Impact of truncating historical data on prediction ability of dairy sheep selection candidates

Along the last decades, the genetic evaluation methodology has evolved, improving breeding value estimates. Many breeding programmes have historical phenotypic records and large number of generations, but to make use of them could result in more inconveniences than benefits. In this study, the prediction ability of genotyped young animals was assessed by simultaneously evaluating the removal of historical data, two pedigree deepness and two methodologies (traditional BLUP and single-step genomic BLUP or ssGBLUP), using milk yield records of 40 years of three Latxa dairy sheep populations. The linear regression method was used to compare predictions of young rams before and after progeny testing, with six cut-off points, by intervals of 4 years (from 1992 to 2012), and statistics of ratio of accuracies, bias, and dispersion were calculated. The prediction accuracy of selection candidates, when genomic information was included, was the highest in all Latxa populations (between 0.54 and 0.69 with full data set). Nevertheless, the deletion of historical phenotypic data resulted on moderate accuracy gain in the bigger data size populations (mean gain 2.5%), and the smaller population took advantage of a moderate data deletion (2.7% gain by removing data until 2004), reducing accuracy when more records were removed. The bias of validation individuals was lower when the breeding value was predicted based on genomic information (between 2.1 and 13.9), being lower when the biggest amount of data was deleted in the bigger data size populations (5.2% reduction), and the smaller population was benefited from data deletion between 1996 and 2008 (3.8% bias reduction). Meanwhile, the slope of estimated genetic trend was lower when less data were included, and an overestimation of the unknown parent group estimates was observed. The results indicated that ssGBLUP evaluations were outstanding, compared with traditional BLUP evaluations, while the depth of pedigree had a very small influence, and deletion of historical phenotypic data was beneficial. Thus, Latxa routine genetic evaluations would benefit from truncating phenotypic records between 2000 and 2004, the use of two pedigree generations and the implementation of ssGBLUP methodology.

Converting estimated breeding values from the observed to probability scale for health traits

Dairy cattle health traits are paramount from a welfare and economic viewpoint; therefore, modern breeding programs prioritize the genetic improvement of these traits. Estimated breeding values for health traits are published as the probability of animals staying healthy. They are obtained using threshold models, which assume that the observed binary phenotype (i.e., healthy or sick) is dictated by an underlying normally distributed liability exceeding or not a threshold. This methodology requires significant computing time and faces convergence challenges as it implies a nonlinear system of equations. Linear models have more straightforward computations and provide a robust approximation to threshold models; thus, they could be used to overcome the mentioned challenges. However, linear models yield estimated breeding values on the observed scale, requiring an approximation to the liability scale analogous to that from threshold models to later obtain the estimated breeding values on the probability scale. In addition, the robustness of the approximation of linear to threshold models depends on the amount of information and the incidence of the trait, with extreme incidence (i.e., ≤ 5%) deviating from optimal approximation. Our objective was to test a transformation from the observed to the liability and then to the probability scale in the genetic evaluation of health traits with moderate and very low (extreme) incidence. Data comprised displaced abomasum (5.1M), ketosis (3.6M), lameness (5M), and mastitis (6.3M) records from a Holstein population with a pedigree of 6M animals, of which 1.7M were genotyped. Univariate threshold and linear models were performed to predict breeding values. The agreement between estimated breeding values on the probability scale derived from threshold and linear models was assessed using Spearman rank correlations and comparison of estimated breeding values distributions. Correlations were at least 0.95, and estimated breeding value distributions almost entirely overlapped for all the traits but displaced abomasum, the trait with the lowest incidence (2%). Computing time was ∼3x longer for threshold than for linear models. In this Holstein population, the approximation was suboptimal for a trait with extreme incidence (2%). However, when the incidence was ≥6%, the approximation was robust, and its use is recommended along with linear models for analyzing categorical traits in large populations to ease the computational burden.

Modeling missing pedigree with metafounders and validating single-step genomic predictions in a small dairy cattle population with a great influence of foreign genetics

Genetic improvement in small countries rely heavily on foreign genetics. In an importing country such as Uruguay, consideration of unknown parent groups (UPG) for foreign sires is essential. However, the use of UPG in genomic model evaluations may lead to bias in genomic estimated breeding values (GEBV). The objective of this study was to study different models including UPG or metafounders (MF) in the Uruguayan Holstein evaluation and to analyze bias, dispersion, and accuracy of GEBV predictions in BLUP and single-step genomic BLUP (ssGBLUP). A gamma matrix (Γ) was estimated either by using base allele population frequencies obtained by bounded linear regression (MFbounded), or by using 2 values to design Γ (i.e., a single value for the diagonal and a different value for the off-diagonal [MFrobust]). Both Γ estimators performed well in terms of GEBV predictions, but MFbounded was the best option. There is, however, some bias whose origin was not completely understood. UPG or MF seem to model correctly genetic progress for unknown parents except for the very first groups (earlier time period). As for validation bulls, bias was observed across all models, whereas for validation cows it was only observed with UPG in BLUP. Overdispersion was found in all models, but it was mostly detected in validation bulls. Ratio of accuracies indicated that ssGBLUP gave better predictions than BLUP.

Unknown parent groups and truncated pedigree in single-step genomic evaluations of Murrah buffaloes

Missing pedigree may produce bias in genomic evaluations. Thus, strategies to deal with this problem have been proposed as using unknown parent groups (UPG) or truncated pedigrees. The aim of this study was to investigate the impact of modeling missing pedigree under ssGBLUP evaluations for productive and reproductive traits in dairy buffalos using different approaches: 1) traditional BLUP without UPG (BLUP), 2) traditional BLUP including UPG (BLUP/UPG), 3) ssGBLUP without UPG (ssGBLUP), 4) ssGBLUP including UPG in the A and A22 matrices (ssGBLUP/A_UPG), 5) ssGBLUP including UPG in all elements of the H matrix (ssGBLUP/H_UPG), 6) BLUP with pedigree truncation for the last 3 generations (BLUP/truncated), and 7) ssGBLUP with pedigree truncation for the last 3 generations (ssGBLUP/ truncated). UPGs were not used in the scenarios with truncated pedigree. A total of 3,717, 4,126 and 3,823 records of the first lactation for accumulated 305 d milk yield (MY), age at first calving (AFC) and lactation length (LL), respectively were used. Accuracies ranged from 0.27 for LL (BLUP) to 0.46 for MY (BLUP), bias ranged from -0.62 for MY (ssGBLUP) to 0.0002 for AFC (BLUP/truncated), and dispersion ranged from 0.88 for MY (BLUP/ A_UPG) to 1.13 for LL (BLUP). Genetic trend showed genetic gains for all traits across 20 years of selection and the impact of including either genomic information, UPG or pedigree truncation under GEBV accuracies ranged among the evaluated traits. Overall, methods using UPGs, truncation pedigree and genomic information exhibited potential to improve GEBV accuracies, bias and dispersion for all traits compared with other methods. Truncated scenarios promoted high genetic gains. In small populations with few genotyped animals, combining truncated pedigree or UPG with genomic information is a feasible approach to deal with missing pedigrees.

A comparison of genetic and genomic breeding values in Saanen and Alpine goats

Nowadays, several countries are developing or adopting genomic selection in the dairy goat sector. The most used method to estimate breeding values is Single-Step Genomic Best Linear Unbiased Prediction (ssGBLUP) which offers several advantages in terms of computational process and accuracy of the estimated breeding values (EBVs). Saanen and Alpine are the predominant dairy goat breeds in Italy, and both have similar breeding programs where EBVs for productive traits are currently calculated using BLUP. This work describes the implementation of genomic selection for these two breeds in Italy, aligning with the selection practices already carried out in the international landscape. The available dataset included 3 611 genotyped animals, 11 470 lactation records, five traits (milk, protein and fat yields, and fat and protein percentages), and three-generation pedigrees. EBVs were estimated using BLUP, GBLUP, and ssGBLUP both with single and multiple trait approaches. The methods were compared in terms of correlation between EBVs and genetic trends. Results were also validated with the linear regression method excluding part of the phenotypic data. In both breeds, EBVs and GEBVs were strongly correlated and the trend of each trait was similar comparing the three methods. The average increase in accuracy across traits and methods amounted to +13 and +10% from BLUP to ssGBLUP for Alpine and Saanen breeds, respectively. Results indicated higher prediction accuracy and correlation for GBLUP and ssGBLUP compared to BLUP, implying that the use of genotypes increases the accuracy of EBVs, particularly in the absence of phenotypic data. Therefore, ssGBLUP is likely to be the most effective method to enhance genetic gain in Italian Saanen and Alpine goats.

