Selection of core animals in the Algorithm for Proven and Young using a simulation model

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. This method relies on the combination of a sparse approximation of the inverse of the genomic relationship matrix ( G A P Y - 1 ) built with the algorithm for proven and young ( APY ) and an approximation of the prediction error variance of SNP effects which does not require the inversion of the left-hand side (LHS) of the mixed model equations. To test the proposed p-value computing method, we used a reduced genotyped population of 50K genotyped animals and compared the approximated SNP p-values with benchmark p-values obtained with the direct inverse of LHS built with an exact genomic relationship matrix (G - 1 ) . Then, we applied the proposed approximation method to obtain SNP p-values for a larger genotyped population composed of 450K genotyped animals.

RESULTS

The same genomic regions on chromosomes 7 and 20 were identified across all p-value computing methods when using 50K genotyped animals. In terms of computational requirements, obtaining p-values with the proposed approximation reduced the wall-clock time by 38 times and the memory requirement by ten times compared to using the exact inversion of the LHS. When the approximation was applied to a population of 450K genotyped animals, two new significant regions on chromosomes 6 and 14 were uncovered, indicating an increase in GWAS detection power when including more genotypes in the analyses. The process of obtaining p-values with the approximation and 450K genotyped individuals took 24.5 wall-clock hours and 87.66GB of memory, which is expected to increase linearly with the addition of noncore genotyped individuals.

CONCLUSIONS

With the proposed method, obtaining p-values for SNP effects in ssGWAS is computationally feasible in large genotyped populations. The computational cost of obtaining p-values in ssGWAS may no longer be a limitation in extensive populations with many genotyped animals.

Temporal dynamics of genetic parameters and SNP effects for performance and disorder traits in poultry undergoing genomic selection

Accurate genetic parameters are crucial for predicting breeding values and selection responses in breeding programs. Genetic parameters change with selection, reducing additive genetic variance and changing genetic correlations. This study investigates the dynamic changes in genetic parameters for residual feed intake (RFI), gain (GAIN), breast percentage (BP), and femoral head necrosis (FHN) in a broiler population that undergoes selection, both with and without the use of genomic information. Changes in single nucleotide polymorphism (SNP) effects were also investigated when including genomic information. The dataset containing 200,093 phenotypes for RFI, 42,895 for BP, 203,060 for GAIN, and 63,349 for FHN was obtained from 55 mating groups. The pedigree included 1,252,619 purebred broilers, of which 154,318 were genotyped with a 60K Illumina Chicken SNP BeadChip. A Bayesian approach within the GIBBSF90 + software was applied to estimate the genetic parameters for single-, two-, and four-trait models with sliding time intervals. For all models, we used genomic-based (GEN) and pedigree-based approaches (PED), meaning with or without genotypes. For GEN (PED), heritability varied from 0.19 to 0.2 (0.31 to 0.21) for RFI, 0.18 to 0.11 (0.25 to 0.14) for GAIN, 0.45 to 0.38 (0.61 to 0.47) for BP, and 0.35 to 0.24 (0.53 to 0.28) for FHN, across the intervals. Changes in genetic correlations estimated by GEN (PED) were 0.32 to 0.33 (0.12 to 0.25) for RFI-GAIN, -0.04 to -0.27 (-0.18 to -0.27) for RFI-BP, -0.04 to -0.07 (-0.02 to -0.08) for RFI-FHN, -0.04 to 0.04 (0.06 to 0.2) for GAIN-BP, -0.17 to -0.06 (-0.02 to -0.01) for GAIN-FHN, and 0.02 to 0.07 (0.06 to 0.07) for BP-FHN. Heritabilities tended to decrease over time while genetic correlations showed both increases and decreases depending on the traits. Similar to heritabilities, correlations between SNP effects declined from 0.78 to 0.2 for RFI, 0.8 to 0.2 for GAIN, 0.73 to 0.16 for BP, and 0.71 to 0.14 for FHN over the eight intervals with genomic information, suggesting potential epistatic interactions affecting genetic trait architecture. Given rapid genetic architecture changes and differing estimates between genomic and pedigree-based approaches, using more recent data and genomic information to estimate variance components is recommended for populations undergoing genomic selection to avoid potential biases in genetic parameters.

