Genomic evaluation of Brown Swiss dairy cattle with limited national genotype data and integrated external information

This study demonstrated the feasibility of a genomic evaluation for the dairy cattle population for which the small national training population can be complemented with foreign information from international evaluations. National test-day milk yield data records for the Slovenian Brown Swiss cattle population were analyzed. Genomic evaluation was carried out using the single-step genomic best linear unbiased prediction method (ssGBLUP), resulting in genomic estimated breeding values (GEBV). The predominantly female group of genotyped animals, representing the national training population in the single-step genomic evaluation, was further augmented with 7,024 genotypes of foreign progeny-tested sires from an international Brown Swiss InterGenomics genomic evaluation (https://interbull.org/ib/whole_cop). Additionally, the estimated breeding values for the altogether 7,246 genotyped domestic and foreign sires from the 2019 sire multiple across-country evaluation (MACE), were added to the ssGBLUP as external pseudophenotypic information. The ssGBLUP method, with integration of MACE information by avoiding double counting, was then performed, resulting in MACE-enhanced GEBV (GEBVM). The methods were empirically validated with forward prediction. The validation group consisted of 315 domestic males and 1,041 domestic females born after 2012. Increase, inflation, and bias of the GEBV(M) reliability (REL) were assessed for the validation group with a focus on females. All individuals in the validation benefited from genomic evaluations using both methods, but the GEBV(M) REL increased most for the youngest selection candidates. Up to 35 points of GEBV REL could be assigned to national genomic information, and up to 17 points of GEBVM REL could additionally be attributed to the integration of foreign sire genomic and MACE information. Results indicated that the combined foreign progeny-tested sire genomic and external MACE information can be used in the single-step genomic evaluation as an equivalent replacement for domestic phenotypic information. Thus, an equal or slightly higher genomic breeding value REL was obtained sooner than the pedigree-based breeding value REL for the female selection candidates. When the abundant foreign progeny-tested sire genomic and MACE information was used to complement available national genomic and phenotypic information in single-step genomic evaluation, the genomic breeding value REL for young-female selection candidates increased approximately 10 points. Use of international information provides the possibility to upgrade small national training populations and obtain satisfying reliability of genomic breeding values even for the youngest female selection candidates, which will help to increase selection efficiency in the future.</p

Computational strategies for the preconditioned conjugate gradient method applied to ssSNPBLUP, with an application to a multivariate maternal model

Background: The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is one of the single-step evaluations that enable a simultaneous analysis of phenotypic and pedigree information of genotyped and non-genotyped animals with a large number of genotypes. The aim of this study was to develop and illustrate several computational strategies to efficiently solve different ssSNPBLUP systems with a large number of genotypes on current computers. Results: The different developed strategies were based on simplified computations of some terms of the preconditioner, and on splitting the coefficient matrix of the different ssSNPBLUP systems into multiple parts to perform its multiplication by a vector more efficiently. Some matrices were computed explicitly and stored in memory (e.g. the inverse of the pedigree relationship matrix), or were stored using a compressed form (e.g. the Plink 1 binary form for the genotype matrix), to permit the use of efficient parallel procedures while limiting the required amount of memory. The developed strategies were tested on a bivariate genetic evaluation for livability of calves for the Netherlands and the Flemish region in Belgium. There were 29,885,286 animals in the pedigree, 25,184,654 calf records, and 131,189 genotyped animals. The ssSNPBLUP system required around 18 GB Random Access Memory and 12 h to be solved with the most performing implementation. Conclusions: Based on our proposed approaches and results, we showed that ssSNPBLUP provides a feasible approach in terms of memory and time requirements to estimate genomic breeding values using current computers.</p

Genomic prediction using individual-level data and summary statistics from multiple populations

This study presents a method for genomic prediction that uses individual-level data and summary statistics from multiple populations. Genome-wide markers are nowadays widely used to predict complex traits, and genomic prediction using multi-population data are an appealing approach to achieve higher prediction accuracies. However, sharing of individual-level data across populations is not always possible. We present a method that enables integration of summary statistics from separate analyses with the available individual-level data. The data can either consist of individuals with single or multiple (weighted) phenotype records per individual. We developed a method based on a hypothetical joint analysis model and absorption of population-specific information. We show that population-specific information is fully captured by estimated allele substitution effects and the accuracy of those estimates, i.e., the summary statistics. The method gives identical result as the joint analysis of all individual-level data when complete summary statistics are available. We provide a series of easy-to-use approximations that can be used when complete summary statistics are not available or impractical to share. Simulations show that approximations enable integration of different sources of information across a wide range of settings, yielding accurate predictions. The method can be readily extended to multiple-traits. In summary, the developed method enables integration of genome-wide data in the individual-level or summary statistics from multiple populations to obtain more accurate estimates of allele substitution effects and genomic predictions.</p

