Simulation of functional additive and non-additive genetic effects using statistical estimates from quantitative genetic models.

Stochastic simulation software is commonly used to aid breeders designing cost-effective breeding programs and to validate statistical models used in genetic evaluation. An essential feature of the software is the ability to simulate populations with desired genetic and non-genetic parameters. However, this feature often fails when non-additive effects due to dominance or epistasis are modeled, as the desired properties of simulated populations are estimated from classical quantitative genetic statistical models formulated at the population level. The software simulates underlying functional effects for genotypic values at the individual level, which are not necessarily the same as effects from statistical models in which dominance and epistasis are included. This paper provides the theoretical basis and mathematical formulas for the transformation between functional and statistical effects in such simulations. The transformation is demonstrated with two statistical models analyzing individual phenotypes in a single population (common in animal breeding) and plot phenotypes of three-way hybrids involving two inbred populations (observed in some crop breeding programs). We also describe different methods for the simulation of functional effects for additive genetics, dominance, and epistasis to achieve the desired levels of variance components in classical statistical models used in quantitative genetics.

Causal inference and GWAS: Rubin, Pearl, and Mendelian randomization.

Although Genome Wide Analysis (GWAS) have been widely used to understand the genetic architecture of complex quantitative traits, interpreting their results in terms of the biological processes that determine those traits has been difficult or even lacking, because of the variability in responses to the tests of hypotheses within a trait, species, and breed or cross, and the lack of follow-up studies. It is then essential employing appropriate statistical tests that point out to the causal genes responsible of the relevant fraction of the genetic variability observed. We briefly review the main theoretical aspects of the two schools of causal inference (Rubin's Causal Model, RCM, and Pearl's causal inference, PCI). RCM approachs the hypothesis testing from a randomization perspective by considering a wider space of the observation, i.e. the "potential outcomes", rather than the narrower space that results from defining "treatment" effects after observing the data. Next, we discuss the assumptions involved to meet the requirements of randomization for RCM with observational data (non-designed experiments) with special emphasis on the Stable Unit Treatment Analysis (SUTVA). Due to the presence of "confounders" (i.e. systematic fixed effects, environmental permanent effects, interaction among genes, etc.), causal average treatment effects are viewed through the familiar lens of normal linear (or mixed) models. To overcome the difficulties of association analyses, a tests of causal effects is introduced using independent predicted residual breeding values from animal models of genetic evaluation that avoids the effects of population structure and confounder effects. An independent section discusses the issue of whether the additive effects defined at the "gene" level by R. A. Fisher and popularized in D. S. Falconer's textbook of quantitative genetics can be termed causal from either RCM or PCI.

Metabolomic-genomic prediction can improve prediction accuracy of breeding values for malting quality traits in barley.

BACKGROUND: Metabolomics measures an intermediate stage between genotype and phenotype, and may therefore be useful for breeding. Our objectives were to investigate genetic parameters and accuracies of predicted breeding values for malting quality (MQ) traits when integrating both genomic and metabolomic information. In total, 2430 plots of 562 malting spring barley lines from three years and two locations were included. Five MQ traits were measured in wort produced from each plot. Metabolomic features used were 24,018 nuclear magnetic resonance intensities measured on each wort sample. Methods for statistical analyses were genomic best linear unbiased prediction (GBLUP) and metabolomic-genomic best linear unbiased prediction (MGBLUP). Accuracies of predicted breeding values were compared using two cross-validation strategies: leave-one-year-out (LOYO) and leave-one-line-out (LOLO), and the increase in accuracy from the successive inclusion of first, metabolomic data on the lines in the validation population (VP), and second, both metabolomic data and phenotypes on the lines in the VP, was investigated using the linear regression (LR) method. RESULTS: For all traits, we saw that the metabolome-mediated heritability was substantial. Cross-validation results showed that, in general, prediction accuracies from MGBLUP and GBLUP were similar when phenotypes and metabolomic data were recorded on the same plots. Results from the LR method showed that for all traits, except one, accuracy of MGBLUP increased when including metabolomic data on the lines of the VP, and further increased when including also phenotypes. However, in general the increase in accuracy of MGBLUP when including both metabolomic data and phenotypes on lines of the VP was similar to the increase in accuracy of GBLUP when including phenotypes on the lines of the VP. Therefore, we found that, when metabolomic data were included on the lines of the VP, accuracies substantially increased for lines without phenotypic records, but they did not increase much when phenotypes were already known. CONCLUSIONS: MGBLUP is a useful approach to combine phenotypic, genomic and metabolomic data for predicting breeding values for MQ traits. We believe that our results have significant implications for practical breeding of barley and potentially many other species.

