2023 BioMed Central Ltd unless otherwise stated. 2007. 2015. 1 of van den Berg et al. The accuracy of the estimated effect of one effective segment, accounting for simultaneous fitting of all segments, can be found from selection index theory by including the estimated effects of the other \(M_{e} - 1\) segments as an information source. 2019). (4), so it is not limited to marker information but can be applied for any source of information). First, we ignore the reduction in residual variance that results from fitting all markers simultaneously and from joint analysis of the two populations, in order to mathematically demonstrate the equivalence of the SIT and FI approaches for this case. 2018. 1989;49:21727. Genet Sel Evol. Miyable ex Shirai f. sp. [3], Harris and Johnson [11], and Eq. (2b) and (3b) into Eq. However, the full increase in accuracy from merging the two subpopulations when also accounting for the additional reduction in residual variance follows from Eq. and transmitted securely. The effect of phenotypic data in the predictive ability of GWFP was explored by creating five validation sets using contrasting sets of phenotypic data between training set and validation set (Figure 3A). 2010). Falconer DS, Mackay FC.. While we will never know the exact breeding value, for performance traits it is possible to make good estimates. The https:// ensures that you are connecting to the sharing sensitive information, make sure youre on a federal Plant Breeding. The breeding value includes a genomic component for residual feed intake (RFI) combined with maintenance requirements calculated from either a genomic or pedigree estimated breeding value (EBV) for body weight (BW) predicted using conformation traits. Accounting for the effect of fitting all markers simultaneously in the SIT approach can be accommodated by including the effect of the other \(M_{e} - 1\) segments as an information source in the index, as illustrated in Appendix 10, and gives identical accuracy predictions as accounting for this effect in the FI approach. 2016. Anim Sci. Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. Hence, we draw no conclusions on the superiority of Eq. School of Forest Resources and Conservation, University of Florida, Gainesville, FL 32611, USA, 4 In this study, the GWFP_Fam_Ind approach showed similar accuracy to GEBV for most traits, with the addition of lower needs for phenotypic and genotypic data for the model development. Dekkers JCM. Cite this article. Linear models for the prediction of animal breeding values. The genotype of an animal, however, cannot be influenced by these environmental factors. Dekkers et al. de Almeida Filho et al. Predicted ability was estimated by calculating a Pearsons correlation between the phenotypic values and the estimated breeding values, and prediction accuracy was estimated by calculating a Pearsons correlation between the real breeding value and the estimated breeding value. 2017. Exploitation of data from breeding programs supports rapid implementation of genomic selection for key agronomic traits in perennial ryegrass, Genome-wide regression and prediction with the BGLR statistical package. Voss-Fels KP, Cooper M, Hayes BJ.. 2017. The GEBV requires significant more resources (labor, economic, and computational) to collect and analyze data. 2017; Amadeu et al. These two approaches have resulted in slightly different results when considering the combination of pedigree and genomic information. Because we ignore the reduction in residual variance here, we use \(q^{2} h^{2} /M_{e}\) rather than \(r^{2} h^{2}\) in the denominator, as explained above for Eq. Genetic change due to selection based on EBV will be lower than if selection had been on true breeding value. The same interpretation is suggested by Eq. 2018; Pembleton et al. 2001) as an alternative method to marker-assisted selection. J Anim Sci. Bayesian methods have been proposed to successfully cope with these challenges. Before A total of 4740 polymorphic SNPs (CCLONES_real) and an average of 5000 polymorphic SNPs for CCLONES_sim and CCLONES_sim_prog (average across simulated replicates) were used in the analyses. (3a) and (3b) account for it when we add the FI for the markers (i.e., \(\theta_{M}\)) of the two subpopulations. 