Genomic Relationship Matrices Research Articles

A comparison of methods to estimate genomic relationships using pedigree and markers in livestock populations.

Accurate prediction of breeding values depends on capturing the variability in genome sharing of relatives with the same pedigree relationship. Here, we compare two approaches to set up genomic relationship matrices for precision of genomic relationships (GR) and accuracy of estimated breeding values (GEBV). Real and simulated data (pigs, 60k SNP) were analysed, and GR were estimated using two approaches: (i) identity by state, corrected with either the observed (GVR-O ) or the base population (GVR-B ) allele frequencies and (ii) identity by descent using linkage analysis (GIBD-L ). Estimators were evaluated for precision and empirical bias with respect to true pedigree IBD GR. All three estimators had very low bias. GIBD-L displayed the lowest sampling error and the highest correlation with true genome-shared values. GVR-B approximated GIBD-L 's correlation and had lower error than GVR-O . Accuracy of GEBV for selection candidates was significantly higher when GIBD-L was used and identical between GVR-O and GVR-B . In real data, GIBD-L 's sampling standard deviation was the closest to the theoretical value for each pedigree relationship. Use of pedigree to calculate GR improved the precision of estimates and the accuracy of GEBV.

GenoMatrix: A Software Package for Pedigree-Based and Genomic Prediction Analyses on Complex Traits.

Genomic and pedigree-based best linear unbiased prediction methodologies (G-BLUP and P-BLUP) have proven themselves efficient for partitioning the phenotypic variance of complex traits into its components, estimating the individuals' genetic merits, and predicting unobserved (or yet-to-be observed) phenotypes in many species and fields of study. The GenoMatrix software, presented here, is a user-friendly package to facilitate the process of using genome-wide marker data and parentage information for G-BLUP and P-BLUP analyses on complex traits. It provides users with a collection of applications which help them on a set of tasks from performing quality control on data to constructing and manipulating the genomic and pedigree-based relationship matrices and obtaining their inverses. Such matrices will be then used in downstream analyses by other statistical packages. The package also enables users to obtain predicted values for unobserved individuals based on the genetic values of observed related individuals. GenoMatrix is available to the research community as a Windows 64bit executable and can be downloaded free of charge at: http://compbio.ufl.edu/software/genomatrix/.

Crossbreed evaluations in single-step genomic best linear unbiased predictor using adjusted realized relationship matrices1

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

Differential contribution of genomic regions to marked genetic variation and prediction of quantitative traits in broiler chickens.

BackgroundGenome-wide association studies in humans have found enrichment of trait-associated single nucleotide polymorphisms (SNPs) in coding regions of the genome and depletion of these in intergenic regions. However, a recent release of the ENCyclopedia of DNA elements showed that ~80 % of the human genome has a biochemical function. Similar studies on the chicken genome are lacking, thus assessing the relative contribution of its genic and non-genic regions to variation is relevant for biological studies and genetic improvement of chicken populations.MethodsA dataset including 1351 birds that were genotyped with the 600K Affymetrix platform was used. We partitioned SNPs according to genome annotation data into six classes to characterize the relative contribution of genic and non-genic regions to genetic variation as well as their predictive power using all available quality-filtered SNPs. Target traits were body weight, ultrasound measurement of breast muscle and hen house egg production in broiler chickens. Six genomic regions were considered: intergenic regions, introns, missense, synonymous, 5′ and 3′ untranslated regions, and regions that are located 5 kb upstream and downstream of coding genes. Genomic relationship matrices were constructed for each genomic region and fitted in the models, separately or simultaneously. Kernel-based ridge regression was used to estimate variance components and assess predictive ability. Contribution of each class of genomic regions to dominance variance was also considered.ResultsVariance component estimates indicated that all genomic regions contributed to marked additive genetic variation and that the class of synonymous regions tended to have the greatest contribution. The marked dominance genetic variation explained by each class of genomic regions was similar and negligible (~0.05). In terms of prediction mean-square error, the whole-genome approach showed the best predictive ability.ConclusionsAll genic and non-genic regions contributed to phenotypic variation for the three traits studied. Overall, the contribution of additive genetic variance to the total genetic variance was much greater than that of dominance variance. Our results show that all genomic regions are important for the prediction of the targeted traits, and the whole-genome approach was reaffirmed as the best tool for genome-enabled prediction of quantitative traits.