Estimation and consequences of direct-maternal genetic and environmental covariances in models for genetic evaluation in broilers.

BACKGROUND: Maternal effects influence juvenile traits such as body weight and early growth in broilers. Ignoring significant maternal effects leads to reduced accuracy and inflated predicted breeding values. Including genetic and environmental direct-maternal covariances into prediction models in broilers can increase the accuracy and limit inflation of predicted breeding values better than simply adding maternal effects to the model. To test this hypothesis, we applied a model accounting for direct-maternal genetic covariance and direct-maternal environmental covariance to estimate breeding values. RESULTS: This model, and simplified versions of it, were tested using simulated broiler populations and then was applied to a large broiler population for validation. The real population analyzed consisted of a commercial line of broilers, for which body weight at a common slaughter age was recorded for 41 selection rounds. The direct-maternal genetic covariance was negative whereas the direct-maternal environmental covariance was positive. Simulated populations were created to mimic the real population. The predictive ability of the models was assessed by cross-validation, where the validation birds were all from the last five selection rounds. Accuracy of prediction was defined as the correlation between the predicted breeding values estimated without the phenotypic records of the validation population and a predictor. The predictors were the breeding values estimated using all the phenotypic information and the phenotypes corrected for the fixed effects, and for the simulated data, the true breeding values. In the real data, adding the environmental covariance, with or without also adding the genetic covariance, increased the accuracy, or reduced deflation of breeding values compared with a model not including dam-offspring covariance. Nevertheless, in the simulated data, reduction in the inflation of breeding values was possible and was associated with a gain in accuracy of up to 6% compared with a model not including both forms of direct-maternal covariance. CONCLUSIONS: In this paper, we propose a simple approach to estimate the environmental direct-maternal covariance using standard software for REML analysis. The genetic covariance between dam and offspring was negative whereas the corresponding environmental covariance was positive. Considering both covariances in models for genetic evaluation increased the accuracy of predicted breeding values.

Improvement of genomic prediction in advanced wheat breeding lines by including additive-by-additive epistasis.

KEY MESSAGE: Including additive and additive-by-additive epistasis in a NOIA parametrization did not yield orthogonal partitioning of genetic variances, nevertheless, it improved predictive ability in a leave-one-out cross-validation for wheat grain yield. Additive-by-additive epistasis is the principal non-additive genetic effect in inbred wheat lines and is potentially useful for developing cultivars based on total genetic merit; nevertheless, its practical benefits have been highly debated. In this article, we aimed to (i) evaluate the performance of models including additive and additive-by-additive epistatic effects for variance components (VC) estimation of grain yield in a wheat-breeding population, and (ii) to investigate whether including additive-by-additive epistasis in genomic prediction enhance wheat grain yield predictive ability (PA). In total, 2060 sixth-generation (F6) lines from Nordic Seed A/S breeding company were phenotyped in 21 year-location combinations in Denmark, and genotyped using a 15 K-Illumina-BeadChip. Three models were used to estimate VC and heritability at plot level: (i) "I-model" (baseline), (ii) "I + GA-model", extending I-model with an additive genomic effect, and (iii) "I + GA + GAA-model", extending I + GA-model with an additive-by-additive genomic effects. The I + GA-model and I + GA + GAA-model were based on the Natural and Orthogonal Interactions Approach (NOIA) parametrization. The I + GA + GAA-model failed to achieve orthogonal partition of genetic variances, as revealed by a change in estimated additive variance of I + GA-model when epistasis was included in the I + GA + GAA-model. The PA was studied using leave-one-line-out and leave-one-breeding-cycle-out cross-validations. The I + GA + GAA-model increased PA significantly (16.5%) compared to the I + GA-model in leave-one-line-out cross-validation. However, the improvement due to including epistasis was not observed in leave-one-breeding-cycle-out cross-validation. We conclude that epistatic models can be useful to enhance predictions of total genetic merit. However, even though we used the NOIA parameterization, the variance partition into orthogonal genetic effects was not possible.

