- Open Access
Impacts of both reference population size and inclusion of a residual polygenic effect on the accuracy of genomic prediction
© Liu et al; licensee BioMed Central Ltd. 2011
- Received: 6 October 2010
- Accepted: 17 May 2011
- Published: 17 May 2011
The purpose of this work was to study the impact of both the size of genomic reference populations and the inclusion of a residual polygenic effect on dairy cattle genetic evaluations enhanced with genomic information.
Direct genomic values were estimated for German Holstein cattle with a genomic BLUP model including a residual polygenic effect. A total of 17,429 genotyped Holstein bulls were evaluated using the phenotypes of 44 traits. The Interbull genomic validation test was implemented to investigate how the inclusion of a residual polygenic effect impacted genomic estimated breeding values.
As the number of reference bulls increased, both the variance of the estimates of single nucleotide polymorphism effects and the reliability of the direct genomic values of selection candidates increased. Fitting a residual polygenic effect in the model resulted in less biased genome-enhanced breeding values and decreased the correlation between direct genomic values and estimated breeding values of sires in the reference population.
Genetic evaluation of dairy cattle enhanced with genomic information is highly effective in increasing reliability, as well as using large genomic reference populations. We found that fitting a residual polygenic effect reduced the bias in genome-enhanced breeding values, decreased the correlation between direct genomic values and sire's estimated breeding values and made genome-enhanced breeding values more consistent in mean and variance as is the case for pedigree-based estimated breeding values.
- Reference Population
- Milk Yield
- Single Nucleotide Polymorphism Marker
- Genomic Prediction
- Somatic Cell Score
With the availability of the bovine genome sequence and the development of high-density arrays of single nucleotide polymorphism (SNP) markers, the accuracy of genetic predictions has improved compared to conventional breeding value estimations based on phenotypic data and pedigree [1–9]. In order to model genetic variation for quantitative traits, Meuwissen et al.  have proposed a genetic evaluation model that includes a large number of SNP markers simultaneously. This genomic model assumes that, all the loci that affect the trait are in linkage disequilibrium (LD) with at least one SNP marker and thus marker genotypes can be used as predictors for breeding values. A main advantage of the availability of genome-enhanced breeding values (GEBV) in dairy cattle comes from the improved accuracy in pre-selecting animals for breeding. Therefore, more and more countries have been implementing genomic evaluations in dairy cattle breeding. The genomic BLUP model, which has been used to include high-density SNP data in most of the dairy cattle applications [11–17], assumes that all SNP contribute equally to the genetic variance, because field data results support the infinitesimal model [11, 15, 18].
The reliability of genomic predictions strongly depends on the number of genotyped bulls in the reference population that is used to estimate SNP effects [15, 18]. The increase in genomic reliability appears to be approximately linearly correlated with the number of reference bulls . However, little is known on how the size of reference populations impacts the estimation of SNP effects. A German national genomic dataset has been used to study this question. Genomic models [10, 15–17, 19] usually assume that a given SNP marker chip, such as the Illumina Bovine54K (Illumina Inc., San Diego, CA), explains all the genetic variation of a trait, and as a consequence no residual polygenic effect (RPG) is typically fitted in genomic prediction [10, 15–17, 19]. Fitting the RPG effect can account for the fact that SNP markers may not explain all the genetic variance [13, 20, 21]. Including the RPG effect in the genomic model can also render the estimates of SNP effect less biased and more persistent over generations . To investigate the impact of including an RPG effect on genomic prediction, a larger dataset from the EuroGenomics reference population  was used. The objectives of this study were to investigate (1) the impact of the size of a genomic reference population using German reference bulls on the estimation of SNP effects and on direct genomic values (DGV) and (2) the impact of including an RPG effect on the accuracy of genomic prediction using EuroGenomics reference bulls.