Integrating Nonadditive Genomic Relationship Matrices into the Study of Genetic Architecture of Complex Traits.

The study of genetic architecture of complex traits has been dramatically influenced by implementing genome-wide analytical approaches during recent years. Of particular interest are genomic prediction strategies which make use of genomic information for predicting phenotypic responses instead of detecting trait-associated loci. In this work, we present the results of a simulation study to improve our understanding of the statistical properties of estimation of genetic variance components of complex traits, and of additive, dominance, and genetic effects through best linear unbiased prediction methodology. Simulated dense marker information was used to construct genomic additive and dominance matrices, and multiple alternative pedigree- and marker-based models were compared to determine if including a dominance term into the analysis may improve the genetic analysis of complex traits. Our results showed that a model containing a pedigree- or marker-based additive relationship matrix along with a pedigree-based dominance matrix provided the best partitioning of genetic variance into its components, especially when some degree of true dominance effects was expected to exist. Also, we noted that the use of a marker-based additive relationship matrix along with a pedigree-based dominance matrix had the best performance in terms of accuracy of correlations between true and estimated additive, dominance, and genetic effects.

Genome wide association and genomic prediction for growth traits in juvenile farmed Atlantic salmon using a high density SNP array.

BackgroundThe genetic architecture of complex traits in farmed animal populations is of interest from a scientific and practical perspective. The use of genetic markers to predict the genetic merit (breeding values) of individuals is commonplace in modern farm animal breeding schemes. Recently, high density SNP arrays have become available for Atlantic salmon, which facilitates genomic prediction and association studies using genome-wide markers and economically important traits. The aims of this study were (i) to use a high density SNP array to investigate the genetic architecture of weight and length in juvenile Atlantic salmon; (ii) to assess the utility of genomic prediction for these traits, including testing different marker densities; (iii) to identify potential candidate genes underpinning variation in early growth.ResultsA pedigreed population of farmed Atlantic salmon (n = 622) were measured for weight and length traits at one year of age, and genotyped for 111,908 segregating SNP markers using a high density SNP array. The heritability of both traits was estimated using pedigree and genomic relationship matrices, and was comparable at around 0.5 and 0.6 respectively. The results of the GWA analysis pointed to a polygenic genetic architecture, with no SNPs surpassing the genome-wide significance threshold, and one SNP associated with length at the chromosome-wide level. SNPs surpassing an arbitrary threshold of significance (P < 0.005, ~ top 0.5 % of markers) were aligned to an Atlantic salmon reference transcriptome, identifying 109 SNPs in transcribed regions that were annotated by alignment to human, mouse and zebrafish protein databases. Prediction of breeding values was more accurate when applying genomic (GBLUP) than pedigree (PBLUP) relationship matrices (accuracy ~ 0.7 and 0.58 respectively) and 5,000 SNPs were sufficient for obtaining this accuracy increase over PBLUP in this specific population.ConclusionsThe high density SNP array can effectively capture the additive genetic variation in complex traits. However, the traits of weight and length both appear to be very polygenic with only one SNP surpassing the chromosome-wide threshold. Genomic prediction using the array is effective, leading to an improvement in accuracy compared to pedigree methods, and this improvement can be achieved with only a small subset of the markers in this population. The results have practical relevance for genomic selection in salmon and may also provide insight into variation in the identified genes underpinning body growth and development in salmonid species.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-015-2117-9) contains supplementary material, which is available to authorized users.

Compression distance can discriminate animals by genetic profile, build relationship matrices and estimate breeding values

BackgroundGenetic relatedness is currently estimated by a combination of traditional pedigree-based approaches (i.e. numerator relationship matrices, NRM) and, given the recent availability of molecular information, using marker genotypes (via genomic relationship matrices, GRM). To date, GRM are computed by genome-wide pair-wise SNP (single nucleotide polymorphism) correlations.ResultsWe describe a new estimate of genetic relatedness using the concept of normalised compression distance (NCD) that is borrowed from Information Theory. Analogous to GRM, the resultant compression relationship matrix (CRM) exploits numerical patterns in genome-wide allele order and proportion, which are known to vary systematically with relatedness. We explored properties of the CRM in two industry cattle datasets by analysing the genetic basis of yearling weight, a phenotype of moderate heritability. In both Brahman (Bos indicus) and Tropical Composite (Bos taurus by Bos indicus) populations, the clustering inferred by NCD was comparable to that based on SNP correlations using standard principal component analysis approaches. One of the versions of the CRM modestly increased the amount of explained genetic variance, slightly reduced the ‘missing heritability’ and tended to improve the prediction accuracy of breeding values in both populations when compared to both NRM and GRM. Finally, a sliding window-based application of the compression approach on these populations identified genomic regions influenced by introgression of taurine haplotypes.ConclusionsFor these two bovine populations, CRM reduced the missing heritability and increased the amount of explained genetic variation for a moderately heritable complex trait. Given that NCD can sensitively discriminate closely related individuals, we foresee CRM having possible value for estimating breeding values in highly inbred populations.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-015-0158-9) contains supplementary material, which is available to authorized users.

