An Efficient Method to Calculate Genomic Prediction Accuracy for New Individuals.

Diagonal elements of the coefficient matrix are necessary to calculate the genomic prediction accuracy. Here an improved methodology is described, to update the inverse of the coefficient matrix (C) for new individuals with a genotype, with and without phenotypes. Computational performance is significantly improved by re-using parts of the coefficient matrix inverse calculations that do not change from one animal to another, in combination with updated calculations for those that do change. This method expedites calculation of accuracy for new individuals with genotypes, without re-doing the whole population, by using the previously calculated matrices.

Estimates of genetic trend for single-step genomic evaluations.

BACKGROUND: A common measure employed to evaluate the efficacy of livestock improvement schemes is the genetic trend, which is calculated as the means of predicted breeding values for animals born in successive time periods. This implies that different cohorts refer to the same base population. For genetic evaluation schemes integrating genomic information with records for all animals, genotyped or not, this is often not the case: expected means for pedigree founders are zero whereas values for genotyped animals are expected to sum to zero at the (mean) time corresponding to the frequencies that are used to center marker allele counts when calculating genomic relationships. METHODS: The paper examines estimates of genetic trends from single-step genomic evaluations. After a review of methods which propose to align pedigree-based and genomic relationship matrices, simulation is used to illustrate the effects of alignments and choice of assumed gene frequencies on trajectories of genetic trends. RESULTS: The results show that methods available to alleviate differences between the founder populations implied by the two types of relationship matrices perform well; in particular, the meta-founder approach is advantageous. An application to data from routine genetic evaluation of Australian sheep is shown, confirming their effectiveness for practical data. CONCLUSIONS: Aligning pedigree and genomic relationship matrices for single step genetic evaluation for populations under selection is essential. Fitting meta-founders is an effective and simple method to avoid distortion of estimates of genetic trends.

Study of the optimum haplotype length to build genomic relationship matrices.

BACKGROUND: As genomic data becomes more abundant, genomic prediction is more routinely used to estimate breeding values. In genomic prediction, the relationship matrix ([Formula: see text]), which is traditionally used in genetic evaluations is replaced by the genomic relationship matrix ([Formula: see text]). This paper considers alternative ways of building relationship matrices either using single markers or haplotypes of different lengths. We compared the prediction accuracies and log-likelihoods when using these alternative relationship matrices and the traditional [Formula: see text] matrix, for real and simulated data. METHODS: For real data, we built relationship matrices using 50k genotype data for a population of Brahman cattle to analyze three traits: scrotal circumference (SC), age at puberty (AGECL) and weight at first corpus luteum (WTCL). Haplotypes were phased with hsphase and imputed with BEAGLE. The relationship matrices were built using three methods based on haplotypes of different lengths. The log-likelihood was considered to define the optimum haplotype lengths for each trait and each haplotype-based relationship matrix. RESULTS: Based on simulated data, we showed that the inverse of [Formula: see text] matrix and the inverse of the haplotype relationship matrices for methods using one-single nucleotide polymorphism (SNP) phased haplotypes provided coefficients of determination (R2) close to 1, although the estimated genetic variances differed across methods. Using real data and multiple SNPs in the haplotype segments to build the relationship matrices provided better results than the [Formula: see text] matrix based on one-SNP haplotypes. However, the optimal haplotype length to achieve the highest log-likelihood depended on the method used and the trait. The optimal haplotype length (7 to 8 SNPs) was similar for SC and AGECL. One of the haplotype-based methods achieved the largest increase in log-likelihood for SC, i.e. from -1330 when using [Formula: see text] to -1325 when using haplotypes with eight SNPs. CONCLUSIONS: Building the relationship matrix by using haplotypes that comprise multiple SNPs will increase the accuracy of estimated breeding values. However, the optimum haplotype length that shows the correct relationship among individuals for each trait can be derived from the data.

BESSiE: a software for linear model BLUP and Bayesian MCMC analysis of large-scale genomic data.