German national genomic and phenotypic data
Genomic and phenotypic data§ used for routine genomic evaluation and for the validation study in January 2010 for German Holstein bulls
Year of birth
Data for routine genomic evaluation
Data for genomic validation study
Nb of genotyped animals
Nb of bulls in reference population
Nb of bulls with daughters
Scenarios to study the impact of the residual polygenic effect
To investigate the impact of including an RPG effect on GEBV, another dataset was used, which originated from the EuroGenomics collaboration . This dataset comprised 17,429 genotyped Holstein bulls, representing 21.4 million daughters from the EuroGenomics countries i.e. France, Germany, Nordic countries and The Netherlands . The total number of genotyped animals in the German Holstein population, including domestic candidates, was 26,191. Deregressed Multiple Across Country Evaluation (MACE) EBV from the April 2010 Interbull evaluation were used as dependent variables. In order to apply the Interbull genomic validation test , the genotyped bulls were divided into two groups: 14,494 reference bulls born before September 2003 and 1,377 German national validation bulls born between September 2003 and December 2004. The GEBV and parental average of pedigree-based EBV of the validation bulls were compared to their actual deregressed MACE EBV to evaluate the predictive ability of the genomic model. To investigate the impact of including an RPG effect on genomic predictions, three different percentages of residual polygenic variance to total genetic variance were considered, 5%, 10% and 15%. These three scenarios were compared to a scenario with a very small residual polygenic variance by setting the heritability of the RPG effect to 0.0001 , which was equivalent to 0.02% of the total genetic variance for milk yield. In order to determine the optimal residual polygenic variance for each trait in the German Holstein breed, a genomic validation study was conducted according to the Interbull genomic validation test , in which SNP effects were estimated using genotypic and phenotypic information of older bulls and the resulting GEBV of younger validation bulls were compared to their daughters' actual performance, i.e. deregressed EBV of the validation bulls. Observed regression coefficients of validation bulls' DRP on GEBV were compared to their expected value of 1. The scenario with observed regression coefficients close or equal to the expectation of 1 was chosen as the one with the most optimal residual polygenic variance.
In the literature [25, 26], some concern has been raised that, under the BLUP genomic model, estimated SNP marker effects may model mainly family relationships. Solberg et al.  have suggested fitting an RPG effect to reduce this problem. In order to investigate whether incorporation of an RPG effect into the genomic model would reduce the correlation of animal DGV with EBV of sires in reference population, milk yield was analysed for the scenarios of residual polygenic variance of 0.02%, 5%, 10% and 20%.
A genomic model for German Holstein cattle
Where q i is the DRP of bull i, μ is a general mean, ν i is the RPG effect of bull i, p is the number of fitted SNP, z ij is a genotype indicator (-1 or 1 for the two homozygotes and 0 for the heterozygote) of marker j of bull i, u j is the random regression coefficient for marker j, and e i is the residual effect of bull i. The total additive genetic variance, , was obtained from a conventional pedigree-based analysis, e.g. for milk production traits  and for female fertility traits , and was partitioned into two components: the residual polygenic variance , where w is the proportion of additive genetic variance explained by the RPG effect, and additive genetic variance explained by the p markers . We assumed that all markers contribute equal genetic variance. The proportion of residual polygenic variance w was assumed to vary across traits. The optimal w value was determined by applying the Interbull genomic validation test . Residual variance associated with the deregressed EBV q i was , where is the error variance obtained from the pedigree-based evaluation and φ i is the EDC for bull i. The RPG was fitted in the same way as in conventional genetic evaluations, i.e. using full pedigree and the same grouping procedures of phantom parents .
Since the BLUP SNP model (1) has a large number of parameters, i.e. SNP effects that need to be estimated simultaneously, a Gauss-Seidel iteration with residual updating  was applied to estimate all the effects of model (1). To further improve convergence, the SNP were processed in descending order of heterozygosity.
Genomic validation using German national data
Realised reliabilities§ of genomic EBV of German Holstein bulls using the German national reference population
Somatic cell score
Rear leg set
Body condition score
When the genomic reference population for German Holstein cattle was switched from the German national to the EuroGenomics reference population, the number of reference bulls increased from 5,025 to 17,429. Additionally, the dependent variable DRP was derived from MACE EBV, which included phenotypic information from foreign countries, in contrast to German national EBV. In comparison to the validation results from the German national reference population in Table 2, when the larger EuroGenomics reference population was used the gain in reliability over pedigree-based EBV was 12% greater on average across four of the analyzed traits, protein yield, somatic cell score, udder depth and non-return rate. A significant gain in genomic reliability has also been reported in another genomic validation study using the EuroGenomics reference population .
Effect of the genomic reference population size
Impact of reference population size on the SNP effect estimates for milk yield
Phenotypic data of milk yield from conventional evaluations
Nb of reference bulls
Variance of SNP effect estimates§
Estimate of largest SNP effect$
Correlation of SNP effect estimates between evaluations
Correlations of DGV of milk yield of genotyped German Holstein animals compared to the February 2010 genomic evaluation with 5025 reference bulls
Phenotypic data from conventional evaluation
Nb of reference bulls
Common reference bulls in this run and the February 2010 run
Reference bulls in the February 2010 run but not in this run
Common candidates in this run and the February 2010 run
Candidates with a sire in both reference populations?
