Review: Opportunities and challenges for small populations of dairy cattle in the era of genomics

In modern dairy cattle breeding, genomic breeding programs have the potential to increase efficiency and genetic gain. At the same time, the requirements and the availability of genotypes and phenotypes present a challenge. The set-up of a large enough reference population for genomic prediction is problematic for numerically small breeds but also for hard to measure traits. The first part of this study is a review of the current literature on strategies to overcome the lack of reference data. One solution is the use of combined reference populations from different breeds, different countries, or different research populations. Results reveal that the level of relationship between the merged populations is the most important factor. Compiling closely related populations facilitates the accurate estimation of marker effects and thus results in high accuracies of genomic prediction. Consequently, mixed reference populations of the same breed, but from different countries are more promising than combining different breeds, especially if those are more distantly related. The use of female reference information has the potential to enlarge the reference population size. Including females is advisable for small populations and difficult traits, and maybe combined with genotyping females and imputing those that are un-genotyped.The efficient use of imputation for un-genotyped individuals requires a set of genotyped related animals and well-considered selection strategies which animals to choose for genotyping and phenotyping. Small populations have to find ways to derive additional advantages from the cost-intensive establishment of genomic breeding schemes. Possible solutions may be the use of genomic information for inbreeding control, parentage verification, within-herd selection, adjusted mating plans or conservation strategies.The second part of the paper deals with the issue of high-quality phenotypes against the background of new, difficult and hard to measure traits. The use of contracted herds for phenotyping is recommended, as additional traits, when compared to standard traits used in dairy cattle breeding can be measured at set moments in time. This can be undertaken even for the recording of health traits, thus resulting in complete contemporary groups for health traits. Future traits to be recorded and used in genomic breeding programs, at least partly will be traits for which traditional selection based on widespread phenotyping is not possible. Enabling phenotyping of sufficient numbers to enable genomic selection will rely on cooperation between scientists from different disciplines and may require multidisciplinary approaches.     

The value of cows in reference populations for genomic selection of new functional traits

Today, almost all reference populations consist of progeny tested bulls. However, older progeny tested bulls do not have reliable estimated breeding values (EBV) for new traits. Thus, to be able to select for these new traits, it is necessary to build a reference population. We used a deterministic prediction model to test the hypothesis that the value of cows in reference populations depends on the availability of phenotypic records. To test the hypothesis, we investigated different strategies of building a reference population for a new functional trait over a 10-year period. The trait was either recorded on a large scale (30 000 cows per year) or on a small scale (2000 cows per year). For large-scale recording, we compared four scenarios where the reference population consisted of 30 sires; 30 sires and 170 test bulls; 30 sires and 2000 cows; or 30 sires, 2000 cows and 170 test bulls in the first year with measurements of the new functional trait. In addition to varying the make-up of the reference population, we also varied the heritability of the trait (h2 = 0.05 v. 0.15). The results showed that a reference population of test bulls, cows and sires results in the highest accuracy of the direct genomic values (DGV) for a new functional trait, regardless of its heritability. For small-scale recording, we compared two scenarios where the reference population consisted of the 2000 cows with phenotypic records or the 30 sires of these cows in the first year with measurements of the new functional trait. The results showed that a reference population of cows results in the highest accuracy of the DGV whether the heritability is 0.05 or 0.15, because variation is lost when phenotypic data on cows are summarized in EBV of their sires. The main conclusions from this study are: (i) the fewer phenotypic records, the larger effect of including cows in the reference population; (ii) for small-scale recording, the accuracy of the DGV will continue to increase for several years, whereas the increases in the accuracy of the DGV quickly decrease with large-scale recording; (iii) it is possible to achieve accuracies of the DGV that enable selection for new functional traits recorded on a large scale within 3 years from commencement of recording; and (iv) a higher heritability benefits a reference population of cows more than a reference population of bulls.     

Review: How to improve genomic predictions in small dairy cattle populations

This paper reviews strategies and methods to improve accuracies of genomic predictions from the perspective of a numerically small population. Improvements are realized by influencing one or both of the main factors: (1) improve or increase genomic connections to phenotypic records in training data. (2) Models and strategies to focus genomic predictions on markers closer to the causative variants. Combining populations into a joint reference population results in high improvements when combining populations of the same breed and diminishes as the genetic distance between populations increases. For distantly related breeds sophisticated Bayesian variable selection models in combination with denser markers sets or functional subsets of markers is needed. This is expected to be further improved by the efficient use of sequence information. In addition predictions can be improved by the use of phenotypes of genotyped and non-genotyped cows directly. For a small population the optimal approach will combine the above components.     