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. In particular, core definitions based on random choice or on the contribution to the genomic relationship matrix (G_CONTR) calculated using Principal Component Analysis were tested. Core sizes able to explain 90, 95, 98, and 99% of the total variance of the genomic relationship matrix (G) were used. Analyzed phenotypes were three simulated traits for 3 000 individuals, and milkability records for 136 406 Italian Simmental cows. The number of genotypes was 4 100 for the simulated dataset, and 11 636 for the Simmental data, respectively. The G_CONTR values in Simmental dataset were moderately correlated with the analyzed phenotype, and they showed a decreasing trend according to the year of birth of genotyped animals. The accuracy increased as the size of the core increased in both datasets. The inclusion in the core of animals with largest G_CONTR values led to the lowest accuracies (0.50 and 0.71 for the simulated and Simmental datasets, respectively; average across traits and core sizes). On the contrary, the selection of animals with the lowest rank according to their contribution to the G provided slightly higher accuracies, especially in the simulated dataset (0.68 for the simulated dataset, and 0.76 for the Simmental data; average across traits and core sizes). In real data, particularly for larger sizes of core animals, the criteria of choice appear less important, confirming the results of earlier studies. Anyway, the inclusion in the core of animals with the lowest values of G_CONTR led to increases in accuracy. These are preliminary results based on a small sample size that need to be confirmed on a larger number of genotypes.

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. distant generations or accumulating phenotypes from recent to past generations. Data comprised pedigree of 825K birds hatched over 12 overlapping generations, phenotypes for body weight (BW; 820K), residual feed intake (RF; 200K) and weight gain during a trial period (WG; 200K), and breast meat percent (BP; 43K). A total of 154K birds (last six generations) had genotypes. The number of animals that maximize predictive ability was assessed based on the number of largest eigenvalues explaining 99% of variation in the genomic relationship matrix (1Me = 7,131), twice (2Me), or a fraction of this number (i.e., 0.75, 0.50, or 0.25Me). Equivalency between IP and GEBV was measured by correlating these two sets of predictions. GEBV were obtained as if generation 12 (validation animals) was part of the evaluation. IP were derived from GEBV of animals from generations 8 to 11 or generations 11, 10, 9, or 8. IP predictive ability was defined as the correlation between IP and adjusted phenotypes. The IP predictive ability increased from 0.25Me to 1Me (11%, on average); the change from 1Me to 2Me was negligible (0.6%). The correlation IP-GEBV was the same when IP were derived from a subset of 1Me animals chosen randomly across generations (8 to 11) or from generation 11 (0.98 for BW, 0.99 for RF, WG, and BP). A marginal decline in the correlation was observed when IP were based on GEBV of animals from generation 8 (0.95 for BW, 0.98 for RF, WG, and BP). Predictive ability had a similar trend; from generation 11 to 8, it changed from 0.32 to 0.31 for BW, from 0.39 to 0.38 for BP, and was constant at 0.33(0.22) for RF(WG). Predictive ability had a slight to moderate increase accumulating up to four generations of phenotypes. 1Me animals provide accurate IP, equivalent to GEBV. A minimum decay in predictive ability is observed when IP are derived from GEBV of animals from four generations back, possibly because of strong selection or the model not being completely additive.

Optimisation of the core subset for the APY approximation of genomic relationships

BACKGROUND

By entering the era of mega-scale genomics, we are facing many computational issues with standard genomic evaluation models due to their dense data structure and cubic computational complexity. Several scalable approaches have been proposed to address this challenge, such as the Algorithm for Proven and Young (APY). In APY, genotyped animals are partitioned into core and non-core subsets, which induces a sparser inverse of the genomic relationship matrix. This partitioning is often done at random. While APY is a good approximation of the full model, random partitioning can make results unstable, possibly affecting accuracy or even reranking animals. Here we present a stable optimisation of the core subset by choosing animals with the most informative genotype data.