Single-step SNPBLUP evaluation in six German beef cattle breeds

The implementation of genomic selection for six German beef cattle populations was evaluated. Although the multiple-step implementation of genomic selection is the status quo in most national dairy cattle evaluations, the breeding structure of German beef cattle, coupled with the shortcoming and complexity of the multiple-step method, makes single step a more attractive option to implement genomic selection in German beef cattle populations. Our objective was to develop a national beef cattle single-step genomic evaluation in five economically important traits in six German beef cattle populations and investigate its impact on the accuracy and bias of genomic evaluations relative to the current pedigree-based evaluation. Across the six breeds in our study, 461,929 phenotyped and 14,321 genotyped animals were evaluated with a multi-trait single-step model. To validate the single-step model, phenotype data in the last 2 years were removed in a forward validation study. For the conventional and single-step approaches, the genomic estimated breeding values of validation animals and other animals were compared between the truncated and the full evaluations. The correlation of the GEBVs between the full and truncated evaluations in the validation animals was slightly higher in the single-step evaluation. The regression of the full GEBVs on truncated GEBVs was close to the optimal value of 1 for both the pedigree-based and the single-step evaluations. The SNP effect estimates from the truncated evaluation were highly correlated with those from the full evaluation, with values ranging from 0.79 to 0.94. The correlation of the SNP effect was influenced by the number of genotyped animals shared between the full and truncated evaluations. The regression coefficients of the SNP effect of the full evaluation on the truncated evaluation were all close to the expected value of 1, indicating unbiased estimates of the SNP markers for the production traits. The Manhattan plot of the SNP effect estimates identified chromosomal regions harbouring major genes for muscling and body weight in breeds of French origin. Based on the regression intercept and slope of the GEBVs of validation animals, the single-step evaluation was neither inflated nor deflated across the six breeds. Overall, the single-step model resulted in a more accurate and stable evaluation. However, due to the small number of genotyped individuals, the single-step method only provided slightly better results when compared to the pedigree-based method.

The importance of historically popular sires on the accuracy of genomic predictions of young animals in the US Holstein population

The dairy industry is known for its extensive use of artificial insemination, which has resulted in a population where most animals can be traced back to only a few sires. Due to their relatedness to the population, old influential sires could still contribute to the accuracy of genomic predictions. The objective of the study was to identify the impact of historically influential sires on the recent population. This was tested by constructing a genomic relationship matrix using recursion with different sets of sires. Differences in prediction accuracies with different sets are indicative of how important each set is. Recursion coefficients linking young animals to those sets reveal the relative importance of specific sires to the prediction accuracy of recent animals. The data included ∼10 million scores for stature and fore udder attachment (FUA) measured from 1983. Genotypes of 569,404 animals were available. Sire sets included the 100 most popular sires born within different time periods. Computations were with single-step genomic BLUP. In general, the younger sires had higher prediction accuracies than the oldest sires, even though they generally have fewer progeny. The accuracy of evaluation for stature was increased from 0.54 with the most popular sires born before 1981 to 0.69 with sires born from 2001 to 2010, while the accuracy for FUA increased from 0.47 to 0.61. The accuracy achieved using the overall 100 most used sires was 0.66 for stature and 0.58 for FUA. All 100 sires from each period were combined in a subset to determine the importance of each sire relative to all 400 animals in the combined subset. The highest relative impact of a sire that was born within the different time sets was 1.97 for Valiant (before 1981), 1.94 for Blackstar (1981 to 1990), 4.38 for Shottle (1991 to 2000), and 3.09 for Planet (2001 to 2010). The 3 sires among the 400 with the greatest impact were Shottle, Goldwyn (3.73), and Planet. The relative impact of a sire was not strongly related to the number of progeny. For instance, the relative impact of Durham with 34K progeny was 2.29, whereas the impact of O Man with 15K progeny was 3.13. The impact of a sire is also influenced by whether it was used as a sire of sires. Results show that younger sires are more relevant to the accuracy of breeding value prediction in the recent population.

A genome-wide association study for loin depth and muscle pH in pigs from intensely selected purebred lines

BACKGROUND

Genome-wide association studies (GWAS) aim at identifying genomic regions involved in phenotype expression, but identifying causative variants is difficult. Pig Combined Annotation Dependent Depletion (pCADD) scores provide a measure of the predicted consequences of genetic variants. Incorporating pCADD into the GWAS pipeline may help their identification. Our objective was to identify genomic regions associated with loin depth and muscle pH, and identify regions of interest for fine-mapping and further experimental work. Genotypes for ~ 40,000 single nucleotide morphisms (SNPs) were used to perform GWAS for these two traits, using de-regressed breeding values (dEBV) for 329,964 pigs from four commercial lines. Imputed sequence data was used to identify SNPs in strong ([Formula: see text] 0.80) linkage disequilibrium with lead GWAS SNPs with the highest pCADD scores.

RESULTS

Fifteen distinct regions were associated with loin depth and one with loin pH at genome-wide significance. Regions on chromosomes 1, 2, 5, 7, and 16, explained between 0.06 and 3.55% of the additive genetic variance and were strongly associated with loin depth. Only a small part of the additive genetic variance in muscle pH was attributed to SNPs. The results of our pCADD analysis suggests that high-scoring pCADD variants are enriched for missense mutations. Two close but distinct regions on SSC1 were associated with loin depth, and pCADD identified the previously identified missense variant within the MC4R gene for one of the lines. For loin pH, pCADD identified a synonymous variant in the RNF25 gene (SSC15) as the most likely candidate for the muscle pH association. The missense mutation in the PRKAG3 gene known to affect glycogen content was not prioritised by pCADD for loin pH.

CONCLUSIONS

For loin depth, we identified several strong candidate regions for further statistical fine-mapping that are supported in the literature, and two novel regions. For loin muscle pH, we identified one previously identified associated region. We found mixed evidence for the utility of pCADD as an extension of heuristic fine-mapping. The next step is to perform more sophisticated fine-mapping and expression quantitative trait loci (eQTL) analysis, and then interrogate candidate variants in vitro by perturbation-CRISPR assays.

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.

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.

Leveraging low-density crossbred genotypes to offset crossbred phenotypes and their impact on purebred predictions

The objectives of this study were to 1) investigate the predictability and bias of genomic breeding values (GEBV) of purebred (PB) sires for CB performance when CB genotypes imputed from a low-density panel are available, 2) assess if the availability of those CB genotypes can be used to partially offset CB phenotypic recording, and 3) investigate the impact of including imputed CB genotypes in genomic analyses when using the algorithm for proven and young (APY). Two pig populations with up to 207,375 PB and 32,893 CB phenotypic records per trait and 138,026 PB and 32,893 CB genotypes were evaluated. PB sires were genotyped for a 50K panel, whereas CB animals were genotyped for a low-density panel of 600 SNP and imputed to 50K. The predictability and bias of GEBV of PB sires for backfat thickness (BFX) and average daily gain recorded (ADGX) recorded on CB animals were assessed when CB genotypes were available or not in the analyses. In the first set of analyses, direct inverses of the genomic relationship matrix (G) were used with phenotypic datasets truncated at different time points. In the next step, we evaluated the APY algorithm with core compositions differing in the CB genotype contributions. After that, the performance of core compositions was compared with an analysis using a random PB core from a purely PB genomic set. The number of rounds to convergence was recorded for all APY analyses. With the direct inverse of G in the first set of analyses, adding CB genotypes imputed from a low-density panel (600 SNP) did not improve predictability or reduce the bias of PB sires' GEBV for CB performance, even for sires with fewer CB progeny phenotypes in the analysis. That indicates that the inclusion of CB genotypes primarily used for inferring pedigree in commercial farms is of no benefit to offset CB phenotyping. When CB genotypes were incorporated into APY, a random core composition or a core with no CB genotypes reduced bias and the number of rounds to convergence but did not affect predictability. Still, a PB random core composition from a genomic set with only PB genotypes resulted in the highest predictability and the smallest number of rounds to convergence, although bias increased. Genotyping CB individuals for low-density panels is a valuable identification tool for linking CB phenotypes to pedigree; however, the inclusion of those CB genotypes imputed from a low-density panel (600 SNP) might not benefit genomic predictions for PB individuals or offset CB phenotyping for the evaluated CB performance traits. Further studies will help understand the usefulness of those imputed CB genotypes for traits with lower PB-CB genetic correlations and traits not recorded in the PB environment, such as mortality and disease traits.