A simple method for genomic selection of moderately sized dairy cattle populations

An efficient algorithm for genomic selection of moderately sized populations based on single nucleotide polymorphism chip technology is described. A total of 995 Israeli Holstein bulls with genetic evaluations based on daughter records were genotyped for either the BovineSNP50 BeadChip or the BovineSNP50 v2 BeadChip. Milk, fat, protein, somatic cell score, female fertility, milk production persistency and herd-life were analyzed. The 400 markers with the greatest effects on each trait were first selected based on individual analysis of each marker with the genetic evaluations of the bulls as the dependent variable. The effects of all 400 markers were estimated jointly using a 'cow model,' estimated from the data truncated to exclude lactations with freshening dates after September 2006. Genotype probabilities for each locus were computed for all animals with missing genotypes. In Method I, genetic evaluations were computed by analysis of the truncated data set with the sum of the marker effects subtracted from each record. Genomic estimated breeding values for the young bulls with genotypes, but without daughter records, were then computed as their parent averages combined with the sum of each animal's marker effects. Method II genomic breeding values were computed based on regressions of estimated breeding values of bulls with daughter record on their parent averages, sum of marker effects and birth year. Method II correlations of the current breeding values of young bulls without daughter records in the truncated data set were higher than the correlations of the current breeding values with the parent averages for fat and protein production, persistency and herd-life. Bias of evaluations, estimated as a difference between the mean of current breeding values of the young bulls and their genomic evaluations, was reduced for milk production traits, persistency and herd-life. Bias for milk production traits was slightly negative, as opposed to the positive bias of parent averages. Correlations of Method II with the means of daughter records adjusted for fixed effects were higher than parent averages for fat, protein, fertility, persistency and herd-life. Reducing the number of markers included in the analysis from 400 to 300 did not reduce correlations of genomic breeding values for protein with current breeding values, but did slightly reduce correlations with means of daughter records. Method II has the advantages as compared with the method of VanRaden in that genotypes of cows can be readily incorporated into the Method II analysis, and it is more effective for moderately sized populations.     

Integrating genomic selection into dairy cattle breeding programmes: a review

Extensive genetic progress has been achieved in dairy cattle populations on many traits of economic importance because of efficient breeding programmes. Success of these programmes has relied on progeny testing of the best young males to accurately assess their genetic merit and hence their potential for breeding. Over the last few years, the integration of dense genomic information into statistical tools used to make selection decisions, commonly referred to as genomic selection, has enabled gains in predicting accuracy of breeding values for young animals without own performance. The possibility to select animals at an early stage allows defining new breeding strategies aimed at boosting genetic progress while reducing costs. The first objective of this article was to review methods used to model and optimize breeding schemes integrating genomic selection and to discuss their relative advantages and limitations. The second objective was to summarize the main results and perspectives on the use of genomic selection in practical breeding schemes, on the basis of the example of dairy cattle populations. Two main designs of breeding programmes integrating genomic selection were studied in dairy cattle. Genomic selection can be used either for pre-selecting males to be progeny tested or for selecting males to be used as active sires in the population. The first option produces moderate genetic gains without changing the structure of breeding programmes. The second option leads to large genetic gains, up to double those of conventional schemes because of a major reduction in the mean generation interval, but it requires greater changes in breeding programme structure. The literature suggests that genomic selection becomes more attractive when it is coupled with embryo transfer technologies to further increase selection intensity on the dam-to-sire pathway. The use of genomic information also offers new opportunities to improve preservation of genetic variation. However, recent simulation studies have shown that putting constraints on genomic inbreeding rates for defining optimal contributions of breeding animals could significantly reduce achievable genetic gain. Finally, the article summarizes the potential of genomic selection to include new traits in the breeding goal to meet societal demands regarding animal health and environmental efficiency in animal production.     

