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Abstract: Management of inbreeding is one of the crucial parts of breeding programs in livestock populations. Traditionally, the inbreeding coefficient is calculated using pedigree data; however, it can also be estimated from genomic data. Nowadays, various approaches to estimating genomic-based inbreeding coefficients are increasingly integrated into research and breeding practices. These genomic estimators can supplement or replace pedigree-based coefficients. Each genomic-based inbreeding coefficient has its own properties and different ranges of values, and some of them need specific settings for calculation. Moreover, depending on the methodological approach, genomic estimators are sensitive to the population structure, genotyping technology applied, and the quality control of obtained genomic data. It is important to consider all these factors when calculating and especially when interpreting the final genomic inbreeding values. For these reasons, using genomic-based inbreeding coefficients can be more challenging than using pedigree-based ones. In this review, we comprehensively evaluate the most commonly used genomic estimators of individual inbreeding in livestock, providing an in-depth analysis of their advantages and limitations while offering insights into the methodological considerations and best practices for their accurate calculation and interpretation.

Management of inbreeding is one of the crucial parts of breeding programs in livestock populations. Traditionally, the inbreeding coefficient is calculated using pedigree data; however, it can also be estimated from genomic data. Nowadays, various approaches to estimating genomic-based inbreeding coefficients are increasingly integrated into research and breeding practices. These genomic estimators can supplement or replace pedigreebased coefficients. Each genomic-based inbreeding coefficient has its own properties and different ranges of values, and some of them need specific settings for calculation. Moreover, depending on the methodological approach, genomic estimators are sensitive to the population structure, genotyping technology applied, and the quality control of obtained genomic data. It is important to consider all these factors when calculating and especially when interpreting the final genomic inbreeding values. For these reasons, using genomic-based inbreeding coefficients can be more challenging than using pedigree-based ones. In this review, we comprehensively evaluate the most commonly used genomic estimators of individual inbreeding in livestock, providing an in-depth analysis of their advantages and limitations while offering insights into the methodological considerations and best practices for their accurate calculation and interpretation. [ABSTRACT FROM AUTHOR]

Simple Summary: Chronic progressive lymphedema is an incurable disease in draught horse breeds, particularly prevalent in breeds with genealogical relationships with Belgian draught horses. In this follow-up study, we analysed the heritabilities of this condition in Rhenish German draught horses and in addition, evaluated the genetic and phenotypic correlations with body size, skinfold thickness, and hoof characteristics. Furthermore, we studied heritabilities of chronic progressive lymphedema with models assuming censored data due to the progressive course of the disease. We found high heritabilities of chronic progressive lymphedema in the Rhenish German draught horses, even when we regarded all horses of any age. Over all age groups, the heritability of the score for chronic progressive lymphedema across all four limbs was 0.595 ± 0.131 in the threshold animal model based on pedigree data. Using a genomic relationship matrix yielded very similar estimates, but with slightly smaller standard errors. When assuming censored data for horses with an age below 7 and 8 years, heritabilities reached values of 0.774 ± 0.157 and 0.788 ± 0.168, respectively. Particularly, horses with higher cannon bone circumference, larger frames, and higher skinfold thickness appeared to be disposed to chronic progressive lymphedema. Horses with softer hoof horns seemed to be more susceptible to chronic progressive lymphedema than horses with harder hoof horns. This study showed that genetic disposition to chronic progressive lymphedema is the most important issue and therefore, breeding measures should be initiated to reduce the prevalence of severe cases of this incurable disease in Rhenish German draught horses. Chronic progressive lymphedema (CPL) is a prevalent and progressive disease in Rhenish German draught horses. The objective of our follow-up study was to evaluate the heritability of this disease in Rhenish German draught horses using pedigree-based and genomic relationship matrices. We employed linear and threshold animal models. Models included the random animal effect and effects of breeding association, coat colour, sex, and age within sex, and farm-related factors, on CPL scores. In addition, we estimated heritabilities in models assuming censoring for data when horses were below an age of 1–15 years. The heritabilities of CPL scores across all ages were 0.595 ± 0.131 and 0.482 ± 0.105 in the threshold and linear animal model with pedigree-based relationship matrices, respectively. The restriction of data to horses with a minimum age at examination or accounting for censored data in younger animals showed an increase in heritabilities of CPL scores up to 0.788 ± 0.168 (threshold model) and 0.752 ± 0.153 (linear model) at an age of 7–8 years. Analyses including genomic relationship matrices yielded very similar estimates, but with smaller standard errors than pedigree-based analyses. Heritabilities in threshold models for CPL prevalence (CPL-bin-score) and the number of affected limbs (CPL-bin-sum) were 0.176–0.189 ± 0.061–0.064 and 0.375–0.433 ± 0.164–0.170, respectively. We were able to show moderately to highly positive genetic correlations between the CPL score and cannon bone circumference (0.529–0.825), height at withers (0.338–0.555), and skinfold thickness (0.241–0.517). Using the dichotomous trait for the CPL score and the genomic relationship matrix resulted in corresponding estimates of 0.868, 0.793, and 0.784, respectively. This study showed the great importance of additive genetic variation influencing the expression of chronic progressive lymphedema in Rhenish German draught horses. Therefore, further research is warranted to implement breeding programmes in a small breeding population that exploit the potential of additive genetic differences among animals for reducing the prevalence and severity of lesions of this incurable disease. [ABSTRACT FROM AUTHOR]

Genotype-environment interaction is pervasive in forest genetics. Delineation of spatial breeding zones (BZs) is fundamental for accommodating genotype-environment interaction. Here we developed a BZ classification pipeline for the forest tree Eucalyptus globulus in 2 Australian regions based on phenotypic, genomic, and pedigree data, as well on a detailed environmental characterization ("envirotyping") and spatial mapping of BZs. First, the factor analytic method was used to model additive genetic variance and site–site genetic correlations (rB) in stem volume across 48 trials of 126,467 full-sib progeny from 2 separate breeding programs. Thirty-three trials were envirotyped using 145 environmental variables (EVs), involving soil and landscape (71), climate (73), and management (1) EVs. Next, sparse partial least squares-discriminant analysis was used to identify EVs that were required to predict classification of sites into 5 non-exclusive BZ classes based on rB. Finally, these BZs were spatially mapped across the West Australian and "Green Triangle" commercial estates by enviromic prediction using EVs for 80 locations and 15 sets of observed climate data to represent temporal variation. The factor analytic model explained 85.9% of estimated additive variance. Our environmental classification system produced within-zone mean rB between 0.76 and 0.84, which improves upon the existing values of 0.62 for Western Australia and 0.67 for Green Triangle as regional BZs. The delineation of 5 BZ classes provides a powerful framework for increasing genetic gain by matching genotypes to current and predicted future environments. [ABSTRACT FROM AUTHOR]

