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.

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.

Local and global patterns of admixture and population structure in Iranian native cattle.

BACKGROUND: Two separate domestication events gave rise to humped zebu cattle in India and humpless taurine cattle in the Fertile Crescent of the Near and Middle East. Iran covers the Eastern side of the Fertile Crescent and exhibits a variety of native cattle breeds, however, only little is known about the admixture patterns of Iranian cattle and their contribution to the formation of modern cattle breeds. RESULTS: Genome-wide data (700 k chip) of eight Iranian cattle breeds (Sarabi N = 19, Kurdi N = 7, Taleshi N = 7, Mazandarani N = 10, Najdi N = 7, Pars N = 7, Kermani N = 9, and Sistani N = 9) were collected from across Iran. For a local assessment, taurine (Holstein and Jersey) and indicine (Brahman) outgroup samples were used. For the global perspective, 134 world-wide cattle breeds were included. Between breed variation amongst Iranian cattle explained 60 % (p < 0.001) of the total molecular variation and 82.88 % (p < 0.001) when outgroups were included. Several migration edges were observed within the Iranian cattle breeds. The highest indicine proportion was found in Sistani. All Iranian breeds with higher indicine ancestry were more admixed with a complex migration pattern. Nineteen founder populations most accurately explained the admixture of 44 selected representative cattle breeds (standard error 0.4617). Low levels of African ancestry were identified in Iranian cattle breeds (on average 7.5 %); however, the signal did not persist through all analyses. Admixture and migration analyses revealed minimal introgression from Iranian cattle into other taurine cattle (Holstein, Hanwoo, Anatolian breeds). CONCLUSION: The eight Iranian cattle breeds feature a discrete genetic composition which should be considered in conservation programs aimed at preserving unique species and genetic diversity. Despite a complex admixture pattern among Iranian cattle breeds, there was no strong introgression from other world-wide cattle breeds into Iranian cattle and vice versa. Considering Iran's central location of cattle domestication, Iranian cattle might represent a local domestication event that remained contained and did not contribute to the formation of modern breeds, or genetics of the ancestral population that gave rise to modern cattle is too diluted to be linked directly to any current cattle breeds.

Genome-wide association study of body weight in Australian Merino sheep reveals an orthologous region on OAR6 to human and bovine genomic regions affecting height and weight.

BACKGROUND: Body weight (BW) is an important trait for meat production in sheep. Although over the past few years, numerous quantitative trait loci (QTL) have been detected for production traits in cattle, few QTL studies have been reported for sheep, with even fewer on meat production traits. Our objective was to perform a genome-wide association study (GWAS) with the medium-density Illumina Ovine SNP50 BeadChip to identify genomic regions and corresponding haplotypes associated with BW in Australian Merino sheep. METHODS: A total of 1781 Australian Merino sheep were genotyped using the medium-density Illumina Ovine SNP50 BeadChip. Among the 53 862 single nucleotide polymorphisms (SNPs) on this array, 48 640 were used to perform a GWAS using a linear mixed model approach. Genotypes were phased with hsphase; to estimate SNP haplotype effects, linkage disequilibrium blocks were identified in the detected QTL region. RESULTS: Thirty-nine SNPs were associated with BW at a Bonferroni-corrected genome-wide significance threshold of 1 %. One region on sheep (Ovis aries) chromosome 6 (OAR6) between 36.15 and 38.56 Mb, included 13 significant SNPs that were associated with BW; the most significant SNP was OAR6_41936490.1 (P = 2.37 × 10(-16)) at 37.69 Mb with an allele substitution effect of 2.12 kg, which corresponds to 0.248 phenotypic standard deviations for BW. The region that surrounds this association signal on OAR6 contains three genes: leucine aminopeptidase 3 (LAP3), which is involved in the processing of the oxytocin precursor; NCAPG non-SMC condensin I complex, subunit G (NCAPG), which is associated with foetal growth and carcass size in cattle; and ligand dependent nuclear receptor corepressor-like (LCORL), which is associated with height in humans and cattle. CONCLUSIONS: The GWAS analysis detected 39 SNPs associated with BW in sheep and a major QTL region was identified on OAR6. In several other mammalian species, regions that are syntenic with this region have been found to be associated with body size traits, which may reflect that the underlying biological mechanisms share a common ancestry. These findings should facilitate the discovery of causative variants for BW and contribute to marker-assisted selection.

hsphase: an R package for pedigree reconstruction, detection of recombination events, phasing and imputation of half-sib family groups.