The long-term effects of genomic selection: 1. Response to selection, additive genetic variance, and genetic architecture

Background

Genomic selection has revolutionized genetic improvement in animals and plants, but little is known about its long-term effects. Here, we investigated the long-term effects of genomic selection on response to selection, genetic variance, and the genetic architecture of traits using stochastic simulations. We defined the genetic architecture as the set of causal loci underlying each trait, their allele frequencies, and their statistical additive effects. We simulated a livestock population under 50 generations of phenotypic, pedigree, or genomic selection for a single trait, controlled by either only additive, additive and dominance, or additive, dominance, and epistatic effects. The simulated epistasis was based on yeast data.

Results

Short-term response was always greatest with genomic selection, while response after 50 generations was greater with phenotypic selection than with genomic selection when epistasis was present, and was always greater than with pedigree selection. This was mainly because loss of genetic variance and of segregating loci was much greater with genomic and pedigree selection than with phenotypic selection. Compared to pedigree selection, selection response was always greater with genomic selection. Pedigree and genomic selection lost a similar amount of genetic variance after 50 generations of selection, but genomic selection maintained more segregating loci, which on average had lower minor allele frequencies than with pedigree selection. Based on this result, genomic selection is expected to better maintain genetic gain after 50 generations than pedigree selection. The amount of change in the genetic architecture of traits was considerable across generations and was similar for genomic and pedigree selection, but slightly less for phenotypic selection. Presence of epistasis resulted in smaller changes in allele frequencies and less fixation of causal loci, but resulted in substantial changes in statistical additive effects across generations.

Conclusions

Our results show that genomic selection outperforms pedigree selection in terms of long-term genetic gain, but results in a similar reduction of genetic variance. The genetic architecture of traits changed considerably across generations, especially under selection and when non-additive effects were present. In conclusion, non-additive effects had a substantial impact on the accuracy of selection and long-term response to selection, especially when selection was accurate.

Removing data and using metafounders alleviates biases for all traits in Lacaune dairy sheep predictions

Bias in dairy genetic evaluations, when it exists, has to be understood and properly addressed. The origin of biases is not always clear. We analyzed 40 yr of records from the Lacaune dairy sheep breeding program to evaluate the extent of bias, assess possible corrections, and emit hypotheses on its origin. The data set included 7 traits (milk yield, fat and protein contents, somatic cell score, teat angle, udder cleft, and udder depth) with records from 600,000 to 5 million depending on the trait, ∼1,900,000 animals, and ∼5,900 genotyped elite artificial insemination rams. For the ∼8% animals with missing sire, we fit 25 unknown parent groups. We used the linear regression method to compare "partial" and "whole" predictions of young rams before and after progeny testing, with 7 cut-off points, and we obtained estimates of their bias, (over)dispersion, and accuracy in early proofs. We tried (1) several scenarios as follows: multiple or single trait, the "official" (routine) evaluation, which is a mixture of both single and multiple trait, and "deletion" of data before 1990; and (2) several models as follows: BLUP and single-step genomic (SSG)BLUP with fixed unknown parent groups or metafounders, where, for metafounders, their relationship matrix gamma was estimated using either a model for inbreeding trend, or base allele frequencies estimated by peeling. The estimate of gamma obtained by modeling the inbreeding trend resulted in an estimated increase of inbreeding, based on markers, faster than the pedigree-based one. The estimated genetic trends were similar for most models and scenarios across all traits, but were shrunken when gamma was estimated by peeling. This was due to shrinking of the estimates of metafounders in the latter case. Across scenarios, all traits showed bias, generally as an overestimate of genetic trend for milk yield and an underestimate for the other traits. As for the slope, it showed overdispersion of estimated breeding values for all traits. Using multiple-trait models slightly reduced the overestimate of genetic trend and the overdispersion, as did including genomic information (i.e., SSGBLUP) when the gamma matrix was estimated by the model for inbreeding trend. However, only deletion of historical data before 1990 resulted in elimination of both kind of biases. The SSGBLUP resulted in more accurate early proofs than BLUP for all traits. We considered that a snowball effect of small errors in each genetic evaluation, combined with selection, may have resulted in biased evaluations. Improving statistical methods reduced some bias but not all, and a simple solution for this data set was to remove historical records.

Validation of single-step genomic predictions using the linear regression method for milk yield and heat tolerance in a Thai-Holstein population

Background and Aim:

Genomic selection improves accuracy and decreases the generation interval, increasing the selection response. This study was conducted to assess the benefits of using single-step genomic best linear unbiased prediction (ssGBLUP) for genomic evaluations of milk yield and heat tolerance in Thai-Holstein cows and to test the value of old phenotypic data to maintain the accuracy of predictions.

Materials and Methods:

The dataset included 104,150 milk yield records collected from 1999 to 2018 from 15,380 cows. The pedigree contained 33,799 animals born between 1944 and 2016, of which 882 were genotyped. Analyses were performed with and without genomic information using ssGBLUP and BLUP, respectively. Statistics for bias, dispersion, the ratio of accuracies, and the accuracy of estimated breeding values were calculated using the linear regression (LR) method. A partial dataset excluded the phenotypes of the last generation, and 66 bulls were identified as validation individuals.

Results:

Bias was considerable for BLUP (0.44) but negligible (−0.04) for ssGBLUP; dispersion was similar for both techniques (0.84 vs. 1.06 for BLUP and ssGBLUP, respectively). The ratio of accuracies was 0.33 for BLUP and 0.97 for ssGBLUP, indicating more stable predictions for ssGBLUP. The accuracy of predictions was 0.18 for BLUP and 0.36 for ssGBLUP. Excluding the first 10 years of phenotypic data (i.e., 1999-2008) decreased the accuracy to 0.09 for BLUP and 0.32 for ssGBLUP. Genomic information doubled the accuracy and increased the persistence of genomic estimated breeding values when old phenotypes were removed.

Conclusion:

The LR method is useful for estimating accuracies and bias in complex models. When the population size is small, old data are useful, and even a small amount of genomic information can substantially improve the accuracy. The effect of heat stress on first parity milk yield is small.

