(2a), we find: Note that \(r^{2}\) appears on both sides of the equal signs in Eq. The most obvious piece of phenotypic information we can use is the animal's own phenotype. The simulated genome had 12 chromosomes, each with 100 cM, and 10,000 polymorphic loci were randomly selected to represent the entire genome, and only the scenario exhibiting an absence of dominance (d2 = 0.0) and h2 = 0.25 were used for analyses in this study. Models considering different Bayesian methods were similar in predicting GEBV in traits measured in the real breeding population and the simulated population in this study. Subsequently, 42 individuals were selected from G2 and used in crosses to the next generation (G3, CCLONES_sim_prog), a population composed of 1176 individuals and 71 families. Plant Breeding. [4] (see also Appendix A in Wientjes et al. 2021;53:55. (2012). (6) for both \(\theta_{M,1}\) and \(\theta_{M,2}\) and simplifying the result yields a FI-based prediction of the reliability of GEBV based on the full reference population (see Appendix 13) that is equal to: Alternatively, we can derive \(r^{2}\) based on SIT. For one group of individuals phenotypic and genotypic data were pooled at the family level and used as the training set for GWFP models. Large commercial breeding companies have been applying genomic prediction; however, the success of the process depends strongly on the species and the breeding program scheme (Voss-Fels et al. (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. 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. 2019. 6 of Dekkers et al. The number of individuals per family ranged from 1 to 20, with an average of 13 trees per family (standard deviation = 5). The . Additive Genetic Value E Residual Effect 314 +14 +3 +11 306 +6 +7 -1 302 +2 -3 +5 293 -7 +4 -11 289 -11 -7 -4 . Miyable ex Shirai f. sp. Genomic prediction in pigs using data from a commercial crossbred population: insights from the Duroc x (Landrace x Yorkshire) three-way crossbreeding system. 2018. Finally, GWFP models could be exploited in scenarios when remnant seeds might be available for the same family, and the goal would be to predict the performance of the family or individuals within the family. 2013. Transmitted ability is often used as a substitute for one-half breeding value. Invited review: Genomic selection in dairy cattle: progress and challenges. All phenotypic and genotypic data utilized in this study have been previously published as a standard data set for development of genomic prediction methods (Resende et al. (2014). Hence, we can find the reliability for the combined reference population by replacing \(\theta_{M,i}\) in Eq. Five families exhibiting genotypic segregation ratios 1:1 (A and B) and 1:2:1 (C and D) for single nucleotide polymorphisms were included in the analysis. 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. Breeding values define the superiority or inferiority of the offspring of an animal. (2012), reported a slightly greater predictive ability in the real population for rust incidence with Bayesian methods over RR-BLUP, because fewer genes with large effects control this trait. (4) in the previous paragraph ignores a potential reduction in residual variance due to the merger of pedigree and marker information. 0.6297) in Eq. Your privacy choices/Manage cookies we use in the preference centre. The pedigree-based EBV relates to FI for \(g_{G}\), because pedigree information captures the full genetic effect. With n equal to 15 individuals the Ne is 1.88, which is 94% of this maximum of 2. Norman A, Taylor J, Edwards J, Kuchel H.. [3]. The validation set was the single family not included in the training group. They are calculated differently to our conventional Estimated Breeding Values (EBVs). GEBV: genomic estimated breeding values individual trees; GWFP_Fam_Ind: genome-wide family prediction using 59 family pools as training set, while different individuals from the same families were used as validation