Residual Polygenic Effect Research Articles

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

BackgroundIn this study, computationally efficient methods to approximate the reliabilities of genomic estimated breeding values (GEBV) in a single-step genomic prediction model including a residual polygenic (RPG) effect are described. In order to calculate the reliabilities of the genotyped animals, a single nucleotide polymorphism best linear unbiased prediction (SNPBLUP) or a genomic BLUP (GBLUP), was used, where two alternatives to account for the RPG effect were tested. In the direct approach, the genomic model included the RPG effect, while in the blended method, it did not but an index was used to weight the genomic and pedigree-based BLUP (PBLUP) reliabilities. In order to calculate the single-step GBLUP reliabilities for the breeding values for the non-genotyped animals, a simplified weighted-PBLUP model that included a general mean and additive genetic effects with weights accounting for the non-genomic and genomic information was used. We compared five schemes for the weights. Two datasets, i.e., a small (Data 1) one and a large (Data 2) one were used.ResultsFor the genotyped animals in Data 1, correlations between approximate reliabilities using the blended method and exact reliabilities ranged from 0.993 to 0.996 across three lactations. The slopes observed by regressing the reliabilities of GEBV from the exact method on those from the blended method were 1.0 for all three lactations. For Data 2, the correlations and slopes ranged, respectively, from 0.980 to 0.986 and from 0.91 to 0.96, and for the non-genotyped animals in Data 1, they ranged, respectively, from 0.987 to 0.994 and from 0.987 to 1, which indicate that the approximations were in line with the exact results. The best approach achieved correlations of 0.992 to 0.994 across lactations.ConclusionsOur results demonstrate that the approximated reliabilities calculated using our proposed approach are in good agreement with the exact reliabilities. The blended method for the genotyped animals is computationally more feasible than the direct method when RPG effects are included, particularly for large-scale datasets. The approach can serve as an effective strategy to estimate the reliabilities of GEBV in large-scale single-step genomic predictions.

35 Young Scholar Award Talk: Computing Strategies for National Beef Cattle Evaluations

Abstract The constantly growing size of the national beef cattle evaluations datasets creates computational challenges to estimate breeding values and their accuracies under the single-step methodology timely and in a robust way. This study aims to present strategies for making weekly national single-step beef cattle evaluations computationally feasible. The process for estimating breeding values in single-step can be divided into two parts. In the first part, hereafter called genomic setup, the genotype file is read, and the inverse of the genomic relationship matrix is calculated using the Algorithm for Proven and Young (APY). The genotype file is read in a stream-unformatted format, and the markers are stored bit-wise. A residual polygenic effect can be fitted with an algorithm whose computing cost is constant with the number of genotyped animals. The calculation of is done using parallel computing and optimized matrix algebra procedures. The second part estimates breeding values by iteration on data with a block diagonal preconditioner. Finally, the accuracy of the estimated breeding values is calculated by combining the pedigree and genomic information in terms of effective daughter contributions. For an Angus dataset with 10 million animals in the pedigree and 500,000 genotypes, the genomic setup took 4 hours. With the same dataset, solutions for a three-trait model with maternal effects including birth weight, weaning weight, and post-weaning gain were obtained after 12 hours. The approximation of the accuracies of breeding values took less than one hour. Our results show that weekly national beef cattle evaluations are computationally feasible.