BACKGROUND: The advent of genomic marker data has triggered the development of various Bayesian algorithms for estimation of marker effects, but software packages implementing these algorithms are not readily available, or are limited to a single algorithm, uni-variate analysis or a limited number of factors. Moreover, script based environments like R may not be able to handle large-scale genomic data or exploit model properties which save computing time or memory (RAM). RESULTS: BESSiE is a software designed for best linear unbiased prediction (BLUP) and Bayesian Markov chain Monte Carlo analysis of linear mixed models allowing for continuous and/or categorical multivariate, repeated and missing observations, various random and fixed factors and large-scale genomic marker data. BESSiE covers the algorithms genomic BLUP, single nucleotide polymorphism (SNP)-BLUP, BayesA, BayesB, BayesC[Formula: see text] and BayesR for estimating marker effects and/or summarised genomic values. BESSiE is parameter file driven, command line operated and available for Linux environments. BESSiE executable, manual and a collection of examples can be downloaded http://turing.une.edu.au/~agbu-admin/BESSiE/ . CONCLUSION: BESSiE allows the user to compare several different Bayesian and BLUP algorithms for estimating marker effects from large data sets in complex models with the same software by small alterations in the parameter file. The program has no hard-coded limitations for number of factors, observations or genetic markers.

A multi-trait, meta-analysis for detecting pleiotropic polymorphisms for stature, fatness and reproduction in beef cattle.

Polymorphisms that affect complex traits or quantitative trait loci (QTL) often affect multiple traits. We describe two novel methods (1) for finding single nucleotide polymorphisms (SNPs) significantly associated with one or more traits using a multi-trait, meta-analysis, and (2) for distinguishing between a single pleiotropic QTL and multiple linked QTL. The meta-analysis uses the effect of each SNP on each of n traits, estimated in single trait genome wide association studies (GWAS). These effects are expressed as a vector of signed t-values (t) and the error covariance matrix of these t values is approximated by the correlation matrix of t-values among the traits calculated across the SNP (V). Consequently, t'V-1t is approximately distributed as a chi-squared with n degrees of freedom. An attractive feature of the meta-analysis is that it uses estimated effects of SNPs from single trait GWAS, so it can be applied to published data where individual records are not available. We demonstrate that the multi-trait method can be used to increase the power (numbers of SNPs validated in an independent population) of GWAS in a beef cattle data set including 10,191 animals genotyped for 729,068 SNPs with 32 traits recorded, including growth and reproduction traits. We can distinguish between a single pleiotropic QTL and multiple linked QTL because multiple SNPs tagging the same QTL show the same pattern of effects across traits. We confirm this finding by demonstrating that when one SNP is included in the statistical model the other SNPs have a non-significant effect. In the beef cattle data set, cluster analysis yielded four groups of QTL with similar patterns of effects across traits within a group. A linear index was used to validate SNPs having effects on multiple traits and to identify additional SNPs belonging to these four groups.

Accuracies of genomically estimated breeding values from pure-breed and across-breed predictions in Australian beef cattle.

BACKGROUND: The major obstacles for the implementation of genomic selection in Australian beef cattle are the variety of breeds and in general, small numbers of genotyped and phenotyped individuals per breed. The Australian Beef Cooperative Research Center (Beef CRC) investigated these issues by deriving genomic prediction equations (PE) from a training set of animals that covers a range of breeds and crosses including Angus, Murray Grey, Shorthorn, Hereford, Brahman, Belmont Red, Santa Gertrudis and Tropical Composite. This paper presents accuracies of genomically estimated breeding values (GEBV) that were calculated from these PE in the commercial pure-breed beef cattle seed stock sector. METHODS: PE derived by the Beef CRC from multi-breed and pure-breed training populations were applied to genotyped Angus, Limousin and Brahman sires and young animals, but with no pure-breed Limousin in the training population. The accuracy of the resulting GEBV was assessed by their genetic correlation to their phenotypic target trait in a bi-variate REML approach that models GEBV as trait observations. RESULTS: Accuracies of most GEBV for Angus and Brahman were between 0.1 and 0.4, with accuracies for abattoir carcass traits generally greater than for live animal body composition traits and reproduction traits. Estimated accuracies greater than 0.5 were only observed for Brahman abattoir carcass traits and for Angus carcass rib fat. Averaged across traits within breeds, accuracies of GEBV were highest when PE from the pooled across-breed training population were used. However, for the Angus and Brahman breeds the difference in accuracy from using pure-breed PE was small. For the Limousin breed no reasonable results could be achieved for any trait. CONCLUSION: Although accuracies were generally low compared to published accuracies estimated within breeds, they are in line with those derived in other multi-breed populations. Thus PE developed by the Beef CRC can contribute to the implementation of genomic selection in Australian beef cattle breeding.