The increasing use of genomic selection (GS) in plant and animal breeding programs has led to the development of software that fits models based on unique scenarios. Accordingly, several R packages have been developed for GS. The lmekin function from the coxme R package was one of the first functions implemented in R to fit models with random family effects using the pedigree-based relationship matrix. The function allows the user to provide the covariance structures for the random effects; thus, the GBLUP model can be fitted. This fitting process consists of replacing, in the traditional BLUP model, the additive relationship matrix derived from a pedigree by the additive relationship matrix derived from markers. Thus, the objective of this study was to employ the lmekin function in the context of genomic prediction by comparing the results of this function with those obtained using five R packages for GS: rrBLUP, BGLR, sommer, lme4qtl, and lme4GS. The comparisons were performed considering the computational times and predicted values for a wheat dataset and simulated big data. In addition, we implemented a 5-fold cross-validation scheme through considering the values predicted by the lmekin function for the wheat dataset. The results indicated that the lmekin function was effective in predicting genomic breeding values considering multiple random effects and relatively small sample sizes. The rrBLUP package processed the fastest for the scenario with only one genetic random effect, and the high temporal efficiency of the sommer package was confirmed for the scenario with more than one genetic random effect. Differences in computational times occurred because of the different algorithms implemented in the packages to estimate the variance components. [ABSTRACT FROM AUTHOR]

Abstract Background Carcass traits are crucial for broiler ducks, but carcass traits can only be measured postmortem. Genomic selection (GS) is an effective approach in animal breeding to improve selection and reduce costs. However, the performance of genomic prediction in duck carcass traits remains largely unknown. Results In this study, we estimated the genetic parameters, performed GS using different models and marker densities, and compared the estimation performance between GS and conventional BLUP on 35 carcass traits in an F2 population of ducks. Most of the cut weight traits and intestine length traits were estimated to be high and moderate heritabilities, respectively, while the heritabilities of percentage slaughter traits were dynamic. The reliability of genome prediction using GBLUP increased by an average of 0.06 compared to the conventional BLUP method. The Permutation studies revealed that 50K markers had achieved ideal prediction reliability, while 3K markers still achieved 90.7% predictive capability would further reduce the cost for duck carcass traits. The genomic relationship matrix normalized by our true variance method instead of the widely used $$\sum {2p}_{i}(1-{p}_{i})$$ ∑ 2 p i ( 1 - p i ) could achieve an increase in prediction reliability in most traits. We detected most of the bayesian models had a better performance, especially for BayesN. Compared to GBLUP, BayesN can further improve the predictive reliability with an average of 0.06 for duck carcass traits. Conclusion This study demonstrates genomic selection for duck carcass traits is promising. The genomic prediction can be further improved by modifying the genomic relationship matrix using our proposed true variance method and several Bayesian models. Permutation study provides a theoretical basis for the fact that low-density arrays can be used to reduce genotype costs in duck genome selection.

Abstract Accurate estimate of relatedness is important for genetic data analyses, such as heritability estimation and association mapping based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to biased heritability estimations and spurious associations. Individual-level genotype data are often used to estimate kinship coefficient between individuals. The commonly used sample correlation-based genomic relationship matrix (scGRM) method estimates kinship coefficient by calculating the average sample correlation coefficient among all single nucleotide polymorphisms (SNPs), where the observed allele frequencies are used to calculate both the expectations and variances of genotypes. Although this method is widely used, a substantial proportion of estimated kinship coefficients are negative, which are difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists bias in the estimated kinship coefficient using the scGRM method when the observed allele frequencies are regarded as true frequencies. This leads to negative bias for the average estimate of kinship among all individuals, which explains the estimated negative kinship coefficients. Based on this observation, we propose an unbiased estimation method, UKin, which can reduce kinship estimation bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to compare UKin with scGRM and three other kinship estimating methods: rGRM, tsGRM, and KING. Our results demonstrate that both bias and root mean square error in kinship coefficient estimation could be reduced by using UKin. We further investigated the performance of UKin, KING, and three GRM-based methods in calculating the SNP-based heritability, and show that UKin can improve estimation accuracy for heritability regardless of the scale of SNP panel.

Global environmental change is happening at unprecedented rates. Coral reefs are among the ecosystems most threatened by global change. For wild populations to persist, they must adapt. Knowledge shortfalls about corals' complex ecological and evolutionary dynamics, however, stymie predictions about potential adaptation to future conditions. Here, we review adaptation through the lens of quantitative genetics. We argue that coral adaptation studies can benefit greatly from "wild" quantitative genetic methods, where traits are studied in wild populations undergoing natural selection, genomic relationship matrices can replace breeding experiments, and analyses can be extended to examine genetic constraints among traits. In addition, individuals with advantageous genotypes for anticipated future conditions can be identified. Finally, genomic genotyping supports simultaneous consideration of how genetic diversity is arrayed across geographic and environmental distances, providing greater context for predictions of phenotypic evolution at a metapopulation scale. [ABSTRACT FROM AUTHOR]

This study aimed to assess the impact of differential weighting in genomic regions harboring candidate causal loci on the genomic prediction accuracy and dispersion for growth and carcass‐related traits in Nelore cattle. The dataset contained 168 793 phenotypic records for adjusted weight at 450 days of age (W450), 83 624 for rib eye area (REA), 24 480 for marbling (MAR) and 82 981 for subcutaneous backfat thickness (BFT) and rump fat thickness (RFT). The pedigree harbored information from 244 254 animals born between 1977 and 2016, including 6283 sires and 50 742 dams. Animals (n = 7769) were genotyped with the low‐density panel (Clarifide® Nelore 3.0), and the genotypes were imputed to a panel containing 735 044 markers. A linear animal model was applied to estimate the genetic parameters and to perform the weighted single‐step genome‐wide association study (WssGWAS). A total of seven models for genomic prediction were evaluated combining the SNP weights obtained in the iterations of the WssGWAS and the candidate QTL. The heritability estimated for W450 (0.35) was moderate, and for carcass‐related traits, the estimates were moderate for REA (0.27), MAR (0.28) and RFT (0.28), and low for BFT (0.18). The prediction accuracy for W450 incorporating reported QTL previously described in the literature along with different SNPs weights was like those described for the default ssGBLUP model. The use of the ssGWAS to weight the SNP effects displayed limited advantages for the REA prediction accuracy. Comparing the ssGBLUP with the BLUP model, a meaningful improvement in the prediction accuracy from 0.09 to 0.63 (700%) was observed for MAR. The highest prediction accuracy was obtained for BFT and RFT in all evaluated models. The application of information obtained from the WssGWAS is an alternative to reduce the genomic prediction dispersion for growth and carcass‐related traits, except for MAR. Furthermore, the results obtained herein pointed out that is possible to improve the prediction accuracy and reduce the genomic prediction dispersion for growth and carcass‐related traits in young animals. [ABSTRACT FROM AUTHOR]