set; GWFP_Fam_Fam: genome-wide family prediction using 59 family pools as the training and validation population, but different full-sib individuals were pooled in both sets; GWFP: genome-wide family prediction using 63 family pools in a 10-fold cross validation scheme. ibreeder Livestock Trading Platform Launch, Maidenlands British Blues Review / Testimonial, Its been a busy year at Scawfell Genetics, Profile: Steven OKane On-Farm Collection. To accomplish this, we translate the reliability of predictions based on deviations of genomic relationships from pedigree relationships, \(r_{D}^{2}\), into an FI that refers to the full genetic effect by solving Eq. Therefore, the definition of the optimum number of families, and number of individuals per family are a crucial point for the genomic prediction process. [3], (see their Eq. The SIT and FI approaches are equivalent when these sources are accounted for. Higher predictive ability obtained with GWFP would motivate the application of genomic prediction in these situations. F D, Ashraf BH, Pedersen MG, Janss L, Byrne S, et al. Marker effects were estimated at the individual (GEBV) and family (GWFP) levels with two distinct whole-genome regression approaches using the package BGLR (Perez and de los Campos, 2014) in R (R Development Core Team 2018): (1) Bayes B which considers that markers have heterogeneous variances, i.e., many loci with no genetic variance and a few loci explain a large portion of the genetic variation (Meuwissen et al. 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 . Get the best quality genetics from your bull? In dairy cattle, genomic prediction can double the genetic gain compared with selection based on progeny test (Xu et al. Nearly all reported models only included additive effects. (3b) with \(\theta_{M}\)=1.5, which yields \(r^{2}\)=0.5114. Goddard M. Genomic selection: prediction of accuracy and maximisation of long term response. Genomic selection (GS) plays an essential role in livestock genetic improvement programs. 2020; Esfandyari et al, 2020). J Anim Breed Genet. When studying the effect of size and composition of training population in blueberry (Vaccinium spp. Genet Sel Evol 54, 13 (2022). 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. Marker effects were estimated to compute genomic estimated breeding values (GEBV) at the individual and family (GWFP) levels. In summary, the base population was created (G0=1000 diploid individuals) by randomly sampling 2000 haplotypes from a population with an effective size of Ne = 10,000 (Johnson et al. Predictive ability was always greater for GWFP methods in both populations and all traits, except for the scenario GWFP_Fam_Ind that showed similar or lower accuracy than GEBV for most traits (Figure 4). Epub 2009 Sep 11. These results revealed great potential for using GWFP in breeding programs that select family bulks as the selection unit, GWFP is well suited for crops that are routinely genotyped and phenotyped at the plot-level. Terms and Conditions, A prediction of \(r_{G}^{2}\) using the FI approach that accounts for (and assumes)a reduction in residual variance due to the merger of genomic and pedigree information follows from solving Eq. Anim Sci. Book However, while it is clear that the residual variance decreases when merging two subpopulations into a single reference population, we are not sure whether this decrease also occurs when merging pedigree and genomic data in a single GP, for example with single step GP [1, 12]. (4), but refers to \(r_{M}^{2}\) rather than \(r^{2}\). 2010;93:74352. government site. (9), where \(r_{D}^{2}\) is calculated from Eqs. Genomic prediction showed to be a powerful tool to achieve higher genetic gain in plant breeding in many other species (Crossa et al. Predictions of the accuracy of genomic prediction: connecting R, $$r^{2} = \frac{{\sigma_{s}^{2} }}{{\sigma_{s}^{2} + \left( {\sigma_{P}^{2} - \sigma_{s}^{2} } \right)/n}},$$, \(\left( {\sigma_{P}^{2} - \sigma_{s}^{2} } \right)/n\), \(\sigma_{s}^{2} = \frac{1}{4}h^{2} \sigma_{p}^{2}\), \(r^{2} = nh^{2} /\left[ {nh^{2} + \left( {4 - h^{2} } \right)} \right]\), $$r^{2} = \frac{{h^{2} /M_{e} }}{{h^{2} /M_{e} + \left( {1 - h^{2} /M_{e} } \right)/N}} = \frac{{Nh^{2} /M_{e} }}{{Nh^{2} /M_{e} + 1 - h^{2} /M_{e} }}.$$, $$r^{2} \approx \frac{{Nh^{2} /M_{e} }}{{Nh^{2} /M_{e} + 1}}.$$, $$r^{2} = q^{2} r_{M}^{2} = q^{2} \frac{{\frac{{Nq^{2} h^{2} }}{{M_{e} }}}}{{\frac{{Nq^{2} h^{2} }}{{M_{e} }} + 1 - \frac{{q^{2} h^{2} }}{{M_{e} }}}} = q^{2} \frac{{\theta_{M} }}{{ \theta_{M} + 1 - q^{2} h^{2} /M_{e} }},$$, $$r^{2} \approx q^{2} \frac{{Nq^{2} h^{2} /M_{e} }}{{Nq^{2} h^{2} /M_{e} + 1}} = q^{2} \frac{{\theta_{M} }}{{\theta_{M} + 1 }}$$, \(\left( {M_{e} - 1} \right) r^{2} h^{2} /M_{e}\), $$1 - q^{2} h^{2} /M_{e} - \left( {M_{e} - 1} \right)r^{2} h^{2} /M_{e} = 1 - h^{2} (q^{2} - r^{2} + r^{2} M_{e} )/M_{e} ,$$, \(h^{2} \left( {q^{2} - r^{2} } \right)/M_{e} \ll 1\), $$r^{2} \approx q^{2} \frac{{Nq^{2} h^{2} /M_{e} }}{{Nq^{2} h^{2} /M_{e} + 1 - r^{2} h^{2} }} = q^{2} \frac{{\theta_{M} }}{{\theta_{M} + 1 - r^{2} h^{2} }}.$$, $$r^{2} = \frac{{1 + \theta_{M} - \sqrt {\left( {1 + \theta_{M} } \right)^{2} - 4h^{2} q^{2} \theta_{M} } }}{{2h^{2} }}.$$, \(r^{2} = \left[ {1 + \theta_{M} - \sqrt {\left( {1 + \theta_{M} } \right)^{2} - 4h^{2} q^{4} \theta_{M} } } \right]/2q^{2} h^{2}\), $$r^{2} = \frac{\theta }{{\theta + 1 - r^{2} h^{2} }},$$, \(\theta_{M} /\left( {\theta_{M} + 1 - r^{2} h^{2} } \right)\), $$r_{i}^{2} = q^{2} r_{M,i}^{2} = q^{2} \frac{{\theta_{M,i} }}{{\theta_{M,i} + 1 - q^{2} h^{2} /M_{e} }},$$, \(\theta_{M,i} = N_{i} q^{2} h^{2} /M_{e}\), $$\theta_{M,i} = \frac{{r_{i}^{2} \left( {1 - q^{2} h^{2} /M_{e} } \right)}}{{q^{2} - r_{i}^{2} }}.$$, \(\theta_{M} = \theta_{M,1} + \theta_{M,2}\), $$r^{2} = q^{2} r_{M}^{2} = q^{2} \frac{{\theta_{M,1} + \theta_{M,2} }}{{\theta_{M,1} + \theta_{M,2} + 1 - q^{2} h^{2} /M_{E} }}.$$, $$r^{2} = \frac{{r_{1}^{2} + r_{2}^{2} - 2r_{1}^{2} r_{2}^{2} /q^{2} }}{{1 - r_{1}^{2} r_{2}^{2} /q^{4} }}.$$, $$r_{G}^{2} = \frac{{r_{A}^{2} + r_{D}^{2} - 2r_{A}^{2} r_{D}^{2} }}{{1 - r_{A}^{2} r_{D}^{2} }}.$$, $$\theta_{{D_{G} }} = \frac{{r_{D}^{2} \left( {1 - r_{D}^{2} h^{2} } \right)}}{{1 - r_{D}^{2} }}.$$, $$\theta_{G} = \theta_{A} + \theta_{{D_{G} }} .$$, \(\theta = \theta_{G} = \theta_{A} + \theta_{{D_{G} }}\), $$r_{G}^{2} = \frac{{1 + \theta_{G} - \sqrt {\left( {1 + \theta_{G} } \right)^{2} - 4h^{2} \theta_{G} } }}{{2h^{2} }}.$$, $$\begin{aligned} \left[ {\begin{array}{*{20}c} {b_{1} } \\ {b_{2} } \\ \end{array} } \right] & = {\mathbf{b}} = {\mathbf{P}}^{ - 1} {\mathbf{g}} = \left[ {\begin{array}{*{20}c} {\frac{{q^{2} h^{2} }}{{M_{e} }} + \frac{{1 - \frac{{q^{2} h^{2} }}{{M_{e} }}}}{N}} & {\frac{{r^{2} h^{2} \left( {M_{e} - 1} \right)}}{{M_{e} N}}} \\ {\frac{{r^{2} h^{2} \left( {M_{e} - 1} \right)}}{{M_{e} N}}} & {\frac{{r^{2} h^{2} \left( {M_{e} - 1} \right)}}{{M_{e} N}}} \\ \end{array} } \right]^{ - 1} \left[ {\begin{array}{*{20}c} {q^{2} h^{2} /M_{e} } \\ 0 \\ \end{array} } \right] \\ & = \frac{N}{{Nq^{2} h^{2} + M_{e} - q^{2} h^{2} - r^{2} h^{2} \left( {M_{e} - 1} \right)}} \left[ {\begin{array}{*{20}c} {q^{2} h^{2} } \\ { - q^{2} h^{2} } \\ \end{array} } \right] \\ \end{aligned}$$, $$\begin{aligned} r^{2} & = \frac{{{\mathbf{b^{\prime}g}}}}{{h^{2} /M_{e} }} = \frac{1}{{h^{2} /M_{e} }} \frac{N}{{Nq^{2} h^{2} + M_{e} - q^{2} h^{2} - r^{2} h^{2} \left( {M_{e} - 1} \right)}} \left[ {\begin{array}{*{20}c} {q^{2} h^{2} } & { - q^{2} h^{2} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {q^{2} h^{2} /M_{e} } \\ 0 \\ \end{array} } \right]. Hence, the two subpopulations have independent sampling errors, which allows FI of the two subpopulations to be summed to obtain FI of the full reference population, as in van den Berg et al. (2015) studied the effect of the number of families in the accuracy of genomic . Breeders may also be interested in employing the GWFP_Fam_Ind approach, where family bulks are used as training set, but individuals are the selection unit (Figure 6C). 2009. Therefore, the definition of the optimum number of families, and number of individuals per family are a crucial point for the genomic prediction process. The CCLONES_real phenotypic deviation is for the trait stem diameter (E). (5) by \(\theta_{M} = \theta_{M,1} + \theta_{M,2}\), giving: Substituting Eq. 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. EBVs have been introduced to make sure that cattle from a particularbreedor herd are all being scored from the same base point regardless as to an animals management regime, favourable or less favourable location. official website and that any information you provide is encrypted 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). 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. In total, 20,000 Markov chain Monte Carlo iterations were used, of which the first 5000 were discarded as burn-in, and every third sample was kept for parameter estimation. 2008;3:e3395. Xu Y, Liu X, Fu J, Wang H, Wang J, et al. Evaluation of Breeding Values and Variance Components of Birth and Weaning Weights in the Holstein Cows Herd Based on Genetic Information. The effect of number of individuals within families on accuracy of genomic prediction models was also demonstrated in perennial ryegrass (Pembleton et al. Email: Received 2021 Mar 9; Accepted 2021 Jul 2. The relevant solution is: Equation(3b) accounts both for \(q^{2} < 1\) and for the reduction of residual variance because all markers are fitted simultaneously in GP. In the case of the genomic data, the allele frequency (p) was calculated for each SNP per family, considering the reference allele (A) as follows: where pij refers to the allele frequency for SNP i in the j family; nAAij and 2nAaij are number of individuals with genotype AA and Aa respectively for SNP i in the family j; Nij are number of individuals in family j with non-missing genotype data for SNP i. Kumar S, Chagn D, Bink MC, Volz RK, Whitworth C, et al. True genetic value (TBV) is never known exactly, we cannot see genes and breeding values. (1) The value of an individual as a (genetic) parent. 2017; Lara et al. The contribution of dominance to phenotype prediction in a pine breeding and simulated population. Print [3] referred to the genetic component that is captured by markers, rather than the full genetic component. GEBV, genomic estimated breeding value; GWFP, genome-wide family prediction; CV, cross-validation. Correspondence to Genetic gain from selection for rooting ability and early growth in vegetatively propagated clones of loblolly pine. 2018. Perennial ryegrass is commonly bred using families and GWPF has been exploited in the species for various traits (F et al. Christensen OF, Lund MS. Genomic prediction when some animals are not genotyped. [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). Agronomy Department, University of Florida, Gainesville, FL 32611, USA, 2 The GEBV showed higher accuracy than GWFP for the oligogenic trait, and similar accuracy for the polygenic trait (Figure 5). 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. (4). The basic principle is that because of the high marker density, each quantitative trait loci (QTL) is in linkage disequilibrium (LD) with at least one nearby marker. 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. 2016). Springer Nature. Meuwissen THE, Hayes BJ, Goddard ME.. 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. 2009. The number of families was fixed and limited to 70 families, so we did not focus on studying the effect of a variable number of families. 2013). [3] between predicted accuracies based on SIT vs. FI, and to show that these two approaches are equivalent when the same assumptions are made. The reliability of GEBV follows by analogy. From Eq. Careers. The standard SIT approach (Eq. Cambridge: CABI Publishing; 2014. The authors stated that 4860 individuals per population are necessary to accurately represent the genetic diversity within a ryegrass population. 2012. Thus, \(r^{2}\) is the ratio of the variance in the progeny means that is explained by the sire over the full variance in the progeny means, which is the \(R^{2}\) due to the sire. [3]. 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). 2001) and a mutation rate of 2.5108. Using this concept, we showed that the apparent discrepancy between predictions of the accuracy of GEBV based the SIT vs. FI approaches in Dekkers et al. Derivations of the accuracy of GEBV make use of the concept of effective chromosomal segments [8]. (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. 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 \(g_{G}\). Elshire RJ, Glaubitz JC, Sun Q, Poland JA, Kawamoto K, et al. Second, we account for the reductions in residual variance due to the merger of subpopulations into a joint reference population and due to fitting all markers simultaneously. J Dairy Sci. 2020). 2007 Dec;124(6):323-30. doi: 10.1111/j.1439-0388.2007.00702.x. CAS Mathematical Modeling and Software Tools for Breeding Value Estimation Based on Phenotypic, Pedigree and Genomic Information of Holstein Friesian Cattle in Serbia. All these plant-specific characteristics are key factors affecting predictive ability in genomic prediction due to their influence in breeding methods, effective population size, population structure, and linkage disequilibrium (Lin et al. 2023 Feb 8;13(4):597. doi: 10.3390/ani13040597. Therefore, the additive genetic variance in full-sib families is half of the additive variance between individuals. The other group of individuals was used as the validation set based on two approaches: (1) predicting the performance of individuals trees not included in the training set (GWFP_Fam_Ind), and (2) pooling individuals at the family level to predict performance of families composed of individuals not included in the training set (GWFP_Fam_Fam). The same interpretation is suggested by Eq. statement and (3a), resulting in a quadratic equation in \(r^{2}\). A simulated population (CCLONES_sim) exhibiting similar genetic properties as CCLONES_real was also considered in this study, aiming to assess the efficiency of GWFP for two different traits and to predict the performance of the next generation. Goals of genomic prediction. To derive the corresponding result based on FI, it is essential to distinguish between FI for \(g_{M}\) and FI for \(g_{G}\). 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. Equations(1a) and (1b) ignore that the genotyped markers may capture only a proportion \(q^{2}\) of the full additive genetic variance [4, 9], which has two consequences. Predictive ability was always greater for GWFP methods than GEBV in both the real and simulated populations and for all traits, except when the model was built with family pools, and individual performance was predicted (GWFP_Fam_Ind) (Figure 4). This value is slightly larger than the 0.7728 presented above where we ignored a potential reduction in residual variance when combining pedigree and marker information. In this section, we use the general relationship between reliability and FI (\(\theta\)), as given by van den Berg et al. Animal breeding faces one of the most significant changes of the past decades - the implementation of genomic selection. Second, the SIT approach did not account for the increase in accuracy of GEBV due to a reduction of the residual variance when combining information sources. 2017; Jia et al. Prediction of response to marker-assisted and genomic selection using selection index theory. Although results from simulation studies suggest that different models may yield more accurate genomic estimated breeding values (GEBVs) for different traits, depending on the underlying QTL distribution of the trait, there is so far only little evidence from studies based on real data to support this. Our objective was to investigate the effect of using MFs in genomic prediction for CB performance on estimated variance components, and accuracy and bias of GEBV.