All-breed single-step genomic best linear unbiased predictor evaluations for fertility traits in US dairy cattle.

The US dairy cattle genetic evaluation is currently a multistep process, including multibreed traditional BLUP estimations followed by single-breed SNP effects estimation. Single-step GBLUP (ssGBLUP) combines pedigree and genomic data for all breeds in one analysis. Unknown parent groups (UPG) or metafounders (MF) can be used to address missing pedigree information.

Approximation of reliabilities for random-regression single-step genomic best linear unbiased predictor models.

Random-regression models (RRM) are used in national genetic evaluations for longitudinal traits. The outputs of RRM are an index based on random-regression coefficients and its reliability. The reliabilities are obtained from the inverse of the coefficient matrix of mixed model equations (MME).

Transforming estimated breeding values from observed to probability scale: how to make categorical data analyses more efficient.

Threshold models are often used in genetic analysis of categorical data, such as calving ease. Solutions in the liability scale are easily transformed into probabilities; therefore, estimated breeding values are published as the probability of expressing the category of main interest and are the industry's gold standard because they are easy to interpret and use for selection. However, because threshold models involve nonlinear equations and probability functions, implementing such a method is complex.

Marker effect p-values for single-step GWAS with the algorithm for proven and young in large genotyped populations.

Background: Single-nucleotide polymorphism (SNP) effects can be backsolved from ssGBLUP genomic estimated breeding values (GEBV) and used for genome-wide association studies (ssGWAS). However, obtaining p-values for those SNP effects relies on the inversion of dense matrices, which poses computational limitations in large genotyped populations. In this study, we present a method to approximate SNP p-values for ssGWAS with many genotyped animals.

Comparing algorithms to approximate accuracies for single-step genomic best linear unbiased predictor.

The exact accuracy of estimated breeding values can be calculated based on the prediction error variances obtained from the diagonal of the inverse of the left-hand side (LHS) of the mixed model equations (MME). However, inverting the LHS is not computationally feasible for large datasets, especially if genomic information is available. Thus, different algorithms have been proposed to approximate accuracies.

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, F coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy-Weinberg equilibrium.

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.

Single-step genomic predictions for crossbred Holstein and Jersey cattle in the United States.

In the dairy cattle sector, the number of crossbred genotypes increased in the last years, and therefore, the need for accurate genomic evaluations for crossbred animals has also increased. Thus, this study aimed to investigate the feasibility of including crossbred genotypes in multibreed, single-step genomic BLUP (ssGBLUP) evaluations. The Council of Dairy Cattle Breeding provided more than 47 million lactation records registered between 2000 and 2021 in purebred Holstein and Jersey and their crosses.

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.

Derivation of indirect predictions using genomic recursions across generations in a broiler population.

Genomic estimated breeding values (GEBV) of animals without phenotypes can be indirectly predicted using recursions on GEBV of a subset. To maximize predictive ability of indirect predictions (IP), the subset must represent the independent chromosome segments segregating in the population. We aimed to 1) determine the number of animals needed in recursions to maximize predictive ability, 2) evaluate equivalency IP-GEBV, and 3) investigate trends in predictive ability of IP derived from recent vs.

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.

Efficient ways to combine data from broiler and layer chickens to account for sequential genomic selection.

In broiler breeding, superior individuals for growth become parents and are later evaluated for reproduction in an independent evaluation; however, ignoring broiler data can produce inaccurate and biased predictions. This research aimed to determine the most accurate, unbiased, and time-efficient approach for jointly evaluating reproductive and broiler traits. The data comprised a pedigree with 577K birds, 146K genotypes, phenotypes for three reproductive (egg production [EP], fertility [FE], hatch of fertile eggs [HF]; 9K each), and four broiler traits (body weight [BW], breast meat percent [BP], fat percent [FP], residual feed intake [RF]; up to 467K).

Strategies for choosing core animals in the algorithm for proven and young and their impact on the accuracy of single-step genomic predictions in cattle.

Nowadays, in some populations, the number of genotyped animals is too large to obtain the inverse of the genomic relationship matrix. The algorithm for proven and young animals (APY) can be used to overcome this problem. In the present work, different strategies for defining core animals in APY were tested using either simulated or real data.

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.

Impact of blending the genomic relationship matrix with different levels of pedigree relationships or the identity matrix on genetic evaluations.