Impact of blending the genomic relationship matrix with different levels of pedigree relationships or the identity matrix on genetic evaluations

Evaluations using single-step genomic BLUP require blending the genomic relationship matrix (G) with a positive definite matrix to ensure nonsingularity for solving the mixed model equations. Many organizations blend G with a proportion of the numerator relationship matrix for genotyped animals (A22) to improve stability and possibly add a residual polygenic effect. However, when nearly all the polygenic variance is explained by G, blending with A22 may cause inflation and add excess computing time; thus, blending with an identity matrix (I) multiplied by a small value may be a better solution. The objective of this study was to evaluate changes in reliability and inflation of genomic estimated breeding values, convergence rate, elapsed wall-clock time for blending G with different levels of A22 or I, and develop a more time-efficient blending method. A US Holstein cattle data set was used with 9.7 million animals in the pedigree, 569,404 animals with genotypes, and 10.1 million stature phenotypes. Blending G by adding a small value to the diagonal elements had comparable performance to A22 with fewer rounds to convergence required to solve the system of equations. Reliability and inflation of genomic estimated breeding values ranged from 0.63 to 0.68 and 0.86 to 0.89 for all blending scenarios tested. The current blending default in the BLUPF90 software is to replace G with (1 – β)G + βA22, where β equals 0.05. In this study, β values of 0.30, 0.20, 0.05, 0.01, 0.005, and 0.001 were evaluated with A22 and I. Negligible differences in elapsed computing time between the blending types and levels were observed. Subsequently, the current blending algorithm used in the BLUPF90 family of programs was optimized, reducing the blending time from approximately 2 h to 5 min for A22 and less than 1 s for I. The new time difference between blending with A22 or I is negligible and not computationally critical. The results indicate that blending G with A22 does not have clear advantages over blending with a small proportion of I.

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

BackgroundSingle-step genomic predictions obtained from a breeding value model require calculating the inverse of the genomic relationship matrix ({mathbf{G}}^{-1}). The Algorithm for Proven and Young (APY) creates a sparse representation of {mathbf{G}}^{-1} with a low computational cost. APY consists of selecting a group of core animals and expressing the breeding values of the remaining animals as a linear combination of those from the core animals plus an error term. The objectives of this study were to: (1) extend APY to marker effects models; (2) derive equations for marker effect estimates when APY is used for breeding value models, and (3) show the implication of selecting a specific group of core animals in terms of a marker effects model.ResultsWe derived a family of marker effects models called APY-SNP-BLUP. It differs from the classic marker effects model in that the row space of the genotype matrix is reduced and an error term is fitted for non-core animals. We derived formulas for marker effect estimates that take this error term in account. The prediction error variance (PEV) of the marker effect estimates depends on the PEV for core animals but not directly on the PEV of the non-core animals. We extended the APY-SNP-BLUP to include a residual polygenic effect and accommodate non-genotyped animals. We show that selecting a specific group of core animals is equivalent to select a subspace of the row space of the genotype matrix. As the number of core animals increases, subspaces corresponding to different sets of core animals tend to overlap, showing that random selection of core animals is algebraically justified.ConclusionsThe APY-(ss)GBLUP models can be expressed in terms of marker effect models. When the number of core animals is equal to the rank of the genotype matrix, APY-SNP-BLUP is identical to the classic marker effects model. If the number of core animals is less than the rank of the genotype matrix, genotypes for non-core animals are imputed as a linear combination of the genotypes of the core animals. For estimating SNP effects, only relationships and estimated breeding values for core animals are needed.

Practical implementation of genetic groups in single-step genomic evaluations with Woodbury matrix identity–based genomic relationship inverse

The growing amount of genomic information in dairy cattle has increased computational and modeling challenges in the single-step evaluations. The computational challenges are due to the dense inverses of genomic (G) and pedigree (A22) relationship matrices of genotyped animals in the single-step mixed model equations. An equivalent mixed model equation is given by single-step genomic BLUP that are based on the T matrix (ssGTBLUP), where these inverses are avoided by expressing G-1 through a product of 2 rectangular matrices, and (A22)-1 through sparse matrix blocks of the inverse of full relationship matrix A-1. A proper way to account genetic groups through unknown parent groups (UPG) after the Quaas-Pollak transformation (QP) is one key factor in a single-step model. When the UPG effects are incompletely accounted, the iterative solving method may have convergence problems. In this study, we investigated computational and predictive performance of ssGTBLUP with residual polygenic (RPG) effect and UPG. The QP transformation used A-1 and, in the complete form, T and (A22)-1 matrices as well. The models were tested with official Nordic Holstein milk production test-day data and model. The results show that UPG can be easily implemented in ssGTBLUP having RPG. The complete QP transformation was computationally feasible when preconditioned conjugate gradient iteration and iteration on data without explicitly setting up G or A22 matrices were used. Furthermore, for good convergence of the preconditioned conjugate gradient method, a complete QP transformation was necessary.

Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling

Calculation of individual animal reliability of estimated genomic breeding value by SNP-BLUP requires inversion of the mixed model equations (MME). When the SNP-BLUP model includes a residual polygenic (RPG) effect, the size of the MME will be at least the number of genotyped animals (n) plus the number of SNP markers (m). Inversion of the MME in SNP-BLUP involves computations proportional to the cube of the MME size; that is, (n + m)3, which can present a considerable computational burden. We introduce a full Monte Carlo (MC) sampling-based method for approximating reliability in the SNP-BLUP model and compare its performance to the genomic BLUP (GBLUP) model. The performance of the full MC approach was evaluated using 2 data sets, including 19,757 and 222,619 genotyped animals selected from populations with 231,186 and 13.35 million pedigree animals, respectively. Genotypes were available in the data sets for 11,729 and 50,240 SNP markers. An advantage of the full MC approximation method was its low computational demand. A drawback was its tendency to overestimate reliability for animals with low reliability, especially when the weight of the RPG effect was high. The overestimation can be lessened by increasing the number of MC samples.

Snp_blup_rel: software for calculating individual animal SNP-BLUP model reliabilities

The snp_blup_rel program computes model reliabilities for genomic breeding values. The program assumes a single trait SNP-BLUP model where the breeding value can include a residual polygenic (RPG) effect. The reliability calculation requires elements of the inverse of the mixed model equations (MME). The calculation has three steps: 1) MME calculation, 2) MME coefficient matrix inversion, and 3) reliability computation. When needed, the inverted matrix can be saved after step 2. Step 3 can be used separately to new genotypes which do not contribute information to Step 2. When an RPG effect is included, an approximate method based on Monte Carlo sampling is applied. This reduces the MME matrix size and allows including many genotyped individuals. The program is written in Fortran 90/95, and uses LAPACK subroutines which enable multi-threaded parallel computing. The program is efficient in terms of computing time and memory requirements, and can be used to analyze even large genomic data. Thus, the program can be used in calculating model reliabilities for large national genomic evaluations.

Using Monte Carlo method to include polygenic effects in calculation of SNP-BLUP model reliability

An SNP-BLUP model is computationally scalable even for large numbers of genotyped animals. When genetic variation cannot be completely captured by SNP markers, a more accurate model is obtained by fitting a residual polygenic effect (RPG) as well. However, inclusion of the RPG effect increases the size of the SNP-BLUP mixed model equations (MME) by the number of genotyped animals. Consequently, the calculation of model reliabilities requiring elements of the inverted MME coefficient matrix becomes more computationally challenging with increasing numbers of genotyped animals. We present a Monte Carlo (MC)-based sampling method to estimate the reliability of the SNP-BLUP model including the RPG effect, where the MME size depends on the number of markers and MC samples. We compared reliabilities calculated using different RPG proportions and different MC sample sizes in analyzing 2 data sets. Data set 1 (data set 2) contained 19,757 (222,619) genotyped animals, with 11,729 (50,240) SNP markers, and 231,186 (13.35 million) pedigree animals. Correlations between the correct and the MC-calculated reliabilities were above 98% even with 5,000 MC samples and an 80% RPG proportion in both data sets. However, more MC samples were needed to achieve a small maximum absolute difference and mean squared error, particularly when the RPG proportion exceeded 20%. The computing time for MC SNP-BLUP was shorter than for GBLUP. In conclusion, the MC-based approach can be an effective strategy for calculating SNP-BLUP model reliability with an RPG effect included.

