A relationship matrix including full pedigree and genomic information

An Expectation-Maximization Algorithm for Combining a Sample of Partially Overlapping Covariance Matrices

The generation of unprecedented amounts of data brings new challenges in data management, but also an opportunity to accelerate the identification of processes of multiple science disciplines. One of these challenges is the harmonization of high-dimensional unbalanced and heterogeneous data. In this manuscript, we propose a statistical approach to combine incomplete and partially-overlapping pieces of covariance matrices that come from independent experiments. We assume that the data are a random sample of partial covariance matrices sampled from Wishart distributions and we derive an expectation-maximization algorithm for parameter estimation. We demonstrate the properties of our method by (i) using simulation studies and (ii) using empirical datasets. In general, being able to make inferences about the covariance of variables not observed in the same experiment is a valuable tool for data analysis since covariance estimation is an important step in many statistical applications, such as multivariate analysis, principal component analysis, factor analysis, and structural equation modeling.

Genomic prediction in Brazilian Guzerá cattle: application of a single-step approach to productive and reproductive traits

This study aimed to investigate the feasibility of genomic prediction for productive and reproductive traits in Guzerá cattle using single-step genomic best linear unbiased prediction (ssGBLUP). Evaluations included the 305-day cumulative yields (first lactation, in kg) of milk, lactose, protein, fat, and total solids; adjusted body weight (kg) at the ages of 450, 365, and 210 days; and age at first calving (in days), from a database containing 197,283 measurements from Guzerá males and females born between 1954 and 2018. The pedigree included 433,823 animals spanning up to 14 overlapping generations. A total of 1618 animals were genotyped. The analyses were performed using ssGBLUP and traditional BLUP methods. Predictive ability and bias were accessed using cross-validation: predictive ability was similar between the methods and ranged from 0.27 to 0.47 for the genomic-based model and from 0.30 to 0.45 for the pedigree-based model; the bias was also similar between the methods, ranging from 0.88 to 1.35 in the genomic-based model and from 0.96 to 1.41 in the pedigree-based model. The individual accuracies of breeding values were evidently increased in the genomic evaluation, with values ranging from 0.41 to 0.56 in the genomic-based model and from 0.26 to 0.54 in the pedigree-based model. Even based on a small number of genotyped animals and a small database for some traits, the results suggest that ssGBLUP is feasible and may be applied to national genetic evaluation of the breed to increase the accuracy of breeding values without greatly impacting predictive ability and bias.

Reliabilities of estimated breeding values in models with metafounders

BACKGROUND

Reliabilities of best linear unbiased predictions (BLUP) of breeding values are defined as the squared correlation between true and estimated breeding values and are helpful in assessing risk and genetic gain. Reliabilities can be computed from the prediction error variances for models with a single base population but are undefined for models that include several base populations and when unknown parent groups are modeled as fixed effects. In such a case, the use of metafounders in principle enables reliabilities to be derived.

METHODS

We propose to compute the reliability of the contrast of an individual's estimated breeding value with that of a metafounder based on the prediction error variances of the individual and the metafounder, their prediction error covariance, and their genetic relationship. Computation of the required terms demands only little extra work once the sparse inverse of the mixed model equations is obtained, or they can be approximated. This also allows the reliabilities of the metafounders to be obtained. We studied the reliabilities for both BLUP and single-step genomic BLUP (ssGBLUP), using several definitions of reliability in a large dataset with 1,961,687 dairy sheep and rams, most of which had phenotypes and among which 27,000 rams were genotyped with a 50K single nucleotide polymorphism (SNP) chip. There were 23 metafounders with progeny sizes between 100,000 and 2000 individuals.

RESULTS

In models with metafounders, directly using the prediction error variance instead of the contrast with a metafounder leads to artificially low reliabilities because they refer to a population with maximum heterozygosity. When only one metafounder is fitted in the model, the reliability of the contrast is shown to be equivalent to the reliability of the individual in a model without metafounders. When there are several metafounders in the model, using a contrast with the oldest metafounder yields reliabilities that are on a meaningful scale and very close to reliabilities obtained from models without metafounders. The reliabilities using contrasts with ssGBLUP also resulted in meaningful values.

CONCLUSIONS

This work provides a general method to obtain reliabilities for both BLUP and ssGBLUP when several base populations are included through metafounders.

A computationally efficient method for approximating reliabilities in large-scale single-step genomic prediction

BACKGROUND

In this study, computationally efficient methods to approximate the reliabilities of genomic estimated breeding values (GEBV) in a single-step genomic prediction model including a residual polygenic (RPG) effect are described. In order to calculate the reliabilities of the genotyped animals, a single nucleotide polymorphism best linear unbiased prediction (SNPBLUP) or a genomic BLUP (GBLUP), was used, where two alternatives to account for the RPG effect were tested. In the direct approach, the genomic model included the RPG effect, while in the blended method, it did not but an index was used to weight the genomic and pedigree-based BLUP (PBLUP) reliabilities. In order to calculate the single-step GBLUP reliabilities for the breeding values for the non-genotyped animals, a simplified weighted-PBLUP model that included a general mean and additive genetic effects with weights accounting for the non-genomic and genomic information was used. We compared five schemes for the weights. Two datasets, i.e., a small (Data 1) one and a large (Data 2) one were used.

RESULTS

For the genotyped animals in Data 1, correlations between approximate reliabilities using the blended method and exact reliabilities ranged from 0.993 to 0.996 across three lactations. The slopes observed by regressing the reliabilities of GEBV from the exact method on those from the blended method were 1.0 for all three lactations. For Data 2, the correlations and slopes ranged, respectively, from 0.980 to 0.986 and from 0.91 to 0.96, and for the non-genotyped animals in Data 1, they ranged, respectively, from 0.987 to 0.994 and from 0.987 to 1, which indicate that the approximations were in line with the exact results. The best approach achieved correlations of 0.992 to 0.994 across lactations.

CONCLUSIONS

Our results demonstrate that the approximated reliabilities calculated using our proposed approach are in good agreement with the exact reliabilities. The blended method for the genotyped animals is computationally more feasible than the direct method when RPG effects are included, particularly for large-scale datasets. The approach can serve as an effective strategy to estimate the reliabilities of GEBV in large-scale single-step genomic predictions.

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

Genomic estimated breeding values (GEBV) of animals without phenotypes can be indirectly predicted using recursions on GEBV of a subset. To maximize predictive ability of indirect predictions (IP), the subset must represent the independent chromosome segments segregating in the population. We aimed to 1) determine the number of animals needed in recursions to maximize predictive ability, 2) evaluate equivalency IP-GEBV, and 3) investigate trends in predictive ability of IP derived from recent vs. distant generations or accumulating phenotypes from recent to past generations. Data comprised pedigree of 825K birds hatched over 12 overlapping generations, phenotypes for body weight (BW; 820K), residual feed intake (RF; 200K) and weight gain during a trial period (WG; 200K), and breast meat percent (BP; 43K). A total of 154K birds (last six generations) had genotypes. The number of animals that maximize predictive ability was assessed based on the number of largest eigenvalues explaining 99% of variation in the genomic relationship matrix (1Me = 7,131), twice (2Me), or a fraction of this number (i.e., 0.75, 0.50, or 0.25Me). Equivalency between IP and GEBV was measured by correlating these two sets of predictions. GEBV were obtained as if generation 12 (validation animals) was part of the evaluation. IP were derived from GEBV of animals from generations 8 to 11 or generations 11, 10, 9, or 8. IP predictive ability was defined as the correlation between IP and adjusted phenotypes. The IP predictive ability increased from 0.25Me to 1Me (11%, on average); the change from 1Me to 2Me was negligible (0.6%). The correlation IP-GEBV was the same when IP were derived from a subset of 1Me animals chosen randomly across generations (8 to 11) or from generation 11 (0.98 for BW, 0.99 for RF, WG, and BP). A marginal decline in the correlation was observed when IP were based on GEBV of animals from generation 8 (0.95 for BW, 0.98 for RF, WG, and BP). Predictive ability had a similar trend; from generation 11 to 8, it changed from 0.32 to 0.31 for BW, from 0.39 to 0.38 for BP, and was constant at 0.33(0.22) for RF(WG). Predictive ability had a slight to moderate increase accumulating up to four generations of phenotypes. 1Me animals provide accurate IP, equivalent to GEBV. A minimum decay in predictive ability is observed when IP are derived from GEBV of animals from four generations back, possibly because of strong selection or the model not being completely additive.

