Comparison of BLUPF90IOD3 and MiXBLUP implementations of the single-step model applied to the Polish national dairy cattle evaluation

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This study compared two widely used software implementations, MiXBLUP and BLUPF90IOD3, for the prediction of breeding values using the single-step G-BLUP model based on data from the Polish national evaluation for stature. Four core animal sets were tested, which differed in the selection of bulls and cows. The GEBVs were predicted and validated using different subsets of the population. Both software packages resulted in high correlations (0.89 and 0.97) between full and truncated dataset predictions and similar validation performance, with MiXBLUP exhibiting slightly greater consistency across different sets of core animals. The ranking of the top 50 bulls remained stable across the implementations. This study concludes that both software implementations provide comparable GEBV predictions, suggesting that software choice should consider computational efficiency, cost, and modeling flexibility, with MiXBLUP offering additional options for GEBV estimation. Animal Science Animal Behavior Biostatistics BLUPF90IOD3 GEBV G-BLUP MiXBLUP single-step Figures Figure 1 INTRODUCTION For several years, the single-step approach to predict breeding values has become increasingly popular, and in many countries, work is underway to implement it into the routine evaluation system for dairy cattle. The growing importance of the single-step model is due to the possibility of integrating phenotypic, genomic, and pedigree data, which results in the prediction of breeding values for all individuals under one unified model without the need to conduct two separate evaluations (i.e., a conventional and a genomic).. In national genomic evaluations of dairy cattle, two forms of a single-step model are used – the single-step G-BLUP fitting a random animal additive genetic effect with a relationship matrix defined by the pedigree and/or SNP genotype information (Aguilar et al., 2010; Christensen & Lund, 2010) and the single-step SNP-BLUP fitting both a random animal additive effect defined above and a random SNP effect (Liu et al., 2014). The primary purpose of our study was to compare the breeding values from the G-BLUP model predicted by two software implementations that are most widely used on a national scale, MiXBLUP (Vandenplas et al., 2022) and BLUPF90IOD3 (Aguilar et al., 2018) using the same model parametrization and a dataset. This was done by considering various sets of core animals using data from the Polish national evaluation for stature. MATERIALS AND METHODS Data The analyzed data represent the active population of animals that entered the Polish national genetic evaluation for stature ( \(\:{h}^{2}=0.54)\) from December 2021. It includes 1,098,611 cow phenotypes and 141,397 pseudophenotypes expressed by deregressed proofs (DRP) from the multiple across-country evaluation (MACE) carried out by Interbull. DRPs were adjusted for the phenotypes of bulls’ daughters born in Poland. Most genotyped individuals were genotyped using various versions of the EuroG MDIllumina genotyping microarray, which was custom-designed for the EuroGenomics Cooperative. Individuals genotyped with other commercial platforms were imputed to EuroG MD using the Fimpute software (Sargolzaei et al., 2014). The SNP preselection criteria followed the procedure used in the national genomic evaluation in Poland. The criteria comprised a minor allele frequency of at least 0.01 and a technical quality of genotyping expressed by a minimum call rate of 99%. After editing, 46,118 SNPs remained for further analysis. The genomic data contained 42,134 cow genotypes and 47,108 bull genotypes. Full pedigree information was truncated after the fifth generation using the Relax2 software (Stranden and Vuori, 2006) prune 5 option. It resulted in 1,555,995 individuals and 33 Unknown Parent Groups (UPGs) based on birth year, country of origin, and sex. Prediction of breeding values The prediction of genomically enhanced breeding values (GEBV) was based on the following single-step G-BLUP model: $$\:\varvec{y}=\varvec{X}\varvec{b}+\varvec{W}\varvec{a}+\varvec{e}$$ 1 , where \(\:\varvec{y}\) is the vector of dependent variables represented by cows’ measured phenotypes for stature and bulls' pseudophenotypes expressed by their MACE DRPs (Jairath et al., 1998), \(\:\varvec{b}\) represents a vector of fixed effects including age at calving, lactation phase, and herd corresponding to cows’ phenotypes as well as corresponding phantom codes of the fixed effects for bulls’ DRPs, \(\:\varvec{a}\) represents a vector of breeding values, and \(\:\varvec{e}\) is the vector of residuals. The underlying covariance structure of the random effects is given by \(\:\varvec{a}\sim\varvec{N}\left(0,{\varvec{H}}_{G}{\sigma\:}_{a}^{2}\right)\) and \(\:\varvec{e}\sim\varvec{N}\left(0,\varvec{R}{\sigma\:}_{e}^{2}\right)\) . \(\:{\varvec{H}}_{G}\) is given by \(\:\left[\begin{array}{cc}{\varvec{A}}_{11}&\:{\varvec{A}}_{12}\\\:{\varvec{A}}_{21}&\:{\varvec{A}}_{22}\end{array}\right]+\left[\begin{array}{cc}{\varvec{A}}_{12}{\varvec{A}}_{22}^{-1}\left(\varvec{G}-{\varvec{A}}_{22}\right){\varvec{A}}_{22}^{-1}{\varvec{A}}_{21}&\:{\varvec{A}}_{12}{\varvec{A}}_{22}^{-1}\left(\varvec{G}-{\varvec{A}}_{22}\right)\\\:\left(\varvec{G}-{\varvec{A}}_{22}\right){\varvec{A}}_{22}^{-1}{\varvec{A}}_{21}&\:\varvec{G}-{\varvec{A}}_{22}\end{array}\right]\) (Lourenco et al., 2020), where \(\:{\varvec{A}}_{11}\) , \(\:{\varvec{A}}_{12}/{\varvec{A}}_{21}\) , and \(\:{\varvec{A}}_{22}\) are the components of the numerator relationship matrix constructed based on the pedigree corresponding to non-genotyped animals, the covariance between non-genotyped and genotyped animals, as well as between genotyped animals, respectively, while \(\:\varvec{G}\) represents the genomic relationship matrix between genotyped animals. \(\:\varvec{R}\) is a diagonal matrix containing 1.00 for cows with phenotypes or \(\:{n}_{i}\) for bulls with MACE DRPs, with \(\:{n}_{i}\) representing a difference in effective daughter contributions of i-th bull between the MACE and the national evaluation. \(\:\varvec{X}\) and \(\:\varvec{W}\) denote the corresponding design matrices. For solving the mixed model equations corresponding to model ( 1 ) an inverse of the genomic covariance matrix ( \(\:\varvec{G}\) ) is required. Following (Misztal, 2016) the inverse was approximated as: \(\:{\varvec{G}}^{-1}\approx\:\left[\begin{array}{cc}{\varvec{G}}_{cc}^{-1}&\:0\\\:0&\:0\end{array}\right]+\left[\begin{array}{c}-{\varvec{G}}_{cc}^{-1}{\varvec{G}}_{cn}\\\:\varvec{I}\end{array}\right]{\varvec{M}}_{nn}^{-1}\left[\begin{array}{cc}-{\varvec{G}}_{cn}^{T}{\varvec{G}}_{cc}^{-1}&\:\varvec{I}\end{array}\right]\) , where \(\:{\varvec{G}}_{cc}\) represents the genomic relationship matrix for the subgroup of animals defined as core individuals, \(\:{\varvec{G}}_{cn}\) is the genomic relationship matrix between core and non-core individuals, and \(\:{\varvec{M}}_{nn}\) is a diagonal matrix with nonzero elements corresponding to the variance of the mendelian sampling effect for each non-core individual. Four sets of genotyped animals were used as the core individuals. The All_male set was composed of all bulls with phenotypes, the Male_20K set was composed of 20,000 bulls randomly selected from the active population, the Female_30K set was composed of 30,000 cows randomly selected from the active population, and the Random_20K set was composed of 20,000 individuals (bulls and cows) randomly selected from the active population. The random choice of core animals was performed using a custom-written R script using the sample function. The first three sets were chosen to represent markedly different scenarios that would allow for a better understanding of the impact of the selected core animals for prediction. The random selection resembles the scenario used in practical applications. The computations were performed using two software packages, MiXBLUP and BLUPF90IOD3, which implement the PCG solver with an equivalent convergence criterion (Vandenplas et al., 2021; Masuda, 2019). The corresponding and equivalent stopping criteria were given by 1E-07 for MiXBLUP and 1E-14 for BLUPF90IOD3. The difference between programs was due to because of the differences in software implementation. Validation of predictions The validation of GEBV prediction followed the GEBVtest method (Mäntysaari et al., 2010) adopted by the Interbull organization ( www.interbull.org ) and was based on the following linear regression model: $$\:{\varvec{G}\varvec{E}\varvec{B}\varvec{V}}_{full}=\:{b}_{0}+\:{b}_{1}{\varvec{G}\varvec{E}\varvec{B}\varvec{V}}_{trunc}+\varvec{\epsilon\:}$$ 2 , where \(\:{\varvec{G}\varvec{E}\varvec{B}\varvec{V}}_{full}\) is the vector of GEBV predicted by Eq. ( 1 ) for the complete data set and \(\:{\varvec{G}\varvec{E}\varvec{B}\varvec{V}}_{trunc}\) represents a vector of GEBVs predicted by Eq. ( 1 ) for the validation dataset. Three validation sets were defined: all_validation – composed of all bulls born between 2014 and 2017 with Effected Daughter Contributions (EDC) over 20; daughters_in_PL – a subset of all_validation set composed only of bulls with daughters in Poland; young – comprising genotyped young bulls born after 2017. The validation model ( 2 ) was fitted using the lm function in the R software (R Core Team, 2021). RESULTS The correlation coefficients between the GEBVs predicted by the full and each of the three validation datasets were very similar across software implementations, the core animal, and the validation sets (Table 1 ). They varied between 0.89 for the scenario with Female_30K and Daughters_in_PL set predicted by BLUPF90IOD3 and 0.97 for the scenario with Male_20K and young set, regardless of the software. Considering validation, the estimated regression intercepts \(\:\left({\widehat{\beta\:}}_{0}\right)\) varied not only between software implementations, but also between validation scenarios, and core animal sets. Albeit similarities of intercepts were not expected, as the various subsets of data were not corrected for the genetic base. Moreover, from the validation perspective, the most important quantities are \(\:{\widehat{\beta\:}}_{1}\:\) and \(\:{R}^{2}\) that remained stable across software implementations for each validation scenario (Table 2 -Table 4). Note, that slope estimates obtained for the young dataset were very close to unity, which is due to the fact that young bulls have no daughter information in both, the full as well as in the truncated set. For MiXBLUP, the number of iterations to convergence ranged between 364 for Random_20K , truncated dataset, and 551 for Female_30K , full dataset, and for each scenario, the full dataset required more iterations than the truncated dataset. For most scenarios, the convergence of BLUPF90IOD3 required more iterations than MiXBLUP and was more variable across the datasets. The lowest number of 284 iterations was needed to converge the Random_20K truncated data set, while 707 iterations were required to converge for the full version of this scenario. Surprisingly, the smaller, i.e., truncated, dataset does not always result in faster convergence of the BLUPF90IOD3 solver. A summary of the number of iterations required for each scenario is presented in Table 5 . Further similarities between the programs extend to their high robustness towards different sets of core animals (Fig. 1 ), since among the top 50 ranked bulls, 45 and 44 were also present in the top 50 group defined by the other three scenarios for MiXBLUP and BLUPF90IOD3 implementations, respectively. Within each scenario, there were almost no differences in bull rankings, so the numbers of common bulls were 49 and 48. Table 1 Pearson correlations of GEBVs predicted between the full and the truncated datasets calculated for all. All validation bulls represent bulls with EDC over 20 and born between 2014 and 2017. Validation bulls with daughters in Poland represent bulls with EDC over 20 and born between 2014 and 2017. Genotyped young bulls represent bulls born after 2017. All validation 2,975 bulls Daughters in PL 711 bulls Young 1,737 bulls MiXBLUP BLUPF90IOD3 MiXBLUP BLUPF90IOD3 MiXBLUP BLUPF90IOD3 Male_20K 0.92 ± 0.002 0.92 ± 0.002 0.90 ± 0.005 0.90 ± 0.005 0.97 ± 0.001 0.97 ± 0.001 Random_20K 0.92 ± 0.002 0.92 ± 0.002 0.90 ± 0.005 0.90 ± 0.005 0.96 ± 0.001 0.95 ± 0.002 Female_30K 0.92 ± 0.002 0.92 ± 0.002 0.90 ± 0.005 0.89 ± 0.006 0.95 ± 0.002 0.94 ± 0.002 All_male 0.93 ± 0.002 0.93 ± 0.002 0.90 ± 0.005 0.90 ± 0.005 0.96 ± 0.001 0.96 ± 0.001 Table 2 Validation results of GEBV prediction for bulls born between 2013 and 2017 with EDC > 20. 