Combining pedigree and genomic information to improve prediction quality: an example in sorghum

Key messageThe use of a kinship matrix integrating pedigree- and marker-based relationships optimized the performance of genomic prediction in sorghum, especially for traits of lower heritability.Selection based on genome-wide markers has become an active breeding strategy in crops. Genomic prediction models can make use of pedigree information to account for the residual polygenic effects not captured by markers. Our aim was to evaluate the impact of using pedigree and genomic information on prediction quality of breeding values for different traits in sorghum. We explored BLUP models that use weighted combinations of pedigree and genomic relationship matrices. The optimal weighting factor was empirically determined in order to maximize predictive ability after evaluating a range of candidate weights. The phenotypic data consisted of testcross evaluations of sorghum parental lines across multiple environments. All lines were genotyped, and full pedigree information was available. The performance of the best predictive combined matrix was compared to that of models fitting the component matrices independently. Model performance was assessed using cross-validation technique. Fitting a combined pedigree–genomic matrix with the optimal weight always yielded the largest increases in predictive ability and the largest reductions in prediction bias relative to the simple G-BLUP. However, the weight that optimized prediction varied across traits. The benefits of including pedigree information in the genomic model were more relevant for traits with lower heritability, such as grain yield and stay-green. Our results suggest that the combination of pedigree and genomic relatedness can be used to optimize predictions of complex traits in crops when the additive variation is not fully explained by markers.

Short communication: Genomic prediction using different single-step methods in the Finnish red dairy cattle population

Single-step genomic prediction models utilizing both genotyped and nongenotyped animals are likely to become the prevailing tool in genetic evaluations of livestock. Various single-step prediction models have been proposed, based either on estimation of individual marker effects or on direct prediction via a genomic relationship matrix. In this study, a classical pedigree-based animal model, a regular single-step genomic BLUP (ssGBLUP) model, algorithm for proven and young (APY) with 2 strategies for choosing core animals, and a single-step Bayesian regression (ssBR) model were compared for 305-d production traits (milk, fat, protein) in the Finnish red dairy cattle population. A residual polygenic effect with 10% of total genetic variance was included in the single-step models to reduce inflation of genomic predictions. Validation reliability was calculated as the squared Pearson correlation coefficient between genomically enhanced breeding value (GEBV) and yield deviation for masked records for 2,056 validation cows from the last year in the data set investigated. The results showed that gains of 0.02 to 0.04 on validation reliability were achieved by using single-step methods compared with the classical animal model. The regular ssGBLUP model and ssBR model with an extra polygenic effect yielded the same results. The APY methods yielded similar reliabilities as the regular ssGBLUP and ssBR. Exact prediction error variance of GEBV could be obtained by ssBR to avoid any approximation methods used for ssGBLUP when inversion left-hand side of mixed model equations is computationally infeasible for large data sets.

Single-step SNP-BLUP with on-the-fly imputed genotypes and residual polygenic effects

BackgroundSingle-step genomic best linear unbiased prediction (BLUP) evaluation combines relationship information from pedigree and genomic marker data. The inclusion of the genomic information into mixed model equations requires the inverse of the combined relationship matrix {mathbf{H}}, which has a dense matrix block for genotyped animals.MethodsTo avoid inversion of dense matrices, single-step genomic BLUP can be transformed to single-step single nucleotide polymorphism BLUP (SNP-BLUP) which have observed and imputed marker coefficients. Simple block LDL type decompositions of the single-step relationship matrix {mathbf{H}} were derived to obtain different types of linearly equivalent single-step genomic mixed model equations with different sets of reparametrized random effects. For non-genotyped animals, the imputed marker coefficient terms in the single-step SNP-BLUP were calculated on-the-fly during the iterative solution using sparse matrix decompositions without storing the imputed genotypes. Residual polygenic effects were added to genotyped animals and transmitted to non-genotyped animals using relationship coefficients that are similar to imputed genotypes. The relationships were further orthogonalized to improve convergence of iterative methods.ResultsAll presented single-step SNP-BLUP models can be solved efficiently using iterative methods that rely on iteration on data and sparse matrix approaches. The efficiency, accuracy and iteration convergence of the derived mixed model equations were tested with a small dataset that included 73,579 animals of which 2885 were genotyped with 37,526 SNPs.ConclusionsInversion of the large and dense genomic relationship matrix was avoided in single-step evaluation by using fully orthogonalized single-step SNP-BLUP formulations. The number of iterations until convergence was smaller in single-step SNP-BLUP formulations than in the original single-step GBLUP when heritability was low, but increased above that of the original single-step when heritability was high.