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.

Host genetic control on rumen microbiota and its impact on dairy traits in sheep

BACKGROUND

Milk yield and fine composition in sheep depend on the volatile and long-chain fatty acids, microbial proteins, vitamins produced through feedstuff digestion by the rumen microbiota. In cattle, the host genome has been shown to have a low to moderate genetic control on rumen microbiota abundance but a high control on dairy traits with heritabilities higher than 0.30. There is little information on the genetic correlations and quantitative trait loci (QTL) that simultaneously affect rumen microbiota abundance and dairy traits in ruminants, especially in sheep. Thus, our aim was to quantify the effect of the host genetics on rumen bacterial abundance and the genetic correlations between rumen bacterial abundance and several dairy traits, and to identify QTL that are associated with both rumen bacterial abundance and milk traits.

RESULTS

Our results in Lacaune sheep show that the heritability of rumen bacterial abundance ranges from 0 to 0.29 and that the heritability of 306 operational taxonomic units (OTU) is significantly different from 0. Of these 306 OTU, 96 that belong mainly to the Prevotellaceae, Lachnospiraceae and Ruminococcaceae bacterial families show strong genetic correlations with milk fatty acids and proteins (absolute values ranging from 0.33 to 0.99). Genome-wide association studies revealed a QTL for alpha-lactalbumin concentration in milk on Ovis aries chromosome (OAR) 11, and six QTL for rumen bacterial abundances i.e., for two OTU belonging to the genera Prevotella (OAR3 and 5), Rikeneleaceae_RC9_gut_group (OAR5), Ruminococcus (OAR5), an unknown genus of order Clostridia UCG-014 (OAR10), and CAG-352 (OAR11). None of these detected regions are simultaneously associated with rumen bacterial abundance and dairy traits, but the bacterial families Prevotellaceae, Lachnospiraceae and F082 show colocalized signals on OAR3, 5, 15 and 26.

CONCLUSIONS

In Lacaune dairy sheep, rumen microbiota abundance is partially controlled by the host genetics and is poorly genetically linked with milk protein and fatty acid compositions, and three main bacterial families, Prevotellaceae, Lachnospiraceae and F082, show specific associations with OAR3, 5, 15 and 26.

Single-step genomic BLUP with many metafounders

Single-step genomic BLUP (ssGBLUP) model for routine genomic prediction of breeding values is developed intensively for many dairy cattle populations. Compatibility between the genomic (G) and the pedigree (A) relationship matrices remains an important challenge required in ssGBLUP. The compatibility relates to the amount of missing pedigree information. There are two prevailing approaches to account for the incomplete pedigree information: unknown parent groups (UPG) and metafounders (MF). unknown parent groups have been used routinely in pedigree-based evaluations to account for the differences in genetic level between groups of animals with missing parents. The MF approach is an extension of the UPG approach. The MF approach defines MF which are related pseudo-individuals. The MF approach needs a Γ matrix of the size number of MF to describe relationships between MF. The UPG and MF can be the same. However, the challenge in the MF approach is the estimation of Γ having many MF, typically needed in dairy cattle. In our study, we present an approach to fit the same amount of MF as UPG in ssGBLUP with Woodbury matrix identity (ssGTBLUP). We used 305-day milk, protein, and fat yield data from the DFS (Denmark, Finland, Sweden) Red Dairy cattle population. The pedigree had more than 6 million animals of which 207,475 were genotyped. We constructed the preliminary gamma matrix (Γpre) with 29 MF which was expanded to 148 MF by a covariance function (Γ148). The quality of the extrapolation of the Γpre matrix was studied by comparing average off-diagonal elements between breed groups. On average relationships among MF in Γ148 were 1.8% higher than in Γpre. The use of Γ148 increased the correlation between the G and A matrices by 0.13 and 0.11 for the diagonal and off-diagonal elements, respectively. [G]EBV were predicted using the ssGTBLUP and Pedigree-BLUP models with the MF and UPG. The prediction reliabilities were slightly higher for the ssGTBLUP model using MF than UPG. The ssGBLUP MF model showed less overprediction compared to other models.

A Note on the Conditioning of the -1 Matrix Used in Single-Step GBLUP

The single-step genomic BLUP (ssGBLUP) is used worldwide for the simultaneous genetic evaluation of genotyped and non-genotyped animals. It is easily extendible to all BLUP models by replacing the pedigree-based additive genetic relationship matrix (A) with an augmented pedigree-genomic relationship matrix (H). Theoretically, H does not introduce any artificially inflated variance. However, inflated genetic variances have been observed due to the incomparability between the genomic relationship matrix (G) and A used in H. Usually, G is blended and tuned with A22 (the block of A for genotyped animals) to improve its numerical condition and compatibility. If deflation/inflation is still needed, a common approach is weighting G-1-A22-1 in the form of τG-1-ωA22-1, added to A-1 to form H-1. In some situations, this can violate the conditional properties upon which H is built. Different ways of weighting the H-1 components (A-1, G-1, A22-1, and H-1 itself) were studied to avoid/minimise the violations of the conditional properties of H. Data were simulated on ten populations and twenty generations. Responses to weighting different components of H-1 were measured in terms of the regression of phenotypes on the estimated breeding values (the lower the slope, the higher the inflation) and the correlation between phenotypes and the estimated breeding values (predictive ability). Increasing the weight on H-1 increased the inflation. The responses to weighting G-1 were similar to those for H-1. Increasing the weight on A-1 (together with A22-1) was not influential and slightly increased the inflation. Predictive ability is a direct function of the slope of the regression line and followed similar trends. Responses to weighting G-1-A22-1 depend on the inflation/deflation of evaluations from A-1 to H-1 and the compatibility of the two matrices with the heritability used in the model. One possibility is a combination of weighting G-1-A22-1 and weighting H-1. Given recent advances in ssGBLUP, conditioning H-1 might become an interim solution from the past and then not be needed in the future.

Genomic selection for resistance to mammalian bark stripping and associated chemical compounds in radiata pine

The integration of genomic data into genetic evaluations can facilitate the rapid selection of superior genotypes and accelerate the breeding cycle in trees. In this study, 390 trees from 74 control-pollinated families were genotyped using a 36K Axiom SNP array. A total of 15,624 high-quality SNPs were used to develop genomic prediction models for mammalian bark stripping, tree height, and selected primary and secondary chemical compounds in the bark. Genetic parameters from different genomic prediction methods-single-trait best linear unbiased prediction based on a marker-based relationship matrix (genomic best linear unbiased prediction), multitrait single-step genomic best linear unbiased prediction, which integrated the marker-based and pedigree-based relationship matrices (single-step genomic best linear unbiased prediction) and the single-trait generalized ridge regression-were compared to equivalent single- or multitrait pedigree-based approaches (ABLUP). The influence of the statistical distribution of data on the genetic parameters was assessed. Results indicated that the heritability estimates were increased nearly 2-fold with genomic models compared to the equivalent pedigree-based models. Predictive accuracy of the single-step genomic best linear unbiased prediction was higher than the ABLUP for most traits. Allowing for heterogeneity in marker effects through the use of generalized ridge regression did not markedly improve predictive ability over genomic best linear unbiased prediction, arguing that most of the chemical traits are modulated by many genes with small effects. Overall, the traits with low pedigree-based heritability benefited more from genomic models compared to the traits with high pedigree-based heritability. There was no evidence that data skewness or the presence of outliers affected the genomic or pedigree-based genetic estimates.