2014). Prez-Cabal M, Vazquez AI, Gianola D, Rosa GJ, Weigel KA.. Second, using the FI approach, the FI based on pedigree follows from Eq. Moreover, GWFP_Fam_Fam exhibited similar or greater predictive ability than GWFP for most traits in both populations, except for rust (Figure 4). This result is similar to Eq. While it is not possible to determine an animal's true breeding value, it is possible to estimate it. Performance and environmental influences of anEBV. The site is secure. Association studies using family pools of outcrossing crops based on allele-frequency estimates from DNA sequencing. (4) for \(r^{2}\), giving: Using \(\theta_{G}\)=2.7590 in Eq. However, the minimum number of individuals per family to obtain reasonable accurate estimates of family allele frequency and family phenotypic mean was found to be six. F D, Ashraf BH, Pedersen MG, Janss L, Byrne S, et al. [3]: This result ignores a potential increase in the reliability that would result if combining pedigree and genomic information in a single GP analysis leads to a reduction of the residual variance (proof that this occurs is not straightforward and not given). Springer Nature. TheEstimatedBreedingValueconsiders two elements, the performanceestimateand environmental factors, with the performance estimation affording guidance on parts of the animal that you cannot actually see but which are influenced by genetics. 2007). Ly AMM, Marsman M, Verhagen J, Grasman RP, Wagenmakers EJ. Hallauer AR, Carena MJ, Miranda Filho JB.. Accuracy of genome-enabled prediction in a dairy cattle population using different cross-validation layouts. 2014. (2015) studied the effect of the number of families in the accuracy of genomic prediction for heading date in ryegrass; the authors found high accuracies with a low number of families (<100). 2019) . Animal Breeding and Genomics, Animal Sciences Group, Wageningen University and Research, Wageningen, The Netherlands, Department of Animal Science, Iowa State University, Ames, IA, USA, You can also search for this author in NCI CPTC Antibody Characterization Program. 2007 Dec;124(6):323-30. doi: 10.1111/j.1439-0388.2007.00702.x. For the extreme scenarios (Low and High), the training sets did not have the extreme phenotypic values and alleles frequencies, which could have resulted in poor estimations of markers effects. 2022;2467:45-76. doi: 10.1007/978-1-0716-2205-6_2. The power of genomic estimated breeding values for selection when using a finite population size in genetic improvement of tetraploid potato Catja Selga, Fredrik Reslow, Paulino Prez-Rodrguez, Rodomiro Ortiz G3 Genes|Genomes|Genetics, Volume 12, Issue 1, January 2022, jkab362, https://doi.org/10.1093/g3journal/jkab362 Published: 21 October 2021 PMC Massman JM, Jung HJG, Bernardo R.. Using the genomic relationship matrix to predict the accuracy of genomic selection. Genomic selection for fruit quality traits in apple (Malus domestica Borkh. Disclaimer. J Anim Breed Genet. Average allele frequency deviation (AD) and family mean phenotypic deviation (E and F) in CCLONES_real (real breeding population composed of 63 families) (A, C, and E) and CCLONES_sim (simulated breeding population exhibiting similar genetic properties of CCLONES_real) (B, D, and F) calculated by increasing the number of individuals from 1 to 15. (2a), results in the following residual variance [2, 4, 9]: where, the first term on the left-hand side is the phenotypic variance, the second term is the variance of the true effect of the focal segment, and the third term is the variance of the estimated effects of the remaining \(\left( {M_{e} - 1} \right)\) segments. Genomic Prediction of Complex Traits in an Allogamous Annual Crop: The Case of Maize Single-Cross Hybrids. 2021;53:55. Once the marker effects are estimated, breeding values of young selection candidates can be predicted with reported accuracies up to 0.85. The breakup of LD between markers and QTL across generations advocates frequent re-estimation of marker effects to maintain the accuracy of GEBVs at an acceptable level. Derivations of the accuracy of GEBV make use of the concept of effective chromosomal segments [8]. Both sets of traits from the simulated CCLONES population exhibited very similar accuracies for all schemes (Figure 4). So, n=6 appears adequate to represent genetically a full-sib family, corroborating our results. 2016, 2019). Pioneer studies implementing genomic prediction in plants were performed in major crop species with traditional hybrid selection such as maize (Combs and Bernardo 2013; Massman et al. (2014). In the following, without loss of generality, we assume that \(\sigma_{P}^{2} = 1\), so that additive genetic variance is equal to \(h^{2}\). (3b) with \(\theta_{M}\)=1.5, which yields \(r^{2}\)=0.5114. Funding for this work was received from the authors home institutions and, in the case of JCMD, also from USDA National Institute for Food and Agriculture award number 2017-67015-26299. Hence, analogous to the derivation of the reliability of EBV based on a progeny test, the reliability of the GEBV can be found as the \(R^{2}\) due to a single segment: In the second term of this expression, the numerator represents the contribution of the focal segment to the variance of the mean phenotype of the \(N\) individuals, while the denominator represents the full variance of this mean. Consider a reference population of size \(N\), split into two non-overlapping subpopulations