Assessment of yield stability in sorghum using univariate and multivariate statistical approaches

The experiment was carried out to estimate GEI in sorghum for grain yield using univariate and multivariate statistical approaches based on two sets of performance trials (T1 and T2). While T1 consisted of 15 genotypes and tested in 8 environments, T2 that consisted of 13 genotypes was carried out in 13 environments. Because the combined ANOVA of each trial revealed significant differences among the genotypes, among the environments and GEI, the five univariate stability estimates: CV(i), S(i)(2), W(i)(2), sigma(i)(2), b(i) and Sd(i)(2) were evaluated for ranking the genotypes. There was positive rank-correlation between CVi and S(i)(2) and among W(i)(2), sigma(i)(2), b(i). Sd(i)(2) had significant positive rank-correlation with sigma(i)(2) and bi in T1 but weak rank-correlation with the remaining parameters in both trials. The three types of univariate stability estimates and the only multivariate stability estimate, the AMMI analysis declared genotypes 2 and 5 to be the most stable in T1, but they gave quite unrelated ranking in T2. Because of the lack of correspondence among the tested stability estimates in the two trials, it was difficult to reach a conclusion on producing genotype recommendation based on the univariate statistical approach. However, as GEI has multivariate nature, the multivariate approach is believed to give more robust inference. Hence, some stable genotypes were suggested using the AMMI model for sorghum growing dry lowlands of the country.     

Predictive and postdictive success of statistical analyses of yield trials

Summary The accuracy of a yield trial can be increased by improved experimental techniques, more replicates, or more efficient statistical analyses. The third option involves nominal fixed costs, and is therefore very attractive. The statistical analysis recommended here combines the Additive main effects and multiplicative interaction (AMMI) model with a predictive assessment of accuracy. AMMI begins with the usual analysis of variance (ANOVA) to compute genotype and environment additive effects. It then applies principal components analysis (PCA) to analyze non-additive interaction effects. Tests with a New York soybean yield trial show that the predictive accuracy of AMMI with only two replicates is equal to the predictive accuracy of means based on five replicates. The effectiveness of AMMI increases with the size of the yield trial and with the noisiness of the data. Statistical analysis of yield trials with the AMMI model has a number of promising implications for agronomy and plant breeding research programs.This research was supported by the Rhizobotany Project of the USDA-ARS     

Interpreting genotype × environment interaction in tropical maize using linked molecular markers and environmental covariables

An understanding of the genetic and environmental basis of genotype×environment interaction (GEI) is of fundamental importance in plant breeding. In mapping quantitative trait loci (QTLs), suitable genetic populations are grown in different environments causing QTLs×environment interaction (QEI). The main objective of the present study is to show how Partial Least Squares (PLS) regression and Factorial Regression (FR) models using genetic markers and environmental covariables can be used for studying QEI related to GEI. Biomass data were analyzed from a multi-environment trial consisting of 161 lines from a F_3:4 maize segregating population originally created with the purpose of mapping QTLs loci and investigating adaptation differences between highland and lowland tropical maize. PLS and FR methods detected 30 genetic markers (out of 86) that explained a sizeable proportion of the interaction of maize lines over four contrasting environments involving two low-altitude sites, one intermediate-altitude site, and one high-altitude site for biomass production. Based on a previous study, most of the 30 markers were associated with QTLs for biomass and exhibited significant QEI. It was found that marker loci in lines with positive GEI for the highland environments contained more highland alleles, whereas marker loci in lines with positive GEI for intermediate and lowland environments contained more lowland alleles. In addition, PLS and FR models identified maximum temperature as the most-important environmental covariable for GEI. Using a stepwise variable selection procedure, a FR model was constructed for GEI and QEI that exclusively included cross products between genetic markers and environmental covariables. Higher maximum temperature in low- and intermediate-altitude sites affected the expression of some QTLs, while minimum temperature affected the expression of other QTLs. Received: 10 January 1999 / Accepted: 12 March 1999     