A method to obtain exact single-step GBLUP for non-genotyped descendants when the genomic relationship matrix of ancestors is not available

BACKGROUND

Single-step genomic best linear unbiased prediction (GBLUP) involves a joint analysis of individuals with genotype information, and their ancestors, descendants, or contemporaries, without recorded genotypes. Livestock applications typically represent populations with fewer individuals with genotypes relative to the number not genotyped. Most breeding programmes are structured, consisting of a nucleus tier in which selection drives genetic gains that are propagated through descendants that represent parents in multiplier and commercial tiers. In some cases, the genotypes in the nucleus tier are proprietary to a breeding company, and not publicly available for a whole industry analysis. Bayesian inference involves combining a defined description of prior information with new information to generate a posterior distribution that contains all available information on parameters of interest. A natural extension of Bayesian analysis would be to use information from the posterior distribution to define the prior distribution in a subsequent analysis.

METHODS

We derive the mixed model equations for inference on breeding values for non genotyped individuals in that subset of the population that is of current interest, using only data on the performance of current individuals and their immediate pedigree, along with prior information defined from the posterior distribution of an external BLUP or single-step GBLUP analysis of the ancestors of the current population.

DISCUSSION

Identical estimates of breeding values and their prediction error covariances for current animals of interest in the multiplier or commercial tier can be obtained without requiring neither the genomic relationship matrix nor genotypes of any of their ancestors in the nucleus tier, as can be obtained from a single analysis using pedigree, performance, and genomic information from all tiers. The Bayesian analysis of the current population does not require explicit information on unselected genotyped animals in the external population.

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.

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

BACKGROUND

At the beginning of genomic selection, some Chinese companies genotyped pigs with different single nucleotide polymorphism (SNP) arrays. The obtained genomic data are then combined and to do this, several imputation strategies have been developed. Usually, only additive genetic effects are considered in genetic evaluations. However, dominance effects that may be important for some traits can be fitted in a mixed linear model as either 'classical' or 'genotypic' dominance effects. Their influence on genomic evaluation has rarely been studied. Thus, the objectives of this study were to use a dataset from Canadian Yorkshire pigs to (1) compare different strategies to combine data from two SNP arrays (Affymetrix 55K and Illumina 42K) and identify the most appropriate strategy for genomic evaluation and (2) evaluate the impact of dominance effects (classical' and 'genotypic') and inbreeding depression effects on genomic predictive abilities for average daily gain (ADG), backfat thickness (BF), loin muscle depth (LMD), days to 100 kg (AGE100), and the total number of piglets born (TNB) at first parity.

RESULTS

The reliabilities obtained with the additive genomic models showed that the strategy used to combine data from two SNP arrays had little impact on genomic evaluations. Models with classical or genotypic dominance effect showed similar predictive abilities for all traits. For ADG, BF, LMD, and AGE100, dominance effects accounted for a small proportion (2 to 11%) of the total genetic variance, whereas for TNB, dominance effects accounted for 11 to 20%. For all traits, the predictive abilities of the models increased significantly when genomic inbreeding depression effects were included in the model. However, the inclusion of dominance effects did not change the predictive ability for any trait except for TNB.

CONCLUSIONS

Our study shows that it is feasible to combine data from different SNP arrays for genomic evaluation, and that all combination methods result in similar accuracies. Regardless of how dominance effects are fitted in the genomic model, there is no impact on genetic evaluation. Models including inbreeding depression effects outperform a model with only additive effects, even if the trait is not strongly affected by dominant genes.

Phenomic selection in wheat breeding: prediction of the genotype-by-environment interaction in multi-environment breeding trials

Phenomic prediction of wheat grain yield and heading date in different multi-environmental trial scenarios is accurate. Modelling the genotype-by-environment interaction effect using phenomic data is a potentially low-cost complement to genomic prediction. The performance of wheat cultivars in multi-environmental trials (MET) is difficult to predict because of the genotype-by-environment interactions (G × E). Phenomic selection is supposed to be efficient for modelling the G × E effect because it accounts for non-additive effects. Here, phenomic data are near-infrared (NIR) spectra obtained from plant material. While phenomic selection has recently been shown to accurately predict wheat grain yield in single environments, its accuracy needs to be investigated for MET. We used four datasets from two winter wheat breeding programs to test and compare the predictive abilities of phenomic and genomic models for grain yield and heading date in different MET scenarios. We also compared different methods to model the G × E using different covariance matrices based on spectra. On average, phenomic and genomic prediction abilities are similar in all different MET scenarios. Better predictive abilities were obtained when G × E effects were modelled with NIR spectra than without them, and it was better to use all the spectra of all genotypes in all environments for modelling the G × E. To facilitate the implementation of phenomic prediction, we tested MET designs where the NIR spectra were measured only on the genotype-environment combinations phenotyped for the target trait. Missing spectra were predicted with a weighted multivariate ridge regression. Intermediate predictive abilities for grain yield were obtained in a sparse testing scenario and for new genotypes, which shows that phenomic selection is an efficient and practicable prediction method for dealing with G × E.

Incorporating kernelized multi-omics data improves the accuracy of genomic prediction

Background

Genomic selection (GS) has revolutionized animal and plant breeding after the first implementation via early selection before measuring phenotypes. Besides genome, transcriptome and metabolome information are increasingly considered new sources for GS. Difficulties in building the model with multi-omics data for GS and the limit of specimen availability have both delayed the progress of investigating multi-omics.

Results

We utilized the Cosine kernel to map genomic and transcriptomic data as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n}\times {n}$$\end{document}n×n symmetric matrix (G matrix and T matrix), combined with the best linear unbiased prediction (BLUP) for GS. Here, we defined five kernel-based prediction models: genomic BLUP (GBLUP), transcriptome-BLUP (TBLUP), multi-omics BLUP (MBLUP, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol M=\mathrm{ratio}\times\boldsymbol G+(1-\mathrm{ratio})\times\boldsymbol T$$\end{document}M=ratio×G+(1-ratio)×T), multi-omics single-step BLUP (mssBLUP), and weighted multi-omics single-step BLUP (wmssBLUP) to integrate transcribed individuals and genotyped resource population. The predictive accuracy evaluations in four traits of the Chinese Simmental beef cattle population showed that (1) MBLUP was far preferred to GBLUP (ratio = 1.0), (2) the prediction accuracy of wmssBLUP and mssBLUP had 4.18% and 3.37% average improvement over GBLUP, (3) We also found the accuracy of wmssBLUP increased with the growing proportion of transcribed cattle in the whole resource population.

Conclusions

We concluded that the inclusion of transcriptome data in GS had the potential to improve accuracy. Moreover, wmssBLUP is accepted to be a promising alternative for the present situation in which plenty of individuals are genotyped when fewer are transcribed.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40104-022-00756-6.

Genetic Parameter Estimation and Genome-Wide Association Analysis of Social Genetic Effects on Average Daily Gain in Purebreds and Crossbreds

Simple Summary

Average daily gain (ADG) is influenced by both an individual’s direct genetic effect (DGE) and by a social genetic effect (SGE) derived from pen mates. Therefore, identifying the DGE and SGE on ADG is essential for a better understanding of pig breeding systems. We conducted this study to elucidate the genetic characteristics and relationships of DGE and SGE on ADG using purebred and crossbred pigs. We found that the DGE and SGE both contributed to ADG in both populations. In addition, the SGE of purebred pigs was highly correlated with the DGE of crossbred pigs. Furthermore, we identified several genomic regions that may be associated with the DGE and SGE on ADG. Our findings will contribute to future genomic evaluation studies of socially affected traits.