Impact of Interbeef on national beef cattle evaluations

Submitted 2020-07-02 | Accepted 2020-08-22 | Available 2020-12-01https://doi.org/10.15414/afz.2020.23.mi-fpap.144-155International evaluation models for beef cattle allow to compare animals’ estimated breeding values (EBV) across different countries, thanks to sires having offspring in more than one country. In this study we aimed to provide an up-to-date picture of the Interbeef international beef cattle evaluations from a national perspective, considering both large and small populations. Limousin age-adjusted weaning weight (AWW) phenotypes were available for 3,115,598 animals from 10 European countries, born between 1972 and 2017. EBV and reliabilities were obtained using a multi-trait animal model including maternal effects where AWW from different countries are modelled as different traits. We investigated the country of origin of the sires with internationally publishable EBV and, among them, the country of origin of the top 100 sires for each country scale. All countries had 20 to 28,557 domestic sires whose EBV were publishable, according to Interbeef’s rules, on the scale of other countries. All countries, except one, had domestic sires that ranked among the top 100 sires on other country scales. Across countries, inclusion of information from relatives recorded in other countries increased the reliability of EBV for domestic animals on average by 9.6 percentage points for direct EBV, and 8.3 percentage points for maternal EBV. In conclusion, international evaluations provide small countries access to a panel of elite foreign sires with EBV on their country scale and a more accurate estimation of EBV of domestic animals, while large countries obtain EBV for their sires on the scale of different countries which helps to better promote them.Keywords: international breeding values, genotype-by-environment interaction, Interbeef, reliabilities, weaning weightReferencesBonifazi, R., Vandenplas, J., Napel, J. ten, Matilainen, K., Veerkamp, R. F., & Calus, M. P. L. (2020). Impact of sub-setting the data of the main Limousin beef cattle population on the estimates of across-country genetic correlations. Genetics Selection Evolution, 52(1), 32. https://doi.org/10.1186/s12711-020-00551-9Bouquet, A., Venot, E., Laloë, D., Forabosco, F., Fogh, A., Pabiou, T., Coffey, M., Eriksson, J-A., Renand, G., & Phocas, F. (2009). Genetic Structure of the European Limousin Cattle Metapopulation Using Pedigree Analyses. Interbull Bullettin, 40, 98–103.Durr, J., & Philipsson, J. (2012). International cooperation: The pathway for cattle genomics. Animal Frontiers, 2(1), 16–21. https://doi.org/10.2527/af.2011-0026Fikse, W. F., & Philipsson, J. (2007). Development of international genetic evaluations of dairy cattle for sustainable breeding programs. Animal Genetic Resources, (41), 29–43. https://doi.org/10.1017/S1014233900002315Goddard, M. (1985). A method of comparing sires evaluated in different countries. Livestock Production Science, 13(4), 321–331. https://doi.org/10.1016/0301-6226(85)90024-7Interbeef. (2020). Interbeef Working Group, ICAR. Retrieved August 20, 2020, from https://www.icar.org/index.php/technical-bodies/working-groups/interbeef-working-group/Jorjani, H., Emanuelson, U., & Fikse, W. F. (2005). Data Subsetting Strategies for Estimation of Across-Country Genetic Correlations. Journal of Dairy Science, 88(3), 1214–1224. https://doi.org/10.3168/jds.S0022-0302(05)72788-0Journaux, L., Wickham, B., Venot, E., & Pabiou, T. (2006). Development of Routine International Genetic Evaluation Services for Beef Cattle as an Extension of Interbull ’s Services. Interbull Bulletin, 35(1), 146–152.MiX99 