Prediction of breeding values for group-recorded traits including genomic information and an individually recorded correlated trait.

Records on groups of individuals could be valuable for predicting breeding values when a trait is difficult or costly to measure on single individuals, such as feed intake and egg production. Adding genomic information has shown improvement in the accuracy of genetic evaluation of quantitative traits with individual records. Here, we investigated the value of genomic information for traits with group records. Besides, we investigated the improvement in accuracy of genetic evaluation for group-recorded traits when including information on a correlated trait with individual records. The study was based on a simulated pig population, including three scenarios of group structure and size. The results showed that both the genomic information and a correlated trait increased the accuracy of estimated breeding values (EBVs) for traits with group records. The accuracies of EBV obtained from group records with a size 24 were much lower than those with a size 12. Random assignment of animals to pens led to lower accuracy due to the weaker relationship between individuals within each group. It suggests that group records are valuable for genetic evaluation of a trait that is difficult to record on individuals, and the accuracy of genetic evaluation can be considerably increased using genomic information. Moreover, the genetic evaluation for a trait with group records can be greatly improved using a bivariate model, including correlated traits that are recorded individually. For efficient use of group records in genetic evaluation, relatively small group size and close relationships between individuals within one group are recommended.

Statistical model and testing designs to increase response to selection with constrained inbreeding in genomic breeding programs for pigs affected by social genetic effects.

BACKGROUND: Social genetic effects (SGE) are the effects of the genotype of one animal on the phenotypes of other animals within a social group. Because SGE contribute to variation in economically important traits for pigs, the inclusion of SGE in statistical models could increase responses to selection (RS) in breeding programs. In such models, increasing the relatedness of members within groups further increases RS when using pedigree-based relationships; however, this has not been demonstrated with genomic-based relationships or with a constraint on inbreeding. In this study, we compared the use of statistical models with and without SGE and compared groups composed at random versus groups composed of families in genomic selection breeding programs with a constraint on the rate of inbreeding. RESULTS: When SGE were of a moderate magnitude, inclusion of SGE in the statistical model substantially increased RS when SGE were considered for selection. However, when SGE were included in the model but not considered for selection, the increase in RS and in accuracy of predicted direct genetic effects (DGE) depended on the correlation between SGE and DGE. When SGE were of a low magnitude, inclusion of SGE in the model did not increase RS, probably because of the poor separation of effects and convergence issues of the algorithms. Compared to a random group composition design, groups composed of families led to higher RS. The difference in RS between the two group compositions was slightly reduced when using genomic-based compared to pedigree-based relationships. CONCLUSIONS: The use of a statistical model that includes SGE can substantially improve response to selection at a fixed rate of inbreeding, because it allows the heritable variation from SGE to be accounted for and capitalized on. Compared to having random groups, family groups result in greater response to selection in the presence of SGE but the advantage of using family groups decreases when genomic-based relationships are used.

Genetic parameters and genomic prediction for feed intake recorded at the group and individual level in different production systems for growing pigs.