of sizes \(N_{1}\) and \(N_{2}\), with \(N = N_{1} + N_{2}\). The squared accuracy of GEBV can be understood as a proportion of the variance explained. ), de Bem Oliveira et al. The genotypic value of a family is equal to the mean breeding value of the two parents: (Va +Va) = Va (ignoring the dominance and epistasis effects), so the additive variance among full-sib families is only 50% of the total additive variance, whereas the other 50% represents the variance within a family, which leads to higher accuracy and heritability (Casler and Brummer 2008; Ashraf et al. Mathematical Modeling and Software Tools for Breeding Value Estimation Based on Phenotypic, Pedigree and Genomic Information of Holstein Friesian Cattle in Serbia. The index for the combined GEBV is: The off-diagonal element of the variance matrix, \(\frac{{r_{1}^{2} r_{2}^{2} }}{{q^{2} }}\), follows from Fig. Goddard M. Genomic selection: prediction of accuracy and maximisation of long term response. Various methods based on genomic estimated breeding values (GEBVs) for selecting parental lines that maximize the genetic gain as well as methods for improving the predictive performance of genomic selection have been proposed.Unfortunately, it remains . Environmental influences include disease burden, supplementary feeding, grass quality, and the presence of parasites, whichbreederscan influence to control an animals growth, health and general development. To derive the reliability while accounting for the fitting of all segments, we can still use the \(R^{2}\) due to a single segment, but we have to remove the variance that is explained by the estimates of the \(M_{e} - 1\) other segments from the residual variance, which is equal to \(\left( {M_{e} - 1} \right) r^{2} h^{2} /M_{e}\), where \(h^{2} /M_{e}\) is the variance of the true effects of the segments, which is multiplied by \(r^{2}\) because we remove the variance of the estimated effects of those segments. 2017) and ryegrass (Lolium perenne L.; F et al. In other words, \(r^{2}\) is equal to \(R^{2}\). Only the 63 families with more than 5 individuals were used for analyses. The prediction of reliability of the total GEBV based on the FI approach then follows from Eq. Crossa J, Prez-Rodrguez P, Cuevas J, Montesinos-Lpez O, Jarqun D, et al. Edwards SM, Buntjer JB, Jackson R, Bentley AR, Lage J, et al. (2b) into Eq. Full-sibs share the same parents, hence the mean genotypic value of a full-sib family is equal to the mean breeding value of the two parents: (Va +Va) = Va. Data collection was described in detail in Resende et al. The https:// ensures that you are connecting to the Cross-validation includes dividing the available data set into validation and training sets. Equation(3a) can be interpreted as \(r^{2} = q^{2} r_{M}^{2}\), where the term \(\theta_{M} /\left( {\theta_{M} + 1 - r^{2} h^{2} } \right)\) on the right-hand side of Eq. Cross-validation schemes are implemented taking sub-samples from the training set to calibrate the model and then fit the model into the remaining part of the training set to estimate and evaluate its predictive ability, i.e., the correlation between GEBVs and phenotypic values (Prez-Cabal et al. In this study, GWFP was tested by pooling individual trees belonging to the same full-sib family. In those species, the family (full or half-sibs) is the basic unit for phenotyping (e.g., plot-level measurement for yield rather than plant level) and selection. [4] (see also Appendix A in Wientjes et al. Introdutction to quantitative genetics. However, \(\theta_{M}\) defined in Eq. 2017; Cericola et al. Therefore, the additive genetic variance in full-sib families is half of the additive variance between individuals. The number of individuals per family ranged from 1 to 20, with an average of 13 trees per family (standard deviation = 5). Note that \(\theta_{{D_{G} }}\) is smaller than \(\theta_{D}\), because the markers provide less information on \(g_{G}\) than on \(g_{M}\). Genomic prediction integrates statistical, genomic, and computational tools to improve the estimation of breeding values and increase genetic gain. 2009. Prediction of total genetic value using genome-wide dense marker maps. A larger number of families can be included in the models, which, for the present population, would likely result in higher predictive abilities as reported in perennial ryegrass for heading date (F et al. government site. Formally, it is the variance of the score function, which then equals the expected information [10]. Animal. Narrow-sense heritability (h2) estimated at the individual level (Resende et al. Although the full sib families average explores only half of additive genetic variance, the error variance is mitigated with larger number of observations due progeny replication, when compared with single observations (Hallauer et al. Allele frequency deviations (Figure 1, AD) and mean phenotypic deviations (Figure 1, E and F) indicated that families with less than six individuals were not providing accurate estimates of the familys genotypic and phenotypic means in both populations. [3], and (ii) the combination of information from two subpopulations, as in van den Berg et al. Accuracy and predictive ability of GEBV and GWFP were obtained with the prediction models built with the CCLONES_sim (G2) population as the training set, and models were validated in the following generation (G3). (4) can be used to predict either \(r_{M}^{2}\) or \(r^{2} .