2,975 validation bulls \(\:{\widehat{\varvec{\beta\:}}}_{0}\) \(\:{\widehat{\varvec{\beta\:}}}_{1}\) R 2 MiXBLUP Male_20K 4.702 0.844 0.851 Random_20K 5.212 0.829 0.849 Female_30K 5.442 0.818 0.846 All_male 4.608 0.856 0.858 BLUPF90IOD3 Male_20K 6.954 0.855 0.851 Random_20K 5.443 0.845 0.850 Female_30K 1.924 0.838 0.831 All_male 16.345 0.867 0.860 \(\:{\widehat{\varvec{\beta\:}}}_{0}\) – intercept \(\:{\widehat{\varvec{\beta\:}}}_{1}\) – slope R 2 – coefficient of determination Table 3 Validation results of GEBV prediction for bulls with daughters in Poland born between 2013 and 2017 with EDC > 20. 711 validation bulls \(\:{\widehat{\varvec{\beta\:}}}_{0}\) \(\:{\widehat{\varvec{\beta\:}}}_{1}\) R 2 MiXBLUP Male_20K 4.677 0.843 0.805 Random_20K 5.175 0.830 0.815 Female_30K 5.205 0.830 0.815 All_male 4.756 0.848 0.808 BLUPF90IOD3 Male_20K 6.861 0.861 0.800 Random_20K 5.378 0.848 0.814 Female_30K 1.615 0.831 0.808 All_male 16.504 0.860 0.808 \(\:{\widehat{\varvec{\beta\:}}}_{0}\) – intercept \(\:{\widehat{\varvec{\beta\:}}}_{1}\) – slope R 2 – coefficient of determination Table 4 Validation results of GEBV prediction for young genotyped bulls born after 2017. 1,737 validation bulls \(\:{\widehat{\varvec{\beta\:}}}_{0}\) \(\:{\widehat{\varvec{\beta\:}}}_{1}\) R 2 MiXBLUP Male_20K 2.356 0.968 0.938 Random_20K 2.273 1.019 0.913 Female_30K 1.877 1.030 0.903 All_male 3.201 0.959 0.930 BLUPF90IOD3 Male_20K 4.828 0.980 0.940 Random_20K 2.656 1.035 0.910 Female_30K 9.839 0.988 0.907 All_male 16.175 0.977 0.931 \(\:{\widehat{\varvec{\beta\:}}}_{0}\) – intercept \(\:{\widehat{\varvec{\beta\:}}}_{1}\) – slope R 2 – coefficient of determination Table 5 The number of iterations performed by each software. Number of iterations MiXBLUP BLUPF90IOD3 Male_20K 438 707 Random_20K 404 435 Female_30K 551 392 All_male 424 459 Male_20K_truncated 426 412 Random_20K_truncated 364 284 Female_30K_truncated 432 531 All_male_truncated 381 549 DISCUSSION This study aimed to compare two software implementations of the G-BLUP model, most commonly used for routine genetic evaluations on a national scale, MiXBLUP and BLUPF90IOD3. Both programs provided very similar performance in terms of the quality of prediction of GEBVs, expressed either by the correlation between GEBVS predicted from truncated and full datasets or by the official criterion applied to national routine evaluations, expressed by the Interbull GEBV validation test. A comparison of different core animal scenarios showed a high compatibility of breeding value estimates. These results are consistent with the APY solver, which assumes that the number of individuals, rather than their detailed composition, is crucial (Misztal et al., 2014; Fragomeni et al., 2015). Studies indicate that the random selection of a large group of core animals provides accuracy comparable to cores created according to more advanced criteria (Misztal et al., 2020), which explains the similar results in our scenarios. Any slight difference between the two software programmes is due to numerical differences in the algorithms rather than substantive errors. Practically, this means that both MiXBLUP and BLUPF90IOD3 can be used interchangeably for routine evaluation, providing reliable results. Finally, our results confirm that, regardless of the choice of software, one obtains reliable predictions of estimated breeding values. Both programs fulfill their role and provide similar results, while the main difference is in the usability and technical aspects rather than in the quality of the results. Regarding the availability of fitting different genetic evaluation models, MiXBLUP, apart from the G-BLUP, also allows for the implementation of the GT-BLUP and the SNP-BLUP solvers, which makes it more flexible in terms of the choice of GEBV estimation procedures. In conclusion, our comparison demonstrated that both G-BLUP implementations are very similar in terms of predicted GEBVs, therefore, the choice of a particular program for routine national genetic evaluation needs to be based on other criteria, such as price, support, computational efficiency, or data modelling flexibility. Declarations COMPETING INTERESTS The author(s) declare none. ACKNOWLEDGEMENTS The computations were carried out on the server of the Center of Genetics of the Polish Federation of Cattle Breeders and Dairy Farmers. 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Genet Selection Evol 53(1). https://doi.org/10.1186/s12711-021-00626-1 Vandenplas J, Veerkamp R, Calus M, Lidauer M, Strandén I, Taskinen M, Schrauf M, Napel JT (2022) 358. MiXBLUP 3.0 – software for large genomic evaluations in animal breeding programs. Proceedings of 12th World Congress on Genetics Applied to Livestock Production, 1498–1501. https://doi.org/10.3920/978-90-8686-940-4_358 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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1","display":"","copyAsset":false,"role":"figure","size":356952,"visible":true,"origin":"","legend":"\u003cp\u003eVenn plot of top the top 50 GEBV bulls for different core animal sets within each software.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8398690/v1/ae7efd8d5b3bf353c8c31c47.jpeg"},{"id":98786026,"identity":"e59b79a5-1ada-4535-b4d1-af74cd4dc3c0","added_by":"auto","created_at":"2025-12-22 12:43:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1115292,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8398690/v1/8bde43c7-8c3f-4bd5-98ca-7baa3e9997b8.