Estimating genomic heritabilities at the level of family-pool samples of perennial ryegrass using genotyping-by-sequencing.

KeymessageBy using the genotyping-by-sequencing method, it is feasible to characterize genomic relationships directly at the level of family pools and to estimate genomic heritabilities from phenotypes scored on family-pools in outbreeding species.Genotyping-by-sequencing (GBS) has recently become a promising approach for characterizing plant genetic diversity on a genome-wide scale. We use GBS to extend the concept of heritability beyond individuals by genotyping family-pool samples by GBS and computing genomic relationship matrices (GRMs) and genomic heritabilities directly at the level of family-pools from pool-frequencies obtained by sequencing. The concept is of interest for species where breeding and phenotyping is not done at the individual level but operates uniquely at the level of (multi-parent) families. As an example we demonstrate the approach using a set of 990 two-parent F2 families of perennial ryegrass (Lolium Perenne). The families were phenotyped as a family-unit in field plots for heading date and crown rust resistance. A total of 728 K single nucleotide polymorphism (SNP) variants were available and were divided in groups of different sequencing depths. GRMs based on GBS data showed diagonal values biased upwards at low sequencing depth, while off-diagonals were little affected by the sequencing depth. Using variants with high sequencing depth, genomic heritability for crown rust resistance was 0.33, and for heading date 0.22, and these genomic heritabilities were biased downwards when using variants with lower sequencing depth. Broad sense heritabilities were 0.61 and 0.66, respectively. Underestimation of genomic heritability at lower sequencing depth was confirmed with simulated data. We conclude that it is feasible to use GBS to describe relationships between family-pools and to estimate genomic heritability directly at the level of F2 family-pool samples, but estimates are biased at low sequencing depth.Electronic supplementary materialThe online version of this article (doi:10.1007/s00122-015-2607-9) contains supplementary material, which is available to authorized users.

A simple method to separate base population and segregation effects in genomic relationship matrices.

BackgroundGenomic selection and estimation of genomic breeding values (GBV) are widely used in cattle and plant breeding. Several studies have attempted to detect population subdivision by investigating the structure of the genomic relationship matrix G. However, the question of how these effects influence GBV estimation using genomic best linear unbiased prediction (GBLUP) has received little attention.MethodsWe propose a simple method to decompose G into two independent covariance matrices, one describing the covariance that results from systematic differences in allele frequencies between groups at the pedigree base (GA*) and the other describing genomic relationships (GS) corrected for these differences. Using this decomposition and Fst statistics, we examined whether observed genetic distances between genotyped subgroups within populations resulted from the heterogeneous genetic structure present at the base of the pedigree and/or from breed divergence. Using this decomposition, we tested three models in a forward prediction validation scenario on six traits using Brown Swiss and dual-purpose Fleckvieh cattle data. Model 0 (M0) used both components and is equivalent to the model using the standard G-matrix. Model 1 (M1) used GS only and model 2 (M2), an extension of M1, included a fixed genetic group effect. Moreover, we analyzed the matrix of contributions of each base group (Q) and estimated the effects and prediction errors of each base group using M0 and M1.ResultsThe proposed decomposition of G helped to examine the relative importance of the effects of base groups and segregation in a given population. We found significant differences between the effects of base groups for each breed. In forward prediction, differences between models in terms of validation reliability of estimated direct genomic values were small but predictive power was consistently lowest for M1. The relative advantage of M0 or M2 in prediction depended on breed, trait and genetic composition of the validation group. Our approach presents a general analogy with the use of genetic groups in conventional animal models and provides proof that standard GBLUP using G yields solutions equivalent to M0, where base groups are considered as correlated random effects within the additive genetic variance assigned to the genetic base.

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

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

Genomic best linear unbiased prediction method reflecting the degree of linkage disequilibrium.