Technical note: Equivalent genomic models with a residual polygenic effect

Routine genomic evaluations in animal breeding are usually based on either a BLUP with genomic relationship matrix (GBLUP) or single nucleotide polymorphism (SNP) BLUP model. For a multi-step genomic evaluation, these 2 alternative genomic models were proven to give equivalent predictions for genomic reference animals. The model equivalence was verified also for young genotyped animals without phenotypes. Due to incomplete linkage disequilibrium of SNP markers to genes or causal mutations responsible for genetic inheritance of quantitative traits, SNP markers cannot explain all the genetic variance. A residual polygenic effect is normally fitted in the genomic model to account for the incomplete linkage disequilibrium. In this study, we start by showing the proof that the multi-step GBLUP and SNP BLUP models are equivalent for the reference animals, when they have a residual polygenic effect included. Second, the equivalence of both multi-step genomic models with a residual polygenic effect was also verified for young genotyped animals without phenotypes. Additionally, we derived formulas to convert genomic estimated breeding values of the GBLUP model to its components, direct genomic values and residual polygenic effect. Third, we made a proof that the equivalence of these 2 genomic models with a residual polygenic effect holds also for single-step genomic evaluation. Both the single-step GBLUP and SNP BLUP models lead to equal prediction for genotyped animals with phenotypes (e.g., reference animals), as well as for (young) genotyped animals without phenotypes. Finally, these 2 single-step genomic models with a residual polygenic effect were proven to be equivalent for estimation of SNP effects, too.

A multiple-SNP approach for genome-wide association study of milk production traits in Chinese Holstein cattle.

The multiple-SNP analysis has been studied by many researchers, in which the effects of multiple SNPs are simultaneously estimated and tested in a multiple linear regression. The multiple-SNP association analysis usually has higher power and lower false-positive rate for detecting causative SNP(s) than single marker analysis (SMA). Several methods have been proposed to simultaneously estimate and test multiple SNP effects. In this research, a fast method called MEML (Mixed model based Expectation-Maximization Lasso algorithm) was developed for simultaneously estimate of multiple SNP effects. An improved Lasso prior was assigned to SNP effects which were estimated by searching the maximum joint posterior mode. The residual polygenic effect was included in the model to absorb many tiny SNP effects, which is treated as missing data in our EM algorithm. A series of simulation experiments were conducted to validate the proposed method, and the results showed that compared with SMMA, the new method can dramatically decrease the false-positive rate. The new method was also applied to the 50k SNP-panel dataset for genome-wide association study of milk production traits in Chinese Holstein cattle. Totally, 39 significant SNPs and their nearby 25 genes were found. The number of significant SNPs is remarkably fewer than that by SMMA which found 105 significant SNPs. Among 39 significant SNPs, 8 were also found by SMMA and several well-known QTLs or genes were confirmed again; furthermore, we also got some positional candidate gene with potential function of effecting milk production traits. These novel findings in our research should be valuable for further investigation.