Abstract

Average daily gain (ADG) is an important growth trait in the pig industry. The direct genetic effect (DGE) has been studied mainly to assess the association between genetic information and economic traits. The social genetic effect (SGE) has been shown to affect ADG simultaneously with the DGE because of group housing systems. We conducted this study to elucidate the genetic characteristics and relationships of the DGE and SGE of purebred Korean Duroc and crossbred pigs by single-step genomic best linear unbiased prediction and a genome-wide association study. We used the genotype, phenotype, and pedigree data of 1779, 6022, and 7904 animals, respectively. Total heritabilities on ADG were 0.19 ± 0.04 and 0.39 ± 0.08 for purebred and crossbred pigs, respectively. The genetic correlation was the greatest (0.77 ± 0.12) between the SGE of purebred and DGE of crossbred pigs. We found candidate genes located in the quantitative trait loci (QTLs) for the SGE that were associated with behavior and neurodegenerative diseases, and candidate genes in the QTLs for DGE that were related to body mass, size of muscle fiber, and muscle hypertrophy. These results suggest that the genomic selection of purebred animals could be applied for crossbred performance.

Genome-Wide Association Study of Parasite Resistance to Gastrointestinal Nematodes in Corriedale Sheep

Selection of genetically resistant animals is one alternative to reduce the negative impact of gastrointestinal nematodes (GIN) on sheep production. The aim of this study was to identify genomic regions associated with GIN resistance in Corriedale sheep by single-step genome-wide association studies (ssGWAS) using 170, 507 and 50K single nucleotide polymorphisms (SNPs). Analysis included 19,547 lambs with faecal egg counts (FEC) records, a pedigree file of 40,056 animals and 454, 711 and 383 genotypes from 170, 507 and 50K SNPs, respectively. Genomic estimated breeding values (GEBV) were obtained with single-step genomic BLUP methodology (ssGBLUP), using a univariate animal model, which included contemporary group, type of birth and age of dam as class fixed effects and age at FEC recording as covariate. The SNP effects as wells as p-values were estimated with POSTGSF90 program. Significance level was defined by a chromosome-wise False Discovery Rate of 5%. Significant genomic regions were identified in chromosomes 1, 3, 12 and 19 with the 170 SNP set, in chromosomes 7, 12 and 24 using the 507 SNP chip and only in chromosome 7 with the 50K SNP chip. Candidate genes located in these regions, using Oar_v4.0 as reference genome, were TIMP3, TLR5, LEPR and TLR9 (170 SNPs), SYNDIG1L and MGRN1 (507 SNP chip) and INO80, TLN2, TSHR and EIF2AK4 (50K SNP chip). These results validate genomic regions associated with FEC previously identified in Corriedale and other breeds and report new candidate regions for further investigation.

Accounting for population structure in genomic predictions of Eucalyptus globulus

Genetic groups have been widely adopted in tree breeding to account for provenance effects within pedigree-derived relationship matrices. However, provenances or genetic groups have not yet been incorporated into single-step genomic BLUP (“HBLUP”) analyses of tree populations. To quantify the impact of accounting for population structure in Eucalyptus globulus, we used HBLUP to compare breeding value predictions from models excluding base population effects and models including either fixed genetic groups or the marker-derived proxies, also known as metafounders. Full-sib families from 2 separate breeding populations were evaluated across 13 sites in the “Green Triangle” region of Australia. Gamma matrices (Γ) describing similarities among metafounders reflected the geographic distribution of populations and the origins of 2 land races were identified. Diagonal elements of Γ provided population diversity or allelic covariation estimates between 0.24 and 0.56. Genetic group solutions were strongly correlated with metafounder solutions across models and metafounder effects influenced the genetic solutions of base population parents. The accuracy, stability, dispersion, and bias of model solutions were compared using the linear regression method. Addition of genomic information increased accuracy from 0.41 to 0.47 and stability from 0.68 to 0.71, while increasing bias slightly. Dispersion was within 0.10 of the ideal value (1.0) for all models. Although inclusion of metafounders did not strongly affect accuracy or stability and had mixed effects on bias, we nevertheless recommend the incorporation of metafounders in prediction models to represent the hierarchical genetic population structure of recently domesticated populations.

Applicability of single-step genomic evaluation with a random regression model for reproductive traits in turkeys (Meleagris gallopavo)

Fertility and hatchability are economically important traits due to their effect on poult output coming from the turkey hatchery. Traditionally, fertility is recorded as the number of fertile eggs set in the incubator (FERT), defined at a time point during incubation by the identification of a developing embryo. Hatchability is recorded as either the number of fertile eggs that hatched (hatch of fertile, HOF) or the number hatched from all the eggs set (hatch of set, HOS). These traits are collected throughout the productive life of the bird and are conventionally cumulated, resulting in each bird having a single record per trait. Genetic evaluations of these traits have been estimated using pedigree relationships. However, the longitudinal nature of the traits and the availability of genomic information have renewed interest in using random regression (RR) to capture the differences in repeatedly recorded traits, as well as in the incorporation of genomic relationships. Therefore, the objectives of this study were: 1) to compare the applicability of a RR model with a cumulative model (CUM) using both pedigree and genomic information for genetic evaluation of FERT, HOF, and HOS and 2) to estimate and compare predictability from the models. For this study, a total of 63,935 biweekly FERT, HOF, and HOS records from 7,211 hens mated to 1,524 toms were available for a maternal turkey line. In total, 4,832 animals had genotypic records, and pedigree information on 11,191 animals was available. Estimated heritability from the CUM model using pedigree information was 0.11 ± 0.02, 0.24 ± 0.02, and 0.24 ± 0.02 for FERT, HOF, and HOS, respectively. With random regression using pedigree relationships, heritability estimates were in the range of 0.04–0.09, 0.11–0.17, and 0.09–0.18 for FERT, HOF, and HOS, respectively. The incorporation of genomic information increased the heritability by an average of 28 and 23% for CUM and RR models, respectively. In addition, the incorporation of genomic information caused predictability to increase by approximately 11 and 7% for HOF and HOS, respectively; however, a decrease in predictability of about 12% was observed for FERT. Our findings suggest that RR models using pedigree and genomic relationships simultaneously will achieve a higher predictability than the traditional CUM model.

Low-density SNP panel for efficient imputation and genomic selection of milk production and technological traits in dairy sheep

The present study aimed to ascertain how different strategies for leveraging genomic information enhance the accuracy of estimated breeding values for milk and cheese-making traits and to evaluate the implementation of a low-density (LowD) SNP chip designed explicitly for that aim. Thus, milk samples from a total of 2,020 dairy ewes from 2 breeds (1,039 Spanish Assaf and 981 Churra) were collected and analyzed to determine 3 milk production and composition traits and 2 traits related to milk coagulation properties and cheese yield. The 2 studied populations were genotyped with a customized 50K Affymetrix SNP chip (Affymetrix Inc.) containing 55,627 SNP markers. The prediction accuracies were obtained using different multitrait methodologies, such as the BLUP model based on pedigree information, the genomic BLUP (GBLUP), and the BLUP at the SNP level (SNP-BLUP), which are based on genotypic data, and the single-step GBLUP (ssGBLUP), which combines both sources of information. All of these methods were analyzed by cross-validation, comparing predictions of the whole population with the test population sets. Additionally, we describe the design of a LowD SNP chip (3K) and its prediction accuracies through the different methods mentioned previously. Furthermore, the results obtained using the LowD SNP chip were compared with those based on the 50K SNP chip data sets. Finally, we conclude that implementing genomic selection through the ssGBLUP model in the current breeding programs would increase the accuracy of the estimated breeding values compared with the BLUP methodology in the Assaf (from 0.19 to 0.39) and Churra (from 0.27 to 0.44) dairy sheep populations. The LowD SNP chip is cost-effective and has proven to be an accurate tool for estimating genomic breeding values for milk and cheese-making traits, microsatellite imputation, and parentage verification. The results presented here suggest that the routine use of this LowD SNP chip could potentially increase the genetic gains of the breeding selection programs of the 2 Spanish dairy sheep breeds considered here.

