce the number of equations to solve, consequently decreasing computing costs; however, the large volume of genotypes is responsible for most of the increase in computations. This study aimed to assess the impact of removing genotypes along with phenotypes and pedigree on the computing performance, reliability, and inflation of genomic predicted breeding value (GEBV) from single-step genomic best linear unbiased predictor for selection candidates. Data from two pig lines, a terminal sire (L1) and a maternal line (L2), were analyzed in this study. Four analyses were implemented: growth and "weaning to finish" mortality on L1, pre-weaning and reproductive traits on L2. Four genotype removal scenarios were proposed: removing genotyped animals without phenotypes and progeny (noInfo), removing genotyped animals based on birth year (Age), the combination of noInfo and Age scenarios (noInfo + Age), and no genotype removal (AllGen). In all scenarios, phenotypes were removed, based on birth year, and three pedigree depths were tested: two and three generations traced back and using the entire pedigree. The full dataset contained 1,452,257 phenotypes for growth traits, 324,397 for weaning to finish mortality, 517,446 for pre-weaning traits, and 7,853,629 for reproductive traits in pure and crossbred pigs. Pedigree files for lines L1 and L2 comprised 3,601,369 and 11,240,865 animals, of which 168,734 and 170,121 were genotyped, respectively. In each truncation scenario, the linear regression method was used to assess the reliability and dispersion of GEBV for genotyped parents (born after 2019). The number of years of data that could be removed without harming reliability depended on the number of records, type of analyses (multitrait vs. single trait), the heritability of the trait, and data structure. All scenarios had similar reliabilities, except for noInfo, which performed better in the growth analysis. Based on the data used in this study, considering the last ten years of phenotypes, tracing three generations back in the pedigree, and removing genotyped animals not contributing own or progeny phenotypes, increases computing efficiency with no change in the ability to predict breeding values.

Recording data for long years is common in animal breeding and genetics. However, the larger the data, the higher the computing cost of the analysis, especially with genomic information. This study aimed to investigate the impact of removing data, namely, genotypes, phenotypes, and pedigree, on the computing performance and prediction ability of genomic breeding values. We tested four scenarios to remove genotyped individuals in pig populations. For each scenario, phenotypes were removed according to birth year, and the pedigree was either kept complete or traced back from two to three generations. Reliabilities for young, genotyped animals did not differ after removing genotypes for older or less important animals. However, using only two generations of data slightly reduces the reliability for young, genotyped animals. The dispersion did not change across the studied scenarios, and its worst value was observed when using only one generation in the pedigree. Using the last ten years of phenotypes, a pedigree depth of three generations, and removing genotyped animals not contributing own or progeny phenotypes reduces computing cost with no change in the ability to predict breeding values.

Impact of interpopulation distance on dominance variance and average heterosis in hybrid populations within species.

Interpopulation improvement for crosses of close populations in crops and livestock depends on the amount of heterosis and the amount of variance of dominance deviations in the hybrids. It has been intuited that the further the distance between populations, the lower the amount of dominance variation and the higher the heterosis. Although experience in speciation and interspecific crosses shows, however, that this is not the case when populations are so distant-here we confine ourselves to the case of not-too-distant populations typical in crops and livestock. We present equations that relate the distance between 2 populations, expressed as Nei's genetic distance or as correlation of allele frequencies, quadratically to the amount of dominance deviations across all possible crosses and linearly to the expected heterosis averaging all possible crosses. The amount of variation of dominance deviations decreases with genetic distance until the point where allele frequencies are uncorrelated, and then increases for negatively correlated frequencies. Heterosis always increases with Nei's genetic distance. These expressions match well and complete previous theoretical and empirical findings. In practice, and for close enough populations, they mean that unless frequencies are negatively correlated, selection for hybrids will be more efficient when populations are distant.

Reliabilities of estimated breeding values in models with metafounders.

BACKGROUND: Reliabilities of best linear unbiased predictions (BLUP) of breeding values are defined as the squared correlation between true and estimated breeding values and are helpful in assessing risk and genetic gain. Reliabilities can be computed from the prediction error variances for models with a single base population but are undefined for models that include several base populations and when unknown parent groups are modeled as fixed effects. In such a case, the use of metafounders in principle enables reliabilities to be derived. METHODS: We propose to compute the reliability of the contrast of an individual's estimated breeding value with that of a metafounder based on the prediction error variances of the individual and the metafounder, their prediction error covariance, and their genetic relationship. Computation of the required terms demands only little extra work once the sparse inverse of the mixed model equations is obtained, or they can be approximated. This also allows the reliabilities of the metafounders to be obtained. We studied the reliabilities for both BLUP and single-step genomic BLUP (ssGBLUP), using several definitions of reliability in a large dataset with 1,961,687 dairy sheep and rams, most of which had phenotypes and among which 27,000 rams were genotyped with a 50K single nucleotide polymorphism (SNP) chip. There were 23 metafounders with progeny sizes between 100,000 and 2000 individuals. RESULTS: In models with metafounders, directly using the prediction error variance instead of the contrast with a metafounder leads to artificially low reliabilities because they refer to a population with maximum heterozygosity. When only one metafounder is fitted in the model, the reliability of the contrast is shown to be equivalent to the reliability of the individual in a model without metafounders. When there are several metafounders in the model, using a contrast with the oldest metafounder yields reliabilities that are on a meaningful scale and very close to reliabilities obtained from models without metafounders. The reliabilities using contrasts with ssGBLUP also resulted in meaningful values. CONCLUSIONS: This work provides a general method to obtain reliabilities for both BLUP and ssGBLUP when several base populations are included through metafounders.