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eComparison of BLUPF90IOD3 and MiXBLUP implementations of the single-step model applied to the Polish national dairy cattle evaluation\u003c/p\u003e","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eFor several years, the single-step approach to predict breeding values has become increasingly popular, and in many countries, work is underway to implement it into the routine evaluation system for dairy cattle. The growing importance of the single-step model is due to the possibility of integrating phenotypic, genomic, and pedigree data, which results in the prediction of breeding values for all individuals under one unified model without the need to conduct two separate evaluations (i.e., a conventional and a genomic).. In national genomic evaluations of dairy cattle, two forms of a single-step model are used \u0026ndash; the single-step G-BLUP fitting a random animal additive genetic effect with a relationship matrix defined by the pedigree and/or SNP genotype information (Aguilar et al., 2010; Christensen \u0026amp; Lund, 2010) and the single-step SNP-BLUP fitting both a random animal additive effect defined above and a random SNP effect (Liu et al., 2014).\u003c/p\u003e \u003cp\u003eThe primary purpose of our study was to compare the breeding values from the G-BLUP model predicted by two software implementations that are most widely used on a national scale, MiXBLUP (Vandenplas et al., 2022) and BLUPF90IOD3 (Aguilar et al., 2018) using the same model parametrization and a dataset. This was done by considering various sets of core animals using data from the Polish national evaluation for stature.\u003c/p\u003e"},{"header":"MATERIALS AND METHODS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eData\u003c/h2\u003e \u003cp\u003eThe analyzed data represent the active population of animals that entered the Polish national genetic evaluation for stature (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{h}^{2}=0.54)\\)\u003c/span\u003e\u003c/span\u003e from December 2021. It includes 1,098,611 cow phenotypes and 141,397 pseudophenotypes expressed by deregressed proofs (DRP) from the multiple across-country evaluation (MACE) carried out by Interbull. DRPs were adjusted for the phenotypes of bulls\u0026rsquo; daughters born in Poland. Most genotyped individuals were genotyped using various versions of the EuroG MDIllumina genotyping microarray, which was custom-designed for the EuroGenomics Cooperative. Individuals genotyped with other commercial platforms were imputed to EuroG MD using the Fimpute software (Sargolzaei et al., 2014). The SNP preselection criteria followed the procedure used in the national genomic evaluation in Poland. The criteria comprised a minor allele frequency of at least 0.01 and a technical quality of genotyping expressed by a minimum call rate of 99%. After editing, 46,118 SNPs remained for further analysis. The genomic data contained 42,134 cow genotypes and 47,108 bull genotypes. Full pedigree information was truncated after the fifth generation using the Relax2 software (Stranden and Vuori, 2006) prune 5 option. It resulted in 1,555,995 individuals and 33 Unknown Parent Groups (UPGs) based on birth year, country of origin, and sex.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003ePrediction of breeding values\u003c/h3\u003e\n\u003cp\u003eThe prediction of genomically enhanced breeding values (GEBV) was based on the following single-step G-BLUP model:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\varvec{y}=\\varvec{X}\\varvec{b}+\\varvec{W}\\varvec{a}+\\varvec{e}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{y}\\)\u003c/span\u003e\u003c/span\u003e is the vector of dependent variables represented by cows\u0026rsquo; measured phenotypes for stature and bulls' pseudophenotypes expressed by their MACE DRPs (Jairath et al., 1998), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{b}\\)\u003c/span\u003e\u003c/span\u003e represents a vector of fixed effects including age at calving, lactation phase, and herd corresponding to cows\u0026rsquo; phenotypes as well as corresponding phantom codes of the fixed effects for bulls\u0026rsquo; DRPs, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{a}\\)\u003c/span\u003e\u003c/span\u003e represents a vector of breeding values, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{e}\\)\u003c/span\u003e\u003c/span\u003e is the vector of residuals. The underlying covariance structure of the random effects is given by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{a}\\sim\\varvec{N}\\left(0,{\\varvec{H}}_{G}{\\sigma\\:}_{a}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{e}\\sim\\varvec{N}\\left(0,\\varvec{R}{\\sigma\\:}_{e}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{H}}_{G}\\)\u003c/span\u003e\u003c/span\u003e is given by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left[\\begin{array}{cc}{\\varvec{A}}_{11}\u0026amp;\\:{\\varvec{A}}_{12}\\\\\\:{\\varvec{A}}_{21}\u0026amp;\\:{\\varvec{A}}_{22}\\end{array}\\right]+\\left[\\begin{array}{cc}{\\varvec{A}}_{12}{\\varvec{A}}_{22}^{-1}\\left(\\varvec{G}-{\\varvec{A}}_{22}\\right){\\varvec{A}}_{22}^{-1}{\\varvec{A}}_{21}\u0026amp;\\:{\\varvec{A}}_{12}{\\varvec{A}}_{22}^{-1}\\left(\\varvec{G}-{\\varvec{A}}_{22}\\right)\\\\\\:\\left(\\varvec{G}-{\\varvec{A}}_{22}\\right){\\varvec{A}}_{22}^{-1}{\\varvec{A}}_{21}\u0026amp;\\:\\varvec{G}-{\\varvec{A}}_{22}\\end{array}\\right]\\)\u003c/span\u003e\u003c/span\u003e (Lourenco et al., 2020), where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{A}}_{11}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{A}}_{12}/{\\varvec{A}}_{21}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{A}}_{22}\\)\u003c/span\u003e\u003c/span\u003e are the components of the numerator relationship matrix constructed based on the pedigree corresponding to non-genotyped animals, the covariance between non-genotyped and genotyped animals, as well as between genotyped animals, respectively, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{G}\\)\u003c/span\u003e\u003c/span\u003e represents the genomic relationship matrix between genotyped animals. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{R}\\)\u003c/span\u003e\u003c/span\u003e is a diagonal matrix containing 1.00 for cows with phenotypes or \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{n}_{i}\\)\u003c/span\u003e\u003c/span\u003e for bulls with MACE DRPs, with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{n}_{i}\\)\u003c/span\u003e\u003c/span\u003e representing a difference in effective daughter contributions of i-th bull between the MACE and the national evaluation. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{X}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{W}\\)\u003c/span\u003e\u003c/span\u003e denote the corresponding design matrices. For solving the mixed model equations corresponding to model (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) an inverse of the genomic covariance matrix (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{G}\\)\u003c/span\u003e\u003c/span\u003e) is required. Following (Misztal, 2016) the inverse was approximated as: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}}^{-1}\\approx\\:\\left[\\begin{array}{cc}{\\varvec{G}}_{cc}^{-1}\u0026amp;\\:0\\\\\\:0\u0026amp;\\:0\\end{array}\\right]+\\left[\\begin{array}{c}-{\\varvec{G}}_{cc}^{-1}{\\varvec{G}}_{cn}\\\\\\:\\varvec{I}\\end{array}\\right]{\\varvec{M}}_{nn}^{-1}\\left[\\begin{array}{cc}-{\\varvec{G}}_{cn}^{T}{\\varvec{G}}_{cc}^{-1}\u0026amp;\\:\\varvec{I}\\end{array}\\right]\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}}_{cc}\\)\u003c/span\u003e\u003c/span\u003e represents the genomic relationship matrix for the subgroup of animals defined as \u003cem\u003ecore\u003c/em\u003e individuals, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}}_{cn}\\)\u003c/span\u003e\u003c/span\u003e is the genomic relationship matrix between \u003cem\u003ecore\u003c/em\u003e and \u003cem\u003enon-core\u003c/em\u003e individuals, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{M}}_{nn}\\)\u003c/span\u003e\u003c/span\u003e is a diagonal matrix with nonzero elements corresponding to the variance of the mendelian sampling effect for each \u003cem\u003enon-core\u003c/em\u003e individual. Four sets of genotyped animals were used as the core individuals. The \u003cb\u003eAll_male\u003c/b\u003e set was composed of all bulls with phenotypes, the \u003cb\u003eMale_20K\u003c/b\u003e set was composed of 20,000 bulls randomly selected from the active population, the \u003cb\u003eFemale_30K\u003c/b\u003e set was composed of 30,000 cows randomly selected from the active population, and the \u003cb\u003eRandom_20K\u003c/b\u003e set was composed of 20,000 individuals (bulls and cows) randomly selected from the active population. The random choice of core animals was performed using a custom-written R script using the \u003cem\u003esample\u003c/em\u003e function. The first three sets were chosen to represent markedly different scenarios that would allow for a better understanding of the impact of the selected core animals for prediction. The random selection resembles the scenario used in practical applications.\u003c/p\u003e \u003cp\u003eThe computations were performed using two software packages, MiXBLUP and BLUPF90IOD3, which implement the PCG solver with an equivalent convergence criterion (Vandenplas et al., 2021; Masuda, 2019). The corresponding and equivalent stopping criteria were given by 1E-07 for MiXBLUP and 1E-14 for BLUPF90IOD3. The difference between programs was due to because of the differences in software implementation.\u003c/p\u003e\n\u003ch3\u003eValidation of predictions\u003c/h3\u003e\n\u003cp\u003eThe validation of GEBV prediction followed the GEBVtest method (M\u0026auml;ntysaari et al., 2010) adopted by the Interbull organization (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ewww.interbull.org\u003c/span\u003e\u003cspan address=\"http://www.interbull.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) and was based on the following linear regression model:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{G}\\varvec{E}\\varvec{B}\\varvec{V}}_{full}=\\:{b}_{0}+\\:{b}_{1}{\\varvec{G}\\varvec{E}\\varvec{B}\\varvec{V}}_{trunc}+\\varvec{\\epsilon\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}\\varvec{E}\\varvec{B}\\varvec{V}}_{full}\\)\u003c/span\u003e\u003c/span\u003e is the vector of GEBV predicted by Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) for the complete data set and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}\\varvec{E}\\varvec{B}\\varvec{V}}_{trunc}\\)\u003c/span\u003e\u003c/span\u003e represents a vector of GEBVs predicted by Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) for the validation dataset. Three validation sets were defined: \u003cb\u003eall_validation\u003c/b\u003e \u0026ndash; composed of all bulls born between 2014 and 2017 with Effected Daughter Contributions (EDC) over 20; \u003cb\u003edaughters_in_PL\u003c/b\u003e \u0026ndash; a subset of \u003cb\u003eall_validation\u003c/b\u003e set composed only of bulls with daughters in Poland; \u003cb\u003eyoung\u003c/b\u003e \u0026ndash; comprising genotyped young bulls born after 2017.\u003c/p\u003e \u003cp\u003eThe validation model (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) was fitted using the \u003cem\u003elm\u003c/em\u003e function in the R software (R Core Team, 2021).\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eThe correlation coefficients between the GEBVs predicted by the full and each of the three validation datasets were very similar across software implementations, the core animal, and the validation sets (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). They varied between 0.89 for the scenario with \u003cb\u003eFemale_30K\u003c/b\u003e and \u003cb\u003eDaughters_in_PL\u003c/b\u003e set predicted by BLUPF90IOD3 and 0.97 for the scenario with \u003cb\u003eMale_20K\u003c/b\u003e and \u003cb\u003eyoung\u003c/b\u003e set, regardless of the software. Considering validation, the estimated regression intercepts \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\widehat{\\beta\\:}}_{0}\\right)\\)\u003c/span\u003e\u003c/span\u003e varied not only between software implementations, but also between validation scenarios, and core animal sets. Albeit similarities of intercepts were not expected, as the various subsets of data were not corrected for the genetic base. Moreover, from the validation perspective, the most important quantities are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{1}\\:\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{2}\\)\u003c/span\u003e\u003c/span\u003e that remained stable across software implementations for each validation scenario (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e-Table\u0026nbsp;4). Note, that slope estimates obtained for the \u003cb\u003eyoung\u003c/b\u003e dataset were very close to unity, which is due to the fact that young bulls have no daughter information in both, the full as well as in the truncated set. For MiXBLUP, the number of iterations to convergence ranged between 364 for \u003cb\u003eRandom_20K\u003c/b\u003e, truncated dataset, and 551 for \u003cb\u003eFemale_30K\u003c/b\u003e, full dataset, and for each scenario, the full dataset required more iterations than the truncated dataset. For most scenarios, the convergence of BLUPF90IOD3 required more iterations than MiXBLUP and was more variable across the datasets. The lowest number of 284 iterations was needed to converge the \u003cb\u003eRandom_20K\u003c/b\u003e truncated data set, while 707 iterations were required to converge for the full version of this scenario. Surprisingly, the smaller, i.e., truncated, dataset does not always result in faster convergence of the BLUPF90IOD3 solver. A summary of the number of iterations required for each scenario is presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Further similarities between the programs extend to their high robustness towards different sets of core animals (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), since among the top 50 ranked bulls, 45 and 44 were also present in the top 50 group defined by the other three scenarios for MiXBLUP and BLUPF90IOD3 implementations, respectively. Within each scenario, there were almost no differences in bull rankings, so the numbers of common bulls were 49 and 48.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePearson correlations of GEBVs predicted between the full and the truncated datasets calculated for all. \u003cb\u003eAll validation bulls\u003c/b\u003e represent bulls with EDC over 20 and born between 2014 and 2017. \u003cb\u003eValidation bulls with daughters in Poland\u003c/b\u003e represent bulls with EDC over 20 and born between 2014 and 2017. \u003cb\u003eGenotyped young bulls\u003c/b\u003e represent bulls born after 2017.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eAll validation\u003c/p\u003e \u003cp\u003e2,975 bulls\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eDaughters in PL\u003c/p\u003e \u003cp\u003e711 bulls\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eYoung\u003c/p\u003e \u003cp\u003e1,737 bulls\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eMiXBLUP\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003eMiXBLUP\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003eMiXBLUP\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMale_20K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e0.97\u0026thinsp;\u0026plusmn;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c7\"\u003e \u003cp\u003e0.97\u0026thinsp;\u0026plusmn;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom_20K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e0.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c7\"\u003e \u003cp\u003e0.95\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFemale_30K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e0.95\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c7\"\u003e \u003cp\u003e0.94\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAll_male\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.93\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.93\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e0.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c7\"\u003e \u003cp\u003e0.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValidation results of GEBV prediction for bulls born between 2013 and 2017 with EDC\u0026thinsp;\u0026gt;\u0026thinsp;20.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2,975 validation bulls\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eMiXBLUP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMale_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.702\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.844\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.851\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRandom_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.829\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.849\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFemale_30K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.442\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.818\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.846\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAll_male\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.608\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.856\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.858\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMale_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.954\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.855\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.851\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRandom_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.443\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.845\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.850\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFemale_30K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.924\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.838\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.831\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAll_male\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.867\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.860\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; intercept\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{1}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; slope\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cb\u003eR\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e \u0026ndash; coefficient of determination\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValidation results of GEBV prediction for bulls with daughters in Poland born between 2013 and 2017 with EDC\u0026thinsp;\u0026gt;\u0026thinsp;20.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e711 validation bulls\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eMiXBLUP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMale_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.677\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.805\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRandom_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.815\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFemale_30K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.205\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.815\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAll_male\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.756\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.848\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.808\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMale_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.800\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRandom_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.378\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.848\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.814\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFemale_30K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.615\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.831\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.808\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAll_male\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.504\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.860\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.808\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; intercept\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{1}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; slope\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cb\u003eR\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e \u0026ndash; coefficient of determination\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValidation results of GEBV prediction for young genotyped bulls born after 2017.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1,737 validation bulls\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eMiXBLUP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMale_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.968\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.938\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRandom_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.913\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFemale_30K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.903\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAll_male\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.201\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.959\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.930\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMale_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.828\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.980\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.940\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRandom_20K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.656\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.910\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFemale_30K\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.839\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.988\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.907\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAll_male\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.977\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.931\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; intercept\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\varvec{\\beta\\:}}}_{1}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; slope\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cb\u003eR\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e \u0026ndash; coefficient of determination\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe number of iterations performed by each software.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eNumber of iterations\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eMiXBLUP\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eBLUPF90IOD3\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMale_20K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e438\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e707\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom_20K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e435\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFemale_30K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e551\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e392\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAll_male\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e459\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMale_20K_truncated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e426\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e412\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom_20K_truncated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e284\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFemale_30K_truncated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e432\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e531\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAll_male_truncated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e381\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e549\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThis study aimed to compare two software implementations of the G-BLUP model, most commonly used for routine genetic evaluations on a national scale, MiXBLUP and BLUPF90IOD3. Both programs provided very similar performance in terms of the quality of prediction of GEBVs, expressed either by the correlation between GEBVS predicted from truncated and full datasets or by the official criterion applied to national routine evaluations, expressed by the Interbull GEBV validation test. A comparison of different core animal scenarios showed a high compatibility of breeding value estimates. These results are consistent with the APY solver, which assumes that the number of individuals, rather than their detailed composition, is crucial (Misztal et al., 2014; Fragomeni et al., 2015). Studies indicate that the random selection of a large group of core animals provides accuracy comparable to cores created according to more advanced criteria (Misztal et al., 2020), which explains the similar results in our scenarios. Any slight difference between the two software programmes is due to numerical differences in the algorithms rather than substantive errors. Practically, this means that both MiXBLUP and BLUPF90IOD3 can be used interchangeably for routine evaluation, providing reliable results. Finally, our results confirm that, regardless of the choice of software, one obtains reliable predictions of estimated breeding values. Both programs fulfill their role and provide similar results, while the main difference is in the usability and technical aspects rather than in the quality of the results. Regarding the availability of fitting different genetic evaluation models, MiXBLUP, apart from the G-BLUP, also allows for the implementation of the GT-BLUP and the SNP-BLUP solvers, which makes it more flexible in terms of the choice of GEBV estimation procedures.\u003c/p\u003e \u003cp\u003eIn conclusion, our comparison demonstrated that both G-BLUP implementations are very similar in terms of predicted GEBVs, therefore, the choice of a particular program for routine national genetic evaluation needs to be based on other criteria, such as price, support, computational efficiency, or data modelling flexibility.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCOMPETING INTERESTS\u003c/h2\u003e \u003cp\u003eThe author(s) declare none.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eACKNOWLEDGEMENTS\u003c/h2\u003e \u003cp\u003eThe computations were carried out on the server of the Center of Genetics of the Polish Federation of Cattle Breeders and Dairy Farmers.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAguilar I, Tsuruta S, Masuda Y, Lourenco D, Misztal I (2018) BLUPF90 suite of programs for animal breeding with focus on genomics. \u003cem\u003eProceedings of the 11th World Congress on Genetics Applied to Livestock Production, 751\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAguilar I, Misztal I, Johnson D, Legarra A, Tsuruta S, Lawlor T (2010) Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. 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Proceedings of 12th World Congress on Genetics Applied to Livestock Production, 1498\u0026ndash;1501. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3920/978-90-8686-940-4_358\u003c/span\u003e\u003cspan address=\"10.3920/978-90-8686-940-4_358\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"National Research Institute of Animal Production","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"BLUPF90IOD3, GEBV, G-BLUP, MiXBLUP, single-step","lastPublishedDoi":"10.21203/rs.3.rs-8398690/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8398690/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe integration of phenotypic, genomic, and pedigree data into a single-step model for predicting genomically enhanced estimated breeding values (GEBVs) has become crucial for the accurate genetic evaluation of dairy cattle. This study compared two widely used software implementations, MiXBLUP and BLUPF90IOD3, for the prediction of breeding values using the single-step G-BLUP model based on data from the Polish national evaluation for stature. Four core animal sets were tested, which differed in the selection of bulls and cows. The GEBVs were predicted and validated using different subsets of the population. Both software packages resulted in high correlations (0.89 and 0.97) between full and truncated dataset predictions and similar validation performance, with MiXBLUP exhibiting slightly greater consistency across different sets of core animals. The ranking of the top 50 bulls remained stable across the implementations. This study concludes that both software implementations provide comparable GEBV predictions, suggesting that software choice should consider computational efficiency, cost, and modeling flexibility, with MiXBLUP offering additional options for GEBV estimation.\u003c/p\u003e","manuscriptTitle":"Comparison of BLUPF90IOD3 and MiXBLUP implementations of the single-step model applied to the Polish national dairy cattle evaluation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-22 06:02:06","doi":"10.21203/rs.3.rs-8398690/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f9956067-64b7-402d-a7a7-84b4f2e749dd","owner":[],"postedDate":"December 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":59912631,"name":"Animal Science"},{"id":59912632,"name":"Animal Behavior"},{"id":59912633,"name":"Biostatistics"}],"tags":[],"updatedAt":"2025-12-22T06:02:06+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-22 06:02:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8398690","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8398690","identity":"rs-8398690","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}