Invited review: Unknown-parent groups and metafounders in single-step genomic BLUP

Single-step genomic BLUP (ssGBLUP) is a method for genomic prediction that integrates matrices of pedigree (A) and genomic (G) relationships into a single unified additive relationship matrix whose inverse is incorporated into a set of mixed model equations (MME) to compute genomic predictions. Pedigree information in dairy cattle is often incomplete. Missing pedigree potentially causes biases and inflation in genomic estimated breeding values (GEBV) obtained with ssGBLUP. Three major issues are associated with missing pedigree in ssGBLUP, namely biased predictions by selection, missing inbreeding in pedigree relationships, and incompatibility between G and A in level and scale. These issues can be solved using a proper model for unknown-parent groups (UPG). The theory behind the use of UPG is well established for pedigree BLUP, but not for ssGBLUP. This study reviews the development of the UPG model in pedigree BLUP, the properties of UPG models in ssGBLUP, and the effect of UPG on genetic trends and genomic predictions. Similarities and differences between UPG and metafounder (MF) models, a generalized UPG model, are also reviewed. A UPG model (QP) derived using a transformation of the MME has a good convergence behavior. However, with insufficient data, the QP model may yield biased genetic trends and may underestimate UPG. The QP model can be altered by removing the genomic relationships linking GEBV and UPG effects from MME. This altered QP model exhibits less bias in genetic trends and less inflation in genomic predictions than the QP model, especially with large data sets. Recently, a new model, which encapsulates the UPG equations into the pedigree relationships for genotyped animals, was proposed in simulated purebred populations. The MF model is a comprehensive solution to the missing pedigree issue. This model can be a choice for multibreed or crossbred evaluations if the data set allows the estimation of a reasonable relationship matrix for MF. Missing pedigree influences genetic trends, but its effect on the predictability of genetic merit for genotyped animals should be negligible when many proven bulls are genotyped. The SNP effects can be back-solved using GEBV from older genotyped animals, and these predicted SNP effects can be used to calculate GEBV for young-genotyped animals with missing parents.

Metafounders May Reduce Bias in Composite Cattle Genomic Predictions

Metafounders are pseudo-individuals that act as proxies for animals in base populations. When metafounders are used, individuals from different breeds can be related through pedigree, improving the compatibility between genomic and pedigree relationships. The aim of this study was to investigate the use of metafounders and unknown parent groups (UPGs) for the genomic evaluation of a composite beef cattle population. Phenotypes were available for scrotal circumference at 14 months of age (SC14), post weaning gain (PWG), weaning weight (WW), and birth weight (BW). The pedigree included 680,551 animals, of which 1,899 were genotyped for or imputed to around 30,000 single-nucleotide polymorphisms (SNPs). Evaluations were performed based on pedigree (BLUP), pedigree with UPGs (BLUP_UPG), pedigree with metafounders (BLUP_MF), single-step genomic BLUP (ssGBLUP), ssGBLUP with UPGs for genomic and pedigree relationship matrices (ssGBLUP_UPG) or only for the pedigree relationship matrix (ssGBLUP_UPGA), and ssGBLUP with metafounders (ssGBLUP_MF). Each evaluation considered either four or 10 groups that were assigned based on breed of founders and intermediate crosses. To evaluate model performance, we used a validation method based on linear regression statistics to obtain accuracy, stability, dispersion, and bias of (genomic) estimated breeding value [(G)EBV]. Overall, relationships within and among metafounders were stronger in the scenario with 10 metafounders. Accuracy was greater for models with genomic information than for BLUP. Also, the stability of (G)EBVs was greater when genomic information was taken into account. Overall, pedigree-based methods showed lower inflation/deflation (regression coefficients close to 1.0) for SC14, WWM, and BWD traits. The level of inflation/deflation for genomic models was small and trait-dependent. Compared with regular ssGBLUP, ssGBLUP_MF4 displayed regression coefficient closer to one SC14, PWG, WWM, and BWD. Genomic models with metafounders seemed to be slightly more stable than models with UPGs based on higher similarity of results with different numbers of groups. Further, metafounders can help to reduce bias in genomic evaluations of composite beef cattle populations without reducing the stability of GEBVs.

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.

Automatic Fruit Morphology Phenome and Genetic Analysis: An Application in the Octoploid Strawberry

Automatizing phenotype measurement will decisively contribute to increase plant breeding efficiency. Among phenotypes, morphological traits are relevant in many fruit breeding programs, as appearance influences consumer preference. Often, these traits are manually or semiautomatically obtained. Yet, fruit morphology evaluation can be enhanced using fully automatized procedures and digital images provide a cost-effective opportunity for this purpose. Here, we present an automatized pipeline for comprehensive phenomic and genetic analysis of morphology traits extracted from internal and external strawberry (Fragaria x ananassa) images. The pipeline segments, classifies, and labels the images and extracts conformation features, including linear (area, perimeter, height, width, circularity, shape descriptor, ratio between height and width) and multivariate (Fourier elliptical components and Generalized Procrustes) statistics. Internal color patterns are obtained using an autoencoder to smooth out the image. In addition, we develop a variational autoencoder to automatically detect the most likely number of underlying shapes. Bayesian modeling is employed to estimate both additive and dominance effects for all traits. As expected, conformational traits are clearly heritable. Interestingly, dominance variance is higher than the additive component for most of the traits. Overall, we show that fruit shape and color can be quickly and automatically evaluated and are moderately heritable. Although we study strawberry images, the algorithm can be applied to other fruits, as shown in the GitHub repository.

Genomic predictions for yield traits in US Holsteins with unknown parent groups

The objective of this study was to assess the reliability and bias of estimated breeding values (EBV) from traditional BLUP with unknown parent groups (UPG), genomic EBV (GEBV) from single-step genomic BLUP (ssGBLUP) with UPG for the pedigree relationship matrix (A) only (SS_UPG), and GEBV from ssGBLUP with UPG for both A and the relationship matrix among genotyped animals (A₂₂; SS_UPG2) using 6 large phenotype-pedigree truncated Holstein data sets. The complete data included 80 million records for milk, fat, and protein yields from 31 million cows recorded since 1980. Phenotype-pedigree truncation scenarios included truncation of phenotypes for cows recorded before 1990 and 2000 combined with truncation of pedigree information after 2 or 3 ancestral generations. A total of 861,525 genotyped bulls with progeny and cows with phenotypic records were used in the analyses. Reliability and bias (inflation/deflation) of GEBV were obtained for 2,710 bulls based on deregressed proofs, and on 381,779 cows born after 2014 based on predictivity (adjusted cow phenotypes). The BLUP reliabilities for young bulls varied from 0.29 to 0.30 across traits and were unaffected by data truncation and number of generations in the pedigree. Reliabilities ranged from 0.54 to 0.69 for SS_UPG and were slightly affected by phenotype-pedigree truncation. Reliabilities ranged from 0.69 to 0.73 for SS_UPG2 and were unaffected by phenotype-pedigree truncation. The regression coefficient of bull deregressed proofs on (G)EBV (i.e., GEBV and EBV) ranged from 0.86 to 0.90 for BLUP, from 0.77 to 0.94 for SS_UPG, and was 1.00 ± 0.03 for SS_UPG2. Cow predictivity ranged from 0.22 to 0.28 for BLUP, 0.48 to 0.51 for SS_UPG, and 0.51 to 0.54 for SS_UPG2. The highest cow predictivities for BLUP were obtained with the most extreme truncation, whereas for SS_UPG2, cow predictivities were also unaffected by phenotype-pedigree truncations. The regression coefficient of cow predictivities on (G)EBV was 1.02 ± 0.02 for SS_UPG2 with the most extreme truncation, which indicated the least biased predictions. Computations with the complete data set took 17 h with BLUP, 58 h with SS_UPG, and 23 h with SS_UPG2. The same computations with the most extreme phenotype-pedigree truncation took 7, 36, and 15 h, respectively. The SS_UPG2 converged in fewer rounds than BLUP, whereas SS_UPG took up to twice as many rounds. Thus, the ssGBLUP with UPG assigned to both A and A₂₂ provided accurate and unbiased evaluations, regardless of phenotype-pedigree truncation scenario. Old phenotypes (before 2000 in this data set) did not affect the reliability of predictions for young selection candidates, especially in SS_UPG2.