Detection of quantitative trait loci in Bos indicus and Bos taurus cattle using genome-wide association studies.

BACKGROUND: The apparent effect of a single nucleotide polymorphism (SNP) on phenotype depends on the linkage disequilibrium (LD) between the SNP and a quantitative trait locus (QTL). However, the phase of LD between a SNP and a QTL may differ between Bos indicus and Bos taurus because they diverged at least one hundred thousand years ago. Here, we test the hypothesis that the apparent effect of a SNP on a quantitative trait depends on whether the SNP allele is inherited from a Bos taurus or Bos indicus ancestor. METHODS: Phenotype data on one or more traits and SNP genotype data for 10 181 cattle from Bos taurus, Bos indicus and composite breeds were used. All animals had genotypes for 729 068 SNPs (real or imputed). Chromosome segments were classified as originating from B. indicus or B. taurus on the basis of the haplotype of SNP alleles they contained. Consequently, SNP alleles were classified according to their sub-species origin. Three models were used for the association study: (1) conventional GWAS (genome-wide association study), fitting a single SNP effect regardless of subspecies origin, (2) interaction GWAS, fitting an interaction between SNP and subspecies-origin, and (3) best variable GWAS, fitting the most significant combination of SNP and sub-species origin. RESULTS: Fitting an interaction between SNP and subspecies origin resulted in more significant SNPs (i.e. more power) than a conventional GWAS. Thus, the effect of a SNP depends on the subspecies that the allele originates from. Also, most QTL segregated in only one subspecies, suggesting that many mutations that affect the traits studied occurred after divergence of the subspecies or the mutation became fixed or was lost in one of the subspecies. CONCLUSIONS: The results imply that GWAS and genomic selection could gain power by distinguishing SNP alleles based on their subspecies origin, and that only few QTL segregate in both B. indicus and B. taurus cattle. Thus, the QTL that segregate in current populations likely resulted from mutations that occurred in one of the subspecies and can have both positive and negative effects on the traits. There was no evidence that selection has increased the frequency of alleles that increase body weight.

Fine-mapping the POLL locus in Brahman cattle yields the diagnostic marker CSAFG29.

The POLL locus has been mapped to the centromeric region of bovine chromosome 1 (BTA1) in both taurine breeds and taurine-indicine crosses in an interval of approximately 1 Mb. It has not yet been mapped in pure-bred zebu cattle. Despite several efforts, neither causative mutations in candidate genes nor a singular diagnostic DNA marker has been identified. In this study, we genotyped a total of 68 Brahman cattle and 20 Hereford cattle informative for the POLL locus for 33 DNA microsatellites, 16 of which we identified de novo from the bovine genome sequence, mapping the POLL locus to the region of the genes IFNAR2 and SYNJ1. The 303-bp allele of the new microsatellite, CSAFG29, showed strong association with the POLL allele. We then genotyped 855 Brahman cattle for CSAFG29 and confirmed the association between the 303-bp allele and POLL. To determine whether the same association was found in taurine breeds, we genotyped 334 animals of the Angus, Hereford and Limousin breeds and 376 animals of the Brangus, Droughtmaster and Santa Gertrudis composite taurine-zebu breeds. The association between the 303-bp allele and POLL was confirmed in these breeds; however, an additional allele (305 bp) was also associated but not fully predictive of POLL. Across the data, CSAFG29 was in sufficient linkage disequilibrium to the POLL allele in Australian Brahman cattle that it could potentially be used as a diagnostic marker in that breed, but this may not be the case in other breeds. Further, we provide confirmatory evidence that the scur phenotype generally occurs in animals that are heterozygous for the POLL allele.