BACKGROUND: In breeding programs, recording large-scale feed intake (FI) data routinely at the individual level is costly and difficult compared with other production traits. An alternative approach could be to record FI at the group level since animals such as pigs are normally housed in groups and fed by a shared feeder. However, to date there have been few investigations about the difference between group- and individual-level FI recorded in different environments. We hypothesized that group- and individual-level FI are genetically correlated but different traits. This study, based on the experiment undertaken in purebred DanBred Landrace (L) boars, was set out to estimate the genetic variances and correlations between group- and individual-level FI using a bivariate random regression model, and to examine to what extent prediction accuracy can be improved by adding information of individual-level FI to group-level FI for animals recorded in groups. For both bivariate and univariate models, single-step genomic best linear unbiased prediction (ssGBLUP) and pedigree-based BLUP (PBLUP) were implemented and compared. RESULTS: The variance components from group-level records and from individual-level records were similar. Heritabilities estimated from group-level FI were lower than those from individual-level FI over the test period. The estimated genetic correlations between group- and individual-level FI based on each test day were on average equal to 0.32 (SD = 0.07), and the estimated genetic correlation for the whole test period was equal to 0.23. Our results demonstrate that by adding information from individual-level FI records to group-level FI records, prediction accuracy increased by 0.018 and 0.032 compared with using group-level FI records only (bivariate vs. univariate model) for PBLUP and ssGBLUP, respectively. CONCLUSIONS: Based on the current dataset, our findings support the hypothesis that group- and individual-level FI are different traits. Thus, the differences in FI traits under these two feeding systems need to be taken into consideration in pig breeding programs. Overall, adding information from individual records can improve prediction accuracy for animals with group records.

Genotype by climate zone interactions for fertility, somatic cell score, and production in Iranian Holsteins.

The objective of this study was to investigate genetic variation and genotype by environment (G × E) interactions for fertility (including age at first calving and calving interval), somatic cell score (SCS), and milk production traits for Iranian Holsteins. Different environments were defined based on the climatic zones (cold, semi-cold, and moderate) and considering the herd location. Data were collected between 2003 and 2018 by the National Animal Breeding Center of Iran (Karaj). Variance and covariance components and genetic correlations were estimated using 2 different models, which were analyzed using Bayesian methods. For both models, performance of traits in each climate were considered as different traits. Fertility traits were analyzed using a trivariate model. Furthermore, SCS and production traits were analyzed using trivariate random regression models (records in different climate zones considered as different traits). For the fertility traits, the largest estimates of heritability were observed in cold climate. Fertility performance was always better in cold environment. Genetic correlations between climatic zones ranged from 0.85 to 0.94. For daily measurements of SCS and production traits, heritability ranged from 0.031 to 0.037 and 0.069 to 0.209, respectively. Genetic variances were the highest in the semi-cold and moderate climates for the SCS and production traits, respectively. Furthermore, across the studied climates, 305-d genetic correlation ranged from 0.756 to 0.884 for SCS and from 0.925 to 0.957 for the production traits. The structure of genetic correlation within each climate indicated a negative correlation between early and late lactation for SCS, especially in the cold climate and for milk production in the moderate climate. For fat percentage, in all climatic zones, the lowest genetic correlations were observed between early and mid-lactation. In addition, for protein production in the cold climate, a negative correlation was observed between early and late lactation. Results indicated heterogeneous variance components for all the studied traits across various climatic zones. Estimated genetic correlations for SCS revealed that the genetic expression of animals may vary by climatic zone. Results indicated the existence of G × E interaction due to the climatic condition, only for SCS. Therefore, in Iranian Holsteins, the effect of G × E interactions should not be neglected, especially for SCS, as different sires might be optimal for use in different climatic zones.

The relative effect of genomic information on efficiency of Bayesian analysis of the mixed linear model with unknown variance.

