Technical note: Genetic principal component models for multitrait single-step genomic evaluation.

A reparameterization of the multivariate linear mixed model in genetic evaluation to principal components is described. This yields an equivalent model with a sparser coefficient matrix in the mixed model equations and, thus, reduced computational requirements to solve them. It is especially advantageous for analyses incorporating genomic relationship information with many nonzero elements in the inverse of the relationship matrix. Moreover, the framework lends itself directly to dimension reduction and, thus, further computational savings by omitting genetic principal components with negligible eigenvalues. The potential impact on computational demands is illustrated for an application to single-step genomic evaluation of Australian sheep.

Managing the rate of increase in average co-ancestry in a rolling front tree breeding strategy.

In breeding forest trees, as for livestock, the goal is to capture as much genetic gain as possible for the breeding objective, while limiting long- and short-term inbreeding. The Southern Tree Breeding Association (STBA) is responsible for breeding Australia's two main commercial forest tree species and has adopted algorithms and methods commonly used in animal breeding to achieve this balance. Discrete generation breeding is the norm for most tree breeding programmes. However, the STBA uses an overlapping generation strategy, with a new stream of breeding initiated each year. A feature of the species bred by the STBA (Pinus radiata and Eucalyptus globulus) is the long interval (up to 7 years) between when an individual is mated and when its progeny is first assessed in field trials and performance data included in the national performance database. Mate selection methods must therefore recognize the large pool of unmeasured progeny generated over recent years of crossing. In addition, the substantial delay between when an individual is selected in a field trial and when it is clonally copied into a mating facility (breeding arboretum) means that selection and mating must occur as a two-step process. In this article, we describe modifications to preselection and mate selection algorithms that allow unmeasured progeny (juveniles) to be recognized. We also demonstrate that the addition of hypothetical new progeny to the juvenile pool is important for computing the increase in average co-ancestry in the population. Methods outlined in this article may have relevance to animal breeding programmes where between mating and progeny measurement, new rounds of mating are initiated.

Estimation of accuracies and expected genetic change from selection for selection indexes that use multiple-trait predictions of breeding values.

Procedures are described for estimating selection index accuracies for individual animals and expected genetic change from selection for the general case where indexes of EBVs predict an aggregate breeding objective of traits that may or may not have been measured. Index accuracies for the breeding objective are shown to take an important general form, being able to be expressed as the product of the accuracy of the index function of true breeding values and the accuracy with which that function predicts the breeding objective. When the accuracies of the individual EBVs of the index are known, prediction error variances (PEVs) and covariances (PECs) for the EBVs within animal are able to be well approximated, and index accuracies and expected genetic change from selection estimated with high accuracy. The procedures are suited to routine use in estimating index accuracies in genetic evaluation, and for providing important information, without additional modelling, on the directions in which a population will move under selection.

Genomic evaluations using similarity between haplotypes.

Long-range phasing and haplotype library imputation methodologies are accurate and efficient methods to provide haplotype information that could be used in prediction of breeding value or phenotype. Modelling long haplotypes as independent effects in genomic prediction would be inefficient due to the many effects that need to be estimated and phasing errors, even if relatively low in frequency, exacerbate this problem. One approach to overcome this is to use similarity between haplotypes to model covariance of genomic effects by region or of animal breeding values. We developed a simple method to do this and tested impact on genomic prediction by simulation. Results show that the diagonal and off-diagonal elements of a genomic relationship matrix constructed using the haplotype similarity method had higher correlations with the true relationship between pairs of individuals than genomic relationship matrices built using unphased genotypes or assumed unrelated haplotypes. However, the prediction accuracy of such haplotype-based prediction methods was not higher than those based on unphased genotype information.

Accuracy of prediction of genomic breeding values for residual feed intake and carcass and meat quality traits in Bos taurus, Bos indicus, and composite beef cattle.

The aim of this study was to assess the accuracy of genomic predictions for 19 traits including feed efficiency, growth, and carcass and meat quality traits in beef cattle. The 10,181 cattle in our study had real or imputed genotypes for 729,068 SNP although not all cattle were measured for all traits. Animals included Bos taurus, Brahman, composite, and crossbred animals. Genomic EBV (GEBV) were calculated using 2 methods of genomic prediction [BayesR and genomic BLUP (GBLUP)] either using a common training dataset for all breeds or using a training dataset comprising only animals of the same breed. Accuracies of GEBV were assessed using 5-fold cross-validation. The accuracy of genomic prediction varied by trait and by method. Traits with a large number of recorded and genotyped animals and with high heritability gave the greatest accuracy of GEBV. Using GBLUP, the average accuracy was 0.27 across traits and breeds, but the accuracies between breeds and between traits varied widely. When the training population was restricted to animals from the same breed as the validation population, GBLUP accuracies declined by an average of 0.04. The greatest decline in accuracy was found for the 4 composite breeds. The BayesR accuracies were greater by an average of 0.03 than GBLUP accuracies, particularly for traits with known genes of moderate to large effect mutations segregating. The accuracies of 0.43 to 0.48 for IGF-I traits were among the greatest in the study. Although accuracies are low compared with those observed in dairy cattle, genomic selection would still be beneficial for traits that are hard to improve by conventional selection, such as tenderness and residual feed intake. BayesR identified many of the same quantitative trait loci as a genomewide association study but appeared to map them more precisely. All traits appear to be highly polygenic with thousands of SNP independently associated with each trait.

Technical note: updating the inverse of the genomic relationship matrix.

A computing strategy to update the inverse of the genomic relationship matrix when new genotypes become available is described. It is shown that re-using results of previous computations can result in substantial reductions in computing time required. For instance, when the number of individuals increased by about 1% for matrices larger than 15,000, the time required for updating was less than 7% of that used for direct inversion from scratch.

Analysing quantitative parent-of-origin effects with examples from ultrasonic measures of body composition In Australian beef cattle.

Parent-of-origin effects arise when an individual's genes are modified during gametogenesis. Commonly known as imprinting, affected genes may be completely, or partially, suppressed. Individual loci in mice, human and sheep are known to be imprinted, and the quantitative effects of imprinted loci have been found for many carcass traits in cattle and pigs. Differentiating between five types of loci - direct additive loci and partially and completely imprinted loci by sires and dams - is not possible as their effects are confounded such that only three of seven parameters can be estimated. An analysis of Australian Hereford and Angus heifers and bulls for four ultrasonic measures of body composition - eye muscle area, rib fat, rump fat and intramuscular fat per cent - found parent-of-origin effects for both parents in most trait-gender data sets and that they were an average of 28% of the total genetic variance. No parent-of-origin effects were found for Hereford bull intramuscular fat per cent and the maternal parent-of-origin effects were not significant for Angus Heifer eye muscle area.

Genetic variants affecting meat and milk production traits appear to have effects on reproduction traits in cattle.

Polymorphisms located in the genes ABCG2, DGAT1, LEP, PRLR, RORC, CAPN1 and CAST previously have been associated with milk or meat production traits. In this study, these polymorphisms were examined for significant effects on reproductive traits [age at puberty (AGECL), post-partum anoestrus interval (PPAI) and the ability ovulate prior to weaning (PW)] and on a panel of correlated traits such as weight, growth and serum concentration of insulin-like growth factor I. The effects of the polymorphisms were examined in two samples of tropically adapted beef cattle: Brahman (N = 932) and Tropical Composites (N = 1097). A polymorphism in the gene DGAT1 was associated with age at puberty in the combined sample (P = 0.042), and two polymorphisms in CAPN1 were associated with PPAI (P = 0.033) and with the ability ovulate PW (P = 0.017). The favourable allele for reproductive traits was not always the favourable allele associated with production traits. The effects of these polymorphisms on reproductive traits were small compared to their effects on the traits for which they were originally discovered.

Genome-wide association studies of female reproduction in tropically adapted beef cattle.

The genetics of reproduction is poorly understood because the heritabilities of traits currently recorded are low. To elucidate the genetics underlying reproduction in beef cattle, we performed a genome-wide association study using the bovine SNP50 chip in 2 tropically adapted beef cattle breeds, Brahman and Tropical Composite. Here we present the results for 3 female reproduction traits: 1) age at puberty, defined as age in days at first observed corpus luteum (CL) after frequent ovarian ultrasound scans (AGECL); 2) the postpartum anestrous interval, measured as the number of days from calving to first ovulation postpartum (first rebreeding interval, PPAI); and 3) the occurrence of the first postpartum ovulation before weaning in the first rebreeding period (PW), defined from PPAI. In addition, correlated traits such as BW, height, serum IGF1 concentration, condition score, and fatness were also examined. In the Brahman and Tropical Composite cattle, 169 [false positive rate (FPR) = 0.262] and 84 (FPR = 0.581) SNP, respectively, were significant (P < 0.001) for AGECL. In Brahman, 41% of these significant markers mapped to a single chromosomal region on BTA14. In Tropical Composites, 16% of these significant markers were located on BTA5. For PPAI, 66 (FPR = 0.67) and 113 (FPR = 0.432) SNP were significant (P < 0.001) in Brahman and Tropical Composite, respectively, whereas for PW, 68 (FPR = 0.64) and 113 (FPR = 0.432) SNP were significant (P < 0.01). In Tropical Composites, the largest concentration of PPAI markers were located on BTA5 [19% (PPAI) and 23% (PW)], and BTA16 [17% (PPAI) and 18% (PW)]. In Brahman cattle, the largest concentration of markers for postpartum anestrus was located on BTA3 (14% for PPAI and PW) and BTA14 (17% PPAI). Very few of the significant markers for female reproduction traits for the Brahman and Tropical Composite breeds were located in the same chromosomal regions. However, fatness and BW traits as well as serum IGF1 concentration were found to be associated with similar genome regions within and between breeds. Clusters of SNP associated with multiple traits were located on BTA14 in Brahman and BTA5 in Tropical Composites.

A single nucleotide polymorphism in suppressor of cytokine signalling-2 is associated with growth and feed conversion efficiency in pigs.

Feed efficiency and growth are the most important traits in pig production, and very few genetic markers have been reported to be associated with feed efficiency. The suppressor of cytokine signalling-2 (encoded by SOCS2) is the main negative regulator of somatic growth, and the knockout of SOCS2 and naturally mutant mice have high-growth phenotypes. Porcine SOCS2 was selected as a primary positional candidate for feed efficiency, because it is located on chromosome 5q, in the vicinity of a Quantitative Trait Locus (QTL) region for food conversion ratio in pigs. Here, we report five single nucleotide polymorphisms identified by sequencing of the promoter region and exon 1. One PCR-RFLP assay was designed for genotyping the polymorphism c.1667A > G (GenBank Accession No AY312266). Association analyses were performed in an Australian mapping resource pedigree population (PRDC-US43) for food conversion ratio, backfat, IGF1 level and growth traits and showed significant effects on average daily gain on test (ADG2) (P < 0.01) and marginal association with food conversion ratio (FCR) (P < 0.08).

Predicting genetic merit for mastitis and fertility in dairy cattle using genome wide selection and high density SNP screens.

Two novel methods for genome wide selection (GWS) were examined for predicting the genetic merit of animals using SNP information alone. A panel of 1,546 dairy bulls with reliable EBVs was genotyped for 15,380 SNPs that spanned the whole bovine genome. Two complexity reduction methods were used, partial least squares (PLS) and regression using a genetic algorithm (GAR), to find optimal solutions of EBVs against SNP information. Extensive internal cross-validation was used tofind the best predictive models followed by external validation (without direct use of the pedigree or SNP location). Both PLS and GAR provided both accurate fit to the training data set for somatic cell count (SCC) (max r = 0.83) and fertility (max r = 0.88) and showed an accuracy of prediction of r = 0.47 for SCC, and r = 0.72 for fertility. This is the first empirical demonstration that genome wide selection can account for a very high proportion of additive genetic variation in fitness traits whilst exploiting only a small percentage of available SNP information, without use of pedigree or QTL mapping. PLS was computationally more efficient than GAR.

Combining the meiosis Gibbs sampler with the random walk approach for linkage and association studies with a general complex pedigree and multimarker loci.

A linkage analysis for finding inheritance states and haplotype configurations is an essential process for linkage and association mapping. The linkage analysis is routinely based upon observed pedigree information and marker genotypes for individuals in the pedigree. It is not feasible for exact methods to use all such information for a large complex pedigree especially when there are many missing genotypic data. Proposed Markov chain Monte Carlo approaches such as a single-site Gibbs sampler or the meiosis Gibbs sampler are able to handle a complex pedigree with sparse genotypic data; however, they often have reducibility problems, causing biased estimates. We present a combined method, applying the random walk approach to the reducible sites in the meiosis sampler. Therefore, one can efficiently obtain reliable estimates such as identity-by-descent coefficients between individuals based on inheritance states or haplotype configurations, and a wider range of data can be used for mapping of quantitative trait loci within a reasonable time.

A sampling algorithm for segregation analysis.

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated.

Estimating genotypes with independently sampled descent graphs.

A method for estimating genotypic and identity-by-descent probabilities in complex pedigrees is described. The method consists of an algorithm for drawing independent genotype samples which are consistent with the pedigree and observed genotype. The probability distribution function for samples obtained using the algorithm can be evaluated up to a normalizing constant, and combined with the likelihood to produce a weight for each sample. Importance sampling is then used to estimate genotypic and identity-by-descent probabilities. On small but complex pedigrees, the genotypic probability estimates are demonstrated to be empirically unbiased. On large complex pedigrees, while the algorithm for obtaining genotype samples is feasible, importance sampling may require an infeasible number of samples to estimate genotypic probabilities with accuracy.

Restricted maximum likelihood analysis of linkage between genetic markers and quantitative trait loci for a granddaughter design.

A REML for the estimation of location and variance of a single quantitative trait locus, together with polygenic and residual variance, is described for the analysis of a granddaughter design. The method is based on a mixed linear model that includes the allelic effects of the quantitative trait locus, which are assumed to be normally distributed. Information from four marker loci situated on a single chromosome was available to derive the covariances at the linked quantitative trait locus. A derivative-free algorithm is described that makes use of the specific structure of the granddaughter design. The procedure has been applied to simulated data for a granddaughter design with 50 grandsire families of 40 sires each. Error variance was 60, and total additive genetic variance equaled 40; the quantitative trait locus explained either 10 or 25% of the latter variance. The size of the marker bracket containing the quantitative trait locus was either 10 or 30 cM. The power of detecting the quantitative trait locus ranged from 19 to 99%. Estimates of total genetic variance and variance explained by the quantitative trait locus were found to be empirically unbiased. A small bias was found in location estimates, especially when markers were not fully informative. The accuracy of parameter estimates was greatly improved by the use of information from individual daughters.

Assessing the efficiency of multiplicative mixed model equations to account for heterogeneous variance across herds in carcass scan traits from beef cattle.

Data (n = 2,658) from live animal ultrasonic measures from 17 Angus herds were used to evaluate a multiplicative mixed model that incorporates scaling factors to correct for across-herd heterogeneity of variance. Traits included were ribeye muscle area (EMA), surface fat at the P8 site (P8), surface fat between the 12th and 13th ribs (RIB12), and weight at scanning (WEIGHT). Cattle ranged in age from 501 to 698 d and represented 291 contemporary groups. Data were initially analyzed using single-trait, animal model, Method R procedures to estimate variance components and heritabilities (h2). These estimates were incorporated into a multiplicative mixed model that simultaneously estimates breeding values (EBV) and heterogeneity factors. Re-estimation of h2 after scaling the data with the correction factors was explored to obtain a measure of the improvement in the genetic evaluation and to detect changes in ranking of individuals and herds. Initial h2 estimates for EMA, P8, RIB12, and WEIGHT were .36, .39, .29, and .48, respectively. Scaling factors ranged from .25 for P8 in a herd with eight records to 1.96 for RIB12 in a herd with 86 individuals. Re-estimates of h2 increased by an average of 4.2% for all the traits as a result of correcting for heterogeneity. Deviations of new scaling factors were within expectations. Correlations between EBV with and without heterogeneity correction were greater than .97 for all the traits. However, some substantial re-rankings of herds were observed for some traits in the smaller herds.

Multiple-trait genetic evaluation for one polychotomous trait and several continuous traits with missing data and unequal models.

A method for multiple-trait genetic evaluation for categorical and continuous traits was generalized to a polychotomous rather than a binary trait and to several continuous traits rather than one. Any missing data pattern was allowed. Breeding values were estimated based on an animal model with fixed and random effects differing among traits. Equations in location parameters were solved iteratively within each Fisher scoring step. In each round of scoring, new solutions of the residual covariances among the categorical and the continuous traits were computed based on maximum likelihood estimation and used to reevaluate all partial regression coefficients of liability on the continuous traits for each missing data pattern. Simulation was used to assess the estimation of the residual covariances. The other dispersion parameters were treated as known because their estimation has been treated elsewhere and is analogous to restricted maximum likelihood.

Use of multiple genetic markers in prediction of breeding values.

Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.

Gametic imprinting effects on rate and composition of pig growth.

Genetic improvement schemes in livestock are based on the assumption that the expression of relevant genes is independent of parent of origin. Until now no evidence has been found to reject this assumption. The present study on three purebred pig populations, however, shows that a significant proportion of the phenotypic variance in backfat thickness (5-7%) can be explained by genes subject to paternal imprinting. The implication is that there are genes affecting backfat that are expressed only when derived from the paternal gamete. Paternal imprinted effects explained 1-4% of the phenotypic variation for growth rate. Maternal imprinted effects were heavily confounded with heritable maternal environmental effects. When modelled separately, these effects explained 2-5% and 3-4% of the phenotypic variance in backfat thickness and growth rate, respectively. Gametic imprinting may have consequences for the optimization of breeding programmes, especially in crossbreeding systems with specialized sire and dam lines.