Genetic parameters and genome-wide association study of digital cushion thickness in Holstein cows

The digital cushion is linked to the development of claw horn lesions (CHL) in dairy cattle. The objectives of this study were to (1) estimate genetic parameters for digital cushion thickness (DCT), (2) estimate the genetic correlation between DCT and CHL, and (3) identify candidate genes associated with DCT. A cohort of 2,352 Holstein dairy cows were prospectively enrolled on 4 farms and assessed at 4 time points: before calving, immediately after calving, in early lactation, and in late lactation. At each time point, CHL was recorded by veterinary surgeons, and ultrasonographic images of the digital cushion were stored and retrospectively measured at 2 anatomical locations. Animals were genotyped and pedigree details extracted from the national database. Genetic parameters were estimated following a single-step approach implemented in AIREMLF90. Four traits were analyzed: the 2 DCT measurements, sole lesions (sole hemorrhage and sole ulcers), and white line lesions. All traits were analyzed with univariate linear mixed models; bivariate models were fit to estimate the genetic correlation between traits within and between time points. Single-marker and window-based genome-wide association analyses of DCT traits were conducted at each time point; candidate genes were mapped near (<0.2 Mb) or within the genomic markers or windows with the largest effects. Heritability estimates of DCT ranged from 0.14 to 0.44 depending on the location of DCT measurement and assessment time point. The genetic correlation between DCT and sole lesions was generally negative, notably between DCT immediately after calving and sole lesions in early or late lactation, and between DCT in early or late lactation and sole lesion severity in early or late lactation. Digital cushion thickness was not genetically correlated with white line lesions. A polygenic background to DCT was found; genes associated with inflammation, fat metabolism, and bone development were mapped near or within the top markers and windows. The moderate heritability of DCT provides an opportunity to use selective breeding to change DCT in a population. The negative genetic correlation between DCT and sole lesions at different stages of production lends support to current hypotheses of sole lesion pathogenesis. Highlighted candidate genes provide information regarding the complex genetic background of DCT in Holstein cows, but further studies are needed to explore and corroborate these findings.

Weighted Single-Step GWAS Identifies Genes Influencing Fillet Color in Rainbow Trout

The visual appearance of the fish fillet is a significant determinant of consumers' purchase decisions. Depending on the rainbow trout diet, a uniform bright white or reddish/pink fillet color is desirable. Factors affecting fillet color are complex, ranging from the ability of live fish to accumulate carotenoids in the muscle to preharvest environmental conditions, early postmortem muscle metabolism, and storage conditions. Identifying genetic markers of fillet color is a desirable goal but a challenging task for the aquaculture industry. This study used weighted, single-step GWAS to explore the genetic basis of fillet color variation in rainbow trout. We identified several SNP windows explaining up to 3.5%, 2.5%, and 1.6% of the additive genetic variance for fillet redness, yellowness, and whiteness, respectively. SNPs are located within genes implicated in carotenoid metabolism (β,β-carotene 15,15'-dioxygenase, retinol dehydrogenase) and myoglobin homeostasis (ATP synthase subunit β, mitochondrial (ATP5F1B)). These genes are involved in processes that influence muscle pigmentation and postmortem flesh coloration. Other identified genes are involved in the maintenance of muscle structural integrity (kelch protein 41b (klh41b), collagen α-1(XXVIII) chain (COL28A1), and cathepsin K (CTSK)) and protection against lipid oxidation (peroxiredoxin, superoxide dismutase 2 (SOD2), sestrin-1, Ubiquitin carboxyl-terminal hydrolase-10 (USP10)). A-to-G single-nucleotide polymorphism in β,β-carotene 15,15'-dioxygenase, and USP10 result in isoleucine-to-valine and proline-to-leucine non-synonymous amino acid substitutions, respectively. Our observation confirms that fillet color is a complex trait regulated by many genes involved in carotenoid metabolism, myoglobin homeostasis, protection against lipid oxidation, and maintenance of muscle structural integrity. The significant SNPs identified in this study could be prioritized via genomic selection in breeding programs to improve fillet color in rainbow trout.

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

Background

Single-step genomic predictions obtained from a breeding value model require calculating the inverse of the genomic relationship matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathbf{G}}^{-1})$$\end{document}(G-1). The Algorithm for Proven and Young (APY) creates a sparse representation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}^{-1}$$\end{document}G-1 with a low computational cost. APY consists of selecting a group of core animals and expressing the breeding values of the remaining animals as a linear combination of those from the core animals plus an error term. The objectives of this study were to: (1) extend APY to marker effects models; (2) derive equations for marker effect estimates when APY is used for breeding value models, and (3) show the implication of selecting a specific group of core animals in terms of a marker effects model.

Results

We derived a family of marker effects models called APY-SNP-BLUP. It differs from the classic marker effects model in that the row space of the genotype matrix is reduced and an error term is fitted for non-core animals. We derived formulas for marker effect estimates that take this error term in account. The prediction error variance (PEV) of the marker effect estimates depends on the PEV for core animals but not directly on the PEV of the non-core animals. We extended the APY-SNP-BLUP to include a residual polygenic effect and accommodate non-genotyped animals. We show that selecting a specific group of core animals is equivalent to select a subspace of the row space of the genotype matrix. As the number of core animals increases, subspaces corresponding to different sets of core animals tend to overlap, showing that random selection of core animals is algebraically justified.

Conclusions

The APY-(ss)GBLUP models can be expressed in terms of marker effect models. When the number of core animals is equal to the rank of the genotype matrix, APY-SNP-BLUP is identical to the classic marker effects model. If the number of core animals is less than the rank of the genotype matrix, genotypes for non-core animals are imputed as a linear combination of the genotypes of the core animals. For estimating SNP effects, only relationships and estimated breeding values for core animals are needed.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12711-022-00741-7.

Correcting for base-population differences and unknown parent groups in single-step genomic predictions of Norwegian Red Cattle

Bias and inflation in genomic evaluation with the single-step methods have been reported in several studies. Incompatibility between the base-populations of the pedigree-based and the genomic relationship matrix (G) could be a reason for these biases. Inappropriate ways of accounting for missing parents could be another reason for biases in genetic evaluations with or without genomic information. To handle these problems, we fitted and evaluated a fixed covariate (J) that contains ones for genotyped animals and zeros for unrelated non-genotyped animals, or pedigree-based regression coefficients for related non-genotyped animals. We also evaluated alternative ways of fitting the J covariate together with genetic groups on biases and stability of breeding value estimates, and of including it into G as a random effect. In a whole vs. partial data set comparison, four scenarios were investigated for the partial data: genotypes missing, phenotypes missing, both genotypes and phenotypes missing, and pedigree missing. Fitting J either as fixed or random reduced level-bias and inflation and increased stability of genomic predictions as compared to the basic model where neither J nor genetic groups were fitted. In most models, genomic predictions were largely biased for scenarios with missing genotype and phenotype information. The biases were reduced for models which combined group and J effects. Models with these corrected group covariates performed better than the recently published model where genetic groups were encapsulated and fitted as random via the Quaas and Pollak transformation. In our Norwegian Red cattle data, a model which combined group and J regression coefficients was preferred because it showed least bias and highest stability of genomic predictions across the scenarios.

Identification of Genomic Regions and Candidate Genes for Litter Traits in French Large White Pigs Using Genome-Wide Association Studies

The reproductive traits of sows are one of the important economic traits in pig production, and their performance directly affects the economic benefits of the entire pig industry. In this study, a total of 895 French Large White pigs were genotyped by GeneSeek Porcine 50K SNP Beadchip and four phenotypic traits of 1407 pigs were recorded, including total number born (TNB), number born alive (NBA), number healthy piglets (NHP) and litter weight born alive (LWB). To identify genomic regions and genes for these traits, we used two approaches: a single-locus genome-wide association study (GWAS) and a single-step GWAS (ssGWAS). Overall, a total of five SNPs and 36 genomic regions were identified by single-locus GWAS and ssGWAS, respectively. Notably, fourof all five significant SNPs were located in 10.72–11.06 Mb on chromosome 7, were also identified by ssGWAS. These regions explained the highest or second highest genetic variance in the TNB, NBA and NHP traits and harbor the protein coding gene ENSSSCG00000042180. In addition, several candidate genes associated with litter traits were identified, including JARID2, PDIA6, FLRT2 and DICER1. Overall, these novel results reflect the polygenic genetic architecture of the litter traits and provide a theoretical reference for the following implementation of molecular breeding.