Background: Carcass traits are crucial for broiler ducks, but carcass traits can only be measured postmortem. Genomic selection (GS) is an effective approach in animal breeding to improve selection and reduce costs. However, the performance of genomic prediction in duck carcass traits remains largely unknown. Results: In this study, we estimated the genetic parameters, performed GS using different models and marker densities, and compared the estimation performance between GS and conventional BLUP on 35 carcass traits in an F2 population of ducks. Most of the cut weight traits and intestine length traits were estimated to be high and moderate heritabilities, respectively, while the heritabilities of percentage slaughter traits were dynamic. The reliability of genome prediction using GBLUP increased by an average of 0.06 compared to the conventional BLUP method. The Permutation studies revealed that 50K markers had achieved ideal prediction reliability, while 3K markers still achieved 90.7% predictive capability would further reduce the cost for duck carcass traits. The genomic relationship matrix normalized by our true variance method instead of the widely used ∑ 2 p i (1 - p i) could achieve an increase in prediction reliability in most traits. We detected most of the bayesian models had a better performance, especially for BayesN. Compared to GBLUP, BayesN can further improve the predictive reliability with an average of 0.06 for duck carcass traits. Conclusion: This study demonstrates genomic selection for duck carcass traits is promising. The genomic prediction can be further improved by modifying the genomic relationship matrix using our proposed true variance method and several Bayesian models. Permutation study provides a theoretical basis for the fact that low-density arrays can be used to reduce genotype costs in duck genome selection. [ABSTRACT FROM AUTHOR]

To develop a breed assignment model, three main steps are generally followed: 1) The selection of breed informative single nucleotide polymorphism (SNP); 2) The training of a model, based on a reference population, that allows to classify animals to their breed of origin; and 3) The validation of the developed model on external animals i.e., that were not used in previous steps. However, there is no consensus in the literature about which methodology to follow for the first step, nor about the number of SNP to be selected. This can raise many questions when developing the model and lead to the use of sophisticated methodologies for selecting SNP (e.g., with iterative algorithms, partitions of SNP, or combination of several methods). Therefore, it may be of interest to avoid the first step by the use of all the available SNP. For this purpose, we propose the use of a genomic relationship matrix (GRM), combined or not with a machine learning method, for breed assignment. We compared it with a previously developed model based on selected informative SNP. Four methodologies were investigated: 1) The PLS_NSC methodology: selection of SNP based on a partial least square-discriminant analysis (PLS-DA) and breed assignment by classification based on the nearest shrunken centroids (NSC) method; 2) Breed assignment based on the highest mean relatedness of an animal to the reference populations of each breed (referred to mean_GRM); 3) Breed assignment based on the highest SD of the relatedness of an animal to the reference populations of each breed (referred to SD_GRM) and 4) The GRM_SVM methodology: the use of means and SD of the relatedness defined in mean_GRM and SD_GRM methodologies combined with the linear support vector machine (SVM), a machine learning method used for classification. Regarding mean global accuracies, results showed that the use of mean_GRM or GRM_SVM was not significantly different (Bonferroni corrected P > 0.0083) than the model based on a reduced SNP panel (PLS_NSC). Moreover, the mean_GRM and GRM_SVM methodology were more efficient than PLS_NSC as it was faster to compute. Therefore, it is possible to bypass the selection of SNP and, by the use of a GRM, to develop an efficient breed assignment model. In routine, we recommend the use of GRM_SVM over mean_GRM as it gave a slightly increased global accuracy, which can help endangered breeds to be maintained. The script to execute the different methodologies can be accessed on [ABSTRACT FROM AUTHOR]

Accurate estimate of relatedness is important for genetic data analyses, such as heritability estimation and association mapping based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to biased heritability estimations and spurious associations. Individual-level genotype data are often used to estimate kinship coefficient between individuals. The commonly used sample correlation-based genomic relationship matrix (scGRM) method estimates kinship coefficient by calculating the average sample correlation coefficient among all single nucleotide polymorphisms (SNPs), where the observed allele frequencies are used to calculate both the expectations and variances of genotypes. Although this method is widely used, a substantial proportion of estimated kinship coefficients are negative, which are difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists bias in the estimated kinship coefficient using the scGRM method when the observed allele frequencies are regarded as true frequencies. This leads to negative bias for the average estimate of kinship among all individuals, which explains the estimated negative kinship coefficients. Based on this observation, we propose an unbiased estimation method, UKin, which can reduce kinship estimation bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to compare UKin with scGRM and three other kinship estimating methods: rGRM, tsGRM, and KING. Our results demonstrate that both bias and root mean square error in kinship coefficient estimation could be reduced by using UKin. We further investigated the performance of UKin, KING, and three GRM-based methods in calculating the SNP-based heritability, and show that UKin can improve estimation accuracy for heritability regardless of the scale of SNP panel. [ABSTRACT FROM AUTHOR]

GBLUP, the most widely used genomic prediction (GP) method, consumes large and increasing amounts of computational resources as the training population size increases due to the inverse of the genomic relationship matrix (GRM). Therefore, in this study, we developed a new genomic prediction method (RHEPCG) that avoids the direct inverse of the GRM by combining randomized Haseman–Elston (HE) regression (RHE-reg) and a preconditioned conjugate gradient (PCG). The simulation results demonstrate that RHEPCG, in most cases, not only achieves similar predictive accuracy with GBLUP but also significantly reduces computational time. As for the real data, RHEPCG shows similar or better predictive accuracy for seven traits of the Arabidopsis thaliana F2 population and four traits of the Sorghum bicolor RIL population compared with GBLUP. This indicates that RHEPCG is a practical alternative to GBLUP and has better computational efficiency.

ABSTRACT: The detrimental effects of increased homozygosity due to inbreeding have prompted the development of methods to reduce inbreeding. The detection of runs of homozygosity (ROH), or contiguous stretches of homozygous marker genotypes, can be used to describe and quantify the level of inbreeding in an individual. The estimation of inbreeding coefficients can be calculated based on pedigree information, ROH, or the genomic relationship matrix. The aim of this study was to detect and describe ROH in the turkey genome and compare estimates of pedigree-based inbreeding coefficients (FPED) with genomic-based inbreeding coefficients estimated from ROH (FROH) and the genomic relationship matrix (FGRM). A total of 2,616,890 pedigree records were available. Of these records, 6,371 genotyped animals from three purebred turkey (Meleagris gallopavo) lines between 2013 and 2019 were available, and these were obtained using a dense single nucleotide polymorphism array (56,452 SNPs). The overall mean length of detected ROH was 2.87 ± 0.29 Mb with a mean number of 84.87 ± 8.79 ROH per animal. Short ROH with lengths of 1 to 2 Mb long were the most abundant throughout the genome. Mean ROH coverage differed greatly between chromosomes and lines. Considering inbreeding coefficient means across all lines, genomic derived inbreeding coefficients (FROH = 0.27; FGRM = 0.32) were higher than coefficients estimated from pedigree records (FPED = 0.14). Correlations between FROH and FPED, FROH and FGRM, and FPED and FGRM ranged between 0.19 to 0.31, 0.68 to 0.73, and 0.17 to 0.30, respectively. Additionally, correlations between FROH from different lengths and FPED substantially increased with ROH length from -0.06 to 0.33. Results of the current research, including the distribution of ROH throughout the genome and ROH-derived inbreeding estimates, can provide a more comprehensive description of inbreeding in the turkey genome. This knowledge can be used to evaluate genetic diversity, a requirement for genetic improvement, and develop methods to minimize inbreeding in turkey breeding programs.