Full and reduced models for yield trials

Summary Empirical results routinely demonstrate that the reduced Additive Main effects and Multiplicative Interaction (AMMI) model achieves better predictive accuracy for yield trials than does the full treatment means model. It may seem mysterious that treatment means are not the most accurate estimates, but rather that the AMMI model is often more accurate than its data. The statistical explanation involves the Stein effect, whereby a small sacrifice in bias can produce a large gain in accuracy. The corresponding agricultural explanation is somewhat complex, beginning with a yield trial's design and ending with its research purposes and applications. In essence, AMMI selectively recovers pattern related to the treatment design in its model, while selectively relegating noise related to the experimental design in its discarded residual. For estimating the yield of a particular genotype in a particular environment, the AMMI model uses the entire yield trial, rather than only the several replications of this particular trial, as in the treatment means model. This use of more information is the source of AMMI's gain in accuracy.This research was supported by the Rhizobotany Project of the USDA-ARS     

Use of trial clustering to study QTL × environment effects for grain yield and related traits in maize

A population of 300 F_3:4 lines derived from the cross between maize inbred lines F2 and F252 was evaluated for testcross value in a large range of environmental conditions (11 different locations in 2 years: 1995 and 1996) in order to study (1) the magnitude of genotype × environment and (2) the stability of quantitative trait loci (QTL) effects. Several agronomic traits were measured: dry grain yield (DGY), kernel weight, average number of kernels per plant, silking date (SD) and grain moisture at harvest. A large genotype × environment interaction was found, particularly for DGY. A hierarchical classification of trials and an additive main effects and multiplicative interaction (AMMI) model were carried out. Both methods led to the conclusion that trials could be partitioned into three groups consistent with (1) the year of experiment and (2) the water availability (irrigated vs non-irrigated) for the trials sown in 1995. QTL detection was carried out for all the traits in the different groups of trials. Between 9 and 15 QTL were detected for each trait. QTL × group and QTL × trial effects were tested and proved significant for a large proportion of QTL. QTL detection was also performed on coordinates on the first two principal components (PC) of the AMMI model. PC QTL were generally detected in areas where QTL × group and QTL × trial interactions were significant. A region located on chromosome 8 near an SD QTL seemed to play a key role in DGY stability. Our results confirm the key role of water availability and flowering earliness on grain yield stability in maize.     

Genotype by production environment interaction for birth and weaning weights in a population of composite beef cattle

The objectives of the present study were: (1) to evaluate the importance of genotype×production environment interaction for the genetic evaluation of birth weight (BW) and weaning weight (WW) in a population of composite beef cattle in Brazil, and (2) to investigate the importance of sire×contemporary group interaction (S×CG) to model G×E and improve the accuracy of prediction in routine genetic evaluations of this population. Analyses were performed with one, two (favorable and unfavorable) or three (favorable, intermediate, unfavorable) different definitions of production environments. Thus, BW and WW records of animals in a favorable environment were assigned to either trait 1, in an intermediate environment to trait 2 or in an unfavorable environment to trait 3. The (co)variance components were estimated using Gibbs sampling in single-, bi- or three-trait animal models according to the definition of number of production environments. In general, the estimates of genetic parameters for BW and WW were similar between environments. The additive genetic correlations between production environments were close to unity for BW; however, when examining the highest posterior density intervals, the correlation between favorable and unfavorable environments reached a value of only 0.70, a fact that may lead to changes in the ranking of sires across environments. The posterior mean genetic correlation between direct effects was 0.63 in favorable and unfavorable environments for WW. When S×CG was included in two- or three-trait analyses, all direct genetic correlations were close to unity, suggesting that there was no evidence of a genotype×production environment interaction. Furthermore, the model including S×CG contributed to prevent overestimation of the accuracy of breeding values of sires, provided a lower error of prediction for both direct and maternal breeding values, lower squared bias, residual variance and deviance information criterion than the model omitting S×CG. Thus, the model that included S×CG can therefore be considered the best model on the basis of these criteria. The genotype×production environment interaction should not be neglected in the genetic evaluation of BW and WW in the present population of beef cattle. The inclusion of S×CG in the model is a feasible and plausible alternative to model the effects of G×E in the genetic evaluations.     

Optimization of multi-environment trials for genomic selection based on crop models

Key message

We propose a statistical criterion to optimize multi-environment trials to predict genotype × environment interactions more efficiently, by combining crop growth models and genomic selection models.