Direct genetic effects, maternal genetic effects, and maternal genetic sensitivity on prenatal heat stress for calf diseases and corresponding genomic loci in German Holsteins

The aim of this study was to infer the effects of heat stress (HS) of dams during late gestation on direct and maternal genetic parameters for pneumonia (PNEU, 112,563 observations), diarrhea (DIAR, 176,904 observations), and omphalitis (OMPH, 176,872 observations) in Holstein calves kept in large-scale co-operator herds. The genotype dataset included 41,135 SNPs from 19,247 male and female cattle. Temperature-humidity indices (THI) during the last 8 wk of pregnancy were calculated, using the climate data from the nearest public weather station for each herd. Heat load effects were considered for average weekly THI larger than 60. Phenotypically, regression coefficients of calf diseases on prenatal THI during the last 8 wk of gestation were estimated in 8 consecutive runs. The strongest detrimental effects of prenatal HS on PNEU and DIAR were identified for the last week of pregnancy (wk 1). Thus, only wk 1 was considered in ongoing genetic and genomic analyses. In an advanced model considering prenatal HS, random regression coefficients on THI in wk 1 nested within maternal genetic effects (maternal slope effects for heat load) were considered as parameters to infer maternal sensitivity in response to prenatal THI alterations. Direct heritabilities from the advanced model ranged from 0.10 (THI 60) to 0.08 (THI 74) for PNEU and were close to 0.16 for DIAR. Maternal heritabilities for PNEU increased from 0.03 to 0.10 along the THI gradient. For DIAR, the maternal heritability was largest (0.07) at the minimum THI (THI = 60) and decreased to 0.05 at THI 74. Genetic correlations smaller than 0.80 for PNEU and DIAR recorded at THI 60 with corresponding diseases at THI 74 indicated genotype by climate interactions for maternal genetic effects. Genome-wide associations studies were performed using de-regressed proofs of genotyped sires for direct genetic, maternal genetic, and maternal slope effects. Thirty suggestive and 2 significant SNPs were identified from the GWAS. Forty-three genes located close to the suggestive SNPs (±100 kb) were annotated as potential candidate genes. Three biological processes were inferred on the basis of the these genes, addressing the negative regulation of the viral life cycle, innate immune response, and protein ubiquitination. Hence, the genetics of prenatal heat stress mechanisms are associated with immune physiology and disease resistance mechanisms.

Improvement of Genomic Predictions in Small Breeds by Construction of Genomic Relationship Matrix Through Variable Selection

Genomic selection has been increasingly implemented in the animal breeding industry, and it is becoming a routine method in many livestock breeding contexts. However, its use is still limited in several small-population local breeds, which are, nonetheless, an important source of genetic variability of great economic value. A major roadblock for their genomic selection is accuracy when population size is limited: to improve breeding value accuracy, variable selection models that assume heterogenous variance have been proposed over the last few years. However, while these models might outperform traditional and genomic predictions in terms of accuracy, they also carry a proportional increase of breeding value bias and dispersion. These mutual increases are especially striking when genomic selection is performed with a low number of phenotypes and high shrinkage value—which is precisely the situation that happens with small local breeds. In our study, we tested several alternative methods to improve the accuracy of genomic selection in a small population. First, we investigated the impact of using only a subset of informative markers regarding prediction accuracy, bias, and dispersion. We used different algorithms to select them, such as recursive feature eliminations, penalized regression, and XGBoost. We compared our results with the predictions of pedigree-based BLUP, single-step genomic BLUP, and weighted single-step genomic BLUP in different simulated populations obtained by combining various parameters in terms of number of QTLs and effective population size. We also investigated these approaches on a real data set belonging to the small local Rendena breed. Our results show that the accuracy of GBLUP in small-sized populations increased when performed with SNPs selected via variable selection methods both in simulated and real data sets. In addition, the use of variable selection models—especially those using XGBoost—in our real data set did not impact bias and the dispersion of estimated breeding values. We have discussed possible explanations for our results and how our study can help estimate breeding values for future genomic selection in small breeds.

Comparison of different response variables in genomic prediction using GBLUP and ssGBLUP methods in Iranian Holstein cattle

We compared the reliability and bias of genomic evaluation of Holstein bulls for milk, fat, and protein yield with two methods of genomic best linear unbiased prediction (GBLUP) and single-step GBLUP (ssGBLUP). Four response variables of estimated breeding value (EBV), daughter yield deviation (DYD), de-regressed proofs based on Garrick (DRPGR) and VanRaden (DRPVR) were used as dependent variables. The effects of three weighting methods for diagonal elements of the incidence matrix associated with residuals were also explored. The reliability and the absolute deviation from 1 of the regression coefficient of the response variable on genomic prediction (Dev) using GBLUP and ssGBLUP methods were estimated in the validation population. In the ssGBLUP method, the genomic prediction reliability and Dev from un-weighted DRPGR method for milk yield were 0.44 and 0.002, respectively. In the GBLUP method, the corresponding measurements from un-weighted EBV for fat were 0.52 and 0.008, respectively. Moreover, the un-weighted DRPGR performed well in ssGBLUP with fat yield values for reliability and Dev of 0.49 and 0.001, respectively, compared to equivalent protein yield values of 0.38 and 0.056, respectively. In general, the results from ssGBLUP of the un-weighted DRPGR for milk and fat yield and weighted DRPGR for protein yield outperformed other models. The average reliability of genomic predictions for three traits from ssGBLUP was 0.39 which was 0.98% higher than the average reliability from GBLUP. Likewise, the Dev of genomic predictions was lower in ssGBLUP than GBLUP. The average Dev of predictions for three traits from ssGBLUP and GBLUP were 0.110 and 0.144, respectively. In conclusion, genomic prediction using ssGBLUP outperformed GBLUP both in terms of reliability and bias.

Application of Bayesian genomic prediction methods to genome-wide association analyses

Background

Bayesian genomic prediction methods were developed to simultaneously fit all genotyped markers to a set of available phenotypes for prediction of breeding values for quantitative traits, allowing for differences in the genetic architecture (distribution of marker effects) of traits. These methods also provide a flexible and reliable framework for genome-wide association (GWA) studies. The objective here was to review developments in Bayesian hierarchical and variable selection models for GWA analyses.

Results

By fitting all genotyped markers simultaneously, Bayesian GWA methods implicitly account for population structure and the multiple-testing problem of classical single-marker GWA. Implemented using Markov chain Monte Carlo methods, Bayesian GWA methods allow for control of error rates using probabilities obtained from posterior distributions. Power of GWA studies using Bayesian methods can be enhanced by using informative priors based on previous association studies, gene expression analyses, or functional annotation information. Applied to multiple traits, Bayesian GWA analyses can give insight into pleiotropic effects by multi-trait, structural equation, or graphical models. Bayesian methods can also be used to combine genomic, transcriptomic, proteomic, and other -omics data to infer causal genotype to phenotype relationships and to suggest external interventions that can improve performance.

Conclusions

Bayesian hierarchical and variable selection methods provide a unified and powerful framework for genomic prediction, GWA, integration of prior information, and integration of information from other -omics platforms to identify causal mutations for complex quantitative traits.