Single-step GBLUP (HBLUP) efficiently combines genomic, pedigree, and phenotypic information for holistic genetic analyses of disjunct breeding populations. We combined data from two independent multigenerational Eucalyptus globulus breeding populations to provide direct comparisons across the programs and indirect predictions in environments where pedigreed families had not been evaluated. Despite few known pedigree connections between the programs, genomic relationships provided the connectivity required to create a uni- fied relationship matrix, H, which was used to compare pedigree-based and HBLUP models. Stem volume data from 48 sites spread across three regions of southern Australia and wood quality data across 20 sites provided comparisons of model accuracy. Genotyping proved valuable for correcting pedigree errors and HBLUP more precisely defines relationships within and among populations, with relationships among the genotyped individuals used to connect the pedigrees of the two programs. Cryptic relationships among the native range populations provided evidence of population structure and evidence of the origin of landrace populations. HBLUP across programs improved the prediction accuracy of parents and genotyped individuals and enabled breeding value predictions to be directly compared and inferred in regions where little to no testing has been undertaken. The impact of incorporating genetic groups in the estimation of H will further align traditional genetic evaluation pipelines with approaches that incorporate marker-derived relationships into prediction models. [ABSTRACT FROM AUTHOR]

Abstract Background Genomic prediction is an advanced method for estimating genetic values, which has been widely accepted for genetic evaluation in animal and disease-risk prediction in human. It estimates genetic values with genome-wide distributed SNPs instead of pedigree. The key step of it is to construct genomic relationship matrix (GRM) via genome-wide SNPs; however, usually the calculation of GRM needs huge computer memory especially when the SNP number and sample size are big, so that sometimes it will become computationally prohibitive even for super computer clusters. We herein developed an integrative algorithm to compute GRM. To avoid calculating GRM for the whole genome, ICGRM freely divides the genome-wide SNPs into several segments and computes the summary statistics related to GRM for each segment that requires quite few computer RAM; then it integrates these summary statistics to produce GRM for whole genome. Results It showed that the computer memory of ICGRM was reduced by 15 times (from 218Gb to 14Gb) after the genome SNPs were split into 5 to 200 parts in terms of the number of SNPs in our simulation dataset, making it computationally feasible for almost all kinds of computer servers. ICGRM is implemented in C/C++ and freely available via https://github.com/mingfang618/CLGRM. Conclusions ICGRM is computationally efficient software to build GRM and can be used for big dataset.

Genotypes are often used to assign parentage in agricultural and ecological settings. Sequencing can be used to obtain genotypes but does not provide unambiguous genotype calls, especially when sequencing depth is low in order to reduce costs. In that case, standard parentage analysis methods no longer apply. A strategy for using low-depth sequencing data for parentage assignment is developed here. It entails the use of relatedness estimates along with a metric termed excess mismatch rate which, for parent-offspring pairs or trios, is the difference between the observed mismatch rate and the rate expected under a model of inheritance and allele reads without error. When more than one putative parent has similar statistics, bootstrapping can provide a measure of the relatedness similarity. Putative parent-offspring trios can be further checked for consistency by comparing the offspring’s estimated inbreeding to half the parent relatedness. Suitable thresholds are required for each metric. These methods were applied to a deer breeding operation consisting of two herds of different breeds. Relatedness estimates were more in line with expectation when the herds were analyzed separately than when combined, although this did not alter which parents were the best matches with each offspring. Parentage results were largely consistent with those based on a microsatellite parentage panel with three discordant parent assignments out of 1561. Two models are investigated to allow the parentage metrics to be calculated with non-random selection of alleles. The tools and strategies given here allow parentage to be assigned from low-depth sequencing data.

Implicit assumption of common (co)variance for all loci in multi-trait Genomic Best Linear Unbiased Prediction (GBLUP) results in a genomic relationship matrix (G) that is common to all traits. When this assumption is violated, Bayesian whole genome regression methods may be superior to GBLUP by accounting for unequal (co)variance for all loci or genome regions. This study aimed to develop a strategy to improve the accuracy of GBLUP for multi-trait genomic prediction, using (co)variance estimates of SNP effects from Bayesian whole genome regression methods. Five generations (G1-G5, test populations) of genotype data were available by simulations based on data of 2,200 Danish Holstein cows (G0, reference population). Two correlated traits with heritabilities of 0.1 or 0.4, and a genetic correlation of 0.45 were generated. First, SNP effects and breeding values were estimated using BayesAS method, assuming (co)variance was the same for SNPs within a genome region, and different between regions. Region size was set as one SNP, 100 SNPs, a whole chromosome or whole genome. Second, posterior (co)variances of SNP effects were used to weight SNPs in construction of G matrices. In general, region size of 100 SNPs led to highest prediction accuracies using BayesAS, and wGBLUP outperformed GBLUP at this region size. Our results suggest that when genetic architectures of traits favor Bayesian methods, the accuracy of multi-trait GBLUP can be as high as the Bayesian method if SNPs are weighted by the Bayesian posterior (co)variances.

Objective Intramuscular fat is one of the meat quality traits that is considered in the selection strategies for Hanwoo (Korean cattle). Different methods are used to estimate the breeding value of selection candidates. In the present work we focused on accuracy of different genotype relationship matrices as described by forni and pedigree based relationship matrix. Methods The data set included a total of 778 animals that were genotyped for BovineSNP50 BeadChip. Among these 778 animals, 72 animals were sires for 706 reference animals and were used as a validation dataset. Single trait animal model (best linear unbiased prediction and genomic best linear unbiased prediction) was used to estimate the breeding values from genomic and pedigree information. Results The diagonal elements for the pedigree based coefficients were slightly higher for the genomic relationship matrices (GRM) based coefficients while off diagonal elements were considerably low for GRM based coefficients. The accuracy of breeding value for the pedigree based relationship matrix (A) was 13% while for GRM (GOF, G05, and Yang) it was 0.37, 0.45, and 0.38, respectively. Conclusion Accuracy of GRM was 1.5 times higher than A in this study. Therefore, genomic information will be more beneficial than pedigree information in the Hanwoo breeding program.