This work focuses on the effects of variable amount of genomic information in the Bayesian estimation of unknown variance components associated with single-step genomic prediction. We propose a quantitative criterion for the amount of genomic information included in the model and use it to study the relative effect of genomic data on efficiency of sampling from the posterior distribution of parameters of the single-step model when conducting a Bayesian analysis with estimating unknown variances. The rate of change of estimated variances was dependent on the amount of genomic information involved in the analysis, but did not depend on the Gibbs updating schemes applied for sampling realizations of the posterior distribution. Simulation revealed a gradual deterioration of convergence rates for the locations parameters when new genomic data were gradually added into the analysis. In contrast, the convergence of variance components showed continuous improvement under the same conditions. The sampling efficiency increased proportionally to the amount of genomic information. In addition, an optimal amount of genomic information in variance-covariance matrix that guaranty the most (computationally) efficient analysis was found to correspond a proportion of animals genotyped ***0.8. The proposed criterion yield a characterization of expected performance of the Gibbs sampler if the analysis is subject to adjustment of the amount of genomic data and can be used to guide researchers on how large a proportion of animals should be genotyped in order to attain an efficient analysis.

Accounting for genetic architecture for body weight improves accuracy of predicting breeding values in a commercial line of broilers.

BLUP (best linear unbiased prediction) is the standard for predicting breeding values, where different assumptions can be made on variance-covariance structure, which may influence predictive ability. Herein, we compare accuracy of prediction of four derived-BLUP models: (a) a pedigree relationship matrix (PBLUP), (b) a genomic relationship matrix (GBLUP), (c) a weighted genomic relationship matrix (WGBLUP) and (d) a relationship matrix based on genomic features that consisted of only a subset of SNP selected on a priori information (GFBLUP). We phenotyped a commercial population of broilers for body weight (BW) in five successive weeks and genotyped them using a 50k SNP array. We compared predictive ability of univariate models using conservative cross-validation method, where each full-sib group was divided into two folds. Results from cross-validation showed, with WGBLUP model, a gain in accuracy from 2% to 7% compared with GBLUP model. Splitting the additive genetic matrix into two matrices, based on significance level of SNP (Gf : estimated with only set of SNP selected on significance level, Gr : estimated with the remaining SNP), led to a gain in accuracy from 1% to 70%, depending on the proportion of SNP used to define Gf . Thus, information from GWAS in models improves predictive ability of breeding values for BW in broilers. Increasing the power of detection of SNP effects, by acquiring more data or improving methods for GWAS, will help improve predictive ability.

Effect of genomic selection and genotyping strategy on estimation of variance components in animal models using different relationship matrices.

BACKGROUND: The traditional way to estimate variance components (VC) is based on the animal model using a pedigree-based relationship matrix (A) (A-AM). After genomic selection was introduced into breeding programs, it was anticipated that VC estimates from A-AM would be biased because the effect of selection based on genomic information is not captured. The single-step method (H-AM), which uses an H matrix as (co)variance matrix, can be used as an alternative to estimate VC. Here, we compared VC estimates from A-AM and H-AM and investigated the effect of genomic selection, genotyping strategy and genotyping proportion on the estimation of VC from the two methods, by analyzing a dataset from a commercial broiler line and a simulated dataset that mimicked the broiler population. RESULTS: VC estimates from H-AM were severely overestimated with a high proportion of selective genotyping, and overestimation increased as proportion of genotyping increased in the analysis of both commercial and simulated data. This bias in H-AM estimates arises when selective genotyping is used to construct the H-matrix, regardless of whether selective genotyping is applied or not in the selection process. For simulated populations under genomic selection, estimates of genetic variance from A-AM were also significantly overestimated when the effect of genomic selection was strong. Our results suggest that VC estimates from H-AM under random genotyping have the expected values. Predicted breeding values from H-AM were inflated when VC estimates were biased, and inflation differed between genotyped and ungenotyped animals, which can lead to suboptimal selection decisions. CONCLUSIONS: We conclude that VC estimates from H-AM are biased with selective genotyping, but are close to expected values with random genotyping.VC estimates from A-AM in populations under genomic selection are also biased but to a much lesser degree. Therefore, we recommend the use of H-AM with random genotyping to estimate VC for populations under genomic selection. Our results indicate that it is still possible to use selective genotyping in selection, but then VC estimation should avoid the use of genotypes from one side only of the distribution of phenotypes. Hence, a dual genotyping strategy may be needed to address both selection and VC estimation.