METHODS

We derived a novel algorithm for optimising the core subset based on a conditional genomic relationship matrix or a conditional single nucleotide polymorphism (SNP) genotype matrix. We compared the accuracy of genomic predictions with different core subsets for simulated and real pig data sets. The core subsets were constructed (1) at random, (2) based on the diagonal of the genomic relationship matrix, (3) at random with weights from (2), or (4) based on the novel conditional algorithm. To understand the different core subset constructions, we visualise the population structure of the genotyped animals with linear Principal Component Analysis and non-linear Uniform Manifold Approximation and Projection.

RESULTS

All core subset constructions performed equally well when the number of core animals captured most of the variation in the genomic relationships, both in simulated and real data sets. When the number of core animals was not sufficiently large, there was substantial variability in the results with the random construction but no variability with the conditional construction. Visualisation of the population structure and chosen core animals showed that the conditional construction spreads core animals across the whole domain of genotyped animals in a repeatable manner.

CONCLUSIONS

Our results confirm that the size of the core subset in APY is critical. Furthermore, the results show that the core subset can be optimised with the conditional algorithm that achieves an optimal and repeatable spread of core animals across the domain of genotyped animals.

A comprehensive study on size and definition of the core group in the proven and young algorithm for single-step GBLUP

Background

The algorithm for proven and young (APY) has been suggested as a solution for recursively computing a sparse representation for the inverse of a large genomic relationship matrix (G). In APY, a subset of genotyped individuals is used as the core and the remaining genotyped individuals are used as noncore. Size and definition of the core are relevant research subjects for the application of APY, especially given the ever-increasing number of genotyped individuals.

Methods

The aim of this study was to investigate several core definitions, including the most popular animals (MPA) (i.e., animals with high contributions to the genetic pool), the least popular males (LPM), the least popular females (LPF), a random set (Rnd), animals evenly distributed across genealogical paths (Ped), unrelated individuals (Unrel), or based on within-family selection (Fam), or on decomposition of the gene content matrix (QR). Each definition was evaluated for six core sizes based on prediction accuracy of single-step genomic best linear unbiased prediction (ssGBLUP) with APY. Prediction accuracy of ssGBLUP with the full inverse of G was used as the baseline. The dataset consisted of 357k pedigreed Duroc pigs with 111k pigs with genotypes and ~ 220k phenotypic records.

Results

When the core size was equal to the number of largest eigenvalues explaining 50% of the variation of G (n = 160), MPA and Ped core definitions delivered the highest average prediction accuracies (~ 0.41−0.53). As the core size increased to the number of eigenvalues explaining 99% of the variation in G (n = 7320), prediction accuracy was nearly identical for all core types and correlations with genomic estimated breeding values (GEBV) from ssGBLUP with the full inversion of G were greater than 0.99 for all core definitions. Cores that represent all generations, such as Rnd, Ped, Fam, and Unrel, were grouped together in the hierarchical clustering of GEBV.

Conclusions

For small core sizes, the definition of the core matters; however, as the size of the core reaches an optimal value equal to the number of largest eigenvalues explaining 99% of the variation of G, the definition of the core becomes arbitrary.

Is single-step genomic REML with the algorithm for proven and young more computationally efficient when less generations of data are present?