Impact of the residual polygenic effect
Impact of assumed variance of the residual polygenic effect on SNP effect estimates for milk yield based on the EuroGenomics reference population
Scenario regarding residual polygenic variance
Variance of SNP effect estimates$
Estimate of the largest SNP effect†
Correlation of SNP effect estimates between scenarios
Impact of the assumed variance of residual polygenic effects on DGV estimates for milk yield of reference bulls in the EuroGenomics reference population
Scenario regarding residual polygenic variance
Correlation of conventional EBV with
Variance of DGV/DGVt divided by variance of EBV
Pearson correlations of deregressed EBV with direct (DGV) or combined genomic value (GEBV) for the validation bulls using the EuroGenomics reference population
Correlation with DGV for scenarios with percent residual polygenic variance
Correlation with GEBV for scenarios with percent residual polygenic variance
Somatic cell score
Body conditional score
Estimates of the coefficient of regression of deregressed EBV on combined genomic value (GEBV) for the validation bulls using the EuroGenomics reference population
Scenarios for percent of residual polygenic variance
Somatic cell score
Body conditional score
Influence of the sires' EBV on direct genomic values
Estimation of SNP effects
Convergence of the BLUP SNP model was improved when the SNP markers were processed in descending order of heterozygosity. The processing order was particularly important when some reference bulls with extremely high or low EBV happened to have extremely high EDC, because those extreme phenotypic values could lead to extreme regression estimates of SNP markers with a low heterozygosity and thus could cause a convergence problem in the estimation of SNP effects. For the currently and most widely used 54 K Illumina BeadChip (Illumina Inc., San Diego, CA), we observed that SNP effects did not converge as well as their sum, i.e. DGV. Due to higher LD, convergence of SNP effects could become even lower for a higher density chip, although the convergence of DGV should remain unchanged. An alternative modelling of marker information from high-density chips should be explored.
The tremendous advances in conventional genetic evaluations during the last decades have formed a solid basis for genomic evaluation and selection in dairy cattle. Genomic validation studies worldwide have demonstrated that the genomic model proposed by Meuwissen et al.  is highly effective to increase the reliability of evaluations in dairy cattle breeding. In this study, we have shown that the size of the genomic reference population is an important factor affecting the reliability of genomic prediction. Fitting a residual polygenic effect in the genomic model is necessary to avoid the variance of DGV being too high, to make the GEBV of candidates less biased, and to reduce the correlation between reference sires' EBV and animals' DGV. The optimal residual polygenic variance appears to differ between traits. Our validation study has clearly shown that genomic evaluation is efficient.
German national organisations FBF and FUGATO (GenoTrack) are thanked for their financial support. The EuroGenomics consortium is kindly acknowledged for providing genomic data. The first author appreciates the helpful discussions with the colleagues of the Interbull Technical Committee and Interbull Genomics Task Force. We appreciate very much the competent review, suggestions and comments by two reviewers and the associate editor which all improved the manuscript considerably.
- Henderson CR: Applications of Linear Models in Animal Breeding. 1984, Guelph: University of Guelph PressGoogle Scholar
- Quaas RL: Computing the diagonal elements of a large numerator relationship matrix. Biometrics. 1976, 32: 949-953. 10.2307/2529279.View ArticleGoogle Scholar
- Schaeffer LR, Kennedy BW: Computing strategies for solving mixed model equations. J Dairy Sci. 1986, 69: 575-579. 10.3168/jds.S0022-0302(86)80441-6.View ArticleGoogle Scholar
- VanRaden PM, Wiggans GR: Derivation, calculation and use of national animal model information. J Dairy Sci. 1991, 74: 2737-2746. 10.3168/jds.S0022-0302(91)78453-1.View ArticlePubMedGoogle Scholar
- Schaeffer LR, Dekkers JCM: Random regression in animal models for test-day production in dairy cattle. Proceedings of the 5th World Congress on Genetics Applied Livestock Production: 7-12 August 1994;Guelph. 1994, 443-446.Google Scholar