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.

Genetic analysis of within-litter variation in piglets' birth weight using genomic or pedigree relationship matrices.

The objective of this study was to estimate the genetic variance for within-litter variation of birth weight (BW0) using genomic (GRM) or pedigree relationship matrices (PRM) and to compare the accuracy of estimated breeding values (EBV) for within-litter variation of BW0 using GRM and PRM. The BW0 and residual variance of BW0 were modeled by the double hierarchical generalized linear model using GRM or PRM. Data came from 2 dam lines: Landrace and Large White. After editing, the data set in Landrace consisted of 748 sows with 1,938 litters and 29,430 piglets and in Large White of 989 sows with 3,320 litters and 51,818 piglets. To construct GRM, 46,466 (Landrace) and 44,826 (Large White) single nucleotide polymorphisms were used, whereas to construct PRM, 5 generations of pedigree were used. The accuracy of EBV with GRM was estimated with 8-fold cross-validation and compared to PRM. Estimated variance components were highly similar for GRM and PRM. The maternal genetic variance in residual variance of BW0 in Landrace was 0.05 with GRM and 0.06 with PRM. In Large White these were 0.04 with GRM and 0.05 with PRM. The genetic coefficient of variation (GCV SDe) was about 0.10 in both dam lines. This indicates a change of 10% in residual SD of BW0 when achieving a genetic response of 1 genetic standard deviation. The genetic correlation between birth weight and its residual variance was about 0.6 in both dam lines. The accuracies of selection for within-litter variation of birth weight were 0.35 with GRM and 0.23 with PRM in Landrace and 0.29 with GRM and 0.34 with PRM in Large White. In this case, using GRM did not significantly increase accuracies of selection. Results, however, show good opportunities to select for reduced within-litter variation of BW0. Genomic selection can increase accuracy of selection when reference populations contain at least 2,000 sows.

Estimates of genetic variance and variance of predicted genetic merits using pedigree or genomic relationship matrices in six Brown Swiss cattle populations for different traits

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.

Locally epistatic genomic relationship matrices for genomic association and prediction.

In plant and animal breeding studies a distinction is made between the genetic value (additive plus epistatic genetic effects) and the breeding value (additive genetic effects) of an individual since it is expected that some of the epistatic genetic effects will be lost due to recombination. In this article, we argue that the breeder can take advantage of the epistatic marker effects in regions of low recombination. The models introduced here aim to estimate local epistatic line heritability by using genetic map information and combining local additive and epistatic effects. To this end, we have used semiparametric mixed models with multiple local genomic relationship matrices with hierarchical designs. Elastic-net postprocessing was used to introduce sparsity. Our models produce good predictive performance along with useful explanatory information.

The effect of rare alleles on estimated genomic relationships from whole genome sequence data.

BackgroundRelationships between individuals and inbreeding coefficients are commonly used for breeding decisions, but may be affected by the type of data used for their estimation. The proportion of variants with low Minor Allele Frequency (MAF) is larger in whole genome sequence (WGS) data compared to Single Nucleotide Polymorphism (SNP) chips. Therefore, WGS data provide true relationships between individuals and may influence breeding decisions and prioritisation for conservation of genetic diversity in livestock. This study identifies differences between relationships and inbreeding coefficients estimated using pedigree, SNP or WGS data for 118 Holstein bulls from the 1000 Bull genomes project. To determine the impact of rare alleles on the estimates we compared three scenarios of MAF restrictions: variants with a MAF higher than 5%, variants with a MAF higher than 1% and variants with a MAF between 1% and 5%.ResultsWe observed significant differences between estimated relationships and, although less significantly, inbreeding coefficients from pedigree, SNP or WGS data, and between MAF restriction scenarios. Computed correlations between pedigree and genomic relationships, within groups with similar relationships, ranged from negative to moderate for both estimated relationships and inbreeding coefficients, but were high between estimates from SNP and WGS (0.49 to 0.99). Estimated relationships from genomic information exhibited higher variation than from pedigree. Inbreeding coefficients analysis showed that more complete pedigree records lead to higher correlation between inbreeding coefficients from pedigree and genomic data. Finally, estimates and correlations between additive genetic (A) and genomic (G) relationship matrices were lower, and variances of the relationships were larger when accounting for allele frequencies than without accounting for allele frequencies.ConclusionsUsing pedigree data or genomic information, and including or excluding variants with a MAF below 5% showed significant differences in relationship and inbreeding coefficient estimates. Estimated relationships and inbreeding coefficients are the basis for selection decisions. Therefore, it can be expected that using WGS instead of SNP can affect selection decision. Inclusion of rare variants will give access to the variation they carry, which is of interest for conservation of genetic diversity.Electronic supplementary materialThe online version of this article (doi:10.1186/s12863-015-0185-0) contains supplementary material, which is available to authorized users.