Development Team. (2017). MiX99: A software package for solving large mixed model equations. Release XI/2017.Moore, S. G., & Hasler, J. F. (2017). A 100-Year Review: Reproductive technologies in dairy science. Journal of Dairy Science, 100(12), 10314–10331. https://doi.org/10.3168/jds.2017-13138Mrode, R. A., & Thompson, R. (2005). Linear models for the prediction of animal breeding values: Second Edition. In Linear Models For the Prediction of Animal Breeding Values: Second Edition.Philipsson, J. (2011). Interbull Developments, Global Genetic Trends and Role in the Era of Genomics. Interbull Bulletin, 44, i–xiii.Phocas, F., Donoghue, K., & Graser, H. U. (2005). Investigation of three strategies for an international genetic evaluation of beef cattle weaning weight. Genetics Selection Evolution, 37(4), 361–380. https://doi.org/10.1051/gse:2005006Quintanilla, R., Laloë, D., & Renand, G. (2002a). Heterogeneity of variances across regions for weaning weight in Charolais breed. 7th World Congress on Genetics Applied to Livestock Production, 19–23. Montpellier, France.Quintanilla, R., Laloë, D., & Renand, G. (2002b). Heteroskedasticity and genotype by environment interaction across European countries for weaning weight in Charolais breed. Proceedings of the 33rd Biennial Session of ICAR, 147–150. Interlaken, Switzerland: EAAP publication N. 107, 2003.Renand, G., Laloë, D., Quintanilla, R., & Fouilloux, M. N. (2003). A first attempt of an international genetic evaluation of beef breeds in Europe. Interbull Bulletin, 31, 151–155.Robinson, G. K. (1986). That BLUP Is a Good Thing: The Estimation of Random Effects. Statistical Science, 6(1), 15–51.Schaeffer, L. R. (1994). Multiple-Country Comparison of Dairy Sires. Journal of Dairy Science, 77(9), 2671–2678. https://doi.org/10.3168/jds.S0022-0302(94)77209-XTier, B., & Meyer, K. (2004). Approximating prediction error covariances among additive genetic effects within animals in multiple-trait and random regression models. Journal of Animal Breeding and Genetics, 121(2), 77–89. https://doi.org/10.1111/j.1439-0388.2003.00444.xVenot, E., Fouilloux, M. N., Forabosco, F., Fogh, A., Pabiou, T., Moore, K., Eriksson, J-A., Renand, G., Laloë, D.(2009). Interbeef genetic evaluation of Charolais and Limousine weaning weights. Interbull Bulletin, 40, 61–67.Venot, E., Pabiou, T., Hjerpe, E., Nilforooshan, M. M. A., Launay, A., & Wickham, B. W. W. (2014). Benefits ofInterbeef international genetic evaluations for weaning weight. 10th World Congress of Genetics Applied to Livestock Production.Venot, E, Pabiou, T., Guerrier, J., Cromie, A., Journaux, L., Flynn, J., & Wickham, B. (2007). Interbeef in Practice: Example of a Joint Genetic Evaluation between France, Ireland and United Kingdom for Pure Bred Limousine Weaning Weights. Interbull Bulletin, 36, 41–47.Venot, E, Pabiou, T., Wickham, B., & Journaux, L. (2006). First Steps Towards a European Joint Genetic Evaluation of the Limousine Breed. Interbull Bulletin, 35, 141–145.Venot, Eric, Fouilloux, M. N., Sullivan, P., & Laloë, D. (2008). Level of Connectedness and Reliability in International Beef Evaluation. Interbull Bulletin, 38(June 2008), 3–7.Vishwanath, R. (2003). Artificial insemination: The state of the art. Theriogenology, 59(2), 571–584. https://doi.org/10.1016/S0093-691X(02)01241-4Wickham, B. W., & Durr, J. W. (2011). A new international infrastructure for beef cattle breeding. Animal Frontiers, 1(2), 53–59. https://doi.org/10.2527/af.2011-0019Wilmink, J. B. M., Meijering, A., & Engel, B. (1986). Conversion of breeding values for milk from foreign populations. Livestock Production Science, 14(3), 223–229. https://doi.org/10.1016/0301-6226(86)90081-3