A phasing and imputation method for pedigreed populations that results in a single-stage genomic evaluation.

BACKGROUND: Efficient, robust, and accurate genotype imputation algorithms make large-scale application of genomic selection cost effective. An algorithm that imputes alleles or allele probabilities for all animals in the pedigree and for all genotyped single nucleotide polymorphisms (SNP) provides a framework to combine all pedigree, genomic, and phenotypic information into a single-stage genomic evaluation. METHODS: An algorithm was developed for imputation of genotypes in pedigreed populations that allows imputation for completely ungenotyped animals and for low-density genotyped animals, accommodates a wide variety of pedigree structures for genotyped animals, imputes unmapped SNP, and works for large datasets. The method involves simple phasing rules, long-range phasing and haplotype library imputation and segregation analysis. RESULTS: Imputation accuracy was high and computational cost was feasible for datasets with pedigrees of up to 25 000 animals. The resulting single-stage genomic evaluation increased the accuracy of estimated genomic breeding values compared to a scenario in which phenotypes on relatives that were not genotyped were ignored. CONCLUSIONS: The developed imputation algorithm and software and the resulting single-stage genomic evaluation method provide powerful new ways to exploit imputation and to obtain more accurate genetic evaluations.

Use of the numerator relationship matrix in genetic analysis of autopolyploid species.

Mixed models incorporating the inverse of a numerator relationship matrix (NRM) are widely used to estimate genetic parameters and to predict breeding values in animal breeding. A simple and quick method to directly calculate the inverse of the NRM has been historically developed for diploid animal species. Mixed models are less used in plant breeding partly because the existing method for diploids is not applicable to autopolyploid species. This is because of the phenomenon of double reduction and the possibility that gametes carry alleles which are identical by descent. This paper generalises the NRM and its inverse for autopolyploid species, so it can be easily incorporated into their genetic analysis. The technique proposed is to first calculate the kinship coefficient matrix and its inverse as a precursor to calculating the NRM and its inverse. This allows the NRM to be calculated for populations containing individuals of mixed ploidy levels. This generalization can also accommodate uncertain parentage by generating the "average" relationship matrix. The possibility that non-inbred parents can produce inbred progeny (double reduction) is also discussed. Rules are outlined that are applicable for any level of ploidy. Examples of use of the matrix are provided using simulated pedigrees.

"SNP Snappy": a strategy for fast genome-wide association studies fitting a full mixed model.

A strategy to reduce computational demands of genome-wide association studies fitting a mixed model is presented. Improvements are achieved by utilizing a large proportion of calculations that remain constant across the multiple analyses for individual markers involved, with estimates obtained without inverting large matrices.

A combined long-range phasing and long haplotype imputation method to impute phase for SNP genotypes.

BACKGROUND: Knowing the phase of marker genotype data can be useful in genome-wide association studies, because it makes it possible to use analysis frameworks that account for identity by descent or parent of origin of alleles and it can lead to a large increase in data quantities via genotype or sequence imputation. Long-range phasing and haplotype library imputation constitute a fast and accurate method to impute phase for SNP data. METHODS: A long-range phasing and haplotype library imputation algorithm was developed. It combines information from surrogate parents and long haplotypes to resolve phase in a manner that is not dependent on the family structure of a dataset or on the presence of pedigree information. RESULTS: The algorithm performed well in both simulated and real livestock and human datasets in terms of both phasing accuracy and computation efficiency. The percentage of alleles that could be phased in both simulated and real datasets of varying size generally exceeded 98% while the percentage of alleles incorrectly phased in simulated data was generally less than 0.5%. The accuracy of phasing was affected by dataset size, with lower accuracy for dataset sizes less than 1000, but was not affected by effective population size, family data structure, presence or absence of pedigree information, and SNP density. The method was computationally fast. In comparison to a commonly used statistical method (fastPHASE), the current method made about 8% less phasing mistakes and ran about 26 times faster for a small dataset. For larger datasets, the differences in computational time are expected to be even greater. A computer program implementing these methods has been made available. CONCLUSIONS: The algorithm and software developed in this study make feasible the routine phasing of high-density SNP chips in large datasets.