Unraveling additive from nonadditive effects using genomic relationship matrices.

The application of quantitative genetics in plant and animal breeding has largely focused on additive models, which may also capture dominance and epistatic effects. Partitioning genetic variance into its additive and nonadditive components using pedigree-based models (P-genomic best linear unbiased predictor) (P-BLUP) is difficult with most commonly available family structures. However, the availability of dense panels of molecular markers makes possible the use of additive- and dominance-realized genomic relationships for the estimation of variance components and the prediction of genetic values (G-BLUP). We evaluated height data from a multifamily population of the tree species Pinus taeda with a systematic series of models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance), using either pedigree- or marker-based information. We show that, compared with the pedigree, use of realized genomic relationships in marker-based models yields a substantially more precise separation of additive and nonadditive components of genetic variance. We conclude that the marker-based relationship matrices in a model including additive and nonadditive effects performed better, improving breeding value prediction. Moreover, our results suggest that, for tree height in this population, the additive and nonadditive components of genetic variance are similar in magnitude. This novel result improves our current understanding of the genetic control and architecture of a quantitative trait and should be considered when developing breeding strategies.

Genomic prediction based on runs of homozygosity.

BackgroundGenomic prediction is based on the accurate estimation of the genomic relationships among and between training animals and selection candidates in order to obtain accurate estimates of the genomic estimated breeding values (GEBV). Various methods have been used to predict GEBV based on population-wide linkage disequilibrium relationships (GIBS) or sometimes on linkage analysis relationships (GLA). Here, we propose a novel method to predict GEBV based on a genomic relationship matrix using runs of homozygosity (GROH). Runs of homozygosity were used to derive probabilities of multi-locus identity by descent chromosome segments. The accuracy and bias of the prediction of GEBV using GROH were compared to those using GIBS and GLA. Comparisons were performed using simulated datasets derived from a random pedigree and a real pedigree of Italian Brown Swiss bulls. The comparison of accuracies of GEBV was also performed on data from 1086 Italian Brown Swiss dairy cattle.ResultsSimulations with various thresholds of minor allele frequency for markers and quantitative trait loci showed that GROH achieved consistently more accurate GEBV (0 to 4% points higher) than GIBS and GLA. The bias of GEBV prediction for simulated data was higher based on the real pedigree than based on a random pedigree. In the analyses with real data, GROH and GLA had similar accuracies. However, GLA achieved a higher accuracy when the prediction was done on the youngest animals. The GIBS matrices calculated with and without standardized marker genotypes resulted in similar accuracies.ConclusionsThe present study proposes GROH as a novel method to estimate genomic relationship matrices and predict GEBV based on runs of homozygosity and shows that it can result in higher or similar accuracies of GEBV prediction than GLA, except for the real data analysis with validation of young animals. Compared to GIBS, GROH resulted in more accurate GEBV predictions.

Genomic prediction of breeding values in the New Zealand sheep industry using a 50K SNP chip.

The aim of genomic prediction is to predict breeding value from genomic data. We describe the development of genomic prediction equations and accuracies for molecular breeding values (MBV) for industry use, focusing on the methodology used to deal with predictions for the New Zealand sheep population structure. This is made up of a mixture of pure and crossbred animals, but principally Romney based. In particular, we used pedigree-based EBV for 8 traits (weaning weight as a direct effect, weaning weight as a maternal effect, live weight at 8 mo, live weight at 12 mo, greasy fleece weight at 12 mo, lamb fleece weight, adult fleece weight, and number of lambs born) and Illumina OvineSNP50 BeadChip genotypes from 13,420 animals to investigate BLUP with different genomic relationship matrices (GRM) based on SNP markers and to investigate varying sets of older animals (training sets) to predict the MBV of younger animals (validation sets). The GRM tested included modifications to account for allele frequency differences between breeds, rescaling so that the mean GRM is equal to the mean of the traditional pedigree numerator relationship matrix A: , and combining of the GRM with A: using a convex combination with a weight estimated by maximizing a conditional restricted likelihood. We found that these modifications were beneficial and recommend using a breed-adjusted GRM combined with A: . Training data sets with Romney, Coopworth, and Perendale animals all together usually predicted better than using just a pure breed training data set for all traits. But predictions for the breed Perendale were more accurate with a Perendale training set for 3 of the 8 traits. We concluded that using a mixed-breed training set for all combinations of traits and breeds was best but advise that increasing the number of Perendale animals genotyped should be a priority to increase the MBV accuracies obtained for that breed.