Efficient computing techniques allow the estimation of variance components for virtually any traditional dataset. When genomic information is available, variance components can be estimated using genomic REML (GREML). If only a portion of the animals have genotypes, single-step GREML (ssGREML) is the method of choice. The genomic relationship matrix (G) used in both cases is dense, limiting computations depending on the number of genotyped animals. The algorithm for proven and young (APY) can be used to create a sparse inverse of G (GAPY~-1) with close to linear memory and computing requirements. In ssGREML, the inverse of the realized relationship matrix (H-1) also includes the inverse of the pedigree relationship matrix, which can be dense with a long pedigree, but sparser with short. The main purpose of this study was to investigate whether costs of ssGREML can be reduced using APY with truncated pedigree and phenotypes. We also investigated the impact of truncation on variance components estimation when different numbers of core animals are used in APY. Simulations included 150K animals from 10 generations, with selection. Phenotypes (h2 = 0.3) were available for all animals in generations 1-9. A total of 30K animals in generations 8 and 9, and 15K validation animals in generation 10 were genotyped for 52,890 SNP. Average information REML and ssGREML with G-1 and GAPY~-1 using 1K, 5K, 9K, and 14K core animals were compared. Variance components are impacted when the core group in APY represents the number of eigenvalues explaining a small fraction of the total variation in G. The most time-consuming operation was the inversion of G, with more than 50% of the total time. Next, numerical factorization consumed nearly 30% of the total computing time. On average, a 7% decrease in the computing time for ordering was observed by removing each generation of data. APY can be successfully applied to create the inverse of the genomic relationship matrix used in ssGREML for estimating variance components. To ensure reliable variance component estimation, it is important to use a core size that corresponds to the number of largest eigenvalues explaining around 98% of total variation in G. When APY is used, pedigrees can be truncated to increase the sparsity of H and slightly reduce computing time for ordering and symbolic factorization, with no impact on the estimates.

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). The pedigree included 1,252,619 birds hatched over 7 years, of which 154,318 from the last 4 years were genotyped. Training populations were constructed adding 1 year of data sequentially, persistency of accuracy over time was evaluated using predictions from birds hatched in the three generations following or in the years after the training populations. In the first generation, before genotypes became available for the training populations (first 3 years of data), accuracies remained almost stable with successive additions of phenotypes and pedigree to the accumulated dataset. The inclusion of 1 year of genotypes in addition to 4 years of phenotypes and pedigree in the training population led to increases in accuracy of 54% for GT, 76% for FE1, 110% for CY, and 38% for FE2; on average, 74% of the increase was due to genomics. Prediction accuracies declined faster without than with genomic information in the training populations. When genotypes were unavailable, the average decline in prediction accuracy across traits was 41% from the first to the second generation of validation, and 51% from the second to the third generation of validation. When genotypes were available, the average decline across traits was 14% from the first to the second generation of validation, and 3% from the second to the third generation of validation. Prediction accuracies in the last three generations were the same when the training population included 5 or 2 years of data, and a decrease of ~7% was observed when the training population included only 1 year of data. Training sets including genomic information provided an increase in accuracy and persistence of genomic predictions compared with training sets without genomic data. The two most recent years of pedigree, phenotypic, and genomic data were sufficient to maintain prediction accuracies in selection candidates. Similar conclusions were obtained using validation populations per year.

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 [M_e]) 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 M_e 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. The dataset included 161,897 phenotypic records for a growth trait (GT) and 27,669 phenotypic records for a fitness trait (FT) related to prolificacy in a population with dimensionality around 5,000. The pedigree included 404,979 animals from 2008 to 2020, of which 55,118 were genotyped. Two single-trait models were used with all ancestral data and sliding subsets of 3-, 2-, and 1-generation intervals. Single-step genomic best linear unbiased prediction (ssGBLUP) was used to compute genomic estimated breeding values (GEBV). Estimated accuracies were calculated by the linear regression (LR) method. The validation population consisted of single generations succeeding the training population and continued forward for all generations available. The average accuracy for the first generation after training with all ancestral data was 0.69 and 0.46 for GT and FT, respectively. The average decay in accuracy from the first generation after training to generation 9 was −0.13 and −0.19 for GT and FT, respectively. The persistence of accuracy improves with more data. Old data have a limited impact on the predictions for young animals for a trait with a large amount of information but a bigger impact for a trait with less information.

Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.

Indirect predictions with a large number of genotyped animals using the algorithm for proven and young

Reliable single-nucleotide polymorphisms (SNP) effects from genomic best linear unbiased prediction BLUP (GBLUP) and single-step GBLUP (ssGBLUP) are needed to calculate indirect predictions (IP) for young genotyped animals and animals not included in official evaluations. Obtaining reliable SNP effects and IP requires a minimum number of animals and when a large number of genotyped animals are available, the algorithm for proven and young (APY) may be needed. Thus, the objectives of this study were to evaluate IP with an increasingly larger number of genotyped animals and to determine the minimum number of animals needed to compute reliable SNP effects and IP. Genotypes and phenotypes for birth weight, weaning weight, and postweaning gain were provided by the American Angus Association. The number of animals with phenotypes was more than 3.8 million. Genotyped animals were assigned to three cumulative year-classes: born until 2013 (N = 114,937), born until 2014 (N = 183,847), and born until 2015 (N = 280,506). A three-trait model was fitted using the APY algorithm with 19,021 core animals under two scenarios: 1) core 2013 (random sample of animals born until 2013) used for all year-classes and 2) core 2014 (random sample of animals born until 2014) used for year-class 2014 and core 2015 (random sample of animals born until 2015) used for year-class 2015. GBLUP used phenotypes from genotyped animals only, whereas ssGBLUP used all available phenotypes. SNP effects were predicted using genomic estimated breeding values (GEBV) from either all genotyped animals or only core animals. The correlations between GEBV from GBLUP and IP obtained using SNP effects from core 2013 were ≥0.99 for animals born in 2013 but as low as 0.07 for animals born in 2014 and 2015. Conversely, the correlations between GEBV from ssGBLUP and IP were ≥0.99 for animals born in all years. IP predictive abilities computed with GEBV from ssGBLUP and SNP predictions based on only core animals were as high as those based on all genotyped animals. The correlations between GEBV and IP from ssGBLUP were ≥0.76, ≥0.90, and ≥0.98 when SNP effects were computed using 2k, 5k, and 15k core animals. Suitable IP based on GEBV from GBLUP can be obtained when SNP predictions are based on an appropriate number of core animals, but a considerable decline in IP accuracy can occur in subsequent years. Conversely, IP from ssGBLUP based on large numbers of phenotypes from non-genotyped animals have persistent accuracy over time.

Variance estimates are similar using pedigree or genomic relationships with or without the use of metafounders or the algorithm for proven and young animals1

With an increase in the number of animals genotyped there has been a shift from using pedigree relationship matrices (A) to genomic ones. As the use of genomic relationship matrices (G) has increased, new methods to build or approximate G have developed. We investigated whether the way variance components are estimated should reflect these changes. We estimated variance components for maternal sow traits by solving with restricted maximum likelihood, with four methods of calculating the inverse of the relationship matrix. These methods included using just the inverse of A (A−1), combining A−1 and the direct inverse of G (HDIRECT−1), including metafounders (HMETA−1), or combining A−1 with an approximated inverse of G using the algorithm for proven and young animals (HAPY−1). There was a tendency for higher additive genetic variances and lower permanent environmental variances estimated with A−1 compared with the three H−1 methods, which supports that G−1 is better than A−1 at separating genetic and permanent environmental components, due to a better definition of the actual relationships between animals. There were limited or no differences in variance estimates between HDIRECT−1, HMETA−1, and HAPY−1. Importantly, there was limited differences in variance components, repeatability or heritability estimates between methods. Heritabilities ranged between <0.01 to 0.04 for stayability after second cycle, and farrowing rate, between 0.08 and 0.15 for litter weight variation, maximum cycle number, total number born, total number still born, and prolonged interval between weaning and first insemination, and between 0.39 and 0.44 for litter birth weight and gestation length. The limited differences in heritabilities suggest that there would be very limited changes to estimated breeding values or ranking of animals across models using the different sets of variance components. It is suggested that variance estimates continue to be made using A−1, however including G−1 is possibly more appropriate if refining the model, for traits that fit a permanent environmental effect.