Avoiding preselection bias in subsequent single-step genomic BLUP evaluations of genomically preselected animals

In animal breeding, parents of the next generation are usually selected in multiple stages, and the initial stages of this selection are called preselection. Preselection reduces the information available for subsequent evaluation of preselected animals and this sometimes leads to bias. The objective of this study was to establish the minimum information required to subsequently evaluate genomically preselected animals without bias arising from preselection, with single-step genomic best linear unbiased prediction (ssGBLUP). We simulated a nucleus of a breeding program in which a recent population of 15 generations was produced. In each generation, parents of the next generation were selected in a single-stage selection based on pedigree BLUP. However, in generation 15, 10% of male and 15% of female offspring were preselected on their genomic estimated breeding values (GEBV). These GEBV were estimated using ssGBLUP, including the pedigree of all animals in generations 0-15, genotypes of all animals in generations 13-15 and phenotypes of all animals in generations 11-14. In subsequent ssGBLUP evaluation of these preselected animals, genotypes and phenotypes from various groups of animals were excluded one after another. We found that GEBV of the preselected animals were only estimated without preselection bias when genotypes and phenotypes of all animals in generations 13 and 14 and of the preselected animals were included in the subsequent evaluation. We also found that genotypes of the animals discarded at preselection only helped in reducing preselection bias in GEBV of their preselected sibs when genotypes of their parents were absent or excluded from the subsequent evaluation. We concluded that to prevent preselection bias in subsequent ssGBLUP evaluation of genomically preselected animals, information representative of the reference data used in the evaluation at preselection and genotypes and phenotypes of the preselected animals are needed in the subsequent evaluation.

Technical note: Automatic scaling in single-step genomic BLUP

Single-step genomic BLUP (ssGBLUP) requires compatibility between genomic and pedigree relationships for unbiased and accurate predictions. Scaling the genomic relationship matrix (G) to have the same averages as the pedigree relationship matrix (i.e., scaling by averages) is one way to ensure compatibility. This requires computing both relationship matrices, calculating averages, and changing G, whereas only the inverses of those matrices are needed in the mixed model equations. Therefore, the compatibility process can add extra computing burden. In the single-step Bayesian regression, the scaling is done by including a mean (μ_g) as a fixed effect in the model. The parameter μ_g can be interpreted as the average of the breeding values of the genotyped animals. In this study, such scaling, called automatic, was implemented in ssGBLUP via Quaas-Pollak transformation of the inverse of the relationship matrix used in ssGBLUP (H), which combines the inverses of the pedigree and genomic relationship matrices. Comparisons involved a simulated data set, and the genomic relationship matrix was computed using different allele frequencies either from the current population (i.e., realized allele frequencies), equal among all the loci, or from the base population. For all of the scenarios, we computed bias [defined as the average difference between true breeding values (TBV) and genomic estimated breeding values (GEBV)], accuracy (defined as the correlation between TBV and GEBV), and dispersion (defined as the regression coefficient of GEBV on TBV). With no scaling, the bias expressed in terms of genetic standard deviations was 0.86, 0.64, and 0.58 with realized, equal, and base population allele frequencies, respectively. With scaling by averages, which is currently used in ssGBLUP, bias was 0.07, 0.08, and 0.03, respectively. With automatic scaling, bias was 0.18 regardless of allele frequencies. Accuracies were similar among scaling methods, but about 0.1 lower in the scenario without scaling. The GEBV were more inflated without any scaling, whereas the automatic scaling performed similarly to the scaling by averages. The average dispersion for those methods was 0.94. When μ_g was treated as random, with the variance equal to differences between pedigree and genomic relationships, the bias was the same as with the scaling by averages. The automatic scaling is biased, especially when μ_g is treated as a fixed effect. The bias may be small in real data with fewer generations, when traits are undergoing weak selection, or when the number of genotyped animals is large.

Autoregressive single-step model for genomic evaluation of longitudinal reproductive traits in portuguese holstein cattle

We investigated the applicability of ssGBLUP methodology under the autoregressive model (H-AR) for genomic evaluation of longitudinal reproductive traits in Portuguese Holstein cattle. The genotype data of 1,230 bulls and 1,645 cows were considered in our study. The reproductive traits evaluated were interval from calving to first service (ICF), calving interval (CI) and daughter pregnancy rate (DPR) measured during the first four parities. Reliability and rank correlation were used to compare the H-AR with the traditional pedigree-based autoregressive models (A-AR). In addition, a validation study was performed considering different scenarios. Higher genomic estimated breeding values (GEBV) reliabilities were obtained for genotyped bulls when evaluated under the H-AR model, with emphasis on bulls with less than 9 daughters. For this group, the averages of GEBV reliabilities corresponded to 0.62, 0.69 and 0.62 for ICF, CI and DPR, respectively, while the averages obtained by the A-AR model were 0.27, 0.15 and 0.16. The validation study was favourable to H-AR. The best results were observed in the scenario where genotyped cows were combined with contributing bulls (genotyped bulls with daughter or relationship information in the population). Overall, the results suggest that ssGBLUP methodology under the autoregressive model is a feasible and applicable approach to be used in genomic analyses of longitudinal reproductive traits in Portuguese Holstein cattle.

The impact of training on data from genetically-related lines on the accuracy of genomic predictions for feed efficiency traits in pigs

Background

Most genomic predictions use a unique population that is split into a training and a validation set. However, genomic prediction using genetically heterogeneous training sets could provide more flexibility when constructing the training sets in small populations. The aim of our study was to investigate the potential of genomic prediction of feed efficiency related traits using training sets that combine animals from two different, but genetically-related lines. We compared realized prediction accuracy and prediction bias for different training set compositions for five production traits.

Results

Genomic breeding values (GEBV) were predicted using the single-step genomic best linear unbiased prediction method in six scenarios applied iteratively to two genetically-related lines (i.e. 12 scenarios). The objective for all scenarios was to predict GEBV of pigs in the last three generations (~ 400 pigs, G7 to G9) of a given line. For each line, a control scenario was set up with a training set that included only animals from that line (target line). For all traits, adding more animals from the other line to the training set did not increase prediction accuracy compared to the control scenario. A small decrease in prediction accuracies was found for average daily gain, backfat thickness, and daily feed intake as the number of animals from the target line decreased in the training set. Including more animals from the other line did not decrease prediction accuracy for feed conversion ratio and residual feed intake, which were both highly affected by selection within lines. However, prediction biases were systematic for these cases and might be reduced with bivariate analyses.

Conclusions

Our results show that genomic prediction using a training set that includes animals from genetically-related lines can be as accurate as genomic prediction using a training set from the target population. With combined reference sets, accuracy increased for traits that were highly affected by selection. Our results provide insights into the design of reference populations, especially to initiate genomic selection in small-sized lines, for which the number of historical samples is small and that are developed simultaneously. This applies especially to poultry and pig breeding and to other crossbreeding schemes.

Symposium review: How to implement genomic selection

Genomic selection was adopted very quickly in the 10 yr after first implementation, and breeders continue to find new uses for genomic testing. Breeding values with higher reliability earlier in life are estimated by combining DNA genotypes for many thousands of loci using existing identification, pedigree, and phenotype databases for millions of animals. Quality control for both new and previous data is greatly improved by comparing genomic and pedigree relationships to correct parent-progeny conflicts and discover many additional ancestors. Many quantitative trait loci and gene tests have been added to previous assays that used only evenly spaced, highly polymorphic markers. Imputation now combines genotypes from many assays of differing marker densities. Prediction models have gradually advanced from normal or Bayesian distributions within trait and breed to single-step, multitrait, or other more complex models, such as multibreed models that may be needed for crossbred prediction. Genomic selection was initially applied to males to predict progeny performance but is now widely applied to females or even embryos to predict their own later performance. The initial focus on additive merit has expanded to include mating programs, genomic inbreeding, and recessive alleles. Many producers now use DNA testing to decide which heifers should be inseminated with elite dairy, beef, or sex-sorted semen, which should be embryo donors or recipients, or which should be sold or kept for breeding. Because some of these decisions are expensive to delay, predictions are now provided weekly instead of every few months. Predictions from international genomic databases are often more accurate and cost-effective than those from within-country databases that were previously designed for progeny testing unless local breeds, conditions, or traits differ greatly from the larger database. Selection indexes include many new traits, often with lower heritability or requiring large initial investments to obtain phenotypes, which provide further incentive to cooperate internationally. The genomic prediction methods developed for dairy cattle are now applied widely to many animal, human, and plant populations and could be applied to many more.

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.