Background: Genomic prediction is an advanced method for estimating genetic values, which has been widely accepted for genetic evaluation in animal and disease-risk prediction in human. It estimates genetic values with genome-wide distributed SNPs instead of pedigree. The key step of it is to construct genomic relationship matrix (GRM) via genome-wide SNPs; however, usually the calculation of GRM needs huge computer memory especially when the SNP number and sample size are big, so that sometimes it will become computationally prohibitive even for super computer clusters. We herein developed an integrative algorithm to compute GRM. To avoid calculating GRM for the whole genome, ICGRM freely divides the genome-wide SNPs into several segments and computes the summary statistics related to GRM for each segment that requires quite few computer RAM; then it integrates these summary statistics to produce GRM for whole genome. Results: It showed that the computer memory of ICGRM was reduced by 15 times (from 218Gb to 14Gb) after the genome SNPs were split into 5 to 200 parts in terms of the number of SNPs in our simulation dataset, making it computationally feasible for almost all kinds of computer servers. ICGRM is implemented in C/C++ and freely available via https://github.com/mingfang618/CLGRM. Conclusions: ICGRM is computationally efficient software to build GRM and can be used for big dataset. [ABSTRACT FROM AUTHOR]

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

The purpose of this study is review and evaluation of computing methods used in genomic selection for animal breeding. Commonly used models include SNP BLUP with extensions (BayesA, etc), genomic BLUP (GBLUP) and single-step GBLUP (ssGBLUP). These models are applied for genomewide association studies (GWAS), genomic prediction and parameter estimation. Solving methods include finite Cholesky decomposition possibly with a sparse implementation, and iterative Gauss–Seidel (GS) or preconditioned conjugate gradient (PCG), the last two methods possibly with iteration on data. Details are provided that can drastically decrease some computations. For SNP BLUP especially with sampling and large number of SNP, the only choice is GS with iteration on data and adjustment of residuals. If only solutions are required, PCG by iteration on data is a clear choice. A genomic relationship matrix (GRM) has limited dimensionality due to small effective population size, resulting in infinite number of generalized inverses of GRM for large genotyped populations. A specific inverse called APY requires only a small fraction of GRM, is sparse and can be computed and stored at a low cost for millions of animals. With APY inverse and PCG iteration, GBLUP and ssGBLUP can be applied to any population. Both tools can be applied to GWAS. When the system of equations is sparse but contains dense blocks, a recently developed package for sparse Cholesky decomposition and sparse inversion called YAMS has greatly improved performance over packages where such blocks were treated as sparse. With YAMS, GREML and possibly single-step GREML can be applied to populations with >50 000 genotyped animals. From a computational perspective, genomic selection is becoming a mature methodology.

Growth traits, such as body weight, directly influence productivity and economic efficiency in the swine industry. In this study, we estimate heritability for body weight traits usinginformation from pedigree and genome-wide single nucleotide polymorphism (SNP) chip data. Four body weight phenotypes were measured in 1,105 F2 progeny from an intercross between Landrace and Jeju native black pigs. All experimental animals were subjected to genotypic analysis using PorcineSNP60K BeadChip platform, and 39,992 autosomal SNP markers filtered by quality control criteria were used to construct genomic relationship matrix for heritability estimation. Restricted maximum likelihood estimates of heritability were obtained using both genomic- and pedigree- relationship matrix in a linear mixed model. The heritability estimates using SNP information were smaller (0.36-0.55) than those which were estimated using pedigree information (0.62-0.97). To investigate effect of common environment, such as maternal effect, on heritability estimation, we included maternal effect as an additional random effect term in the linear mixed model analysis. We detected substantial proportions of phenotypic variance components were explained by maternal effect. And the heritability estimates using both pedigree and SNP information were decreased. Therefore, heritability estimates must be interpreted cautiously when there are obvious common environmental variance components.

Ryegrass single plants, bi-parental family pools, and multi-parental family pools are often genotyped, based on allele-frequencies using genotyping-by-sequencing (GBS) assays. GBS assays can be performed at low-coverage depth to reduce costs. However, reducing the coverage depth leads to a higher proportion of missing data, and leads to a reduction in accuracy when identifying the allele-frequency at each locus. As a consequence of the latter, genomic relationship matrices (GRMs) will be biased. This bias in GRMs affects variance estimates and the accuracy of GBLUP for genomic prediction (GBLUP-GP). We derived equations that describe the bias from low-coverage sequencing as an effect of binomial sampling of sequence reads, and allowed for any ploidy level of the sample considered. This allowed us to combine individual and pool genotypes in one GRM, treating pool-genotypes as a polyploid genotype, equal to the total ploidy-level of the parents of the pool. Using simulated data, we verified the magnitude of the GRM bias at different coverage depths for three different kinds of ryegrass breeding material: individual genotypes from single plants, pool-genotypes from F2 families, and pool-genotypes from synthetic varieties. To better handle missing data, we also tested imputation procedures, which are suited for analyzing allele-frequency genomic data. The relative advantages of the bias-correction and the imputation of missing data were evaluated using real data. We examined a large dataset, including single plants, F2 families, and synthetic varieties genotyped in three GBS assays, each with a different coverage depth, and evaluated them for heading date, crown rust resistance, and seed yield. Cross validations were used to test the accuracy using GBLUP approaches, demonstrating the feasibility of predicting among different breeding material. Bias-corrected GRMs proved to increase predictive accuracies when compared with standard approaches to construct GRMs. Among the imputation methods we tested, the random forest method yielded the highest predictive accuracy. The combinations of these two methods resulted in a meaningful increase of predictive ability (up to 0.09). The possibility of predicting across individuals and pools provides new opportunities for improving ryegrass breeding schemes.

Correct pedigree is essential to produce accurate genetic evaluations of livestock populations. Pedigree validation has traditionally been undertaken using microsatellites and more recently, based on checks on opposing homozygotes using single nucleotide polymorphisms (SNPs). In this study, the genomic relationship matrix was examined to see whether it was a useful tool to forensically validate pedigree and discover unknown pedigree. Using 5,993 genotyped Limousin animals which were imputed to a core set of 38,907 SNPs, the genomic relationships between animals were assessed to validate the reported pedigree. Using already pedigree-verified animals, the genomic relationships between animals of different relationships were shown to be on average 0.58, 0.59, 0.32, 0.32, 0.19, and 0.14 between animals and their parents, full siblings, half siblings, grandparents, great grandparents, and great great grandparents, respectively. Threshold values were defined based on the minimum genomic relationship reported between already pedigree-verified animals; 0.46, 0.41, 0.17, 0.17, 0.07, and 0.05, respectively for animals and their parents, full siblings, half siblings, grandparents, great grandparents, and great great grandparents. Using the wider population and the above genomic relationship threshold values, potential pedigree conflicts were identified within each relationship type. Pedigree error rates of between 0.9% (animal and great great grandparent) and 4.0% (full siblings) were identified. A forensic genomic pedigree validation and discovery system was developed to enable pedigree to be verified for individual genotyped animals. This system verifies not just the parents, but also a wide number of other genotyped relatives and can therefore identify more potential errors in the pedigree than current conventional methods. A novel aspect to this algorithm is that it can also be used to discover closely related animals on the basis of their genomic relationships although they are not recorded as such in the pedigree. This functionality enables missing pedigree information to be discovered and corrected in the pedigree of livestock populations. The methods in this paper demonstrate that the genomic relationship matrix can be a useful tool in the validation and discovery of pedigree in livestock populations. However, the method does rely on being able to define threshold values appropriate to the specific livestock population, which will require sufficient number of animals to be genotyped and pedigree validated before it can be used. [ABSTRACT FROM AUTHOR]