A single-step genomic model with direct estimation of marker effects

Compared with the currently widely used multi-step genomic models for genomic evaluation, single-step genomic models can provide more accurate genomic evaluation by jointly analyzing phenotypes and genotypes of all animals and can properly correct for the effect of genomic preselection on genetic evaluations. The objectives of this study were to introduce a single-step genomic model, allowing a direct estimation of single nucleotide polymorphism (SNP) effects, and to develop efficient computing algorithms for solving equations of the single-step SNP model. We proposed an alternative to the current single-step genomic model based on the genomic relationship matrix by including an additional step for estimating the effects of SNP markers. Our single-step SNP model allowed flexible modeling of SNP effects in terms of the number and variance of SNP markers. Moreover, our single-step SNP model included a residual polygenic effect with trait-specific variance for reducing inflation in genomic prediction. A kernel calculation of the SNP model involved repeated multiplications of the inverse of the pedigree relationship matrix of genotyped animals with a vector, for which numerical methods such as preconditioned conjugate gradients can be used. For estimating SNP effects, a special updating algorithm was proposed to separate residual polygenic effects from the SNP effects. We extended our single-step SNP model to general multiple-trait cases. By taking advantage of a block-diagonal (co)variance matrix of SNP effects, we showed how to estimate multivariate SNP effects in an efficient way. A general prediction formula was derived for candidates without phenotypes, which can be used for frequent, interim genomic evaluations without running the whole genomic evaluation process. We discussed various issues related to implementation of the single-step SNP model in Holstein populations with an across-country genomic reference population.

Estimation of genomic breeding values for residual feed intake in a multibreed cattle population.

Residual feed intake (RFI) is a measure of the efficiency of animals in feed utilization. The accuracies of GEBV for RFI could be improved by increasing the size of the reference population. Combining RFI records of different breeds is a way to do that. The aims of this study were to 1) develop a method for calculating GEBV in a multibreed population and 2) improve the accuracies of GEBV by using SNP associated with RFI. An alternative method for calculating accuracies of GEBV using genomic BLUP (GBLUP) equations is also described and compared to cross-validation tests. The dataset included RFI records and 606,096 SNP genotypes for 5,614 Bos taurus animals including 842 Holstein heifers and 2,009 Australian and 2,763 Canadian beef cattle. A range of models were tested for combining genotype and phenotype information from different breeds and the best model included an overall effect of each SNP, an effect of each SNP specific to a breed, and a small residual polygenic effect defined by the pedigree. In this model, the Holsteins and some Angus cattle were combined into 1 "breed class" because they were the only cattle measured for RFI at an early age (6-9 mo of age) and were fed a similar diet. The average empirical accuracy (0.31), estimated by calculating the correlation between GEBV and actual phenotypes divided by the square root of estimated heritability in 5-fold cross-validation tests, was near to that expected using the GBLUP equations (0.34). The average empirical and expected accuracies were 0.30 and 0.31, respectively, when the GEBV were estimated for each breed separately. Therefore, the across-breed reference population increased the accuracy of GEBV slightly, although the gain was greater for breeds with smaller number of individuals in the reference population (0.08 in Murray Grey and 0.11 in Hereford for empirical accuracy). In a second approach, SNP that were significantly (P < 0.001) associated with RFI in the beef cattle genomewide association studies were used to create an auxiliary genomic relationship matrix for estimating GEBV in Holstein heifers. The empirical (and expected) accuracy of GEBV within Holsteins increased from 0.33 (0.35) to 0.39 (0.36) and improved even more to 0.43 (0.50) when using a multibreed reference population. Therefore, a multibreed reference population is a useful resource to find SNP with a greater than average association with RFI in 1 breed and use them to estimate GEBV in another breed.

Genomic relationships based on X chromosome markers and accuracy of genomic predictions with and without X chromosome markers.