Reliability of genomic evaluation for egg quality traits in layers

Background

Genomic evaluation, based on the use of thousands of genetic markers in addition to pedigree and phenotype information, has become the standard evaluation methodology in dairy cattle breeding programmes over the past several years. Despite the many differences between dairy cattle breeding and poultry breeding, genomic selection seems very promising for the avian sector, and studies are currently being conducted to optimize avian selection schemes. In this optimization perspective, one of the key parameters is to properly predict the accuracy of genomic evaluation in pure line layers.

Results

It was observed that genomic evaluation, whether performed on males or females, always proved more accurate than genetic evaluation. The gain was higher when phenotypic information was narrowed, and an augmentation of the size of the reference population led to an increase in accuracy prediction with regard to genomic evaluation. By taking into account the increase of selection intensity and the decrease of the generation interval induced by genomic selection, the expected annual genetic gain would be higher with ancestry-based genomic evaluation of male candidates than with genetic evaluation based on collaterals. This advantage of genomic selection over genetic selection requires more detailed further study for female candidates.

Conclusions

In conclusion, in the population studied, the genomic evaluation of egg quality traits of breeding birds at birth seems to be a promising strategy, at least for the selection of males.

Invited review: Advances and applications of random regression models: From quantitative genetics to genomics

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits.

Comparison of economic returns among genetic evaluation strategies in a 2-tiered Charolais-sired beef cattle production system1,2

The objective of this study was to estimate economic returns and costs associated with 4 scenarios of genetic evaluation that combine genotypes, phenotypes, and pedigree information from a vertically integrated purebred (PB) and commercial (CM) beef cattle system. Inference was to a genetic evaluation for a production system producing Charolais terminal sires for 10,000 CM cows. The first genetic evaluation scenario, denoted PB_A, modeled a genetic evaluation in which pedigree information and phenotypes are available for PB seedstock animals. Scenario PB_H contained the same information as PB_A with the addition of 25K density (GeneSeek Genomic Profiler LD) single nucleotide polymorphism (SNP) genotypes from PB animals. Scenario PBCM_A contained pedigree records and phenotypes from PB and CM cattle. Scenario PBCM_H contained phenotypes, pedigree, and genotypes from the PB and CM animals. Estimates of prediction error variance, (co)variance, and selection index parameters were used to estimate accuracy of selection candidates (r_TI) and genetic gain resulting from selection on an economic index in US dollars (ΔG). Annual costs and incomes were used to determine the 30-yr cumulative net present value (CNPV) per CM calf resulting from selection in these genetic evaluation scenarios. Adding genotypes and CM production phenotypes to genetic evaluation increased the r_TI of selection candidates and ΔG across all 4 scenarios. Scenario PBCM_H produced the highest annual ΔG in the PB herd at US$11.91 per head. Including CM phenotypes and parentage testing in the genetic evaluation increased the time to breakeven from 12 yr in PB_A to 19 years in PBCM_A after accounting for the cost of that information. Adding CM phenotypes and genotypes increased the breakeven time from 12 yr in PB_H to 18 yr in PBCM_H. Scenario PB_H produced the highest 30-yr CNPV per slaughtered CM calf at US$371.16. These results using field data indicate that economically relevant r_TI and ΔG can be realized by adding 25K SNP genotypes and CM phenotypes to genetic evaluation, but the additional cost of that data significantly delays the economic return to the enterprise.

The impact of truncating data on the predictive ability for single-step genomic best linear unbiased prediction

Simulated and swine industry data sets were utilized to assess the impact of removing older data on the predictive ability of selection candidate estimated breeding values (EBV) when using single-step genomic best linear unbiased prediction (ssGBLUP). Simulated data included thirty replicates designed to mimic the structure of swine data sets. For the simulated data, varying amounts of data were truncated based on the number of ancestral generations back from the selection candidates. The swine data sets consisted of phenotypic and genotypic records for three traits across two breeds on animals born from 2003 to 2017. Phenotypes and genotypes were iteratively removed 1 year at a time based on the year an animal was born. For the swine data sets, correlations between corrected phenotypes (Cp) and EBV were used to evaluate the predictive ability on young animals born in 2016-2017. In the simulated data set, keeping data two generations back or greater resulted in no statistical difference (p-value > 0.05) in the reduction in the true breeding value at generation 15 compared to utilizing all available data. Across swine data sets, removing phenotypes from animals born prior to 2011 resulted in a negligible or a slight numerical increase in the correlation between Cp and EBV. Truncating data is a method to alleviate computational issues without negatively impacting the predictive ability of selection candidate EBV.

Technical note: Impact of pedigree depth on convergence of single-step genomic BLUP in a purebred swine population

In genomic evaluations, it is desirable to have low computing cost while retaining high accuracy of evaluation for young animals. When the population is large but only few animals have phenotypes, especially for low heritability traits, the convergence rate of BLUP or single-step genomic BLUP (ssGBLUP) can be very slow. This study investigates the effect of pedigree truncation on convergence rate and solutions of ssGBLUP for data exhibiting slow convergence. The data consisted of 216,000, 221,000, 732,000, and 579,000 phenotypes on 4 traits. Heritabilities were less than 0.1 for 2 traits and greater than 0.2 for the other 2 traits. The full pedigree consisted of 2.4 million animals. Genotypes were available for 33,000 animals and consisted of 60,000 SNP. Two bivariate animal models were fit using pedigree-based BLUP or ssGBLUP. Either a regular or the algorithm for proven and young (APY) inverse was used for the genomic relationship matrix. Different pedigree depths were analyzed including full pedigree and 1 to 5 ancestral generations. Pedigree depths were defined as n ancestral generations for animals with phenotypes. The number of animals in the reduced pedigrees varied from 226,000 and 760,000 for 1 generation to 228,000 and 767,000 for 5 generations. Genomic EBV (GEBV) for genotyped animals had correlations greater than 0.99 between runs with the full and reduced pedigrees with 2 to 5 generations. A single generation of pedigree was not sufficient to obtain the same GEBV as full pedigree. The convergence rate was the worst with the full pedigree and generally improved with reduced pedigrees. Using ssGBLUP with the APY inverse improved convergence without affecting accuracy. Reducing pedigrees and the APY are important tools to reduce the computational cost in the implementation of ssGBLUP.

A comparison of accuracy validation methods for genomic and pedigree-based predictions of swine litter size traits using Large White and simulated data

The objective of this study was to compare and determine the optimal validation method when comparing accuracy from single-step GBLUP (ssGBLUP) to traditional pedigree-based BLUP. Field data included six litter size traits. Simulated data included ten replicates designed to mimic the field data in order to determine the method that was closest to the true accuracy. Data were split into training and validation sets. The methods used were as follows: (i) theoretical accuracy derived from the prediction error variance (PEV) of the direct inverse (iLHS), (ii) approximated accuracies from the accf90(GS) program in the BLUPF90 family of programs (Approx), (iii) correlation between predictions and the single-step GEBVs from the full data set (GEBV_Full ), (iv) correlation between predictions and the corrected phenotypes of females from the full data set (Y_c ), (v) correlation from method iv divided by the square root of the heritability (Y_ch ) and (vi) correlation between sire predictions and the average of their daughters' corrected phenotypes (Y_cs ). Accuracies from iLHS increased from 0.27 to 0.37 (37%) in the Large White. Approximation accuracies were very consistent and close in absolute value (0.41 to 0.43). Both iLHS and Approx were much less variable than the corrected phenotype methods (ranging from 0.04 to 0.27). On average, simulated data showed an increase in accuracy from 0.34 to 0.44 (29%) using ssGBLUP. Both iLHS and Y_ch approximated the increase well, 0.30 to 0.46 and 0.36 to 0.45, respectively. GEBV_Full performed poorly in both data sets and is not recommended. Results suggest that for within-breed selection, theoretical accuracy using PEV was consistent and accurate. When direct inversion is infeasible to get the PEV, correlating predictions to the corrected phenotypes divided by the square root of heritability is adequate given a large enough validation data set.