Ryegrass single plants, bi-parental family pools, and multi-parental family pools are often genotyped, based on allele-frequencies using genotyping-by-sequencing (GBS) assays. GBS assays can be performed at low-coverage depth to reduce costs. However, reducing the coverage depth leads to a higher proportion of missing data, and leads to a reduction in accuracy when identifying the allele-frequency at each locus. As a consequence of the latter, genomic relationship matrices (GRMs) will be biased. This bias in GRMs affects variance estimates and the accuracy of GBLUP for genomic prediction (GBLUP-GP). We derived equations that describe the bias from low-coverage sequencing as an effect of binomial sampling of sequence reads, and allowed for any ploidy level of the sample considered. This allowed us to combine individual and pool genotypes in one GRM, treating pool-genotypes as a polyploid genotype, equal to the total ploidy-level of the parents of the pool. Using simulated data, we verified the magnitude of the GRM bias at different coverage depths for three different kinds of ryegrass breeding material: individual genotypes from single plants, pool-genotypes from F2 families, and pool-genotypes from synthetic varieties. To better handle missing data, we also tested imputation procedures, which are suited for analyzing allele-frequency genomic data. The relative advantages of the bias-correction and the imputation of missing data were evaluated using real data. We examined a large dataset, including single plants, F2 families, and synthetic varieties genotyped in three GBS assays, each with a different coverage depth, and evaluated them for heading date, crown rust resistance, and seed yield. Cross validations were used to test the accuracy using GBLUP approaches, demonstrating the feasibility of predicting among different breeding material. Bias-corrected GRMs proved to increase predictive accuracies when compared with standard approaches to construct GRMs. Among the imputation methods we tested, the random forest method yielded the highest predictive accuracy. The combinations of these two methods resulted in a meaningful increase of predictive ability (up to 0.09). The possibility of predicting across individuals and pools provides new opportunities for improving ryegrass breeding schemes. [ABSTRACT FROM AUTHOR]

Large yellow croaker accounts for the largest biomass production of any maricultured fish in China. However, very little is known about the genetic parameters of its commercially important traits. As an initial step towards developing a selective breeding programme, genetic parameters of nine quantitative traits were estimated using a marker-based method. Dorsal fin samples were collected to extract genomic DNA, and GBS method was employed to construct the libraries for sequencing. Genetic parameters were estimated by REML method through a genomic relationship matrix (G matrix) constructed by abundant genomewide SNPs. The nine traits were body weight ( BWT), body length ( BL), body height ( BH), length/height ratio ( LTH), body width ( BWH), eviscerated weight ( EW), gonad weight ( GW), eviscerated weight/body weight ratio ( REB) and swim bladder index ( SBI). Estimates of heritability were 0.63 ± 0.11, 0.60 ± 0.11, 0.53 ± 0.11, 0.34 ± 0.11, 0.55 ± 0.11, 0.66 ± 0.11, 0.37 ± 0.10, 0.25 ± 0.08 and 0.71 ± 0.10 for the nine traits respectively. The relatively high heritability values may be derived from calculating the genetic relationship by high-density SNPs. To illustrate that, we had studied on the variation of the heritability estimates with different number of SNPs evenly sampled from 29748 SNPs. The results showed that the estimates of heritability generally decreased when the number of SNPs reduced. There were relatively high phenotypic and genetic correlations between the pairs of BWT, BL, BH, BWH and EW, which indicated that genetic improvement for these traits could be accomplished merely by selecting one trait. The results obtained in this study may provide a reference for the later selective breeding programme. [ABSTRACT FROM AUTHOR]

In pig breeding, the final product is a crossbred (CB) animal, while selection is performed at the purebred (PB) level using mainly PB data. However, incorporating CB data in genetic evaluations is expected to result in greater genetic progress at the CB level. Currently, there is no optimal way to include CB genotypes into the genomic relationship matrix. This is because, in single-step genomic BLUP, which is the most commonly used method, genomic and pedigree relationships must refer to the same base. This may not be the case when several breeds and CB are included. An alternative to overcome this issue may be to use a genomic relationship matrix (G matrix) that accounts for both linkage disequilibrium (LD) and linkage analysis (LA), called GLDLA. The objectives of this study were to further develop the GLDLA matrix approach to utilize both PB and CB genotypes simultaneously, to investigate its performance, and the general added value of including CB genotypes in genomic evaluations. Data were available on Dutch Landrace, Large White, and the F1 cross of those breeds. In total, 7 different G matrix compositions (PB alone, PB together, each PB with the CB, all genotypes across breeds, and GLDLA) were tested on 3 maternal traits: total number born (TNB), live born (LB), and gestation length (GL). Results show that GLDLA gave the greatest prediction accuracy of all the relationship matrices tested for PB prediction, but not for CB prediction. Including CB genotypes in general increased prediction accuracy for all breeds. However, in some cases, these increases in prediction accuracy were not significant (at P < 0.05). To conclude, CB genotypes increased prediction accuracy for some of the traits and breeds, but not for all. The GLDLA matrix had significantly greater prediction accuracy in PB than the other G matrix with both PB and CB genotypes, except in one case. While for CB, the G matrix with genotypes across all breeds gave the greatest accuracy, though this was not significantly different from GLDLA. Computation time was high for GLDLA, and research will be needed to reduce its computational costs to make it feasible for use in routine evaluations. The main conclusion is that inclusion of CB genotypes is beneficial for both PB and CB animals. [ABSTRACT FROM AUTHOR]

A simulation analysis and real phenotype analysis were performed to evaluate the impact of three different relationship matrices on heritability estimation and prediction accuracy in a closed-line breeding of Duroc pigs. The numerator relationship matrix ( NRM), single nucleotide polymorphism ( SNP)-based genomic relationship matrix ( GRM) ( GS), and haplotype-based GRM ( GH) were applied in this study. We used Porcine SNP60 genotype array data (38 114 SNPs) of 831 Duroc pigs with four selection traits. In both heritability estimation and prediction accuracy, the accuracy depended on the number of animals with records. For heritability estimation, a large difference in the results among three relationship matrices was not shown, but the trend of the estimated heritabilities between GRMs, that is GS < GH, was shown in this population. For the accuracy of prediction values in test animals, the accuracies of prediction values obtained by two GRMs were higher than that by the NRM in this population. The accuracies obtained by GRMs using animals with no records were lower than that by the NRM using animals with their performance records, but were close to that by the NRM using animals with full-sib testing records. [ABSTRACT FROM AUTHOR]