Integration of beef cattle international pedigree and genomic estimated breeding values into national evaluations, with an application to the Italian Limousin population

BackgroundInternational evaluations combine data from different countries allowing breeders to have access to larger panels of elite bulls and to increase the accuracy of estimated breeding values (EBV). However, international and national evaluations can use different sources of information to compute EBV (EBVINT and EBVNAT, respectively), leading to differences between them. Choosing one of these EBV results in losing the information that is contained only in the discarded EBV. Our objectives were to define and validate a procedure to integrate publishable sires' EBVINT and their associated reliabilities computed from pedigree-based or single-step international beef cattle evaluations into national evaluations to obtain "blended" EBV. The Italian (ITA) pedigree-based national evaluation was used as a case study to validate the integration procedure.MethodsPublishable sires' international information, i.e. EBVINT and their associated reliabilities, was included in the national evaluation as pseudo-records. Data were available for 444,199 individual age-adjusted weaning weights of Limousin cattle from eight countries and 17,607 genotypes from four countries (ITA excluded). To mimic differences between international and national evaluations, international evaluations included phenotypes (and genotypes) of animals born prior to January 2019, while national evaluations included ITA phenotypes of animals born until April 2019. International evaluations using all available information were considered as reference scenarios. Publishable sires were divided into three groups: sires with >= 15, < 15 and no recorded offspring in ITA.ResultsOverall, for these three groups, integrating either pedigree-based or single-step international information into national pedigree-based evaluations improved the similarity of the blended EBV with the reference EBV compared to national evaluations without integration. For instance, the correlation with the reference EBV for direct (maternal) EBV went from 0.61 (0.79) for a national evaluation without integration to 0.97 (0.88) when integrating single-step international information, on average across all groups of publishable sires.ConclusionsOur proposed one-animal-at-a-time integration procedure yields blended EBV that are in close agreement with full international EBV for all groups of animals analysed. The procedure can be directly applied by countries since it does not rely on specific software and is computationally inexpensive, allowing straightforward integration of publishable sires' EBVINT from pedigree-based or single-step based international beef cattle evaluations into national evaluations

Accelerated matrix-vector multiplications for matrices involving genotype covariates with applications in genomic prediction

In the last decade, a number of methods have been suggested to deal with large amounts of genetic data in genomic predictions. Yet, steadily growing population sizes and the suboptimal use of computational resources are pushing the practical application of these approaches to their limits. As an extension to the C/CUDA library miraculix, we have developed tailored solutions for the computation of genotype matrix multiplications which is a critical bottleneck in the empirical evaluation of many statistical models. We demonstrate the benefits of our solutions at the example of single-step models which make repeated use of this kind of multiplication. Targeting modern Nvidia® GPUs as well as a broad range of CPU architectures, our implementation significantly reduces the time required for the estimation of breeding values in large population sizes. miraculix is released under the Apache 2.0 license and is freely available at https://github.com/alexfreudenberg/miraculix

Efficient large-scale single-step evaluations and indirect genomic prediction of genotyped selection candidates

Background Single-step genomic best linear unbiased prediction (ssGBLUP) models allow the combination of genomic, pedigree, and phenotypic data into a single model, which is computationally challenging for large genotyped populations. In practice, genotypes of animals without their own phenotype and progeny, so-called genotyped selection candidates, can become available after genomic breeding values have been estimated by ssGBLUP. In some breeding programmes, genomic estimated breeding values (GEBV) for these animals should be known shortly after obtaining genotype information but recomputing GEBV using the full ssGBLUP takes too much time. In this study, first we compare two equivalent formulations of ssGBLUP models, i.e. one that is based on the Woodbury matrix identity applied to the inverse of the genomic relationship matrix, and one that is based on marker equations. Second, we present computationally-fast approaches to indirectly compute GEBV for genotyped selection candidates, without the need to do the full ssGBLUP evaluation. Results The indirect approaches use information from the latest ssGBLUP evaluation and rely on the decomposition of GEBV into its components. The two equivalent ssGBLUP models and indirect approaches were tested on a six-trait calving difficulty model using Irish dairy and beef cattle data that include 2.6 million genotyped animals of which about 500,000 were considered as genotyped selection candidates. When using the same computational approaches, the solving phase of the two equivalent ssGBLUP models showed similar requirements for memory and time per iteration. The computational differences between them were due to the preprocessing phase of the genomic information. Regarding the indirect approaches, compared to GEBV obtained from single-step evaluations including all genotypes, indirect GEBV had correlations higher than 0.99 for all traits while showing little dispersion and level bias. Conclusions In conclusion, ssGBLUP predictions for the genotyped selection candidates were accurately approximated using the presented indirect approaches, which are more memory efficient and computationally fast, compared to solving a full ssGBLUP evaluation. Thus, indirect approaches can be used even on a weekly basis to estimate GEBV for newly genotyped animals, while the full single-step evaluation is done only a few times within a year

Invited review: Reliability computation from the animal model era to the single-step genomic model era

The calculation of exact reliabilities involving the inversion of mixed model equations poses a heavy computational challenge when the system of equations is large. This has prompted the development of different approximation methods. We give an overview of the various methods and computational approaches in calculating reliability from the era before the animal model to the era of single-step genomic models. The different methods are discussed in terms of modeling, development, and applicability in large dairy cattle populations. The paper also describes the problems faced in reliability computation. Many details dispersed throughout the literature are presented in this paper. It is clear that a universal solution applicable to every model and input data may not be possible, but we point out several efficient and accurate algorithms developed recently for a variety of very large genomic evaluations