Abstract

Genotype × environment interactions (GEI) are common in plant multi-environment trials (METs). In this context, models developed for genomic selection (GS) that refers to the use of genome-wide information for predicting breeding values of selection candidates need to be adapted. One promising way to increase prediction accuracy in various environments is to combine ecophysiological and genetic modelling thanks to crop growth models (CGM) incorporating genetic parameters. The efficiency of this approach relies on the quality of the parameter estimates, which depends on the environments composing this MET used for calibration. The objective of this study was to determine a method to optimize the set of environments composing the MET for estimating genetic parameters in this context. A criterion called OptiMET was defined to this aim, and was evaluated on simulated and real data, with the example of wheat phenology. The MET defined with OptiMET allowed estimating the genetic parameters with lower error, leading to higher QTL detection power and higher prediction accuracies. MET defined with OptiMET was on average more efficient than random MET composed of twice as many environments, in terms of quality of the parameter estimates. OptiMET is thus a valuable tool to determine optimal experimental conditions to best exploit MET and the phenotyping tools that are currently developed.

     

Simultaneously accounting for population structure, genotype by environment interaction, and spatial variation in marker-trait associations in sugarcane

Few association mapping studies have simultaneously accounted for population structure, genotype by environment interaction (GEI), and spatial variation. In this sugarcane association mapping study we tested models accounting for these factors and identified the impact that each model component had on the list of markers declared as being significantly associated with traits. About 480 genotypes were evaluated for cane yield and sugar content at three sites and scored with DArT markers. A mixed model was applied in analysis of the data to simultaneously account for the impacts of population structure, GEI, and spatial variation within a trial. Two forms of the DArT marker data were used in the analysis: the standard discrete data (0, 1) and a continuous DArT score, which is related to the marker dosage. A large number of markers were significantly associated with cane yield and sugar content. However, failure to account for population structure, GEI, and (or) spatial variation produced both type I and type II errors, which on the one hand substantially inflated the number of significant markers identified (especially true for failing to account for GEI) and on the other hand resulted in failure to detect markers that could be associated with cane yield or sugar content (especially when failing to account for population structure). We concluded that association mapping based on trials from one site or analysis that failed to account for GEI would produce many trial-specific associated markers that would have low value in breeding programs.     

Grain Yield and Charcoal Rot Resistance Stability in Common Beans under Terminal Drought Conditions

Charcoal rot (Macrophomina phaseolina) is a major disease of beans (Phaseolus vulgaris L.) in Mexico. The use of germplasm combining high‐yield stability with resistance to drought and charcoal rot could reduce damage from this disease. In this study, we compared the Eberhart and Russell method and the Additive Main Effect and Multiplicative Interaction (AMMI) model plus biplot analysis for measuring grain yield (GY) and charcoal rot resistance (CHRR) stabilities in 98 F_{8 : 10} recombinant inbred lines (RILs) derived from a cross between bean adapted to the tropics (BAT) 477 (resistant) × Pinto UI‐114 (susceptible). Experiments were conducted from 2007 to 2009 in Isla, Cotaxtla, Río Bravo and Díaz Ordaz, México, under irrigated or terminal drought conditions. anova detected significant differences (P ≤ 0.05) in GY and CHRR among environments, genotypes and genotype × environment interactions (GEI). Most RILs showed good responses to unfavourable environments based on GY (48) and CHRR (40). AMMI anova s for both traits showed that all sources of variation in the model accounted for approximately 49% of the total squared sum. For the first principal component (PC1), we found 13 RILs that were stable for GY, and for the second (PC2), we found 9 that were stable for GI. For CHRR, we detected 14 stable RILs (PC1) and eight (PC2). Biplot analysis showed the largest vectors for Díaz Ordaz (irrigated and drought, 2008), where the highest and most variable GYs were detected. The shortest vectors were found in Isla (drought, 2007) and Río Bravo (irrigated and drought, 2008), where the lowest and least variable GY were found. We found differential responses of RILs to locations, years and soil humidity conditions as well as significant GEI based on GY and CHRR. The two methods were complementary, and both gave us information to select stable, high‐yield germplasm associated with resistance to charcoal rot disease.     