BACKGROUND: Identification of recombination events and which chromosomal segments contributed to an individual is useful for a number of applications in genomic analyses including haplotyping, imputation, signatures of selection, and improved estimates of relationship and probability of identity by descent. Genotypic data on half-sib family groups are widely available in livestock genomics. This structure makes it possible to identify recombination events accurately even with only a few individuals and it lends itself well to a range of applications such as parentage assignment and pedigree verification. RESULTS: Here we present hsphase, an R package that exploits the genetic structure found in half-sib livestock data to identify and count recombination events, impute and phase un-genotyped sires and phase its offspring. The package also allows reconstruction of family groups (pedigree inference), identification of pedigree errors and parentage assignment. Additional functions in the package allow identification of genomic mapping errors, imputation of paternal high density genotypes from low density genotypes, evaluation of phasing results either from hsphase or from other phasing programs. Various diagnostic plotting functions permit rapid visual inspection of results and evaluation of datasets. CONCLUSION: The hsphase package provides a suite of functions for analysis and visualization of genomic structures in half-sib family groups implemented in the widely used R programming environment. Low level functions were implemented in C++ and parallelized to improve performance. hsphase was primarily designed for use with high density SNP array data but it is fast enough to run directly on sequence data once they become more widely available. The package is available (GPL 3) from the Comprehensive R Archive Network (CRAN) or from http://www-personal.une.edu.au/~cgondro2/hsphase.htm.

Detection of recombination events, haplotype reconstruction and imputation of sires using half-sib SNP genotypes.

BACKGROUND: Identifying recombination events and the chromosomal segments that constitute a gamete is useful for a number of applications in genomic analyses. In livestock, genotypic data are commonly available for half-sib families. We propose a straightforward but computationally efficient method to use single nucleotide polymorphism marker genotypes on half-sibs to reconstruct the recombination and segregation events that occurred during meiosis in a sire to form the haplotypes observed in its offspring. These meiosis events determine a block structure in paternal haplotypes of the progeny and this can be used to phase the genotypes of individuals in single half-sib families, to impute haplotypes of the sire if they are not genotyped or to impute the paternal strand of the offspring's sequence based on sequence data of the sire. METHODS: The hsphase algorithm exploits information from opposing homozygotes among half-sibs to identify recombination events, and the chromosomal regions from the paternal and maternal strands of the sire (blocks) that were inherited by its progeny. This information is then used to impute the sire's genotype, which, in turn, is used to phase the half-sib family. Accuracy (defined as R2) and performance of this approach were evaluated by using simulated and real datasets. Phasing results for the half-sibs were benchmarked to other commonly used phasing programs - AlphaPhase, BEAGLE and PedPhase 3. RESULTS: Using a simulated dataset with 20 markers per cM, and for a half-sib family size of 4 and 40, the accuracy of block detection, was 0.58 and 0.96, respectively. The accuracy of inferring sire genotypes was 0.75 and 1.00 and the accuracy of phasing was around 0.97, respectively. hsphase was more robust to genotyping errors than PedPhase 3, AlphaPhase and BEAGLE. Computationally, hsphase was much faster than AlphaPhase and BEAGLE. CONCLUSIONS: In half-sib families of size 8 and above, hsphase can accurately detect block structure of paternal haplotypes, impute genotypes of ungenotyped sires and reconstruct haplotypes in progeny. The method is much faster and more accurate than other widely used population-based phasing programs. A program implementing the method is freely available as an R package (hsphase).