Genomic selection for feed efficiency in dairy cattle

Feed is a major component of variable costs associated with dairy systems and is therefore an important consideration for breeding objectives. As a result, measures of feed efficiency are becoming popular traits for genetic analyses. Already, several countries account for feed efficiency in their breeding objectives by approximating the amount of energy required for milk production, maintenance, etc. However, variation in actual feed intake is currently not captured in dairy selection objectives, although this could be possible by evaluating traits such as residual feed intake (RFI), defined as the difference between actual and predicted feed (or energy) intake. As feed intake is expensive to accurately measure on large numbers of cows, phenotypes derived from it are obvious candidates for genomic selection provided that: (1) the trait is heritable; (2) the reliability of genomic predictions are acceptable to those using the breeding values; and (3) if breeding values are estimated for heifers, rather than cows then the heifer and cow traits need to be correlated. The accuracy of genomic prediction of dry matter intake (DMI) and RFI has been estimated to be around 0.4 in beef and dairy cattle studies. There are opportunities to increase the accuracy of prediction, for example, pooling data from three research herds (in Australia and Europe) has been shown to increase the accuracy of genomic prediction of DMI from 0.33 within country to 0.35 using a three-country reference population. Before including RFI as a selection objective, genetic correlations with other traits need to be estimated. Weak unfavourable genetic correlations between RFI and fertility have been published. This could be because RFI is mathematically similar to the calculation of energy balance and failure to account for mobilisation of body reserves correctly may result in selection for a trait that is similar to selecting for reduced (or negative) energy balance. So, if RFI is to become a selection objective, then including it in an overall multi-trait selection index where the breeding objective is net profit is sensible, as this would allow genetic correlations with other traits to be properly accounted for. If genetic parameters are accurately estimated then RFI is a logical breeding objective. If there is uncertainty in these, then DMI may be preferable.     

Accuracy of predicting genomic breeding values for carcass merit traits in Angus and Charolais beef cattle

Accuracy of predicting genomic breeding values for carcass merit traits including hot carcass weight, longissimus muscle area (REA), carcass average backfat thickness (AFAT), lean meat yield (LMY) and carcass marbling score (CMAR) was evaluated based on 543 Angus and 400 Charolais steers genotyped on the Illumina BovineSNP50 Beadchip. For the genomic prediction within Angus, the average accuracy was 0.35 with a range from 0.32 (LMY) to 0.37 (CMAR) across different training/validation data‐splitting strategies and statistical methods. The within‐breed genomic prediction for Charolais yielded an average accuracy of 0.36 with a range from 0.24 (REA) to 0.46 (AFAT). The across‐breed prediction had the lowest accuracy, which was on average near zero. When the data from the two breeds were combined to predict the breeding values of either breed, the prediction accuracy averaged 0.35 for Angus with a range from 0.33 (REA) to 0.39 (CMAR) and averaged 0.33 for Charolais with a range from 0.18 (REA) to 0.46 (AFAT). The prediction accuracy was slightly higher on average when the data were split by animal's birth year than when the data were split by sire family. These results demonstrate that the genetic relationship or relatedness of selection candidates with the training population has a great impact on the accuracy of predicting genomic breeding values under the density of the marker panel used in this study.     

Multi-generational imputation of single nucleotide polymorphism marker genotypes and accuracy of genomic selection

Availability of high-density single nucleotide polymorphism (SNP) genotyping platforms provided unprecedented opportunities to enhance breeding programmes in livestock, poultry and plant species, and to better understand the genetic basis of complex traits. Using this genomic information, genomic breeding values (GEBVs), which are more accurate than conventional breeding values. The superiority of genomic selection is possible only when high-density SNP panels are used to track genes and QTLs affecting the trait. Unfortunately, even with the continuous decrease in genotyping costs, only a small fraction of the population has been genotyped with these high-density panels. It is often the case that a larger portion of the population is genotyped with low-density and low-cost SNP panels and then imputed to a higher density. Accuracy of SNP genotype imputation tends to be high when minimum requirements are met. Nevertheless, a certain rate of genotype imputation errors is unavoidable. Thus, it is reasonable to assume that the accuracy of GEBVs will be affected by imputation errors; especially, their cumulative effects over time. To evaluate the impact of multi-generational selection on the accuracy of SNP genotypes imputation and the reliability of resulting GEBVs, a simulation was carried out under varying updating of the reference population, distance between the reference and testing sets, and the approach used for the estimation of GEBVs. Using fixed reference populations, imputation accuracy decayed by about 0.5% per generation. In fact, after 25 generations, the accuracy was only 7% lower than the first generation. When the reference population was updated by either 1% or 5% of the top animals in the previous generations, decay of imputation accuracy was substantially reduced. These results indicate that low-density panels are useful, especially when the generational interval between reference and testing population is small. As the generational interval increases, the imputation accuracies decay, although not at an alarming rate. In absence of updating of the reference population, accuracy of GEBVs decays substantially in one or two generations at the rate of 20% to 25% per generation. When the reference population is updated by 1% or 5% every generation, the decay in accuracy was 8% to 11% after seven generations using true and imputed genotypes. These results indicate that imputed genotypes provide a viable alternative, even after several generations, as long the reference and training populations are appropriately updated to reflect the genetic change in the population.     