A comparison of five methods to predict genomic breeding values of dairy bulls from genome-wide SNP markers.

BACKGROUND: Genomic selection (GS) uses molecular breeding values (MBV) derived from dense markers across the entire genome for selection of young animals. The accuracy of MBV prediction is important for a successful application of GS. Recently, several methods have been proposed to estimate MBV. Initial simulation studies have shown that these methods can accurately predict MBV. In this study we compared the accuracies and possible bias of five different regression methods in an empirical application in dairy cattle. METHODS: Genotypes of 7,372 SNP and highly accurate EBV of 1,945 dairy bulls were used to predict MBV for protein percentage (PPT) and a profit index (Australian Selection Index, ASI). Marker effects were estimated by least squares regression (FR-LS), Bayesian regression (Bayes-R), random regression best linear unbiased prediction (RR-BLUP), partial least squares regression (PLSR) and nonparametric support vector regression (SVR) in a training set of 1,239 bulls. Accuracy and bias of MBV prediction were calculated from cross-validation of the training set and tested against a test team of 706 young bulls. RESULTS: For both traits, FR-LS using a subset of SNP was significantly less accurate than all other methods which used all SNP. Accuracies obtained by Bayes-R, RR-BLUP, PLSR and SVR were very similar for ASI (0.39-0.45) and for PPT (0.55-0.61). Overall, SVR gave the highest accuracy.All methods resulted in biased MBV predictions for ASI, for PPT only RR-BLUP and SVR predictions were unbiased. A significant decrease in accuracy of prediction of ASI was seen in young test cohorts of bulls compared to the accuracy derived from cross-validation of the training set. This reduction was not apparent for PPT. Combining MBV predictions with pedigree based predictions gave 1.05 - 1.34 times higher accuracies compared to predictions based on pedigree alone. Some methods have largely different computational requirements, with PLSR and RR-BLUP requiring the least computing time. CONCLUSIONS: The four methods which use information from all SNP namely RR-BLUP, Bayes-R, PLSR and SVR generate similar accuracies of MBV prediction for genomic selection, and their use in the selection of immediate future generations in dairy cattle will be comparable. The use of FR-LS in genomic selection is not recommended.

A primary assembly of a bovine haplotype block map based on a 15,036-single-nucleotide polymorphism panel genotyped in holstein-friesian cattle.

Analysis of data on 1000 Holstein-Friesian bulls genotyped for 15,036 single-nucleotide polymorphisms (SNPs) has enabled genomewide identification of haplotype blocks and tag SNPs. A final subset of 9195 SNPs in Hardy-Weinberg equilibrium and mapped on autosomes on the bovine sequence assembly (release Btau 3.1) was used in this study. The average intermarker spacing was 251.8 kb. The average minor allele frequency (MAF) was 0.29 (0.05-0.5). Following recent precedents in human HapMap studies, a haplotype block was defined where 95% of combinations of SNPs within a region are in very high linkage disequilibrium. A total of 727 haplotype blocks consisting of > or =3 SNPs were identified. The average block length was 69.7 +/- 7.7 kb, which is approximately 5-10 times larger than in humans. These blocks comprised a total of 2964 SNPs and covered 50,638 kb of the sequence map, which constitutes 2.18% of the length of all autosomes. A set of tag SNPs, which will be useful for further fine-mapping studies, has been identified. Overall, the results suggest that as many as 75,000-100,000 tag SNPs would be needed to track all important haplotype blocks in the bovine genome. This would require approximately 250,000 SNPs in the discovery phase.

An algorithm for sampling descent graphs in large complex pedigrees efficiently.

No exact method for determining genotypic and identity-by-descent probabilities is available for large complex pedigrees. Approximate methods for such pedigrees cannot be guaranteed to be unbiased. A new method is proposed that uses the Metropolis-Hastings algorithm to sample a Markov chain of descent graphs which fit the pedigree and known genotypes. Unknown genotypes are determined from each descent graph. Genotypic probabilities are estimated as their means. The algorithm is shown to be unbiased for small complex pedigrees and feasible and consistent for moderately large complex pedigrees.