Genotype‐by‐environment interaction and the Dobzhansky–Muller model of postzygotic isolation

The Dobzhansky–Muller (D–M) model of reproductive isolation (RI) posits that hybrid sterility and inviability result from negative epistatic interactions between alleles at a minimum of two genes. This standard model makes several implicit assumptions, including a lack of environmental effects and genotype‐by‐environment interactions (GEI) involving hybrid sterility and hybrid inviability loci. Here we relax this assumption of the standard D–M model. By doing so, several patterns of the genetic architecture of RI change. First, a novel single‐locus model of postzygotic RI emerges. Several indirect lines of evidence are discussed in support of the model, but we conclude that this new single‐locus model is currently no more supported than previous ones. Second, when multilocus D–M models incorporating GEI are considered, we find that the number of potential negative epistatic interactions increases dramatically over the number predicted by the standard D–M model, even when only the most simple case of two‐allele interactions are considered. Third, these multilocus models suggest that some previous generalizations about the evolutionary genetics of postzygotic RI may not necessarily hold. Our findings also suggest that the evolution of postzygotic RI may be more likely when the expression of traits driving speciation is affected by the environment, since there appears to be a greater spectrum of potential hybrid incompatibilities under the D–M model incorporating GEI.     

我国旱地春小麦产量及主要农艺指标的变异分析

采用4年、13个品种(系)、18个试点组成的全国旱地春小麦区域试验产量资料,通过联合方差分析和基因型及其与环境互作（GGE）双标图分析,研究了基因型、环境、基因型与环境互作效应（GEI）对产量变异的影响及品种的产量稳定性.结果表明：环境对产量变异的影响远大于基因型和GEI,环境引起的产量变异占87.5%～92.0%．互作因素中以地点×基因型的互作效应最大,基因型×年份的互作效应最小.我国旱地春小麦基因型多年多点的平均产量水平为2550 kg·hm^-2.产量三要素中,千粒重受环境的影响最小.影响产量变异的主要环境因子有：≥10 ℃年积温、生育期降雨量、平均气温、海拔、年降雨量和无霜期.产量与单位面积穗数（0.675^**）、穗粒数（0.581^**）、千粒重（0.456^**）呈极显著正相关,产量三要素间也呈正相关（0.244～0.480^**）,处于可同步提高范围.     

Predicting treatment effect from surrogate endpoints and historical trials: an extrapolation involving probabilities of a binary outcome or survival to a specific time

Using multiple historical trials with surrogate and true endpoints, we consider various models to predict the effect of treatment on a true endpoint in a target trial in which only a surrogate endpoint is observed. This predicted result is computed using (1) a prediction model (mixture, linear, or principal stratification) estimated from historical trials and the surrogate endpoint of the target trial and (2) a random extrapolation error estimated from successively leaving out each trial among the historical trials. The method applies to either binary outcomes or survival to a particular time that is computed from censored survival data. We compute a 95% confidence interval for the predicted result and validate its coverage using simulation. To summarize the additional uncertainty from using a predicted instead of true result for the estimated treatment effect, we compute its multiplier of standard error. Software is available for download.     

Genotype and environment effects on rice (Oryza sativa L.) grain arsenic concentration in Bangladesh