Genetic analysis on body weight at different ages in broiler chicken raised in commercial environment.

A multivariate model was developed and used to estimate genetic parameters of body weight (BW) at 1-6 weeks of age of broilers raised in a commercial environment. The development of model was based on the predictive ability of breeding values evaluated from a cross-validation procedure that relied on half-sib correlation. The multivariate model accounted for heterogeneous variances between sexes through standardization applied to male and female BWs differently. It was found that the direct additive genetic, permanent environmental maternal and residual variances for BW increased drastically as broilers aged. The drastic increase in variances over weeks of age was mainly due to scaling effects. The ratio of the permanent environmental maternal variance to phenotypic variance decreased gradually with increasing age. Heritability of BW traits ranged from 0.28 to 0.33 at different weeks of age. The direct genetic effects on consecutive weekly BWs had high genetic correlations (0.85-0.99), but the genetic correlations between early and late BWs were low (0.32-0.57). The difference in variance components between sexes increased with increasing age. In conclusion, the permanent environmental maternal effect on broiler chicken BW decreased with increasing age from weeks 1 to 6. Potential bias of the model that considered identical variances for sexes could be reduced when heterogeneous variances between sexes are accounted for in the model.

Bias in estimates of variance components in populations undergoing genomic selection: a simulation study.

BACKGROUND: After the extensive implementation of genomic selection (GS), the choice of the statistical model and data used to estimate variance components (VCs) remains unclear. A primary concern is that VCs estimated from a traditional pedigree-based animal model (P-AM) will be biased due to ignoring the impact of GS. The objectives of this study were to examine the effects of GS on estimates of VC in the analysis of different sets of phenotypes and to investigate VC estimation using different methods. Data were simulated to resemble the Danish Jersey population. The simulation included three phases: (1) a historical phase; (2) 20 years of conventional breeding; and (3) 15 years of GS. The three scenarios based on different sets of phenotypes for VC estimation were as follows: (1) Pheno1: phenotypes from only the conventional phase (1-20 years); (2) Pheno1 + 2: phenotypes from both the conventional phase and GS phase (1-35 years); (3) Pheno2: phenotypes from only the GS phase (21-35 years). Single-step genomic BLUP (ssGBLUP), a single-step Bayesian regression model (ssBR), and P-AM were applied. Two base populations were defined: the first was the founder population referred to by the pedigree-based relationship (P-base); the second was the base population referred to by the current genotyped population (G-base). RESULTS: In general, both the ssGBLUP and ssBR models with all the phenotypic and genotypic information (Pheno1 + 2) yielded biased estimates of additive genetic variance compared to the P-base model. When the phenotypes from the conventional breeding phase were excluded (Pheno2), P-AM led to underestimation of the genetic variance of P-base. Compared to the VCs of G-base, when phenotypes from the conventional breeding phase (Pheno2) were ignored, the ssBR model yielded unbiased estimates of the total genetic variance and marker-based genetic variance, whereas the residual variance was overestimated. CONCLUSIONS: The results show that neither of the single-step models (ssGBLUP and ssBR) can precisely estimate the VCs for populations undergoing GS. Overall, the best solution for obtaining unbiased estimates of VCs is to use P-AM with phenotypes from the conventional phase or phenotypes from both the conventional and GS phases.

Genetic parameters for body weight and different definitions of residual feed intake in broiler chickens.