Inbreeding has the potential to negatively impact animal performance. Strategies to monitor and mitigate inbreeding depression require that it can be accurately estimated. Here, we used genomewide SNP data to explore 3 alternative measures of genomic inbreeding: the diagonal elements of the genomic relationship matrix (FGRM), the proportion of homozygous SNP (FHOM), and the proportion of the genome covered by runs of homozygosity (FROH). We used 2,111 Brahman (BR) and 2,550 Tropical Composite (TC) cattle with phenotypes recorded for 10 traits of relevance to tropical adaptation. We further explored 3 marker densities ranging from a highdensity chip (729,068 SNP), a medium-density chip (71,726 SNP) specifically designed for Bos indicus cattle, and a low-density chip (18,860 SNP) associated with the measures of inbreeding. Measures of FGRM were highly correlated across the 3 SNP densities and negatively correlated with FHOM and FROH in the BR population. In both populations, there was a strong positive correlation for each measure of inbreeding across the 3 SNP panels. We found significant (P < 0.01) inbreeding depression for various traits, particularly when using the highest-density SNP chip in the BR population, where inbreeding was negatively associated with coat color and coat type such that inbred animals presented shorter, slicker, and lighter coats. Based on FGRM using the medium-density chip, we found that a 1% increase in inbreeding in the BR and TC populations was associated with a decrease of 0.514 and 0.579 kg BW, respectively, in yearlings. In the TC population, a 1% increase in FHOM was associated with a decrease in BCS of -0.636% (P < 0.001). The low-density chip, comprising SNP associated with inbreeding, captured genes, and regions with pleiotropic effects (P < 0.001). However, it did not improve our ability to identify inbreeding depression, relative to the use of higher-density panels. We conclude that where heterogeneous populations are present, such as in tropical environments where composite animals abound, measures of inbreeding that do not depend on allele frequencies, such as FHOM and FROH, are preferable for estimating genomic inbreeding. Finally, the sustainable intensification of livestock systems in tropical regions will rely on genetic safeguards to ensure that productivity is improved while also adapting animals to cope with climate change. The results of this study are a step toward achieving that goal. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The genetic covariance matrix conditional on pedigree is proportional to the pedigree-based additive relationship matrix ( PARM), which is twice the matrix of identity-by-descent ( IBD) probabilities. In genomic prediction, IBD probabilities in the PARM, which are expected genetic similarities between relatives that are derived from the pedigree, are substituted by realized similarities that are derived from genotypes to obtain a genomic additive relationship matrix ( GARM). Different definitions of similarity lead to different GARMs, and two commonly used GARMS are the matrix G, which is based on an allele substitution effect model, and the matrix T, which is based on an allele effect model. We show that although the two matrices T and G are not proportional, they give identical predictions of differences between breeding values. When genomic information is used for variance component estimation, the GARM G x is computed from genotype covariates that have been standardized to have unit variance. That approach is equivalent to fitting a random regression model using the same standardized covariates. We show that under Hardy-Weinberg and linkage equilibria ( LE) that the genetic variance is [ABSTRACT FROM AUTHOR]

The purpose of this study is review and evaluation of computing methods used in genomic selection for animal breeding. Commonly used models include SNP BLUP with extensions (BayesA, etc), genomic BLUP (GBLUP) and single-step GBLUP (ssGBLUP). These models are applied for genomewide association studies (GWAS), genomic prediction and parameter estimation. Solving methods include finite Cholesky decomposition possibly with a sparse implementation, and iterative Gauss–Seidel (GS) or preconditioned conjugate gradient (PCG), the last two methods possibly with iteration on data. Details are provided that can drastically decrease some computations. For SNP BLUP especially with sampling and large number of SNP, the only choice is GS with iteration on data and adjustment of residuals. If only solutions are required, PCG by iteration on data is a clear choice. A genomic relationship matrix (GRM) has limited dimensionality due to small effective population size, resulting in infinite number of generalized inverses of GRM for large genotyped populations. A specific inverse called APY requires only a small fraction of GRM, is sparse and can be computed and stored at a low cost for millions of animals. With APY inverse and PCG iteration, GBLUP and ssGBLUP can be applied to any population. Both tools can be applied to GWAS. When the system of equations is sparse but contains dense blocks, a recently developed package for sparse Cholesky decomposition and sparse inversion called YAMS has greatly improved performance over packages where such blocks were treated as sparse. With YAMS, GREML and possibly single-step GREML can be applied to populations with >50 000 genotyped animals. From a computational perspective, genomic selection is becoming a mature methodology. [ABSTRACT FROM PUBLISHER]

Growth traits, such as body weight, directly influence productivity and economic efficiency in the swine industry. In this study, we estimate heritability for body weight traits usinginformation from pedigree and genome-wide single nucleotide polymorphism (SNP) chip data. Four body weight phenotypes were measured in 1,105 F2 progeny from an intercross between Landrace and Jeju native black pigs. All experimental animals were subjected to genotypic analysis using PorcineSNP60K BeadChip platform, and 39,992 autosomal SNP markers filtered by quality control criteria were used to construct genomic relationship matrix for heritability estimation. Restricted maximum likelihood estimates of heritability were obtained using both genomic- and pedigree- relationship matrix in a linear mixed model. The heritability estimates using SNP information were smaller (0.36-0.55) than those which were estimated using pedigree information (0.62-0.97). To investigate effect of common environment, such as maternal effect, on heritability estimation, we included maternal effect as an additional random effect term in the linear mixed model analysis. We detected substantial proportions of phenotypic variance components were explained by maternal effect. And the heritability estimates using both pedigree and SNP information were decreased. Therefore, heritability estimates must be interpreted cautiously when there are obvious common environmental variance components. [ABSTRACT FROM AUTHOR]

The genomic relationship matrix (GRM) can be inverted by the algorithm for proven and young (APY) based on recursion on a random subset of animals. While a regular inverse has a cubic cost, the cost of the APY inverse can be close to linear. Theory for the APY assumes that the optimal size of the subset (maximizing accuracy of genomic predictions) is due to a limited dimensionality of the GRM, which is a function of the effective population size (Ne). The objective of this study was to evaluate these assumptions by simulation. Six populations were simulated with approximate effective population size (Ne) from 20 to 200. Each population consisted of 10 nonoverlapping generations, with 25,000 animals per generation and phenotypes available for generations 1-9. The last 3 generations were fully genotyped assuming genome length L = 30. The GRM was constructed for each population and analyzed for distribution of eigenvalues. Genomic estimated breeding values (GEBV) were computed by single-step GBLUP, using either a direct or an APY inverse of GRM. The sizes of the subset in APY were set to the number of the largest eigenvalues explaining x% of variation (EIGx, x = 90, 95, 98, 99) in GRM. Accuracies of GEBV for the last generation with the APY inverse peaked at EIG98 and were slightly lower with EIG95, EIG99, or the direct inverse. Most information in the GRM is contained in ~NeL largest eigenvalues, with no information beyond 4NeL. Genomic predictions with the APY inverse of the GRM are more accurate than by the regular inverse. [ABSTRACT FROM AUTHOR]

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 singlestep 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 1.3 h 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. Singlestep genomic BLUP with APY is applicable to millions of genotyped animals. [ABSTRACT FROM AUTHOR]