Evaluations using single-step genomic BLUP require blending the genomic relationship matrix () with a positive definite matrix to ensure nonsingularity for solving the mixed model equations. Many organizations blend with a proportion of the numerator relationship matrix for genotyped animals ( ) to improve stability and possibly add a residual polygenic effect. However, when nearly all the polygenic variance is explained by , blending with may cause inflation and add excess computing time; thus, blending with an identity matrix () multiplied by a small value may be a better solution.

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 ( ) and pedigree relationship matrices for all ( ) and genotyped ( ) animals. The procedure ensures and are compatible so that both matrices refer to the same genetic base ('tuning'). Then is combined with a proportion of ('blending') to avoid singularity problems and to account for the polygenic component not accounted for by markers.

Accounting for population structure in genomic predictions of Eucalyptus globulus.

Genetic groups have been widely adopted in tree breeding to account for provenance effects within pedigree-derived relationship matrices. However, provenances or genetic groups have not yet been incorporated into single-step genomic BLUP ("HBLUP") analyses of tree populations. To quantify the impact of accounting for population structure in Eucalyptus globulus, we used HBLUP to compare breeding value predictions from models excluding base population effects and models including either fixed genetic groups or the marker-derived proxies, also known as metafounders.

On the equivalence between marker effect models and breeding value models and direct genomic values with the Algorithm for Proven and Young.

Background: Single-step genomic predictions obtained from a breeding value model require calculating the inverse of the genomic relationship matrix [Formula: see text]. The Algorithm for Proven and Young (APY) creates a sparse representation of [Formula: see text] with a low computational cost. APY consists of selecting a group of core animals and expressing the breeding values of the remaining animals as a linear combination of those from the core animals plus an error term.

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young.

The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEVs) for genomic best linear unbiased prediction (GBLUP) models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and apply this algorithm for approximating the theoretical reliabilities for single- and multiple-trait models in ssGBLUP. The PEV with APY was calculated by block sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions.

Investigating the persistence of accuracy of genomic predictions over time in broilers.

Accuracy of genomic predictions is an important component of the selection response. The objectives of this research were: 1) to investigate trends for prediction accuracies over time in a broiler population of accumulated phenotypes, genotypes, and pedigrees and 2) to test if data from distant generations are useful to maintain prediction accuracies in selection candidates. The data contained 820K phenotypes for a growth trait (GT), 200K for two feed efficiency traits (FE1 and FE2), and 42K for a carcass yield trait (CY).

Impact of including the cause of missing records on genetic evaluations for growth in commercial pigs.

It is of interest to evaluate crossbred pigs for hot carcass weight (HCW) and birth weight (BW); however, obtaining a HCW record is dependent on livability (LIV) and retained tag (RT). The purpose of this study is to analyze how HCW evaluations are affected when herd removal and missing identification are included in the model and examine if accounting for the reasons for missing traits improves the accuracy of predicting breeding values. Pedigree information was available for 1,965,077 purebred and crossbred animals.

Accounting for Population Structure and Phenotypes From Relatives in Association Mapping for Farm Animals: A Simulation Study.

Population structure or genetic relatedness should be considered in genome association studies to avoid spurious association. The most used methods for genome-wide association studies (GWAS) account for population structure but are limited to genotyped individuals with phenotypes. Single-step GWAS (ssGWAS) can use phenotypes from non-genotyped relatives; however, its ability to account for population structure has not been explored.

Determining the stability of accuracy of genomic estimated breeding values in future generations in commercial pig populations.

Genomic information has a limited dimensionality (number of independent chromosome segments [Me]) related to the effective population size. Under the additive model, the persistence of genomic accuracies over generations should be high when the nongenomic information (pedigree and phenotypes) is equivalent to Me animals with high accuracy. The objective of this study was to evaluate the decay in accuracy over time and to compare the magnitude of decay with varying quantities of data and with traits of low and moderate heritability.

Modeling genetic differences of combined broiler chicken populations in single-step GBLUP.

The introduction of animals from a different environment or population is a common practice in commercial livestock populations. In this study, we modeled the inclusion of a group of external birds into a local broiler chicken population for the purpose of genomic evaluations. The pedigree was composed of 242,413 birds and genotypes were available for 107,216 birds.

Changes in genomic predictions when new information is added.

The stability of genomic evaluations depends on the amount of data and population parameters. When the dataset is large enough to estimate the value of nearly all independent chromosome segments (~10K in American Angus cattle), the accuracy and persistency of breeding values will be high. The objective of this study was to investigate changes in estimated breeding values (EBV) and genomic EBV (GEBV) across monthly evaluations for 1 yr in a large genotyped population of beef cattle.