BACKGROUND: The objectives of this study were to (1) simultaneously estimate genetic parameters for BW, feed intake (FI), and body weight gain (Gain) during a FI test in broiler chickens using multi-trait Bayesian analysis; (2) derive phenotypic and genetic residual feed intake (RFI) and estimate genetic parameters of the resulting traits; and (3) compute a Bayesian measure of direct and correlated superiority of a group selected on phenotypic or genetic residual feed intake. A total of 56,649 male and female broiler chickens were measured at one of two ages ([Formula: see text] or [Formula: see text] days). BW, FI, and Gain of males and females at the two ages were considered as separate traits, resulting in a 12-trait model. Phenotypic RFI ([Formula: see text]) and genetic RFI ([Formula: see text]) were estimated from a conditional distribution of FI given BW and Gain using partial phenotypic and partial genetic regression coefficients, respectively. RESULTS: Posterior means of heritability for BW, FI and Gain were moderately high and estimates were significantly different between males and females at the same age for all traits. In addition, the genetic correlations between male and female traits at the same age were significantly different from 1, which suggests a sex-by-genotype interaction. Genetic correlations between [Formula: see text] and [Formula: see text] were significantly different from 1 at an older age but not at a younger age. CONCLUSIONS: The results of the multivariate Bayesian analyses in this study showed that genetic evaluation for production and feed efficiency traits should take sex and age differences into account to increase accuracy of selection and genetic gain. Moreover, for communicating with stakeholders, it is easier to explain results from selection on [Formula: see text] than selection on [Formula: see text], since [Formula: see text] is genetically independent of production traits and it explains the efficiency of birds in nutrient utilization independently of energy requirements for production and maintenance.

Correction to: Use of genomic information to exploit genotype-by-environment interactions for body weight of broiler chicken in bio-secure and production environments.

After publication of this work [1], we noticed that there was an error: the formula to calculate the standard error of the estimated correlation.

Use of genomic information to exploit genotype-by-environment interactions for body weight of broiler chicken in bio-secure and production environments.

BACKGROUND: The increase in accuracy of prediction by using genomic information has been well-documented. However, benefits of the use of genomic information and methodology for genetic evaluations are missing when genotype-by-environment interactions (G × E) exist between bio-secure breeding (B) environments and commercial production (C) environments. In this study, we explored (1) G × E interactions for broiler body weight (BW) at weeks 5 and 6, and (2) the benefits of using genomic information for prediction of BW traits when selection candidates were raised and tested in a B environment and close relatives were tested in a C environment. METHODS: A pedigree-based best linear unbiased prediction (BLUP) multivariate model was used to estimate variance components and predict breeding values (EBV) of BW traits at weeks 5 and 6 measured in B and C environments. A single-step genomic BLUP (ssGBLUP) model that combined pedigree and genomic information was used to predict EBV. Cross-validations were based on correlation, mean difference and regression slope statistics for EBV that were estimated from full and reduced datasets. These statistics are indicators of population accuracy, bias and dispersion of prediction for EBV of traits measured in B and C environments. Validation animals were genotyped and non-genotyped birds in the B environment only. RESULTS: Several indications of G × E interactions due to environmental differences were found for BW traits including significant re-ranking, heterogeneous variances and different heritabilities for BW measured in environments B and C. The genetic correlations between BW traits measured in environments B and C ranged from 0.48 to 0.54. The use of combined pedigree and genomic information increased population accuracy of EBV, and reduced bias of EBV prediction for genotyped birds compared to the use of pedigree information only. A slight increase in accuracy of EBV was also observed for non-genotyped birds, but the bias of EBV prediction increased for non-genotyped birds. CONCLUSIONS: The G × E interaction was strong for BW traits of broilers measured in environments B and C. The use of combined pedigree and genomic information increased population accuracy of EBV substantially for genotyped birds in the B environment compared to the use of pedigree information only.

Bayesian estimation of direct and correlated responses to selection on linear or ratio expressions of feed efficiency in pigs.