Many computations with SNP data including genomic evaluation, parameter estimation, and genome-wide association studies use an inverse of the genomic relationship matrix. The cost of a regular inversion is cubic and is prohibitively expensive for large matrices. Recent studies in cattle demonstrated that the inverse can be computed in almost linear time by recursion on any subset of ~10,000 individuals. The purpose of this study is to present a theory of why such a recursion works and its implication for other populations. Assume that, because of a small effective population size, the additive information in a genotyped population has a small dimensionality, even with a very large number of SNP markers. That dimensionality is visible as a limited number of effective SNP effects, independent chromosome segments, or the rank of the genomic relationship matrix. Decompose a population arbitrarily into core and noncore individuals, with the number of core individuals equal to that dimensionality. Then, breeding values of noncore individuals can be derived by recursions on breeding values of core individuals, with coefficients of the recursion computed from the genomic relationship matrix. A resulting algorithm for the inversion called "algorithm for proven and young" (APY) has a linear computing and memory cost for noncore animals. Noninfinitesimal genetic architecture can be accommodated through a trait-specific genomic relationship matrix, possibly derived from Bayesian regressions. For populations with small effective population size, the inverse of the genomic relationship matrix can be computed inexpensively for a very large number of genotyped individuals. [ABSTRACT FROM AUTHOR]

Background: Genotyping-by-sequencing (GBS) is becoming an attractive alternative to array-based methods for genotyping individuals for a large number of single nucleotide polymorphisms (SNPs). Costs can be lowered by reducing the mean sequencing depth, but this results in genotype calls of lower quality. A common analysis strategy is tofilter SNPs to just those with sufficient depth, thereby greatly reducing the number of SNPs available. We investigate methods for estimating relatedness using GBS data, including results of low depth, using theoretical calculation, simulation and application to a real data set. Results: We show that unbiased estimates of relatedness can be obtained by using only those SNPs with genotype calls in both individuals. The expected value of this estimator is independent of the SNP depth in each individual, under a model of genotype calling that includes the special case of the two alleles being read at random. In contrast, the estimator of self-relatedness does depend on the SNP depth, and we provide a modification to provide unbiased estimates of self-relatedness. We refer to these methods of estimation as kinship using GBS with depth adjustment (KGD). The estimators can be calculated using matrix methods, which allow efficient computation. Simulation results were consistent with the methods being unbiased, and suggest that the optimal sequencing depth is around 2-4 for relatedness between individuals and 5-10 for self-relatedness. Application to a real data set revealed that some SNP filtering may still be necessary, for the exclusion of SNPs which did not behave in a Mendelian fashion. A simple graphical method (a 'fin plot') is given to illustrate this issue and to guide filtering parameters. Conclusion: We provide a method which gives unbiased estimates of relatedness, based on SNPs assayed by GBS, which accounts for the depth (including zero depth) of the genotype calls. This allows GBS to be applied at read depths which can be chosen to optimise the information obtained. SNPs with excess heterozygosity, often due to (partial) polyploidy or other duplications can be filtered based on a simple graphical method. [ABSTRACT FROM AUTHOR]

Background: Measuring the extent of shared ancestry between individuals or organisms is important in many fields, including forensic science, conservation genetics and animal breeding. The traditional approach is to calculate the expected degree of relatedness between individuals in a pedigree. This assumes that the founders of the pedigree are non-inbred and unrelated to each other, which is rarely the case. In contrast, molecular data allow measurement of actual relatedness without knowledge of a pedigree. Methods to do this have been proposed, but generally do not take the lengths of the genomic regions shared between individuals into account. Results: Two measures based on the extent of haplotype sharing between genomes are proposed. The intercept measure B estimates the fraction of shared genome between individuals, and the product measure C is closely related to the numerator relationship matrix A. Both are based on a model for the joint distribution of markers at the haplotype level. The two measures are compared to the pedigree-based measure A and to vanRaden’s G, a frequently used molecular measure, using a set of data comprising 5037 dairy cattle. The comparison criteria include the ability to capture genealogical relatedness and the prediction accuracy obtained when used in genomic prediction. Both B and C explain around 95 % of the variation in A, whereas G explains around 6 %. G captures genealogical relatedness poorly, particularly for distantly related individuals (second cousins or farther). Both B and C tend to be larger than A but this can be ascribed to the assumption of non-inbred unrelated founders. Using C in linear mixed models results in slightly higher prediction accuracy than G, and using B results in slightly lower prediction accuracy. Conclusions: The two proposed measures of relatedness capture genealogical relatedness well, outperforming vanRaden’s G in this respect. When used in genomic prediction models, the product measure leads to slightly improved prediction accuracy. [ABSTRACT FROM AUTHOR]

The degree of linkage disequilibrium (LD) between markers differs depending on the location of the genome; this difference biases genetic evaluation by genomic best linear unbiased prediction (GBLUP). To correct this bias, we used three GBLUP methods reflecting the degree of LD (GBLUP-LD). In the three GBLUP-LD methods, genomic relationship matrices were conducted from single nucleotide polymorphism markers weighted according to local LD levels. The predictive abilities of GBLUP-LD were investigated by estimating variance components and assessing the accuracies of estimated breeding values using simulation data. When quantitative trait loci (QTL) were located at weak LD regions, the predictive abilities of the three GBLUP-LD methods were superior to those of GBLUP and Bayesian lasso except when the number of QTL was small. In particular, the superiority of GBLUP-LD increased with decreasing trait heritability. The rates of QTL at weak LD regions would increase when selection by GBLUP continues; this consequently decreases the predictive ability of GBLUP. Thus, the GBLUP-LD could be applicable for populations selected by GBLUP for a long time. However, if QTL were located at strong LD regions, the accuracies of three GBLUP-LD methods were lower than GBLUP and Bayesian lasso. [ABSTRACT FROM AUTHOR]

The amount of variance captured in genetic estimations may depend on whether a pedigree-based or genomic relationship matrix is used. The purpose of this study was to investigate the genetic variance as well as the variance of predicted genetic merits ( PGM) using pedigree-based or genomic relationship matrices in Brown Swiss cattle. We examined a range of traits in six populations amounting to 173 population-trait combinations. A main aim was to determine how using different relationship matrices affect variance estimation. We calculated ratios between different types of estimates and analysed the impact of trait heritability and population size. The genetic variances estimated by REML using a genomic relationship matrix were always smaller than the variances that were similarly estimated using a pedigree-based relationship matrix. The variances from the genomic relationship matrix became closer to estimates from a pedigree relationship matrix as heritability and population size increased. In contrast, variances of predicted genetic merits obtained using a genomic relationship matrix were mostly larger than variances of genetic merit predicted using pedigree-based relationship matrix. The ratio of the genomic to pedigree-based PGM variances decreased as heritability and population size rose. The increased variance among predicted genetic merits is important for animal breeding because this is one of the factors influencing genetic progress. [ABSTRACT FROM AUTHOR]