Implication of the order of blending and tuning when computing the genomic relationship matrix in single-step GBLUP.

Single-step genomic BLUP (ssGBLUP) relies on the combination of the genomic ( G $$ \mathbf{G} $$ ) and pedigree relationship matrices for all ( A $$ \mathbf{A} $$ ) and genotyped ( A 22 $$ {\mathbf{A}}_{22} $$ ) animals. The procedure ensures G $$ \mathbf{G} $$ and A 22 $$ {\mathbf{A}}_{22} $$ are compatible so that both matrices refer to the same genetic base ('tuning'). Then G $$ \mathbf{G} $$ is combined with a proportion of A 22 $$ {\mathbf{A}}_{22} $$ ('blending') to avoid singularity problems and to account for the polygenic component not accounted for by markers. This computational procedure has been implemented in the reverse order (blending before tuning) following the sequential research developments. However, blending before tuning may result in less optimal tuning because the blended matrix already contains a proportion of A 22 $$ {\mathbf{A}}_{22} $$ . In this study, the impact of 'tuning before blending' was compared with 'blending before tuning' on genomic estimated breeding values (GEBV), single nucleotide polymorphism (SNP) effects and indirect predictions (IP) from ssGBLUP using American Angus Association and Holstein Association USA, Inc. data. Two slightly different tuning methods were used; one that adjusts the mean diagonals and off-diagonals of G $$ \mathbf{G} $$ to be similar to those in A 22 $$ {\mathbf{A}}_{22} $$ and another one that adjusts based on the average difference between all elements of G $$ \mathbf{G} $$ and A 22 $$ {\mathbf{A}}_{22} $$ . Over 6 million Angus growth records and 5.9 million Holstein udder depth records were available. Genomic information was available on 51,478 Angus and 105,116 Holstein animals. Average realized relationship estimates among groups of animals were similar across scenarios. Scatterplots show that GEBV, SNP effects and IP did not noticeably change for all animals in the evaluation regardless of the order of computations and when using blending parameter of 0.05. Formulas were derived to determine the blending parameter that maximizes changes in the genomic relationship matrix and GEBV when changing the order of blending and tuning. Algebraically, the change is maximized when the blending parameter is equal to 0.5. Overall, tuning G $$ \mathbf{G} $$ before blending, regardless of blending parameter used, had a negligible impact on genomic predictions and SNP effects in this study.

Impacts of additive, dominance, and inbreeding depression effects on genomic evaluation by combining two SNP chips in Canadian Yorkshire pigs bred in China.

BACKGROUND: At the beginning of genomic selection, some Chinese companies genotyped pigs with different single nucleotide polymorphism (SNP) arrays. The obtained genomic data are then combined and to do this, several imputation strategies have been developed. Usually, only additive genetic effects are considered in genetic evaluations. However, dominance effects that may be important for some traits can be fitted in a mixed linear model as either 'classical' or 'genotypic' dominance effects. Their influence on genomic evaluation has rarely been studied. Thus, the objectives of this study were to use a dataset from Canadian Yorkshire pigs to (1) compare different strategies to combine data from two SNP arrays (Affymetrix 55K and Illumina 42K) and identify the most appropriate strategy for genomic evaluation and (2) evaluate the impact of dominance effects (classical' and 'genotypic') and inbreeding depression effects on genomic predictive abilities for average daily gain (ADG), backfat thickness (BF), loin muscle depth (LMD), days to 100 kg (AGE100), and the total number of piglets born (TNB) at first parity. RESULTS: The reliabilities obtained with the additive genomic models showed that the strategy used to combine data from two SNP arrays had little impact on genomic evaluations. Models with classical or genotypic dominance effect showed similar predictive abilities for all traits. For ADG, BF, LMD, and AGE100, dominance effects accounted for a small proportion (2 to 11%) of the total genetic variance, whereas for TNB, dominance effects accounted for 11 to 20%. For all traits, the predictive abilities of the models increased significantly when genomic inbreeding depression effects were included in the model. However, the inclusion of dominance effects did not change the predictive ability for any trait except for TNB. CONCLUSIONS: Our study shows that it is feasible to combine data from different SNP arrays for genomic evaluation, and that all combination methods result in similar accuracies. Regardless of how dominance effects are fitted in the genomic model, there is no impact on genetic evaluation. Models including inbreeding depression effects outperform a model with only additive effects, even if the trait is not strongly affected by dominant genes.