BACKGROUND: This study aimed at (1) deriving Bayesian methods to predict breeding values for ratio (i.e. feed conversion ratio; FCR) or linear (i.e. residual feed intake; RFI) traits; (2) estimating genetic parameters for average daily feed consumption (ADFI), average daily weight gain (ADG), lean meat percentage (LMP) along with the derived traits of RFI and FCR; and (3) deriving Bayesian estimates of direct and correlated responses to selection on RFI, FCR, ADG, ADFI, and LMP. Response to selection was defined as the difference in additive genetic mean of the selected top individuals, expected to be parents of the next generation, and the total population after integrating genetic trends out of the posterior distribution of selection responses. Inferences were based on marginal posterior distributions obtained from the Bayesian method for integration over unknown population parameters and "fixed" environmental effects and for appropriate handling of ratio traits. Terminal line pigs (n = 3724) were used for a multi-variate model for ADFI, ADG, and LMP. RFI was estimated from the conditional distribution of ADFI given ADG and LMP, using either genetic (RFIG) or phenotypic (RFIP) partial regression coefficients. The posterior distribution of the FCR's breeding values was derived from the posterior distribution of "fixed" environmental effects and additive genetic effects on ADFI and ADG. RESULTS: Posterior means of heritability were 0.32, 0.26, 0.56, 0.20, and 0.15 for ADFI, ADG, LMP, RFIP, and RFIG, respectively. Selection against RFIG showed a direct response of - 0.16 kg/d and correlated responses of - 0.16 kg/kg for FCR and - 0.15 kg/d for ADFI, with no effect on other production traits. Selection against FCR resulted in a direct response of - 0.17 kg/kg and correlated responses of - 0.14 kg/d for RFIG, - 0.18 kg/d for ADFI, and 0.98% for LMP. CONCLUSIONS: The Bayesian methodology developed here enables prediction of breeding values for FCR and RFI from a single multi-variate model. In addition, we derived posterior distributions of direct and correlated responses to selection. Genetic parameter estimates indicated a genetic basis for the studied traits and that genetic improvement through selection was possible. Direct selection against FCR or RFIP resulted in unexpected responses in production traits.

Estimation of variance components and prediction of breeding values based on group records from varying group sizes.

BACKGROUND: Records on groups of individuals rather than on single individuals could be valuable for predicting breeding values (BV) of the traits that are difficult or costly to measure individually, such as feed intake in pigs or beef cattle. Here, we present a model, which handles group records from varying group sizes and involves multiple fixed and random effects, for estimating variance components and predicting BV. Moreover, using simulation, we investigated the efficiency of group records for predicting BV in situations with various group sizes and structures, and factors that affect the trait. RESULTS: The results show that the presented model for group records worked well and that variances estimated from group records with varying group sizes were consistent with those estimated from individual records, but with larger standard errors. Ignoring litter and pen effects had very little or no influence on the accuracy of estimated BV (EBV) obtained from group records. However, ignoring litter effects resulted in biased estimates of additive genetic variance and EBV. The presence of litter and pen effects on phenotypes decreased the accuracy of EBV although the prediction model fitted both effects. Having more littermates in the same pen led to a higher accuracy of EBV. The decay of EBV accuracy with increasing group size was more marked for scenarios with litter and pen effects than without. When litters of six individuals were divided into two pens, accuracies of EBV obtained from group records with a size up to 12 (average 9.6) and up to 24 (average 19.2) were 66.6 and 57.6% of those estimated from individual records in the scenario with litter and pen effects on phenotypes. These percentages reached 77.0 and 68.4% in the scenario without litter and pen effects on phenotypes. CONCLUSIONS: Our results indicate that the model works appropriately for the analysis of group records from varying group sizes. Using group records for genetic evaluation of traits such as feed intake in pig is feasible and the efficiency of the resulting estimates depends on the size and structure of the groups and on the magnitude of the variances for litter and pen effects.