Genetic analysis of 38 rice varieties released by the Bangladesh Rice Research Institute (BRRI) identified 34 as indica, 2 as admixed between indica and aus, and 4 as belonging to the aromatic/Group V subpopulation. Indica varieties developed for the two major rice-growing seasons, the wet monsoon (aman) and the dry winter (boro), were not genetically differentiated. The Additive Main Effect and Multiplicative Interaction (AMMI) model was used to assess the effect of genotype (G), environment (E) and genotype-environment interaction (GEI) on grain arsenic (As) concentration when these rice varieties were grown at ten BRRI research stations located across diverse agro-ecological zones in Bangladesh. G, E and GEI, significantly influenced grain As concentration in both seasons. Overall, E accounted for 69%–80%, G 9%–10% and GEI 10%–21% of the observed variability in grain As. One site, Satkhira had the highest mean grain As concentration and the largest interaction principle component analysis (IPCA) scores in both seasons, indicating maximum interaction with genotypes. Site effects were more pronounced in the boro than in the aman season. The soil level of poorly crystalline Fe-oxide (AOFe), the ratio of AOFe to associated As, soil phosphate extractable As and soil pH were important sub-components of E controlling rice grain As concentration. Irrespective of environment, the mean grain As concentration was significantly higher in the boro (0.290 mg As kg^?1) than in the aman (0.154 mg As kg^?1) season (p?<?0.0001), though the reasons for this are unclear. Based on mean grain As concentration and stability across environments, the variety BR3 is currently the best choice for the boro season, while BR 23 and BRRI dhan 38 are the best choices for the aman season. Popular varieties BR 11 (aman) and BRRI dhan 28 and 29 (boro) had grain As concentrations close to the mean value and were fairly stable across environments, while high-yielding, short-duration aman season varieties (BRRI dhan 32, 33 and 39) developed for intensified cropping had relatively high grain As concentrations. Results suggest that genetic approaches to reducing As in rice grain will require the introduction of novel genetic variation and must be accompanied by appropriate management strategies to reduce As availability and uptake by rice.     

Genotype by environment interaction for 450-day weight of Nelore cattle analyzed by reaction norm models

Genotype by environment interactions (GEI) have attracted increasing attention in tropical breeding programs because of the variety of production systems involved. In this work, we assessed GEI in 450-day adjusted weight (W450) Nelore cattle from 366 Brazilian herds by comparing traditional univariate single-environment model analysis (UM) and random regression first order reaction norm models for six environmental variables: standard deviations of herd-year (RRMw) and herd-year-season-management (RRMw-m) groups for mean W450, standard deviations of herd-year (RRMg) and herd-year-season-management (RRMg-m) groups adjusted for 365-450 days weight gain (G450) averages, and two iterative algorithms using herd-year-season-management group solution estimates from a first RRMw-m and RRMg-m analysis (RRMITw-m and RRMITg-m, respectively). The RRM results showed similar tendencies in the variance components and heritability estimates along environmental gradient. Some of the variation among RRM estimates may have been related to the precision of the predictor and to correlations between environmental variables and the likely components of the weight trait. GEI, which was assessed by estimating the genetic correlation surfaces, had values < 0.5 between extreme environments in all models. Regression analyses showed that the correlation between the expected progeny differences for UM and the corresponding differences estimated by RRM was higher in intermediate and favorable environments than in unfavorable environments (p < 0.0001).     

水稻基因型×环境互作效应分析及其与气候因子的关系

利用多年水稻（早籼稻和晚粳稻）区域试验产量结果和有关试验点气候资料,分析 了基因型×环境互作效应结构变化趋势、与主要气候因子以及试点平均产量的关系等．研究表 明,水稻基因型×环境互作效应值在年度间相对稳定,存在着一个相对稳定的数值．单一试点 水平上产生的交互效应值年度间也保持相对稳定．试点的互作效应由固定部分（由土壤等因素引 起）和随机部分（由不确定气候等因素引起）两部分混合组成,两部分约各占５０％．试点互作效应 与试点对品种判别能力的估算参数（Ｄｊ参数）之间均存在着较好的线性相关关系,与试点平均产 量之间则表现出一种不规则状态．与气候因子的相关性分析结果表明,晚粳稻试验点品种×地点 互作效应与１０月份（灌浆成熟期）的平均日照和平均气温有较大的相关性．从总体趋势上看,气 温和日照与试验点互作效应呈负向相关关系．     

Analyzing Variety by Environment Data Using Multiplicative Mixed Models and Adjustments for Spatial Field Trend

The recommendation of new plant varieties for commercial use requires reliable and accurate predictions of the average yield of each variety across a range of target environments and knowledge of important interactions with the environment. This information is obtained from series of plant variety trials, also known as multi-environment trials (MET). Cullis, Gogel, Verbyla, and Thompson (1998) presented a spatial mixed model approach for the analysis of MET data. In this paper we extend the analysis to include multiplicative models for the variety effects in each environment. The multiplicative model corresponds to that used in the multivariate technique of factor analysis. It allows a separate genetic variance for each environment and provides a parsimonious and interpretable model for the genetic covariances between environments. The model can be regarded as a random effects analogue of AMMI (additive main effects and multiplicative interactions). We illustrate the method using a large set of MET data from a South Australian barley breeding program.     