\) A prediction of \(r_{M}^{2}\) is obtained when using \(\theta_{M}\) defined in Eq. Genomic selection in admixed and crossbred populations. 2015, 2016; Biazzi et al. For phenotypic data, CCLONES_sim showed slightly smaller deviations, especially for a lower number of individuals (Figure 1F), compared with CCLONES_real for the trait diameter (Figure 1E). To make an informed choice and as with selecting anything, like for like comparisons need to be made to ensure that an accurate reflection is obtained and that you select the best animal for your requirements. Aguilar I, Misztal I, Johnson DL, Legarra A, Tsuruta S, Lawlor TJ. Both statistical methods yielded high and similar predictive abilities for the four traits (Figure 2, A and B). 0.6297) in Eq. However, only 63 families, with more than five individuals, were used in this study. The accuracy of genomic predictions strongly depends on characteristics of the reference populations, such as number of animals, number of markers, and the heritability of the recorded phenotype. GEBV, genomic estimated breeding value; GWFP, genome-wide family prediction; CV, cross-validation. In this study, Bayes B and Bayes RR were tested to compare their performance in GWFP because prior distributions and assumptions for both methods are contrasting (Prez and de Los Campos 2014). Second, since genomic information predicts only the component that is captured by markers, \(g_{M}\), rather than the full genetic effect, \(g_{G}\), the reliability of the marker-captured component, say \(r_{M}^{2}\), must be multiplied by a factor \(q^{2}\) to obtain the reliability of the prediction of \(g_{G}\). The remaining seeds from the selected families can be used later to test their merits in further replicated field trials. Esfandyari H, F D, Tessema BB, Janss L, Jensen J.. The GWFP approach can also be extended to breeding schemes where family bulks can serve as training sets, while individuals are the selection target. Next we consider the reliability of GEBV when merging the two subpopulations. ibreeder Livestock Trading Platform Launch, Maidenlands British Blues Review / Testimonial, Its been a busy year at Scawfell Genetics, Profile: Steven OKane On-Farm Collection. Using the estimator of the Ne within a full sib family, given by Ne = [2n/(n+1)] (Resende and Barbosa 2006), the maximum (when n goes to infinite) Ne within a full sib family is 2. 2017; Lara et al. FOIA 2011;128:40921. The authors declare that they have no competing interests. 2019. Both Eqs. Fusiforme (h2 = 0.21, oligogenic trait), and (4) diameter at breast height (Diameter) at year 6 (cm) (h2 = 0.31, polygenic trait). An animal's breeding value can be defined as its genetic merit for each trait. Fitting all markers simultaneously reduces the residual variance and, therefore, increases the reliability (Appendix S1 in [4]). . The EBV based on deviations of genomic relationships from pedigree relationships, in contrast, relates to \(g_{M}\) and \(\theta_{M}\). Accessibility (4), using \(\theta = \theta_{G} = \theta_{A} + \theta_{{D_{G} }}\)=2.7590 and \(r^{2} = 0.6297\). Since the introduction of genomic selection in plant breeding, high genetic gains have been realized in different plant breeding programs. Simulated data available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.3126v. This is evident from comparing Eq. Our results show that the SIT and FI approaches for combining information for GP are equivalent and provide identical accuracies when the underlying assumptions are equivalent. Jia C, Zhao F, Wang X, Han J, Zhao H, et al. 2016). van den Berg I, Meuwissen THE, MacLeod IM, Goddard ME. Comparing an individual animal with the benchmark of a herd or particular breed and expressing the difference, either positively or negatively, gives you an animal's EBV or estimated breeding value, which is then expressed as a + or - from the starting point for an average animal of zero. (9) represents the FI due to genomic relationships deviated from pedigree relationships for estimation of \(g_{G}\), rather than \(g_{M}\). From G1, 42 individuals were selected and used in a circular diallel mating design that reproduced the pedigree as in CCLONES_real (G2), comprised of 923 individuals and 71 full-sib families. PLoS One. [3] derived predictions of the accuracy of genomic EBV (GEBV) by combining pedigree and genomic information using two approaches: a derivation based on selection index theory (SIT) vs. a derivation based on Fisher information (FI). (3a), prior to assuming that \(h^{2}(q^{2}-r^{2})/M_{e}\ll 1\). The prediction models for GEBV and GWFP were validated using 10-fold cross-validation and leave-one-out approaches, for both populations and all traits. Additionally, including more than 10 individuals per family will reduce the sampling variability of the allele frequency and phenotypic mean, resulting in higher genomic accuracies (de Bem Oliveira et al. To assess the effect that the validation set structure has in the predictive ability of the models, both populations were divided in three different phenotypic classes for each trait: the smallest 10%, the largest 10%, and values between both extremes. The impact of genetic relationship information on genomic breeding values in German Holstein cattle. Methods Mol Biol. (3a) represents \(r_{M}^{2}\). In the calculation of EBVs, the performance of individual animals within a . 2001). Wray NR, Hill WG. In a genome-wide family prediction (GWFP) approach, the family is the basic unit of selection. After fitting the model described above for each trait, the GWFP and GEBV of family/individual j (gj) were obtained using the following expression: where Zij is the allele frequency/marker dosage of the ith marker on family/individual j, and p is the total number of markers, andm^i is the estimated effect of ith SNP. Note that this term is like Eq. Other traits in CCLONES_real exhibited a similar behavior (data not shown). 2013) and trees (Kumar et al. For creating true breeding values for the single lines of the breeding and diversity set, we assumed varying frequencies of the positive allele for each locus, which differed between the breeding and the diversity set. 2023 Mar 28;55(1):21. doi: 10.1186/s12711-023-00794-2. These estimates are called Estimated Breeding Values (EBVs). the contents by NLM or the National Institutes of Health. Both approaches are based on the assumption that sampling errors, which are inherent to the pedigree-based and genomic information, are independent of each other. This site needs JavaScript to work properly. In this study, families with less than five individuals were removed, and 63 full-sib families were used for analyses. Thus, in their study family variance was accurately represented with six individuals per family in this autotetraploid species. For breeding programs with limited budgets, the GWFP can be an alternative to GEBV due to the reduction in phenotypic and genotypic costs to develop prediction models. 2017; Jia et al. In order to evaluate these aspects, two loblolly pine (Pinus taeda L.) populations were studied: (1) an observed breeding population composed of 63 families (CCLONES_real), and (2) a simulated population that reproduced the same pedigree as CCLONES_real. These training models were used and validated in the G3 generation using GEBV and GWFP, and models were assessed by calculating predictive ability and prediction accuracy. Missing values for allele frequency were imputed at the family level using the average allele frequency for that given SNP across families. Therefore, genetic evaluation can be performed as soon as DNA is obtained, which allows accurate selection in both genders early in life. We assumed that the observed values based on 15 individuals per family provides with a reasonable estimation of allele frequency and phenotypic mean for a diploid species. Therefore, using the numbers from this study as example, considering the significant reduction in costs incurred in DNA extraction and genotyping 56 families (training set for GWFP), instead of 844 individuals (training set for GEBV), the approach GWFP_Fam_Ind could still be an affordable option for implementing genomic prediction in breeding programs that select individual plants, but have limited budgets to phenotype and genotype all individuals in the training set. Hence, to account for the fact that the markers capture only a proportion \(q^{2}\) of the total genetic variance, we have to substitute the \(h^{2}\) in Eq. The SIT and FI approaches for combining information for GEBV are equivalent and provide identical accuracies when the underlying assumptions are equivalent. Thus, when combining pedigree and genomic information, SIT and FI yield the same accuracy predictions on the condition that: (1) we use a genomic FI that refers to the full genetic effect \(g_{G}\), rather than to \(g_{M}\), and (2) a potential reduction in residual variance in GP due to the increased amount of information when merging marker and pedigree data is ignored. 2020. As an alternative class of models, non- and semiparametric . The GWFP approach is well suited for crops that are routinely genotyped and phenotyped at the plot-level, but it can be extended to other breeding programs. Predictive ability obtained with Bayes B using different methods and schemes (Table 1) is presented in Figure 4 for the 63 families from both populations. The latter uses genome-wide markers to estimate the effects of all genes or chromosome positions simultaneously to calculate genomic estimated breeding values (GEBVs), which are used for the . Estimated breeding values reflect the true genetic potential or genetic transmitting ability of animals. This scheme was repeated until the ten subsets were used as validation set. 2018. PB derived most mathematical results. R Foundation for Statistical Computing. If we assume that a single segment explains a negligible proportion of the phenotypic variance, such that \(h^{2} /M_{e} \ll 1\), we find: This result was first derived by Daetwyler et al. Invited review: reliability of genomic predictions for North American Holstein bulls, Measurements of representativeness used in genetic resources conservation and plant breeding. Here, we clarify this apparent contradiction, both for the combination of pedigree and genomic information and for the combination of subpopulations into a joint reference population. Remember, the breeding values we use are simply estimates of an animal's genetic potential. 2016. Genomic prediction has the power to shorten the time of a breeding process, which leads to a higher genetic gain per unit time, and can allow a reduction in phenotyping process and costs (Grattapaglia and Resende 2011; Crossa et al. 2007;124:33141. Besides, relatedness between the training set and the validation set also influence the predictive ability. 1 of Dekkers et al. So we must use observed phenotypes to obtain estimated genetic value (EBV) and estimated transmitting ability (ETA). 2018). Genetica. See PEDIGREE ANALYSIS. Annicchiarico P, Nazzicari N, Li X, Wei Y, Pecetti L, et al. We thank Yvonne C. J. Wientjes for helpful comments on the manuscript. 2012; de Almeida Filho et al. Resende et al. R: A language and environment for statistical computing. Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) when combining information sources have been developed based on selection index theory (SIT) and on Fisher information (FI). (4), as explained in the following). Consider two non-overlapping subpopulations of the same size, with \(N_{1} = N_{2} =\) 1000, \(N =\) 2000, \(h^{2}\)=0.3, \(q^{2}\)=0.8, and \(M_{e}\)=400, such that \(\theta_{M,1} = \theta_{M,2}\)=0.75 based on Eq. The population is composed of 923 individuals from 70 full-sib families obtained by crossing 32 parents in a circular diallel mating design with additional off-diagonal crosses (Baltunis et al. Allele frequencies per family and family phenotypic means were calculated varying the number of individuals per family from one to 15. (9) yields a very complex expression and is, therefore, not shown. A total of 10 families from CCLONES_real and CCLONES_sim with at least 15 individuals were selected to evaluate the minimum number of individuals required to estimate allele frequency and phenotypic family means with the most reasonable accuracy. Corresponding author: Agronomy Department, University of Florida, 2005 SW 23rd Street, Building 350 Off 5, Gainesville, FL 32608, USA. Hence, from Eq. This approach is an analogy of a pseudo-BLUP selection index, where the EBV of the mates of an individuals parents are included as an information source [13]. First, terms associated with genetic value must be described: Genetic value is the effect the genes of the animal have on its production. By definition, effective chromosomal segments are independent, have equal variance, and together explain the full additive genetic variance [8]. In principle, this reduction in residual variance can be accounted for in a SIT-based derivation by extending the pseudo-BLUP derivation of Appendix 10, which yields the identical result as the FI-based approach (\(r^{2}\)=0.5114 here) (derivations not shown due to their complexity). Hence, not only is the value of q2 the same for the two subpopulations, but the markers are also assumed to be associated with the same part of the genome in the two subpopulations. The purpose of anestimatedbreedingvalue. 2018). 2020. However, there are several methodologies to compute these matrices and there is still an unresolved debate on which one provides the best estimate of inbreeding. (9) follows from the general Eq. Evaluation of Breeding Values and Variance Components of Birth and Weaning Weights in the Holstein Cows Herd Based on Genetic Information. Marker effects have been estimated with several different methods that generally aim at reducing the dimensions of the marker data. Both authors read and approved the final manuscript.
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