Comparison of genomic predictions using genomic relationship matrices built with different weighting factors to account for locus-specific variances

Various models have been used for genomic prediction. Bayesian variable selection models often predict more accurate genomic breeding values than genomic BLUP (GBLUP), but GBLUP is generally preferred for routine genomic evaluations because of low computational demand. The objective of this study was to achieve the benefits of both models using results from Bayesian models and genome-wide association studies as weights on single nucleotide polymorphism (SNP) markers when constructing the genomic matrix (G-matrix) for genomic prediction. The data comprised 5,221 progeny-tested bulls from the Nordic Holstein population. The animals were genotyped using the Illumina Bovine SNP50 BeadChip (Illumina Inc., San Diego, CA). Weighting factors in this investigation were the posterior SNP variance, the square of the posterior SNP effect, and the corresponding minus base-10 logarithm of the marker association P-value [−log10(P)] of a t-test obtained from the analysis using a Bayesian mixture model with 4 normal distributions, the square of the estimated SNP effect, and the corresponding −log10(P) of a t-test obtained from the analysis using a classical genome-wide association study model (linear regression model). The weights were derived from the analysis based on data sets that were 0, 1, 3, or 5 yr before performing genomic prediction. In building a G-matrix, the weights were assigned either to each marker (single-marker weighting) or to each group of approximately 5 to 150 markers (group-marker weighting). The analysis was carried out for milk yield, fat yield, protein yield, fertility, and mastitis. Deregressed proofs (DRP) were used as response variables to predict genomic estimated breeding values (GEBV). Averaging over the 5 traits, the Bayesian model led to 2.0% higher reliability of GEBV than the GBLUP model with an original unweighted G-matrix. The superiority of using a GBLUP with weighted G-matrix over GBLUP with an original unweighted G-matrix was the largest when using a weighting factor of posterior variance, resulting in 1.7 percentage points higher reliability. The second best weighting factors were −log10 (P-value) of a t-test corresponding to the square of the posterior SNP effect from the Bayesian model and −log10 (P-value) of a t-test corresponding to the square of the estimated SNP effect from the linear regression model, followed by the square of estimated SNP effect and the square of the posterior SNP effect. In addition, group-marker weighting performed better than single-marker weighting in terms of reducing bias of GEBV, and also slightly increased prediction reliability. The differences between weighting factors and scenarios were larger in prediction bias than in prediction accuracy. Finally, weights derived from a data set having a lag up to 3 yr did not reduce reliability of GEBV. The results indicate that posterior SNP variance estimated from a Bayesian mixture model is a good alternative weighting factor, and common weights on group markers with a size of 30 markers is a good strategy when using markers of the 50,000-marker (50K) chip. In a population with gradually increasing reference data, the weights can be updated once every 3 yr.

A fast method for evaluating opposing homozygosity in large SNP data sets

Optimized algorithms are indispensable for analyzing large SNP data sets. To date, research has focused on the development of methods for calculating genomic relationship matrices. However, little attention has been given to algorithms for calculating the number of opposing homozygous SNP loci (OH) between genotyped individuals, where this parameter can be used to detect pedigree errors, genotyping errors, mixing of DNA samples, or for paternity tests. A recently proposed approach (LOOP) is sufficient for small data sets but not applicable to larger data sets in terms of number of SNPs and genotyped individuals. In this paper we propose a fast method for the calculation of OH in matrix format (OHM). This method is very fast and easy to implement. For example, it can create the OHM for 12,000 individuals genotyped for 40,000 SNPs with only 12% of the real time used by the LOOP approach. Thus, calculation of OHM from a sequence of matrix manipulations substantially increased the speed for determining the number of opposing homozygous SNP loci between all genotyped individuals of a data set. Given the availability of packages facilitating parallel processing this holds even when using R, and therefore allows inference from OHM even for large data sets.