Multi-environment QTL mixed models for drought stress adaptation in wheat

Many quantitative trait loci (QTL) detection methods ignore QTL-by-environment interaction (QEI) and are limited in accommodation of error and environment-specific variance. This paper outlines a mixed model approach using a recombinant inbred spring wheat population grown in six drought stress trials. Genotype estimates for yield, anthesis date and height were calculated using the best design and spatial effects model for each trial. Parsimonious factor analytic models best captured the variance–covariance structure, including genetic correlations, among environments. The 1RS.1BL rye chromosome translocation (from one parent) which decreased progeny yield by 13.8 g m⁻² was explicitly included in the QTL model. Simple interval mapping (SIM) was used in a genome-wide scan for significant QTL, where QTL effects were fitted as fixed environment-specific effects. All significant environment-specific QTL were subsequently included in a multi-QTL model and evaluated for main and QEI effects with non-significant QEI effects being dropped. QTL effects (either consistent or environment-specific) included eight yield, four anthesis, and six height QTL. One yield QTL co-located (or was linked) to an anthesis QTL, while another co-located with a height QTL. In the final multi-QTL model, only one QTL for yield (6 g m⁻²) was consistent across environments (no QEI), while the remaining QTL had significant QEI effects (average size per environment of 5.1 g m⁻²). Compared to single trial analyses, the described framework allowed explicit modelling and detection of QEI effects and incorporation of additional classification information about genotypes. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Empirical best linear unbiased prediction in cultivar trials using factor-analytic variance-covariance structures

 Results of multi-environment trials to evaluate new plant cultivars may be displayed in a two-way table of genotypes by environments. Different estimators are available to fill the cells of such tables. It has been shown previously that the predictive accuracy of the simple genotype by environment mean is often lower than that of other estimators, e.g. least-squares estimators based on multiplicative models, such as the additive main effects multiplicative interaction (AMMI) model, or empirical best-linear unbiased predictors (BLUPs) based on a two-way analysis-of-variance (ANOVA) model. This paper proposes a method to obtain BLUPs based on models with multiplicative terms. It is shown by cross-validation using five real data sets (oilseed rape, Brassica napus L.) that the predictive accuracy of BLUPs based on models with multiplicative terms may be better than that of least-squares estimators based on the same models and also better than BLUPs based on ANOVA models. Received: 18 October 1997 / Accepted: 31 March 1998     

Environment characterization as an aid to wheat improvement: interpreting genotype-environment interactions by modelling water-deficit patterns in North-Eastern Australia

Genotype-environment interactions (GEI) limit genetic gain for complex traits such as tolerance to drought. Characterization of the crop environment is an important step in understanding GEI. A modelling approach is proposed here to characterize broadly (large geographic area, long-term period) and locally (field experiment) drought-related environmental stresses, which enables breeders to analyse their experimental trials with regard to the broad population of environments that they target. Water-deficit patterns experienced by wheat crops were determined for drought-prone north-eastern Australia, using the APSIM crop model to account for the interactions of crops with their environment (e.g. feedback of plant growth on water depletion). Simulations based on more than 100 years of historical climate data were conducted for representative locations, soils, and management systems, for a check cultivar, Hartog. The three main environment types identified differed in their patterns of simulated water stress around flowering and during grain-filling. Over the entire region, the terminal drought-stress pattern was most common (50% of production environments) followed by a flowering stress (24%), although the frequencies of occurrence of the three types varied greatly across regions, years, and management. This environment classification was applied to 16 trials relevant to late stages testing of a breeding programme. The incorporation of the independently-determined environment types in a statistical analysis assisted interpretation of the GEI for yield among the 18 representative genotypes by reducing the relative effect of GEI compared with genotypic variance, and helped to identify opportunities to improve breeding and germplasm-testing strategies for this region.     

Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle

Background

Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated.

Results

Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield.

Conclusions

Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain.