Contrary to QTL and association mapping, GS uses all molecular markers for GP of the performance of the candidates for selection. Therefore, the aim of GS is to predict breeding and/or genetic values. GS combines molecular and phenotypic data in a training population (TRN) to obtain the genomic estimated breeding values (GEBVs’) of individuals in a testing population (TST) that have been genotyped but not phenotyped  . Figure 1 A depicts the two basic populations in a GS program: the TRN data, whose phenotype and genotype are known, and the TST data, whose genetic values are to be predicted. GS is used in place of phenotyping for a few selection cycles. The main advantages of GS over phenotype-based selection in breeding are that it reduces the cost per cycle and the time required for variety development. In terms of cost reduction in maize breeding, the breeder can testcross 50% of all available lines, evaluating them in ﬁrst-stage multi-locational trials, and can then use the phenotypic data to predict the remaining 50% by GS. Figure 1 B shows the advantage of GS over PS for: (i) reducing costs, up to 50%; and (ii) saving time by selecting lines directly for stage II instead going through stage I (used in PS). This signi ﬁcantly reduces the cost of testcross formation and evaluation at each stage of multi-location evaluations. The time ef ﬁciency over PS could come from the second cycle of selection, which uses the TRN from the previous cycle to predict the new doubled haploid (DH) lines, thus excluding testcross formation and ﬁrst-stage multi- location evaluation trials. Based on GS, the best lines could go directly to the second stage of multi-location evaluations.
Several genomic prediction models combining genotype × environment (G×E) interactions have recently been developed and used for genomicselection (GS) in plantbreeding programs. G×E interactions reduce selection accuracy and limit genetic gains in plantbreeding. Two data sets were used to compare the prediction abilities of multienvironment G×E genomicmodels and two kernel methods. Specifically, a linear kernel, or GB (genomic best linear unbiased predictor [GBLUP]), and a nonlinear kernel, or Gaussian kernel (GK), were used to compare the prediction accuracies (PAs) of four genomic prediction models: 1) a single-environment, main genotypic effect model (SM); 2) a multienvironment, main genotypic effect model (MM); 3) a multienvironment, single-variance G×E deviation model (MDs); and 4) a multienvironment, environment-specific variance G×E deviation model (MDe). We evaluated the utility of genomicselection (GS) for 435 individual rubber trees at two sites and genotyped the individuals via genotyping-by-sequencing (GBS) of single-nucleotide polymorphisms (SNPs). Prediction models were used to estimate stem circumference (SC) during the first 4 years of tree development in conjunction with a broad-sense heritability (H 2 ) of 0.60. Applying the model (SM, MM, MDs, and MDe) and kernel method (GB and GK) combinations to the rubber tree data revealed that the multienvironment models were superior to the single-environment genomicmodels, regardless of the kernel (GB or GK) used, suggesting that introducing interactions between markers and environmental conditions increases the proportion of variance explained by the model and, more importantly, the PA. Compared with the classic breeding method (CBM), methods in which GS is incorporated resulted in a 5-fold increase in response to selection for SC with multienvironment GS (MM, MDe, or MDs). Furthermore, GS resulted in a more balanced selection response for SC and contributed to a reduction in selection time when used in conjunction with traditional genetic breeding programs. Given the rapid advances in genotyping methods and their declining costs and given the overall costs of large-scale progeny testing and shortened breeding cycles, we expect GS to be implemented in rubber tree breeding programs.
with zero mean and different variances were fitted for QTL additive effects of different classes of traits. Dominance coefficients fit a single normal distribution with positive mean, indicating prevalence of additive or partial dominant gene action across many traits.
3) To enhance the predictive ability in new line development, we developed and evaluated a novel method for use in genomicselection. Genomicselection procedures have proven useful in estimating breeding value and predicting phenotype with genome-wide molecular marker information. We proposed a new nonparametric method, pRKHS, which combined the features of supervised principal component analysis and reproducing kernel Hilbert spaces regression, with versions for traits with no/low epistasis, pRKHS-NE, to high epistasis, pRKHS-E. Compared to RR-BLUP, BayesA, BayesB, and RKHS, pRKHS delivers greater predictive ability, particularly when epistasis impacts expression in the trait of interest. Beyond prediction, the new method also facilitated inferences about the extent to which epistasis influences trait expression.
ABSTRACT: Genome-wide selection (GWS) is currently a technique of great importance in plantbreeding, since it improves efficiency of genetic evaluations by increasing genetic gains. The process is based on genomic estimated breeding values (GEBVs) obtained through phenotypic and dense marker genomic information. In this context, GEBVs of N individuals are calculated through appropriate models, which estimate the effect of each marker on phenotypes, allowing the early identification of genetically superior individuals. However, GWS leads to statistical challenges, due to high dimensionality and multicollinearity problems. These challenges require the use of statistical methods to approach the regularization of the estimation process. Therefore, we aimed to propose a method denominated as triple categorical regression (TCR) and compare it with the genomic best linear unbiased predictor (G-BLUP) and Bayesian least absolute shrinkage and selection operator (BLASSO) methods that have been widely applied to GWS. The methods were evaluated in simulated populations considering four different scenarios. Additionally, a modification of the G-BLUP method was proposed based on the TCR-estimated (TCR/G-BLUP) results. All methods were applied to real data of cassava (Manihot esculenta) with to increase efficiency of a current breeding program. The methods were compared through independent validation and efficiency measures, such as prediction accuracy, bias, and recovered genomic heritability. The TCR method was suitable to estimate variance components and heritability, and the TCR/G-BLUP method provided efficient GEBV predictions. Thus, the proposed methods provide new insights for GWS.
Another incongruence that exists between the plant breeders’ approach and some of the conclusions presented in various articles is the use of accuracy alone as a method to determine the success of a GS approach. While accuracy is a good system to determine the performances of a model, it does not directly respond to the most important question a breeder has to ask of the data: how many of the top 5% individuals for a given trait were correctly selected? In fact, an accuracy of 0.4 seems to suggest that 40% (i.e., 8 individu- als) were properly selected, which is a level of failure too high for a plantbreeding program. However, this is not necessarily the case and often models with accuracies of 0.4 or 0.5 were instead capable of picking 60% or 70% of the top individuals  . This is proba- bly due to better prediction ability when estimating the extreme values, and higher noise in estimating the average performances. Empirical gain from selection is therefore the only true measure, and predictions must be validated. Hence, it would be preferable if future studies of GS performances in wheat also include the per- centage of top individuals correctly selected. However, it should be kept in mind that the phenotype is only a predictor of true breeding value (TBV), just as GEBV is. So selecting the very same individuals in GS and PS is not necessarily the grail to seek, since the propor- tion of the top 5% TBV selected by PS may not be higher than that selected by GS.
FIGURE 5 | Prediction accuracy (correlation between estimated and observed values) for selection index and its seven component traits. Prediction models built at GS1 were used.
be measured on a single-plant basis in completely outcrossing species without clonal propagation ability. The selection index was constructed by modeling the relationship between yield and other traits that were measurable on a single-plant basis (Table 1). The selection index was based on the data from a past field experiment with a small number of cultivars. We found a similar among-trait correlation structure between the field experiment and the initial breeding population (Table 2), suggesting the applicability of the selection index to this population. The six GS cycles significantly increased the selection index (Table 4), although the prediction accuracy at GS3 and GS5 was low (Table 3). Expected values at these cycles were heavily shrunk to the overall average, and the improvement at each cycle was small, especially during the second year, in which the prediction accuracy of the selection index was the lowest among selection cycles (Table 3). The relation between prediction accuracy and selection response suggested that the degree of improvement of the target trait depended mainly on its prediction accuracy. The realized response to selection at GS4 and GS6 was smaller than that at the other cycles (Figure 3). This may result from the low predictive accuracy at GS3 and GS5 and from deterioration in the accuracy of the prediction models due to the changes in the LD pattern, as discussed later. The values of three traits with relatively high weight in the index (main stem length, number of flower clusters, and test weight) significantly increased in both PS and GS (Tables 1, 4), suggesting that weight in the selection index worked as expected (i.e., the higher weight traits had, the more they would be improved) at each selection cycle. In particular, the large weight of main stem length in the index (Table 1) and high prediction accuracy at GS1 (Table 3) might have led to a significant difference between the initial and Post-GS1 populations (Table 4). GS did not change the number of primary branches, probably because of its small weight in the index
We extracted total genomic DNA from the plants during the first and second cycles of each year and genotyped them as described by Yabe et al. (2014a) . At GS1, we genotyped 274,303 candidate markers based on the raw sequencing reads using an Illumina Hiseq2000 (Illumina, Inc., San Diego, CA). We selected 50,000 markers according to their polymorphism, linkages with other markers, and clarity of the distinction between two genotypes in dominant markers ( Yabe et al., 2014a ). They were used them to build a prediction model. A microarray was developed using the sequencing data obtained at GS1 by the methods described by Yabe et al. (2014a) . After GS1, the microarray markers were used for genotyping. To re-evaluate the quality of the markers, 12 plants genotyped at GS1 were genotyped again at GS2 with the 48 plants from the Post-GS1 population. The markers that were consistent between GS1 and GS2 were considered reliable. At GS2, 11,480 markers were selected on the basis of reliability (i.e., consistency of the marker genotypes between GS1 and GS2) in addition to the same marker selection way as GS1(according to their polymorphism and linkage with other markers). The original prediction model built at GS1 could not be used at GS2 because it was based on 50,000 markers that were not genotyped at GS2. Thus, at GS2, we rebuilt prediction models based on phenotypes and the data for 11,480 marker genotypes collected at GS1. After the first year, a total of 14,598 markers, which included 11,480 markers used at GS2, were used for genotyping. We used 6,373 markers at GS3, 6,225 at GS4, 4,614 at GS5, and 4,417 at GS6 for modeling; markers were
Although methodologically simple the sparse knowl- edge about its functionality made it initially difficult to find starting points for increasing the prediction accuracy. Theoretical studies thus laid the foundation for optimizing breeding with genomicselection by trying to understand the underlying mechanics of this ‘green box’ approach. The driving forces of prediction accuracy that can be most readily influenced by plant breeders are the train- ing population size and heritability (Muir 2007; Hayes et al. 2009), by adequately adjusting the resource alloca- tion (Riedelsheimer and Melchinger 2013; Longin et al. 2015). Recent advances in sequencing technologies made it possible to apply cost effective genotyping methods such as genotyping-by-sequencing (GBS) in various crop spe- cies (Elshire et al. 2011; Poland et al. 2012; Huang et al. 2014) yielding an appropriate large number of markers for genomicselection (Hayes et al. 2009; Schulz-Streeck et al. 2011). The use of dense genome-wide markers increases the chance of markers being in linkage disequilibrium (LD) with QTL influencing the trait of interest (e.g. Meuwis- sen et al. 2001), and determines to some extent how well genetic relationship and genetic architecture are captured by the genomicselection model (Daetwyler et al. 2010; Heslot et al. 2013a). The importance of a close genetic relationship between training and validation populations to achieve a high prediction accuracy (Habier et al. 2013) has been verified numerous times in plantbreeding studies, e.g. with sugar beet (Würschum et al. 2013); rapeseed (Wür- schum et al. 2014), maize (Zhao et al. 2012; Riedelsheimer et al. 2013; Albrecht et al. 2014; Lehermeier et al. 2014), and wheat (Charmet et al. 2014; Crossa et al. 2014), which motivated investigations for an optimal training population construction to reduce phenotyping costs (Rincent et al. 2012; Isidro et al. 2015).
Genomicselection (GS) can be effective in breeding for quantitative traits, such as yield, by reducing the selection cycle duration. Speed breeding (SB) uses extended photoperiod and temperature control to enable rapid generation advancement. Together, GS and SB can syner- gistically reduce the breeding cycle by quickly producing recombinant inbred lines (RILs) and enabling indirect phenotypic selection to improve for key traits, such as height and flow- ering time, prior to field trials. In addition, traits measured under SB (SB traits) correlated with field-based yield could improve yield predic- tion in multivariate GS. A 193-line spring wheat (Triticum aestivum L.) training population (TP), tested for grain yield in the field in multiple envi- ronments, was used to predict grain yield of a 350-line selection candidate (SC) population, across multiple environments. Four SB traits measured on the TP and SC populations were used to derive principal components, which were incorporated into multivariate GS models. Predictive ability was significantly increased by multivariate GS, in some cases being twice as high as univariate GS. Based on these results, an efficient breeding strategy is proposed combining SB and multivariate GS using yield- correlated SB traits for yield prediction. The potential for early indirect SB phenotypic selec- tion for targeted population improvement prior to trials was also investigated. Plant height and flowering time showed strong relative predicted efficiency to indirect selection, in some cases as high as direct field selection. The higher selec- tion intensity and rate of generation turnover under SB may enable a greater rate of genetic gain than direct field phenotyping.
CHAPTER 1. GENERAL INTRODUCTION
1.1. Dissertation Organization
This dissertation is organized into five chapters. Chapter one provides a brief introduction to the central concepts of plantbreeding, phenomic assisted breeding, and the knowledge gap this research intends to fill. Chapters two through four describe original research authored in manuscript format with the intention for submission into scientific journals. Chapter two investigates physio-morphological predictor importance in contrasting agro-management systems and the development of predictive models for placement of candidate cultivars into their adapted management system. Chapter three explores the use of the phenomic predictors for in-season seed yield prediction in the context of germplasm breeding and the performance of such methods to correctly identify top performing accessions. Chapter four includes a genome-wide association study of phenomic traits and seed yield using a diverse panel of soybean. Chapter five summarizes the findings from all chapters and suggests future work. Throughout this work we develop frameworks amendable to any crop species for the development of prescriptive cultivar development and in-season yield prediction to allow optimization of plantbreeding operational efficiencies and drive the rate of genetic gain. Using the prior information on important phenomic predictors, we sought to identify the genomic regions associated with these traits to unravel the genetic architecture controlling seed yield in soybean.
ABSTRACT Allocating resources between population size and replication affects both genetic gain through phenotypic selection and quantitative trait loci detection power and effect estimation accuracy for marker-assisted selection (MAS). It is well known that because alleles are replicated across individuals in quantitative trait loci mapping and MAS, more resources should be allocated to increasing population size compared with phenotypic selection. Genomicselection is a form of MAS using all marker information simultaneously to predict individual genetic values for complex traits and has widely been found superior to MAS. No studies have explicitly investigated how resource allocation decisions affect success of genomicselection. My objective was to study the effect of resource allocation on response to MAS and genomicselection in a single biparental population of doubled haploid lines by using computer simulation. Simulation results were compared with previously derived formulas for the calculation of prediction accuracy under different levels of heritability and population size. Response of prediction accuracy to resource allocation strategies differed between genomicselectionmodels (ridge regression best linear unbiased prediction [RR-BLUP], BayesCp) and multiple linear regression using ordinary least-squares esti- mation (OLS), leading to different optimal resource allocation choices between OLS and RR-BLUP. For OLS, it was always advantageous to maximize population size at the expense of replication, but a high degree of ﬂexibility was observed for RR-BLUP. Prediction accuracy of doubled haploid lines included in the training set was much greater than of those excluded from the training set, so there was little bene ﬁt to phenotyping only a subset of the lines genotyped. Finally, observed prediction accuracies in the simulation compared well to calculated prediction accuracies, indicating these theoretical formulas are useful for making resource allocation decisions.
Due to the fact that the organic sector still has limited acreage, many commercial breeding companies are reluctant to start breeding programmes specifically for this sector. Farmers are therefore looking for alternative options to enhance availability of a broad spectrum of varieties. Specifically in this respect we may learn from the decentralised and farmers’ participatory approaches already applied in developing countries for areas with small and subsistence farmers neglected by the green revolution (e.g. Kudadjie et al., 2004, Zannou et al., 2004). Such approaches offer an opportunity to combine a farmer’s knowledge, daily experience and developed intuition (farmer’s eye) with knowledge, experience and developed breeder’s eye of formal breeders (Ceccarelli, 2000; Desclaux et al., 2006). Morris and Bellon (2004) have described four breedingmodels in which farmers are to a smaller or larger extent involved in the different steps of a breeding process. In contrast to the traditional model adhered by the formal breeding sector of industrialised countries, a complete participatory breeding model involves farmers in all activities relating to the selection of source germplasm, to trait identification (pre-breeding), to cultivar development, and finally to varietal evaluation. In an efficient participatory breeding model, formal breeders involve farmers in the phase of selecting parent lines and in the end phase of evaluating potential varieties. In the participatory varietal selection model, farmers only deal with varietal evaluation at the end.
chance selection of escapes. Moreover, screening of some traits have to be done in a specific season and/or location. Screening for bacterial wilt resistance is carried out in disease endemic locations. Foliar fungal diseases occur in rainy season in Asia and Africa and field screening is possible in that season. While in the other non-rainy season, generations are advanced based on yield and other attributes, consequently, the progress in breeding for disease resistance is often slow with low rate of genetic gains. Improvement of traits such as, oil content and quality through classical breeding was limited as they require efficient and robust phenotyping tools, and moreover for these traits phenotyping has to be done after harvest, drying, and shelling of the pods. Available tools for analyzing seed quality traits are destructive and can usually result in loss of valuable breeding material especially in early segregating generations where the seed material is in limited supply. Consequently, screening for quality traits is often delayed to advanced generations. Reliable and repeatable phenotyping requires practice and skill, a crucial aspect in breeding. However, even with the best available phenotyping tools, there is a possibility of selection bias that may occur due to chance failure of phenotypic screens and chance escapes. High throughput phenotyping tools are now available to screen for diverse traits, but their application is limited due to their high cost and lack of technical knowhow. Consequently, the high throughput phenotyping tools may not be ready for deployment in breeding programs, but they may be useful to establish marker-trait associations (MTA), genome-wide associations and for training genomicselectionmodels which require precise phenotyping (Cobb et al., 2013). Genomic tools, on other hand offer cost-effective, robust, and reliable tools to enhance genetic gain for target traits and it is possible to enhance the efficiency of classical breeding by optimizing the time, resources, and funds.
1 Cowpea Breeding, International Institute of Tropical Agriculture, Kano, Nigeria, 2 Cowpea Breeding, International Institute of
Tropical Agriculture, Ibadan, Nigeria, 3 Department of Nematology, University of California, Riverside, Riverside, CA, USA, 4 Department of Botany and Plant Sciences, University of California, Riverside, Riverside, CA, USA
Cowpea is one of the most important grain legumes in sub-Saharan Africa (SSA). It provides strong support to the livelihood of small-scale farmers through its contributions to their nutritional security, income generation and soil fertility enhancement. Worldwide about 6.5 million metric tons of cowpea are produced annually on about 14.5 million hectares. The low productivity of cowpea is attributable to numerous abiotic and biotic constraints. The abiotic stress factors comprise drought, low soil fertility, and heat while biotic constraints include insects, diseases, parasitic weeds, and nematodes. Cowpea farmers also have limited access to quality seeds of improved varieties for planting. Some progress has been made through conventional breeding at international and national research institutions in the last three decades. Cowpea improvement could also benefit from modern breedingmethods based on molecular genetic tools. A number of advances in cowpea genetic linkage maps, and quantitative trait loci associated with some desirable traits such as resistance to Striga, Macrophomina, Fusarium wilt, bacterial blight, root-knot nematodes, aphids, and foliar thrips have been reported. An improved consensus genetic linkage map has been developed and used to identify QTLs of additional traits. In order to take advantage of these developments single nucleotide polymorphism (SNP) genotyping is being streamlined to establish an efficient workflow supported by genotyping support service (GSS)-client interactions. About 1100 SNPs mapped on the cowpea genome were converted by LGC Genomics to KASP assays. Several cowpea breeding programs have been exploiting these resources to implement molecular breeding, especially for MARS and MABC, to accelerate cowpea variety improvement. The combination of conventional breeding and molecular breeding strategies, with workflow managed through the CGIAR breeding management system (BMS), promises an increase in the number of improved varieties available to farmers, thereby boosting cowpea production and productivity in SSA.
Stream 2 continues the process of further refining and improving existing elite materials. Adapted materials from breeding population 1 are crossed into breeding population 2 where they are further refined using GS + de novo GWAS models, where the fixed effects would include valuable QTL identified based on GWAS performed in Breeding Population 2, the exotic QTL from Stream 1, or any other large effect QTL a breeder might normally target for trait improvement. Output from Stream 2 can be advanced toward variety release or fed back into stream 1 to serve as parents for further crossing and population development. This approach helps the breeders to learn directly from data on new and diverse germplasm and make rapid genetic gain.
Inclusion of dominance effects into genomic prediction models was successfully attempted in animal breeding, too (Wellmann and Bennewitz, 2012; Wittenburg et al., 2011; Toro and Varona, 2010). It was shown that models with dominance can increase both the accuracy of genomicbreeding value prediction as well as prediction of genetic values (Wellmann and Bennewitz, 2012). Thereby prediction of genetic values of individuals profited con- siderably more than prediction of their breeding values. In plantbreeding, individual genotypes, such as single-cross hybrids, can be multiplied ad libitum and can be of tremendous economic value if successful as a variety. In contrast, genotypes in an- imal breeding are confined to a single individual of compara- tively low economic value, at least in respect to their own per- formance. Thus, genomic prediction of genetic values might be of less importance in animal breeding. Mate allocation emerged as a particularly promising application involving estimated domi- nance effects. Here, male and female parents of a paring are chosen such that the contribution of favorable dominance com- binations are maximized (Wellmann and Bennewitz, 2012; Toro and Varona, 2010). This concept closely resembles the concept of specific combining ability in hybrid breeding. However, because of Mendelian sampling, mate allocation is limited to increasing the average performance of the resulting full-sib families, from which individual members can deviate.
One major area where analysis was needed concerned prediction across generations. Selections can be done at the seedling stage if GEBV can be predicted from the pre- vious generations and training data. Because nearly all of the IITA germplasm from C1 and C2 were clonally evalu- ated, we were able to use these data to assess the accuracy of genomic predictions on unevaluated genotypes of the next generation. In general, the accuracy of prediction across generations was greatest when predicting C2, as shown by averaging across prediction models and traits for predictions trained either with C1 (mean = 0.19 ± SE 0.02) or GG + C1 (0.19 ± 0.02). The accuracy was lower on average when we predicted C2 with GG (0.11 ± 0.01) than when we predicted C1 with GG (0.17 ± 0.02). Accuracy was lowest for both plant vigor and RTWT (0.06 ± 0.005) and was highest for MCMDS (0.32 ± 0.03) and DM (0.38 ± 0.01). Most prediction models performed similarly, as shown by the averaged accuracy across traits and train- ing–test combinations, with RF performing worst (0.08 ± 0.01) and BayesA and BayesB performing best (both 0.20 Table 3. Summary of mean genomic best linear unbiased prediction (GBLUP) cross-validated predictive accuracies across populations. Four subset selectionmethods (random vs. STPGA) and the full set were considered. The high- est predictive accuracy across subsets and the full set is indicated in bold.
Some of the factors affecting prediction accuracy, such as trait heritability, genetic architecture, and to a large extent LD, cannot be controlled; however, we can have control of the design of reference data sets, including size and relationships, marker density, and the model used for estimation of effects. Among the factors that are under control of the researcher, the size of the training data set and the strength of genetic relationships between training and validation samples are by far the most important factors affecting prediction accuracy. The model of choice is also important; however, the differ- ences between models reported by simulation studies have not always been conﬁrmed by real data analysis. Empirical analyses have shown only small differences between meth- ods, with a slight advantage of models performing “selection and shrinkage” such as BayesB for traits with “large-effect QTL.” But in general thick-tailed models such as BayesA or Bayesian LASSO perform well across traits and G-BLUP per- forms well for most traits. An important reason is that, due to the fact that p n, there are a multitude of different pre- diction equations that yield about the same likelihood and minimum prediction error rate (Breiman 2001): often we encounter multiple equally-good models.
By increasing the accuracy and intensity of selection and shortening the generation interval, the rate of genetic progress for economically important dairy traits can be approximately doubled.
bulls with high genetic merit. Before progeny testing a young bull, the average estimated breeding value (EBV) of his sire and dam, which is commonly referred to as parent average, was used to select young bulls with the highest genetic merit and had an accuracy (reliability) of only 30 to 40%. In a progeny-testing scheme, a group of elite cows was identi- ﬁ ed as potential dams of young bulls (i.e., bull mothers). Progeny test- ing was necessary because most traits of economic importance in dairy cattle (e.g., milk production) are sex-limited and can be measured only in females. These bull mothers were mated to elite progeny-tested sires from the previous generation for the speciﬁ c purpose of producing bull calves. Once these young bulls reached sexual maturity, which typically occurred at about 12 months of age, they were mated to a large number of cows on commercial farms, with the goal of producing approximately 100 daughters. Approximately 3 years later, the daughters of these young bulls would begin lactating, and this information was used to calculate the EBV of their sires for milk production and other key traits, which typically had reliabilities of 75 to 85%. At this point, these bulls were approxi- mately 4.5 years of age, and the AI companies would decide which bulls should be culled and which bulls should be marketed to dairy farmers for the purpose of siring the next generation of replacement heifers. Overall, progeny-testing schemes are time consuming and costly because the AI companies have to wait many years to obtain genetic predictions with sufﬁ cient accuracy for making selection decisions, and in the meantime, hundreds of bulls are housed “in waiting” while phenotypes are measured on tens of thousands of their daughters. The objective of this review is to describe how genomics will affect genetic progress and breeding pro- grams in the future.
Using mixed model equations and simple correlation structures. Hill and Rosenberger (1985) showed the efficiency o f BLUP for combining information for germplasm evaluation. Similar BLUPs, i.e., assuming random effects as stochastically independent, were reported effective by Piepho (1994) for modeling multi-environment variety trials. Oman (1991) and Gogel et al. (1995) have shown how to fit models o f complex variance-covariance structure to genotype by environment data. Magari and Kang (1997) used mixed model estimation to consider the interaction o f individual genotypes with environments for stability analysis. Interaction-term variance components were estimated for each genotype by using the mixed model equations. The variance components were used as stability measures. They are equivalent to Shukla's stability variances (Shukla, 1972). but it is important to note that they were estimated as parameters o f a mixed model. Piepho (1998) put different well-known stability measures (Kang and Gauch, 1996) into a unifying mixed model perspective.