Application of single step genomic BLUP under different uncertain paternity scenarios using simulated data

The objective of this study was to investigate the application of BLUP and single step genomic BLUP (ssGBLUP) models in different scenarios of paternity uncertainty with different strategies of scaling the G matrix to match the A22 matrix, using simulated data for beef cattle. Genotypes, pedigree, and phenotypes for age at first calving (AFC) and weight at 550 days (W550) were simulated using heritabilities based on real data (0.12 for AFC and 0.34 for W550). Paternity uncertainty scenarios using 0, 25, 50, 75, and 100% of multiple sires (MS) were studied. The simulated genome had a total length of 2,333 cM, containing 735,293 biallelic markers and 7,000 QTLs randomly distributed over the 29 BTA. It was assumed that QTLs explained 100% of the genetic variance. For QTL, the amount of alleles per loci randomly ranged from two to four. The BLUP model that considers phenotypic and pedigree data, and the ssGBLUP model that combines phenotypic, pedigree and genomic information were used for genetic evaluations. Four ways of scaling the mean of the genomic matrix (G) to match to the mean of the pedigree relationship matrix among genotyped animals (A₂₂) were tested. Accuracy, bias, and inflation were investigated for five groups of animals: ALL = all animals; BULL = only bulls; GEN = genotyped animals; FEM = females; and YOUNG = young males. With the BLUP model, the accuracies of genetic evaluations decreased for both traits as the proportion of unknown sires in the population increased. The EBV accuracy reduction was higher for GEN and YOUNG groups. By analyzing the scenarios for YOUNG (from 0 to 100% of MS), the decrease was 87.8 and 86% for AFC and W550, respectively. When applying the ssGBLUP model, the accuracies of genetic evaluation also decreased as the MS in the pedigree for both traits increased. However, the accuracy reduction was less than those observed for BLUP model. Using the same comparison (scenario 0 to 100% of MS), the accuracies reductions were 38 and 44.6% for AFC and W550, respectively. There were no differences between the strategies for scaling the G matrix for ALL, BULL, and FEM groups under the different scenarios with missing pedigree. These results pointed out that the uninformative part of the A₂₂ matrix and genotyped animals with paternity uncertainty did not influence the scaling of G matrix. On the basis of the results, it is important to have a G matrix in the same scale of the A₂₂ matrix, especially for the evaluation of young animals in situations with missing pedigree information. In these situations, the ssGBLUP model is an appropriate alternative to obtain a more reliable and less biased estimate of breeding values, especially for young animals with few or no phenotypic records. For accurate and unbiased genomic predictions with ssGBLUP, it is necessary to assure that the G matrix is compatible with the A₂₂ matrix, even in situations with paternity uncertainty.

Invited review: A perspective on the future of genomic selection in dairy cattle

Genomic evaluation has been successfully implemented in the United States, Canada, Great Britain, Ireland, New Zealand, Australia, France, the Netherlands, Germany, and the Scandinavian countries. Adoption of this technology in the major dairy producing countries has led to significant changes in the worldwide dairy industry. Gradual elimination of the progeny test system has led to a reduction in the number of sires with daughter records and fewer genetic ties between years. As genotyping costs decrease, the number of cows genotyped will continue to increase, and these records will become the basic data used to compute genomic evaluations, most likely via application of "single-step" methodologies. Although genomic selection has been successful in increasing rates of genetic gain, we still know very little about the genetic architecture of quantitative variation. Apparently, a very large number of genes affect nearly all economic traits, in accordance with the infinitesimal model for quantitative traits. Less emphasis in selection goals will be placed on milk production traits, and more on health, reproduction, and efficiency traits and on environmentally friendly production with reduced waste and gas emission. Genetic variance for economic traits is maintained by the increase in frequency of rare alleles, new mutations, and changes in selection goals and management. Thus, it is unlikely that a selection plateau will be reached in the near future.

Crossbreed evaluations in single-step genomic best linear unbiased predictor using adjusted realized relationship matrices

Combining purebreed and crossbreed information is beneficial for genetic evaluation of some livestock species. Genetic evaluations can use relationships based on genomic information, relying on allele frequencies that are breed specific. Single-step genomic BLUP (ssGBLUP) does not account for different allele frequencies, which could limit the genetic gain in crossbreed evaluations. In this study, we tested the performance of different breed-specific genomic relationship matrices () in ssGBLUP for crossbreed evaluations; we also tested the importance of genotyping crossbred animals. Genotypes were available for purebreeds (AA and BB) and crossbreeds (F) in simulated and real pig populations. The number of genotyped animals was, on average, 4,315 for the simulated population and 15,798 for the real population. Cross-validation was performed on 1,200 and 3,117 F animals in the simulated and real populations, respectively. Simulated scenarios were under no artificial selection, mass selection, or BLUP selection. Two genomic relationship matrices were constructed based on breed-specific allele frequencies: 1) , a genomic relationship matrix centered by breed-specific allele frequencies, and 2) , a genomic relationship matrix centered and scaled by breed-specific allele frequencies. All (the across-breed genomic relationship matrix), , and were also tuned to account for selective genotyping. Using breed-specific allele frequencies reduced the number of negative relationships between 2 purebreeds, pulling the average closer to 0, as in the pedigree-based relationship matrix. For simulated populations that included mass selection, genomic EBV (GEBV) in F, when using and , were, on average, 10% more accurate than ; however, after tuning to account for selective genotyping, provided the same accuracy as for breed-specific genomic relationship matrices. For the real population, accuracies for litter size in F were 0.62 for , , and , and tuning had no impact on accuracy, except for , which was 1 percentage point less accurate. Accuracy of GEBV for number of stillborns in F1 was 0.5 for all tested genomic relationship matrices with no changes after tuning. We observed that genotyping F increased accuracies of GEBV for the same animals by up to 39% compared with having genotypes for only AA and BB. In crossbreed evaluations, accounting for breed-specific allele frequencies promoted changes in G that were not influential enough to improve accuracy of GEBV. Therefore, the best performance of ssGBLUP for crossbreed evaluations requires genotypes for pure- and crossbreeds and no breed-specific adjustments in the realized relationship matrix.

Effects of number of training generations on genomic prediction for various traits in a layer chicken population

Background

Genomic estimated breeding values (GEBV) based on single nucleotide polymorphism (SNP) genotypes are widely used in animal improvement programs. It is typically assumed that the larger the number of animals is in the training set, the higher is the prediction accuracy of GEBV. The aim of this study was to quantify genomic prediction accuracy depending on the number of ancestral generations included in the training set, and to determine the optimal number of training generations for different traits in an elite layer breeding line.

Methods

Phenotypic records for 16 traits on 17,793 birds were used. All parents and some selection candidates from nine non-overlapping generations were genotyped for 23,098 segregating SNPs. An animal model with pedigree relationships (PBLUP) and the BayesB genomic prediction model were applied to predict EBV or GEBV at each validation generation (progeny of the most recent training generation) based on varying numbers of immediately preceding ancestral generations. Prediction accuracy of EBV or GEBV was assessed as the correlation between EBV and phenotypes adjusted for fixed effects, divided by the square root of trait heritability. The optimal number of training generations that resulted in the greatest prediction accuracy of GEBV was determined for each trait. The relationship between optimal number of training generations and heritability was investigated.

Results

On average, accuracies were higher with the BayesB model than with PBLUP. Prediction accuracies of GEBV increased as the number of closely-related ancestral generations included in the training set increased, but reached an asymptote or slightly decreased when distant ancestral generations were used in the training set. The optimal number of training generations was 4 or more for high heritability traits but less than that for low heritability traits. For less heritable traits, limiting the training datasets to individuals closely related to the validation population resulted in the best predictions.

Conclusions

The effect of adding distant ancestral generations in the training set on prediction accuracy differed between traits and the optimal number of necessary training generations is associated with the heritability of traits.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-016-0198-9) contains supplementary material, which is available to authorized users.