Use of field data in pig genomic selection schemes: a simulation study

The aim of this study was to test how genetic gain for a trait not measured on the nucleus animals could be obtained within a genomic selection pig breeding scheme. Stochastic simulation of a pig breeding program including a breeding nucleus, a multiplier to produce and disseminate semen and a production tier where phenotypes were recorded was performed to test (1) the effect of obtaining phenotypic records from offspring of nucleus animals, (2) the effect of genotyping production animals with records for the purpose of including them in a genomic selection reference population or (3) to combine the two approaches. None of the tested strategies affected genetic gain if the trait under investigation had a low economic value of only 10% of the total breeding goal. When the relative economic weight was increased to 30%, a combination of the methods was most effective. Obtaining records from offspring of already genotyped nucleus animals had more impact on genetic gain than to genotype more distant relatives with phenotypes to update the reference population. When records cannot be obtained from offspring of nucleus animals, genotyping of production animals could be considered for traits with high economic importance.     

Integration of genomic information into sport horse breeding programs for optimization of accuracy of selection

Reliable selection criteria are required for young riding horses to increase genetic gain by increasing accuracy of selection and decreasing generation intervals. In this study, selection strategies incorporating genomic breeding values (GEBVs) were evaluated. Relevant stages of selection in sport horse breeding programs were analyzed by applying selection index theory. Results in terms of accuracies of indices (r_TI) and relative selection response indicated that information on single nucleotide polymorphism (SNP) genotypes considerably increases the accuracy of breeding values estimated for young horses without own or progeny performance. In a first scenario, the correlation between the breeding value estimated from the SNP genotype and the true breeding value (= accuracy of GEBV) was fixed to a relatively low value of r_mg = 0.5. For a low heritability trait (h² = 0.15), and an index for a young horse based only on information from both parents, additional genomic information doubles r_TI from 0.27 to 0.54. Including the conventional information source ‘own performance’ into the before mentioned index, additional SNP information increases r_TI by 40%. Thus, particularly with regard to traits of low heritability, genomic information can provide a tool for well-founded selection decisions early in life. In a further approach, different sources of breeding values (e.g. GEBV and estimated breeding values (EBVs) from different countries) were combined into an overall index when altering accuracies of EBVs and correlations between traits. In summary, we showed that genomic selection strategies have the potential to contribute to a substantial reduction in generation intervals in horse breeding programs.     

Invited review: overview of new traits and phenotyping strategies in dairy cattle with a focus on functional traits

For several decades, breeding goals in dairy cattle focussed on increased milk production. However, many functional traits have negative genetic correlations with milk yield, and reductions in genetic merit for health and fitness have been observed. Herd management has been challenged to compensate for these effects and to balance fertility, udder health and metabolic diseases against increased production to maximize profit without compromising welfare. Functional traits, such as direct information on cow health, have also become more important because of growing concern about animal well-being and consumer demands for healthy and natural products. There are major concerns about the impact of drugs used in veterinary medicine on the spread of antibiotic-resistant strains of bacteria that can negatively impact human health. Sustainability and efficiency are also increasingly important because of the growing competition for high-quality, plant-based sources of energy and protein. Disruptions to global environments because of climate change may encourage yet more emphasis on these traits. To be successful, it is vital that there be a balance between the effort required for data recording and subsequent benefits. The motivation of farmers and other stakeholders involved in documentation and recording is essential to ensure good data quality. To keep labour costs reasonable, existing data sources should be used as much as possible. Examples include the use of milk composition data to provide additional information about the metabolic status or energy balance of the animals. Recent advances in the use of mid-infrared spectroscopy to measure milk have shown considerable promise, and may provide cost-effective alternative phenotypes for difficult or expensive-to-measure traits, such as feed efficiency. There are other valuable data sources in countries that have compulsory documentation of veterinary treatments and drug use. Additional sources of data outside of the farm include, for example, slaughter houses (meat composition and quality) and veterinary labs (specific pathogens, viral loads). At the farm level, many data are available from automated and semi-automated milking and management systems. Electronic devices measuring physiological status or activity parameters can be used to predict events such as oestrus, and also behavioural traits. Challenges concerning the predictive biology of indicator traits or standardization need to be solved. To develop effective selection programmes for new traits, the development of large databases is necessary so that high-reliability breeding values can be estimated. For expensive-to-record traits, extensive phenotyping in combination with genotyping of females is a possibility.     

Evaluation of the potential use of a meta-population for genomic selection in autochthonous beef cattle populations

This study investigated the potential application of genomic selection under a multi-breed scheme in the Spanish autochthonous beef cattle populations using a simulation study that replicates the structure of linkage disequilibrium obtained from a sample of 25 triplets of sire/dam/offspring per population and using the BovineHD Beadchip. Purebred and combined reference sets were used for the genomic evaluation and several scenarios of different genetic architecture of the trait were investigated. The single-breed evaluations yielded the highest within-breed accuracies. Across breed accuracies were found low but positive on average confirming the genetic connectedness between the populations. If the same genotyping effort is split in several populations, the accuracies were lower when compared with single-breed evaluation, but showed a small advantage over small-sized purebred reference sets over the accuracies of subsequent generations. Besides, the genetic architecture of the trait did not show any relevant effect on the accuracy with the exception of rare variants, which yielded slightly lower results and higher loss of predictive ability over the generations.     

Imputation of genotypes from low- to high-density genotyping platforms and implications for genomic selection

The objective of this study was to quantify the accuracy achievable from imputing genotypes from a commercially available low-density marker panel (2730 single nucleotide polymorphisms (SNPs) following edits) to a commercially available higher density marker panel (51 602 SNPs following edits) in Holstein-Friesian cattle using Beagle, a freely available software package. A population of 764 Holstein-Friesian animals born since 2006 were used as the test group to quantify the accuracy of imputation, all of which had genotypes for the high-density panel; only SNPs on the low-density panel were retained with the remaining SNPs to be imputed. The reference population for imputation consisted of 4732 animals born before 2006 also with genotypes on the higher density marker panel. The concordance between the actual and imputed genotypes in the test group of animals did not vary across chromosomes and was on average 95%; the concordance between actual and imputed alleles was, on average, 97% across all SNPs. Genomic predictions were undertaken across a range of production and functional traits for the 764 test group animals using either their real or imputed genotypes. Little or no mean difference in the genomic predictions was evident when comparing direct genomic values (DGVs) using real or imputed genotypes. The average correlation between the DGVs estimated using the real or imputed genotypes for the 15 traits included in the Irish total merit index was 0.97 (range of 0.92 to 0.99), indicating good concordance between proofs from real or imputed genotypes. Results show that a commercially available high-density marker panel can be imputed from a commercially available lower density marker panel, which will also have a lower cost, thereby facilitating a reduction in the cost of genomic selection. Increased available numbers of genotyped and phenotyped animals also has implications for increasing the accuracy of genomic prediction in the entire population and thus genetic gain using genomic selection.     

Genotyping strategies for genomic selection in small dairy cattle populations

This study evaluated different female-selective genotyping strategies to increase the predictive accuracy of genomic breeding values (GBVs) in populations that have a limited number of sires with a large number of progeny. A simulated dairy population was utilized to address the aims of the study. The following selection strategies were used: random selection, two-tailed selection by yield deviations, two-tailed selection by breeding value, top yield deviation selection and top breeding value selection. For comparison, two other strategies, genotyping of sires and pedigree indexes from traditional genetic evaluation, were included in the analysis. Two scenarios were simulated, low heritability (h² = 0.10) and medium heritability (h² = 0.30). GBVs were estimated using the Bayesian Lasso. The accuracy of predicted GBVs using the two-tailed strategies was better than the accuracy obtained using other strategies (0.50 and 0.63 for the two-tailed selection by yield deviations strategy and 0.48 and 0.63 for the two-tailed selection by breeding values strategy in low- and medium-heritability scenarios, respectively, using 1000 genotyped cows). When 996 genotyped bulls were used as the training population, the sire’ strategy led to accuracies of 0.48 and 0.55 for low- and medium-heritability traits, respectively. The Random strategies required larger training populations to outperform the accuracies of the pedigree index; however, selecting females from the top of the yield deviations or breeding values of the population did not improve accuracy relative to that of the pedigree index. Bias was found for all genotyping strategies considered, although the Top strategies produced the most biased predictions. Strategies that involve genotyping cows can be implemented in breeding programs that have a limited number of sires with a reliable progeny test. The results of this study showed that females that exhibited upper and lower extreme values within the distribution of yield deviations may be included as training population to increase reliability in small reference populations. The strategies that selected only the females that had high estimated breeding values or yield deviations produced suboptimal results.     

Bayesian methods for estimating GEBVs of threshold traits

Estimation of genomic breeding values is the key step in genomic selection (GS). Manymethods have been proposed for continuous traits, but methods for threshold traits arestill scarce. Here we introduced threshold model to the framework of GS, and specifically,we extended the three Bayesian methods BayesA, BayesB and BayesCπ on the basis ofthreshold model for estimating genomic breeding values of threshold traits, and theextended methods are correspondingly termed BayesTA, BayesTB and BayesTCπ. Computingprocedures of the three BayesT methods using Markov Chain Monte Carlo algorithm werederived. A simulation study was performed to investigate the benefit of the presentedmethods in accuracy with the genomic estimated breeding values (GEBVs) for thresholdtraits. Factors affecting the performance of the three BayesT methods were addressed. Asexpected, the three BayesT methods generally performed better than the correspondingnormal Bayesian methods, in particular when the number of phenotypic categories was small.In the standard scenario (number of categories=2, incidence=30%,number of quantitative trait loci=50, h²=0.3), theaccuracies were improved by 30.4%, 2.4%, and 5.7% points,respectively. In most scenarios, BayesTB and BayesTCπ generated similar accuracies andboth performed better than BayesTA. In conclusion, our work proved that threshold modelfits well for predicting GEBVs of threshold traits, and BayesTCπ is supposed to be themethod of choice for GS of threshold traits.     

家畜基因组选择研究进展

近年来,随着基因芯片技术的发展与育种技术的进步,动植物的基因组选择成为研究热点。在家畜育种中,基因组选择凭借其准确性高、世代间隔短和育种成本低等优势被应用于各种经济动物的种畜选择中。本文详细介绍了基因分型技术和基因组育种值估计方法(最小二乘法、RR-BLUP法、GBLUP法、ssGBLUP法、贝叶斯A法、贝叶斯B法等),并对这些育种方法选用的标记范围、准确性以及计算速度进行了比较,总结了我国和其他国家基因组选择在种畜选择中的应用情况及存在的问题,展望了目前国内外在基因组选择上的最新研究动态及进展,以期为其他育种工作者进一步了解基因组选择提供参考。     

Effect of predictor traits on accuracy of genomic breeding values for feed intake based on a limited cow reference population

The genomic breeding value accuracy of scarcely recorded traits is low because of the limited number of phenotypic observations. One solution to increase the breeding value accuracy is to use predictor traits. This study investigated the impact of recording additional phenotypic observations for predictor traits on reference and evaluated animals on the genomic breeding value accuracy for a scarcely recorded trait. The scarcely recorded trait was dry matter intake (DMI, n = 869) and the predictor traits were fat–protein-corrected milk (FPCM, n = 1520) and live weight (LW, n = 1309). All phenotyped animals were genotyped and originated from research farms in Ireland, the United Kingdom and the Netherlands. Multi-trait REML was used to simultaneously estimate variance components and breeding values for DMI using available predictors. In addition, analyses using only pedigree relationships were performed. Breeding value accuracy was assessed through cross-validation (CV) and prediction error variance (PEV). CV groups (n = 7) were defined by splitting animals across genetic lines and management groups within country. With no additional traits recorded for the evaluated animals, both CV- and PEV-based accuracies for DMI were substantially higher for genomic than for pedigree analyses (CV: max. 0.26 for pedigree and 0.33 for genomic analyses; PEV: max. 0.45 and 0.52, respectively). With additional traits available, the differences between pedigree and genomic accuracies diminished. With additional recording for FPCM, pedigree accuracies increased from 0.26 to 0.47 for CV and from 0.45 to 0.48 for PEV. Genomic accuracies increased from 0.33 to 0.50 for CV and from 0.52 to 0.53 for PEV. With additional recording for LW instead of FPCM, pedigree accuracies increased to 0.54 for CV and to 0.61 for PEV. Genomic accuracies increased to 0.57 for CV and to 0.60 for PEV. With both FPCM and LW available for evaluated animals, accuracy was highest (0.62 for CV and 0.61 for PEV in pedigree, and 0.63 for CV and 0.61 for PEV in genomic analyses). Recording predictor traits for only the reference population did not increase DMI breeding value accuracy. Recording predictor traits for both reference and evaluated animals significantly increased DMI breeding value accuracy and removed the bias observed when only reference animals had records. The benefit of using genomic instead of pedigree relationships was reduced when more predictor traits were used. Using predictor traits may be an inexpensive way to significantly increase the accuracy and remove the bias of (genomic) breeding values of scarcely recorded traits such as feed intake.     

Invited review: efficient computation strategies in genomic selection

The purpose of this study is review and evaluation of computing methods used in genomic selection for animal breeding. Commonly used models include SNP BLUP with extensions (BayesA, etc), genomic BLUP (GBLUP) and single-step GBLUP (ssGBLUP). These models are applied for genomewide association studies (GWAS), genomic prediction and parameter estimation. Solving methods include finite Cholesky decomposition possibly with a sparse implementation, and iterative Gauss–Seidel (GS) or preconditioned conjugate gradient (PCG), the last two methods possibly with iteration on data. Details are provided that can drastically decrease some computations. For SNP BLUP especially with sampling and large number of SNP, the only choice is GS with iteration on data and adjustment of residuals. If only solutions are required, PCG by iteration on data is a clear choice. A genomic relationship matrix (GRM) has limited dimensionality due to small effective population size, resulting in infinite number of generalized inverses of GRM for large genotyped populations. A specific inverse called APY requires only a small fraction of GRM, is sparse and can be computed and stored at a low cost for millions of animals. With APY inverse and PCG iteration, GBLUP and ssGBLUP can be applied to any population. Both tools can be applied to GWAS. When the system of equations is sparse but contains dense blocks, a recently developed package for sparse Cholesky decomposition and sparse inversion called YAMS has greatly improved performance over packages where such blocks were treated as sparse. With YAMS, GREML and possibly single-step GREML can be applied to populations with >50 000 genotyped animals. From a computational perspective, genomic selection is becoming a mature methodology.     

Genomic selection: prediction of accuracy and maximisation of long term response

Genomic selection refers to the use of dense markers covering the whole genome to estimate the breeding value of selection candidates for a quantitative trait. This paper considers prediction of breeding value based on a linear combination of the markers. In this case the best estimate of each marker’s effect is the expectation of the effect conditional on the data. To calculate this requires a prior distribution of marker effects. If the marker effects are normally distributed with constant variance, BLUP can be used to calculate the estimated effects of the markers and hence the estimated breeding value (EBV). In this case the model is equivalent to a conventional animal model in which the relationship matrix among the animals is estimated from the markers instead of the pedigree. The accuracy of the EBV can approach 1.0 but a very large amount of data is required. An alternative model was investigated in which only some markers have non-zero effects and these effects follow a reflected exponential distribution. In this case the expected effect of a marker is a non-linear function of the data such that apparently small effects are regressed back almost to zero and consequently these markers can be deleted from the model. The accuracy in this case is considerably higher than when marker effects are normally distributed. If genomic selection is practiced for several generations the response declines in a manner that can be predicted from the marker allele frequencies. Genomic selection is likely to lead to a more rapid decline in the selection response than phenotypic selection unless new markers are continually added to the prediction of breeding value. A method to find the optimum index to maximise long term selection response is derived. This index varies the weight given to a marker according to its frequency such that markers where the favourable allele has low frequency receive more weight in the index.