Genomic evaluation and genome-wide association studies for total number of teats in a combined American and Danish Yorkshire pig populations selected in China

Joint genomic evaluation by combining data recordings and genomic information from different pig herds and populations is of interest for pig breeding companies because the efficiency of genomic selection (GS) could be further improved. In this work, an efficient strategy of joint genomic evaluation combining data from multiple pig populations is investigated. Total Teat Number (TTN), a trait that is equally recorded on 13 060 American Yorkshire (AY) populations (~14.68 teats) and 10 060 Danish Yorkshire (DY) pigs (~14.29 teats), was used to explore the feasibility and accuracy of GS combining datasets from different populations. We first estimated the genetic correlation (rg) of TTN between AY and DY pig populations (rg=0.79, se=0.23). Then we employed the genome-wide association study (GWAS) to identify QTL regions that are significantly associated with TTN and investigate the genetic architecture of TTN in different populations. Our results suggested that the genomic regions controlling TTN are slight different in the two Yorkshire populations, where the candidate QTL regions were on SSC 7 and SSC 8 for AY population and on SSC 7 for DY population. Finally, we explored an optimal way of genomic prediction for TTN via three different Genomic Best Linear Unbiased Prediction (GBLUP) models and we concluded that when TTN across populations are regarded as different, but correlated, traits in a multi-trait model, predictive abilities for both Yorkshire populations improve. As a conclusion, joint genomic evaluation for target traits in multiple pig populations is feasible in practice and more accurate, provided a proper model is used.

Quality of breeding value predictions from longitudinal analyses, with application to residual feed intake in pigs

Background

An important goal in animal breeding is to improve longitudinal traits. The objective of this study was to explore for longitudinal residual feed intake (RFI) data, which estimated breeding value (EBV), or combination of EBV, to use in a breeding program. Linear combinations of EBV (summarized breeding values, SBV) or phenotypes (summarized phenotypes) derived from the eigenvectors of the genetic covariance matrix over time were considered, and the linear regression method (LR method) was used to facilitate the evaluation of their prediction accuracy.

Results

Weekly feed intake, average daily gain, metabolic body weight, and backfat thickness measured on 2435 growing French Large White pigs over a 10-week period were analysed using a random regression model. In this population, the 544 dams of the phenotyped animals were genotyped. These dams did not have own phenotypes. The quality of the predictions of SBV and breeding values from summarized phenotypes of these females was evaluated. On average, predictions of SBV at the time of selection were unbiased, slightly over-dispersed and less accurate than those obtained with additional phenotypic information. The use of genomic information did not improve the quality of predictions. The use of summarized instead of longitudinal phenotypes resulted in predictions of breeding values of similar quality.

Conclusions

For practical selection on longitudinal data, the results obtained with this specific design suggest that the use of summarized phenotypes could facilitate routine genetic evaluation of longitudinal traits.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12711-022-00722-w.

Multivariate and Genome-Wide Analysis of Mid-Infrared Spectra of Non-Coagulating Milk of Sarda Sheep Breed

Milk coagulation ability is crucial for the dairy sheep industry since the whole amount of milk is processed into cheese. Non-coagulating milk (NCM) is defined as milk not forming a curd within the testing time. In sheep milk, it has been reported in literature that up to 20% of milk is NCM. Although the clotting properties of individual milk have been widely studied, little attention has been given to NCM and genomic dissection of this trait. Mid-infrared (MIR) spectra can be exploited both to predict cheese-making aptitude and to discriminate between coagulating milk and NCM. The main goals of this work were (i) to assess the predictivity of MIR spectra for NCM classification and (ii) to conduct a genome-wide association study on coagulation ability. Milk samples from 949 Sarda ewes genotyped and phenotyped for milk coagulation properties (MCPs) served as the training dataset. The validation dataset included 662 ewes. Three classical MCPs were measured: rennet coagulation time (RCT), curd firmness (a30), and curd firming time (k20). Moreover, MIR spectra were acquired and stored in the region between 925.92 and 5,011.54 cm−1. The probability of a sample to be NCM was modeled by step-wise logistic regression on milk spectral information (LR-W), logistic regression on principal component (LR-PC), and canonical discriminant analysis of spectral wave number (DA-W). About 9% of the samples did not coagulate at 30 min. The use of LR-W gave a poorer classification of NCM. The use of LR-PC improved the percentage of correct assignment (45 ± 9%). The DA-W method allows us to reach 75.1 ± 10.3 and 76.5 ± 18.4% of correct assignments of the inner and external validation datasets, respectively. As far as GWA of NCM, 458 SNP associations and 45 candidate genes were detected. The genes retrieved from public databases were mostly linked to mammary gland metabolism, udder health status, and a milk compound also known to affect the ability of milk to coagulate. In particular, the potential involvement of CAPNs deserves further investigation.

Imputation of non-genotyped F1 dams to improve genetic gain in swine crossbreeding programs

This study investigated using imputed genotypes from non-genotyped animals which were not in the pedigree for the purpose of genetic selection and improving genetic gain for economically relevant traits. Simulations were used to mimic a 3-breed crossbreeding system that resembled a modern swine breeding scheme. The simulation consisted of three purebred (PB) breeds A, B, and C each with 25 and 425 mating males and females, respectively. Males from A and females from B were crossed to produce AB females (n = 1,000), which were crossed with males from C to produce crossbreds (CB; n = 10,000). The genome consisted of three chromosomes with 300 quantitative trait loci and ~9,000 markers. Lowly heritable reproductive traits were simulated for A, B, and AB (h2 = 0.2, 0.2, and 0.15, respectively), whereas a moderately heritable carcass trait was simulated for C (h2 = 0.4). Genetic correlations between reproductive traits in A, B, and AB were moderate (rg = 0.65). The goal trait of the breeding program was AB performance. Selection was practiced for four generations where AB and CB animals were first produced in generations 1 and 2, respectively. Non-genotyped AB dams were imputed using FImpute beginning in generation 2. Genotypes of PB and CB were used for imputation. Imputation strategies differed by three factors: 1) AB progeny genotyped per generation (2, 3, 4, or 6), 2) known or unknown mates of AB dams, and 3) genotyping rate of females from breeds A and B (0% or 100%). PB selection candidates from A and B were selected using estimated breeding values for AB performance, whereas candidates from C were selected by phenotype. Response to selection using imputed genotypes of non-genotyped animals was then compared to the scenarios where true AB genotypes (trueGeno) or no AB genotypes/phenotypes (noGeno) were used in genetic evaluations. The simulation was replicated 20 times. The average increase in genotype concordance between unknown and known sire imputation strategies was 0.22. Genotype concordance increased as the number of genotyped CB increased with little additional gain beyond 9 progeny. When mates of AB were known and more than 4 progeny were genotyped per generation, the phenotypic response in AB did not differ (P > 0.05) from trueGeno yet was greater (P < 0.05) than noGeno. Imputed genotypes of non-genotyped animals can be used to increase performance when 4 or more progeny are genotyped and sire pedigrees of CB animals are known.

Genetic Basis for Resistance Against Viral Nervous Necrosis: GWAS and Potential of Genomic Prediction Explored in Farmed European Sea Bass (Dicentrarchus labrax)

Viral nervous necrosis (VNN) is an infectious disease caused by the red-spotted grouper nervous necrosis virus (RGNNV) in European sea bass and is considered a serious concern for the aquaculture industry with fry and juveniles being highly susceptible. To understand the genetic basis for resistance against VNN, a survival phenotype through the challenge test against the RGNNV was recorded in populations from multiple year classes (YC2016 and YC2017). A total of 4,851 individuals from 181 families were tested, and a subset (n∼1,535) belonging to 122 families was genotyped using a ∼57K Affymetrix Axiom array. The survival against the RGNNV showed low to moderate heritability with observed scale estimates of 0.18 and 0.25 obtained using pedigree vs. genomic information, respectively. The genome-wide association analysis showed a strong signal of quantitative trait loci (QTL) at LG12 which explained ∼33% of the genetic variance. The QTL region contained multiple genes (ITPK1, PLK4, HSPA4L, REEP1, CHMP2, MRPL35, and SCUBE) with HSPA4L and/or REEP1 genes being highly relevant with a likely effect on host response in managing disease-associated symptoms. The results on the accuracy of predicting breeding values presented 20–43% advantage in accuracy using genomic over pedigree-based information which varied across model types and applied validation schemes.