Review: Opportunities and challenges for small populations of dairy cattle in the era of genomics

In modern dairy cattle breeding, genomic breeding programs have the potential to increase efficiency and genetic gain. At the same time, the requirements and the availability of genotypes and phenotypes present a challenge. The set-up of a large enough reference population for genomic prediction is problematic for numerically small breeds but also for hard to measure traits. The first part of this study is a review of the current literature on strategies to overcome the lack of reference data. One solution is the use of combined reference populations from different breeds, different countries, or different research populations. Results reveal that the level of relationship between the merged populations is the most important factor. Compiling closely related populations facilitates the accurate estimation of marker effects and thus results in high accuracies of genomic prediction. Consequently, mixed reference populations of the same breed, but from different countries are more promising than combining different breeds, especially if those are more distantly related. The use of female reference information has the potential to enlarge the reference population size. Including females is advisable for small populations and difficult traits, and maybe combined with genotyping females and imputing those that are un-genotyped. The efficient use of imputation for un-genotyped individuals requires a set of genotyped related animals and well-considered selection strategies which animals to choose for genotyping and phenotyping. Small populations have to find ways to derive additional advantages from the cost-intensive establishment of genomic breeding schemes. Possible solutions may be the use of genomic information for inbreeding control, parentage verification, within-herd selection, adjusted mating plans or conservation strategies. The second part of the paper deals with the issue of high-quality phenotypes against the background of new, difficult and hard to measure traits. The use of contracted herds for phenotyping is recommended, as additional traits, when compared to standard traits used in dairy cattle breeding can be measured at set moments in time. This can be undertaken even for the recording of health traits, thus resulting in complete contemporary groups for health traits. Future traits to be recorded and used in genomic breeding programs, at least partly will be traits for which traditional selection based on widespread phenotyping is not possible. Enabling phenotyping of sufficient numbers to enable genomic selection will rely on cooperation between scientists from different disciplines and may require multidisciplinary approaches.

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals.

Practical implications for genetic modeling in the genomics era

Genetic models convert data into estimated breeding values and other information useful to breeders. The goal is to provide accurate and timely predictions of the future performance for each animal (or embryo). Modeling involves defining traits, editing raw data, removing environmental effects, including genetic by environmental interactions and correlations among traits, and accounting for nonadditive inheritance or nonnormal distributions. Data include phenotypes and pedigrees during the last century and genotypes within the last decade. The genomic data can include single nucleotide polymorphisms, quantitative trait loci, insertions, deletions, and haplotypes. Subsets must be selected to reduce computation because total numbers of variants that can be imputed have increased rapidly from thousands to millions. Current computation using 60,671 markers takes just a few days. Nonlinear models can account for the nonnormal distribution of genomic effects, but reliability is usually better than that of linear models only for traits influenced by major genes. Numbers of genotyped animals have also increased rapidly in the joint North American database from a few thousand in 2009 to over 1 million in 2015. Most are young females and will contribute to estimating allele effects in the future, but only about 150,000 have phenotypes so far. Genomic preselection can bias traditional animal models because Mendelian sampling of phenotyped progeny and mates is no longer expected to average zero; however, estimates of bias are small in current US data. Single-step models that combine pedigree and genomic relationships can account for preselection, but approximations are required for affordable computation. Traditional animal models may include all breeds and crossbreds, but most genomic evaluations are still computed within breed. Models that include inbreeding, heterosis, dominance, and interactions can improve predictions for individual matings. Multitrait genomic models may be preferred for traits with many missing records or when foreign records are included as pseudo-observations, but most countries use multitrait traditional evaluations followed by single-trait genomic evaluations. Genomic reliabilities are about 70% for the more heritable traits. Researchers must choose from many available models and explain how the models work so that breeders can more confidently apply the predictions in their selection programs.

Response and inbreeding from a genomic selection experiment in layer chickens

Background

Genomic selection (GS) using estimated breeding values (GS-EBV) based on dense marker data is a promising approach for genetic improvement. A simulation study was undertaken to illustrate the opportunities offered by GS for designing breeding programs. It consisted of a selection program for a sex-limited trait in layer chickens, which was developed by deterministic predictions under different scenarios. Later, one of the possible schemes was implemented in a real population of layer chicken.

Methods

In the simulation, the aim was to double the response to selection per year by reducing the generation interval by 50 %, while maintaining the same rate of inbreeding per year. We found that GS with retraining could achieve the set objectives while requiring 75 % fewer reared birds and 82 % fewer phenotyped birds per year. A multi-trait GS scenario was subsequently implemented in a real population of brown egg laying hens. The population was split into two sub-lines, one was submitted to conventional phenotypic selection, and one was selected based on genomic prediction. At the end of the 3-year experiment, the two sub-lines were compared for multiple performance traits that are relevant for commercial egg production.

Results

Birds that were selected based on genomic prediction outperformed those that were submitted to conventional selection for most of the 16 traits that were included in the index used for selection. However, although the two programs were designed to achieve the same rate of inbreeding per year, the realized inbreeding per year assessed from pedigree was higher in the genomic selected line than in the conventionally selected line.

Conclusions

The results demonstrate that GS is a promising alternative to conventional breeding for genetic improvement of layer chickens.

Ancestral Relationships Using Metafounders: Finite Ancestral Populations and Across Population Relationships

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a "metafounder," a pseudo-individual included as founder of the pedigree and similar to an "unknown parent group." Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given.

Single-step genomic evaluation using multitrait random regression model and test-day data

The objectives of this study were to evaluate the feasibility of use of the test-day (TD) single-step genomic BLUP (ssGBLUP) using phenotypic records of Nordic Red Dairy cows. The critical point in ssGBLUP is how genomically derived relationships (G) are integrated with population-based pedigree relationships (A) into a combined relationship matrix (H). Therefore, we also tested how different weights for genomic and pedigree relationships affect ssGBLUP, validation reliability, and validation regression coefficients. Deregressed proofs for 305-d milk, protein, and fat yields were used for a posteriori validation. The results showed that the use of phenotypic TD records in ssGBLUP is feasible. Moreover, the TD ssGBLUP model gave considerably higher validation reliabilities and validation regression coefficients than the TD model without genomic information. No significant differences were found in validation reliability between the different TD ssGBLUP models according to bootstrap confidence intervals. However, the degree of inflation in genomic enhanced breeding values is affected by the method used in construction of the H matrix. The results showed that ssGBLUP provides a good alternative to the currently used multi-step approach but there is a great need to find the best option to combine pedigree and genomic information in the genomic matrix.

Short communication: Analysis of genomic predictor population for Holstein dairy cattle in the United States--Effects of sex and age

Increased computing time for the ever-growing predictor population and linkage decay between the ancestral population and current animals have become concerns for genomic evaluation systems. The effects on reliability of US genomic evaluations from including cows and bulls in the Holstein predictor population and also from excluding older bulls from the predictor population were examined. Holstein data collected for December 2013 US genomic evaluations were used in cutoff studies to determine reliability gains, regression coefficients, and bias for 5 yield, 3 fitness, 2 fertility, and 18 conformation traits. Three predictor populations were examined based on animal sex: 30,852 cows with traditional evaluations as of August 2012, 21,883 bulls with traditional evaluations as of August 2012, and a combined group of all bulls and cows. Three subsets of the bull predictor population were examined to determine effect of age: bulls born before 1996 excluded (25% of bulls excluded), bulls born before 2001 excluded (50%), and bulls born before 2005 excluded (75%). The validation set for all predictor populations was either bulls or cows first receiving a traditional evaluation between August 2012 and December 2013. Across all traits, the addition of cows to the bull predictor population increased reliability gains by 0.4 percentage points for validation bulls and 4.4 points for validation cows. Across all traits, excluding bulls born before 1996 from the bull-only predictor population decreased gains in genomic reliability by 1.8 percentage points. For 19 of 28 traits, excluding bulls born before 2005 from the predictor population resulted in lower bias in genomic evaluations of validation bulls. Although the contribution of cows and older bulls to improved accuracy of US genomic evaluations is small, a plateau of achievable gain has not yet been reached.