BackgroundAlthough the X chromosome is the second largest bovine chromosome, markers on the X chromosome are not used for genomic prediction in some countries and populations. In this study, we presented a method for computing genomic relationships using X chromosome markers, investigated the accuracy of imputation from a low density (7K) to the 54K SNP (single nucleotide polymorphism) panel, and compared the accuracy of genomic prediction with and without using X chromosome markers.MethodsThe impact of considering X chromosome markers on prediction accuracy was assessed using data from Nordic Holstein bulls and different sets of SNPs: (a) the 54K SNPs for reference and test animals, (b) SNPs imputed from the 7K to the 54K SNP panel for test animals, (c) SNPs imputed from the 7K to the 54K panel for half of the reference animals, and (d) the 7K SNP panel for all animals. Beagle and Findhap were used for imputation. GBLUP (genomic best linear unbiased prediction) models with or without X chromosome markers and with or without a residual polygenic effect were used to predict genomic breeding values for 15 traits.ResultsAveraged over the two imputation datasets, correlation coefficients between imputed and true genotypes for autosomal markers, pseudo-autosomal markers, and X-specific markers were 0.971, 0.831 and 0.935 when using Findhap, and 0.983, 0.856 and 0.937 when using Beagle. Estimated reliabilities of genomic predictions based on the imputed datasets using Findhap or Beagle were very close to those using the real 54K data. Genomic prediction using all markers gave slightly higher reliabilities than predictions without X chromosome markers. Based on our data which included only bulls, using a G matrix that accounted for sex-linked relationships did not improve prediction, compared with a G matrix that did not account for sex-linked relationships. A model that included a polygenic effect did not recover the loss of prediction accuracy from exclusion of X chromosome markers.ConclusionsThe results from this study suggest that markers on the X chromosome contribute to accuracy of genomic predictions and should be used for routine genomic evaluation.

Accuracy of genomic predictions in Bos indicus (Nellore) cattle

BackgroundNellore cattle play an important role in beef production in tropical systems and there is great interest in determining if genomic selection can contribute to accelerate genetic improvement of production and fertility in this breed. We present the first results of the implementation of genomic prediction in a Bos indicus (Nellore) population.MethodsInfluential bulls were genotyped with the Illumina Bovine HD chip in order to assess genomic predictive ability for weight and carcass traits, gestation length, scrotal circumference and two selection indices. 685 samples and 320 238 single nucleotide polymorphisms (SNPs) were used in the analyses. A forward-prediction scheme was adopted to predict the genomic breeding values (DGV). In the training step, the estimated breeding values (EBV) of bulls were deregressed (dEBV) and used as pseudo-phenotypes to estimate marker effects using four methods: genomic BLUP with or without a residual polygenic effect (GBLUP20 and GBLUP0, respectively), a mixture model (Bayes C) and Bayesian LASSO (BLASSO). Empirical accuracies of the resulting genomic predictions were assessed based on the correlation between DGV and dEBV for the testing group.ResultsAccuracies of genomic predictions ranged from 0.17 (navel at weaning) to 0.74 (finishing precocity). Across traits, Bayesian regression models (Bayes C and BLASSO) were more accurate than GBLUP. The average empirical accuracies were 0.39 (GBLUP0), 0.40 (GBLUP20) and 0.44 (Bayes C and BLASSO). Bayes C and BLASSO tended to produce deflated predictions (i.e. slope of the regression of dEBV on DGV greater than 1). Further analyses suggested that higher-than-expected accuracies were observed for traits for which EBV means differed significantly between two breeding subgroups that were identified in a principal component analysis based on genomic relationships.ConclusionsBayesian regression models are of interest for future applications of genomic selection in this population, but further improvements are needed to reduce deflation of their predictions. Recurrent updates of the training population would be required to enable accurate prediction of the genetic merit of young animals. The technical feasibility of applying genomic prediction in a Bos indicus (Nellore) population was demonstrated. Further research is needed to permit cost-effective selection decisions using genomic information.