Updating genetic relationship matrices and their inverses: a methodology note

Most of the calculations for genetic relationship matrices and their inverses utilized in recent (t + 1) evaluations for populations of interest can be avoided by updating these matrices at t evaluations for only new animals. This study describes and develops existing methods for updating pedigree-based and marker-based relationship matrices and their inverses. Updating some of the matrices could benefit from parallel computing.

Current status of genomic evaluation

Early application of genomic selection relied on SNP estimation with phenotypes or de-regressed proofs (DRP). Chips of 50k SNP seemed sufficient for an accurate estimation of SNP effects. Genomic estimated breeding values (GEBV) were composed of an index with parent average, direct genomic value, and deduction of a parental index to eliminate double counting. Use of SNP selection or weighting increased accuracy with small data sets but had minimal to no impact with large data sets. Efforts to include potentially causative SNP derived from sequence data or high-density chips showed limited or no gain in accuracy. After the implementation of genomic selection, EBV by BLUP became biased because of genomic preselection and DRP computed based on EBV required adjustments, and the creation of DRP for females is hard and subject to double counting. Genomic selection was greatly simplified by single-step genomic BLUP (ssGBLUP). This method based on combining genomic and pedigree relationships automatically creates an index with all sources of information, can use any combination of male and female genotypes, and accounts for preselection. To avoid biases, especially under strong selection, ssGBLUP requires that pedigree and genomic relationships are compatible. Because the inversion of the genomic relationship matrix (G) becomes costly with more than 100k genotyped animals, large data computations in ssGBLUP were solved by exploiting limited dimensionality of genomic data due to limited effective population size. With such dimensionality ranging from 4k in chickens to about 15k in cattle, the inverse of G can be created directly (e.g., by the algorithm for proven and young) at a linear cost. Due to its simplicity and accuracy, ssGBLUP is routinely used for genomic selection by the major chicken, pig, and beef industries. Single step can be used to derive SNP effects for indirect prediction and for genome-wide association studies, including computations of the P-values. Alternative single-step formulations exist that use SNP effects for genotyped or for all animals. Although genomics is the new standard in breeding and genetics, there are still some problems that need to be solved. This involves new validation procedures that are unaffected by selection, parameter estimation that accounts for all the genomic data used in selection, and strategies to address reduction in genetic variances after genomic selection was implemented.

Crossbred evaluations using single-step genomic BLUP and algorithm for proven and young with different sources of data1

Genomic selection (GS) is routinely applied to many purebreds and lines of farm species. However, this method can be extended to predictions across purebreds as well as for crossbreds. This is useful for swine and poultry, for which selection in nucleus herds is typically performed on purebred animals, whereas the commercial product is the crossbred animal. Single-step genomic BLUP (ssGBLUP) is a widely applied method that can explore the recently developed algorithm for proven and young (APY). The APY allows for greater efficiency in computing BLUP solutions by exploiting the theory of limited dimensionality of genomic information and chromosome segments (Me). This study investigates the predictivity as a proxy for accuracy across and within 2 purebred pig lines and their crosses, under the application of APY in ssGBLUP setup, and different levels of Me overlapping across populations. The data consisted of approximately 210k phenotypic records for 2 traits (T1 and T2) with moderate heritability. Genotypes for 43k SNP markers were available for approximately 46k animals, from which 26k and 16k belong to 2 pure lines (L1 and L2), and approximately 4k are crossbreds. The complete pedigree had more than 720k animals. Different multivariate ssGBLUP models were applied, either with the regular or APY inverse of the genomic relationship matrix (G). The models included a standard bivariate animal model with 3 lines evaluated as 1 joint line, and for each trait individually, a 3-trait animal model with each line treated as a separate trait. Both models provided the same predictivity across and within the lines. Using either of the pure lines data as a training set resulted in a similar predictivity for the crossbreed animals (0.18 to 0.21). Across-line predictive ability was limited to less than half of the maximum predictivity for each line (L1T1 0.33, L1T2 0.25, L2T1 0.35, L2T2 0.36). For crossbred predictions, APY performed equivalently to regular G inverse when the number of core animals was equal to the number of eigenvalues explaining between 98% and 99% of the variance of G (4k to 8k) including all lines. Predictivity across the lines is achievable because of the shared Me between them. The number of those shared segments can be obtained via eigenvalue decomposition of genomic information available for each line.