XSim version 2: simulation of modern breeding programs

Simulation can be an efficient approach to design, evaluate, and optimize breeding programs. In the era of modern agriculture, breeding programs can benefit from a simulator that integrates various sources of big data and accommodates state-of-the-art statistical models. The initial release of XSim, in which stochastic descendants can be efficiently simulated with a drop-down strategy, has mainly been used to validate genomic selection results. In this article, we present XSim Version 2 that is an open-source tool and has been extensively redesigned with additional features to meet the needs in modern breeding programs. It seamlessly incorporates multiple statistical models for genetic evaluations, such as GBLUP, Bayesian alphabets, and neural networks, and it can effortlessly simulate successive generations of descendants based on complex mating schemes by the aid of its modular design. Case studies are presented to demonstrate the flexibility of XSim Version 2 in simulating crossbreeding in animal and plant populations. Modern biotechnology, including double haploids and embryo transfer, can all be simultaneously integrated into the mating plans that drive the simulation. From a computing perspective, XSim Version 2 is implemented in Julia, which is a computer language that retains the readability of scripting languages (e.g. R and Python) without sacrificing much computational speed compared to compiled languages (e.g. C). This makes XSim Version 2 a simulation tool that is relatively easy for both champions and community members to maintain, modify, or extend in order to improve their breeding programs. Functions and operators are overloaded for a better user interface so they may concatenate, subset, summarize, and organize simulated populations at each breeding step. With the strong and foreseeable demands in the community, XSim Version 2 will serve as a modern simulator bridging the gaps between theories and experiments with its flexibility, extensibility, and friendly interface.

An Appropriate Genetic Approach for Improving Reproductive Traits in Crossbred Thai-Holstein Cattle under Heat Stress Conditions

Thailand is a tropical country affected by global climate change and has high temperatures and humidity that cause heat stress in livestock. A temperature−humidity index (THI) is required to assess and evaluate heat stress levels in livestock. One of the livestock types in Thailand experiencing heat stress due to extreme climate change is crossbred dairy cattle. Genetic evaluations of heat tolerance in dairy cattle have been carried out for reproductive traits. Heritability values for reproductive traits are generally low (<0.10) because environmental factors heavily influence them. Consequently, genetic improvement for these traits would be slow compared to production traits. Positive and negative genetic correlations were found between reproductive traits and reproductive traits and yield traits. Several selection methods for reproductive traits have been introduced, i.e., the traditional method, marker-assisted selection (MAS), and genomic selection (GS). GS is the most promising technique and provides accurate results with a high genetic gain. Single-step genomic BLUP (ssGBLUP) has higher accuracy than the multi-step equivalent for fertility traits or low-heritability traits.

Effect of genotyping strategies on the sustained benefit of single-step genomic BLUP over multiple generations

BACKGROUND

Single-step genomic best linear unbiased prediction (ssGBLUP) allows the inclusion of information from genotyped and ungenotyped individuals in a single analysis. This avoids the need to genotype all candidates with the potential benefit of reducing overall costs. The aim of this study was to assess the effect of genotyping strategies, the proportion of genotyped candidates and the genotyping criterion to rank candidates to be genotyped, when using ssGBLUP evaluation. A simulation study was carried out assuming selection over several discrete generations where a proportion of the candidates were genotyped and evaluation was done using ssGBLUP. The scenarios compared were: (i) three genotyping strategies defined by their protocol for choosing candidates to be genotyped (RANDOM: candidates were chosen at random; TOP: candidates with the best genotyping criterion were genotyped; and EXTREME: candidates with the best and worse criterion were genotyped); (ii) eight proportions of genotyped candidates (p); and (iii) two genotyping criteria to rank candidates to be genotyped (candidates' own phenotype or estimated breeding values). The criteria of the comparison were the cumulated gain and reliability of the genomic estimated breeding values (GEBV).

RESULTS

The genotyping strategy with the greatest cumulated gain was TOP followed by RANDOM, with EXTREME behaving as RANDOM at low p and as TOP with high p. However, the reliability of GEBV was higher with RANDOM than with TOP. This disparity between the trend of the gain and the reliability is due to the TOP scheme genotyping the candidates with the greater chances of being selected. The extra gain obtained with TOP increases when the accuracy of the selection criterion to rank candidates to be genotyped increases.

CONCLUSIONS

The best strategy to maximise genetic gain when only a proportion of the candidates are to be genotyped is TOP, since it prioritises the genotyping of candidates which are more likely to be selected. However, the strategy with the greatest GEBV reliability does not achieve the largest gain, thus reliability cannot be considered as an absolute and sufficient criterion for determining the scheme which maximises genetic gain.

Integrating genomic information and productivity and climate-adaptability traits into a regional white spruce breeding program

Tree improvement programs often focus on improving productivity-related traits; however, under present climate change scenarios, climate change-related (adaptive) traits should also be incorporated into such programs. Therefore, quantifying the genetic variation and correlations among productivity and adaptability traits, and the importance of genotype by environment interactions, including defense compounds involved in biotic and abiotic resistance, is essential for selecting parents for the production of resilient and sustainable forests. Here, we estimated quantitative genetic parameters for 15 growth, wood quality, drought resilience, and monoterpene traits for Picea glauca (Moench) Voss (white spruce). We sampled 1,540 trees from three open-pollinated progeny trials, genotyped with 467,224 SNP markers using genotyping-by-sequencing (GBS). We used the pedigree and SNP information to calculate, respectively, the average numerator and genomic relationship matrices, and univariate and multivariate individual-tree models to obtain estimates of (co)variance components. With few site-specific exceptions, all traits examined were under genetic control. Overall, higher heritability estimates were derived from the genomic- than their counterpart pedigree-based relationship matrix. Selection for height, generally, improved diameter and water use efficiency, but decreased wood density, microfibril angle, and drought resistance. Genome-based correlations between traits reaffirmed the pedigree-based correlations for most trait pairs. High and positive genetic correlations between sites were observed (average 0.68), except for those pairs involving the highest elevation, warmer, and moister site, specifically for growth and microfibril angle. These results illustrate the advantage of using genomic information jointly with productivity and adaptability traits, and defense compounds to enhance tree breeding selection for changing climate.

Accuracy of Genomic Selection for Important Economic Traits of Cashmere and Meat Goats Assessed by Simulation Study

Genomic selection in plants and animals has become a standard tool for breeding because of the advantages of high accuracy and short generation intervals. Implementation of this technology is hindered by the high cost of genotyping and other factors. The aim of this study was to determine an optional marker density panel and reference population size for using genomic selection of goats, with speculation on the number of QTLs that affect the important economic traits of goats. In addition, the effect of buck population size in the reference population on the accuracy of genomic estimated breeding value (GEBV) was discussed. Based on the previous genetic evaluation results of Inner Mongolia White Cashmere Goats, live body weight (LBW, h2 = 0.11) and fiber diameter (FD, h2 = 0.34) were chosen to perform genomic selection in this study. Reasonable genome parameters and generation transmission processes were set, and phenotypic and genotype data of the two traits were simulated. Then, different sizes of the reference population and validation population were selected from progeny. The GEBVs were obtained by six methods, including GBLUP (Genomic Best Linear Unbiased Prediction), ssGBLUP (Single Step Genomic Best Linear Unbiased Prediction), BayesA, BayesB, Bayesian ridge regression, and Bayesian LASSO. The correlation coefficient between the predicted and realized phenotypes from simulation was calculated and used as a measure of the accuracy of GEBV in each trait. The results showed that the medium marker density Panel (45 K) could be used for genomic selection in goats, which can ensure the accuracy of the GEBV. The reference population size of 1,500 can achieve greater genetic progress in genomic selection for fiber diameter and live body weight in goats by comparing with the population size below this level. The accuracy of the GEBV for live body weight and fiber diameter was better when the number of QTLs was 100 and 50, respectively. Additionally, the accuracy of GEBV was discovered to be good when the buck population size was up to 200. Meanwhile, the accuracy of the GEBV for medium heritability traits (FDs) was found to be higher than the accuracy of the GEBV for low heritability traits (LBWs). These findings will provide theoretical guidance for genomic selection in goats by using real data.