- Liu Z, Reinhardt F, Bünger A, Reents R: Derivation and calculation of approximated reliabilities and daughter yield-deviations of a random regression test-day model for genetic evaluation of dairy cattle. J Dairy Sci. 2004, 87: 1896-1907. 10.3168/jds.S0022-0302(04)73348-2.View ArticlePubMedGoogle Scholar
- Liu Z, Jaitner J, Reinhardt F, Pasman E, Rensing S, Reents R: Genetic evaluation of fertility traits of dairy cattle using a multiple-trait animal model. J Dairy Sci. 2008, 91: 4333-4343. 10.3168/jds.2008-1029.View ArticlePubMedGoogle Scholar
- Ducrocq V: An improved model for the French genetic evaluation of dairy bulls on length of productive life of their daughters. Anim Sci. 2005, 80: 249-256.View ArticleGoogle Scholar
- Schaeffer LR: Multiple-country comparison of dairy sires. J Dairy Sci. 1994, 77: 2671-2678. 10.3168/jds.S0022-0302(94)77209-X.View ArticlePubMedGoogle Scholar
- Meuwissen THE, Hayes BJ, Goddard ME: Prediction of total genetic value using genome-wide dense marker maps. Genetics. 2001, 157: 1819-1829.PubMed CentralPubMedGoogle Scholar
- Hayes BJ, Bowman PJ, Chamberlain AJ, Goddard ME: Invited review: Genomic selection in dairy cattle: Progress and challenges. J Dairy Sci. 2009, 92: 433-443. 10.3168/jds.2008-1646.View ArticlePubMedGoogle Scholar
- Loberg A, Dürr JW: Interbull survey on the use of genomic information. Interbull Bull. 2009, 39: 3-13.Google Scholar
- Van Doormaal BJ, Kistemaker GJ, Sullivan PG, Sargolzaei M, Schenkel FS: Canadian implementation of genomic evaluations. Interbull Bull. 2009, 40: 214-218.Google Scholar
- Reinhardt F, Liu Z, Seefried F, Thaller G: Implementation of genomic evaluation in German Holsteins. Interbull Bull. 2009, 40: 219-226.Google Scholar
- VanRaden PM, Van Tassell CP, Wiggans GW, Sonstegard TS, Schnabel RD, Taylor JF, Schenkel F: Invited review: Reliability of genomic predictions for North American Holstein bulls. J Dairy Sci. 2009, 92: 16-24. 10.3168/jds.2008-1514.View ArticlePubMedGoogle Scholar
- VanRaden PM: Efficient methods to compute genomic predictions. J Dairy Sci. 2008, 91: 4414-4423. 10.3168/jds.2007-0980.View ArticlePubMedGoogle Scholar
- Daetwyler HD, Pong-Wong R, Villanueva B, Woolliams JA: The impact of genetic architecture on genome-wide evaluation methods. Genetics. 2010, 185: 1021-1031. 10.1534/genetics.110.116855.PubMed CentralView ArticlePubMedGoogle Scholar
- Lund MS, de Roos APW, de Vries AG, Druet T, Ducrocq V, Fritz S, Guillaume F, Guldbrandtsen B, Liu Z, Reents R, Schrooten C, Seefried FR, Su G: Improving genomic prediction by EuroGenomics collaboration. Proceedings of the 9th World Congress on Genetics Applied Livestock Production: 1-6 August; Leipzig. 2010, 150-Google Scholar
- Strandén I, Garrick DJ: Technical note: Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit. J Dairy Sci. 2009, 92: 2971-2975. 10.3168/jds.2008-1929.View ArticlePubMedGoogle Scholar
- Christensen OF, Lund MS: Genomic prediction when some animals are not genotyped. Genet Sel Evol. 2010, 42: 2-10.1186/1297-9686-42-2.PubMed CentralView ArticlePubMedGoogle Scholar
- Aguilar I, Misztal I, Johnson DL, Legarra A, Tsuruta S, Lawlor TJ: Hot topic: A unified approach to utilise phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. J Dairy Sci. 2010, 93: 734-752.Google Scholar
- Solberg TR, Sonesson AK, Woolliams JA, Ødegard J, Meuwissen THE: Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect. Genet Sel Evol. 2009, 41: 53-10.1186/1297-9686-41-53.PubMed CentralView ArticlePubMedGoogle Scholar
- Ducrocq V, Liu Z: Combining genomic and classical information in national BLUP evaluations. Interbull Bull. 2009, 40: 172-177.Google Scholar
- Mäntysaari E, Liu Z, VanRaden PM: Interbull validation test for genomic evaluations. Interbull Bull. 2010, 41: 10-14.Google Scholar
- Habier D, Fernando RL, Dekkers JCM: The impact of genetic relationship information on genome-assisted breeding values. Genetics. 2007, 177: 2389-2397.PubMed CentralPubMedGoogle Scholar
- Habier D, Tetens J, Seefried FR, Lichtner P, Thaller G: The impact of genetic relationship on genomic breeding values in German Holstein cattle. Genet Sel Evol. 2009, 42: 5-View ArticleGoogle Scholar
- Legarra A, Misztal I: Technical note: Computing strategies in genome-wide selection. J Dairy Sci. 2008, 91: 360-366. 10.3168/jds.2007-0403.View ArticlePubMedGoogle Scholar
- Gianola D, van Kaam BCHM: Reproducing kernel Hilbert spaces regression methods for genomic assisted prediction of quantitative traits. Genetics. 2008, 178: 2289-2303. 10.1534/genetics.107.084285.PubMed CentralView ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.