The quality of the algorithm for proven and young with various sets of core animals in a multibreed sheep population1

The inverses of the pedigree and genomic relationship matrices (A, G) are required for single-step GBLUP (ssGBLUP). While, inverting A is possible for millions of animals at a linear cost, inverting G has a cubic cost and feasible for at most 150,000 animals, using the current conventional algorithms. The algorithm for proven and young (APY) provides approximations of the regular ssGBLUP by splitting genotyped animals into core and noncore groups, with computational costs being cubic for core and linear for noncore animals. The data consisted of 9,406,096 animals in the pedigree, 6,243,753 weaning weight phenotypes, and 46,949 genotyped animals from 5 breeds, composites, and animals with missing breed information from New Zealand. Aiming to find a core sample for a multibreed sheep population that can provide evaluations similar to those from the regular ssGBLUP, different core types, and core sizes were studied. Core types random, composite, oldest, youngest, the most inbred animals in G (GINB), and in A (AINB) were studied in 5K, 10K, and 20K core sizes (K = 1,000). Romney core was studied in 5K and 10K, and Coopworth-Perendale core was studied in 5K. Correlation and regression coefficient (slope) between GEBV from the non-APY and the APY analyses, as indicators for consistency with non-APY and bias from non-APY, showed a large impact of APY on noncore and a small impact on nongenotyped animals. Breed-based 5K cores resulted in large bias from non-APY even for nongenotyped animals. Random and GINB at 20K core size resulted in the highest consistency with non-APY and the lowest bias from non-APY. However, GINB did not perform as well as Random at lower core sizes. The number of animals from a breed in the core sample was very important for the evaluation of that breed. We observed that cores without Texel or Highlander animals resulted in poor evaluations for those breeds. Solving the mixed model equations, within core type, the smallest core size, and within core size, Random core converged in the least number of iterations. However, APY per se did not necessarily reduce the solving time. Random cores performed the best, as they could give a good coverage on the generations and breeds, representative for the genotyped population. Core size 20K performed better than 5K and 10K, and the optimum core size was found to be 18.8K, according to the eigenvalue decomposition of G.

Sparse single-step genomic BLUP in crossbreeding schemes

The algorithm for proven and young animals (APY) efficiently computes an approximated inverse of the genomic relationship matrix, by dividing genotyped animals in the so-called core and noncore animals. The APY leads to computationally feasible single-step genomic Best Linear Unbiased Prediction (ssGBLUP) with a large number of genotyped animals and was successfully applied to real single-breed or line datasets. This study aimed to assess the quality of genomic estimated breeding values (GEBV) when using the APY (GEBVAPY), in comparison to GEBV when using the directly inverted genomic relationship matrix (GEBVDIRECT), for situations based on crossbreeding schemes, including F1 and F2 crosses, such as the ones for pigs and chickens. Based on simulations of a 3-way crossbreeding program, we compared different approximated inverses of a genomic relationship matrix, by varying the size and the composition of the core group. We showed that GEBVAPY were accurate approximations of GEBVDIRECT for multivariate ssGBLUP involving different breeds and their crosses. GEBVAPY as accurate as GEBVDIRECT were obtained when the core groups included animals from different breed compositions and when the core groups had a size between the numbers of the largest eigenvalues explaining 98% and 99% of the variation in the raw genomic relationship matrix.