Estimating single nucleotide polymorphism associations using pedigree data: applications to breast cancer

Background:Pedigrees with multiple genotyped family members have been underutilised in breast cancer (BC) genetic-association studies. We developed a pedigree-based analytical framework to characterise single-nucleotide polymorphism (SNP) associations with BC risk using data from 736 BC families ascertained through multiple affected individuals. On average, eight family members had been genotyped for 24 SNPs previously associated with BC.Methods:Breast cancer incidence was modelled on the basis of SNP effects and residual polygenic effects. Relative risk (RR) estimates were obtained by maximising the retrospective likelihood (RL) of observing the family genotypes conditional on all disease phenotypes. Models were extended to assess parent-of-origin effects (POEs).Results:Thirteen SNPs were significantly associated with BC under the pedigree RL approach. This approach yielded estimates consistent with those from large population-based studies. Logistic regression models ignoring pedigree structure generally gave larger RRs and association P-values. SNP rs3817198 in LSP1, previously shown to exhibit POE, yielded maternal and paternal RR estimates that were similar to those previously reported (paternal RR=1.12 (95% confidence interval (CI): 0.99–1.27), P=0.081, one-sided P=0.04; maternal RR=0.94 (95% CI: 0.84–1.06), P=0.33). No other SNP exhibited POE.Conclusion:Our pedigree-based methods provide a valuable and efficient tool for characterising genetic associations with BC risk or other diseases and can complement population-based studies.

Comparison on genomic predictions using three GBLUP methods and two single-step blending methods in the Nordic Holstein population

BackgroundA single-step blending approach allows genomic prediction using information of genotyped and non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may need to be adjusted because marker-based and pedigree-based relationship matrices may not be on the same scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein population.MethodsThe data consisted of de-regressed proofs (DRP) for 5 214 genotyped and 9 374 non-genotyped bulls. The bulls were divided into a training and a validation population by birth date, October 1, 2001. Five approaches for genomic prediction were used: 1) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted for the difference of scale between the genomic and the pedigree relationship matrices. A set of weights on the pedigree relationship matrix (ranging from 0.05 to 0.40) was used to build the combined relationship matrix in the single-step blending method and the GBLUP method with a polygenetic effect.ResultsAveraged over the 16 traits, reliabilities of genomic breeding values predicted using the GBLUP method with a polygenic effect (relative weight of 0.20) were 0.3% higher than reliabilities from the simple GBLUP method (without a polygenic effect). The adjusted single-step blending and original single-step blending methods (relative weight of 0.20) had average reliabilities that were 2.1% and 1.8% higher than the simple GBLUP method, respectively. In addition, the GBLUP method with a polygenic effect led to less bias of genomic predictions than the simple GBLUP method, and both single-step blending methods yielded less bias of predictions than all GBLUP methods.ConclusionsThe single-step blending method is an appealing approach for practical genomic prediction in dairy cattle. Genomic prediction from the single-step blending method can be improved by adjusting the scale of the genomic relationship matrix.

Semiparametric variance components models for genetic studies with longitudinal phenotypes

In a family-based genetic study such as the Framingham Heart Study (FHS), longitudinal trait measurements are recorded on subjects collected from families. Observations on subjects from the same family are correlated due to shared genetic composition or environmental factors such as diet. The data have a 3-level structure with measurements nested in subjects and subjects nested in families. We propose a semiparametric variance components model to describe phenotype observed at a time point as the sum of a nonparametric population mean function, a nonparametric random quantitative trait locus (QTL) effect, a shared environmental effect, a residual random polygenic effect and measurement error. One feature of the model is that we do not assume a parametric functional form of the age-dependent QTL effect, and we use penalized spline-based method to fit the model. We obtain nonparametric estimation of the QTL heritability defined as the ratio of the QTL variance to the total phenotypic variance. We use simulation studies to investigate performance of the proposed methods and apply these methods to the FHS systolic blood pressure data to estimate age-specific QTL effect at 62cM on chromosome 17.