Heterogeneous Residual Variances Research Articles

Sensitivity of breeding values for carcass traits of meat-type quail to changes in dietary (methionine + cystine):lysine ratio using reaction norm models.

Our objective was to evaluate changes in breeding values for carcass traits of two meat-type quail (Coturnix coturnix) strains (LF1 and LF2) to changes in the dietary (methionine+cystine):lysine ([Met+Cys]:Lys) ratio due to genotype by environment (G×E) interaction via reaction norm. A total of 7000 records of carcass weight and yield were used for analyses. During the initial phase (from hatching to day 21), five diets with increasing (Met+Cys):Lys ratios (0.61, 0.66, 0.71, 0.76 and 0.81), containing 26.1% crude protein and 2900kcalME/kg, were evaluated. Analyses were performed using random regression models that included linear functions of sex (fixed effect) and breeding value (random effect) for carcass weight and yield, without and with heterogeneous residual variance adjustment. Both fixed and random effects were modelled using Legendre polynomials of second order. Genetic variance and heritability estimates were affected by both (Met+Cys):Lys ratio and strain. We observed that a G×E interaction was present, with changes in the breeding value ranking. Therefore, genetic evaluation for carcass traits should be performed under the same (Met+Cys):Lys ratio in which quails are raised.

ANALISIS GGE BIPLOT PADA HASIL KLON-KLON UBI KAYU MENGGUNAKAN METODE RESTRICTED MAXIMUM LIKELIHOOD

The study was conducted in five locations i.e Kediri, Ponorogo, Probolinggo, Malang, and Mojokerto, from November 2010 until August 2011. The planting materials used were 15 cassava clones. The research objective was to compare analysis methods of the genotype × environment interaction, namely: a) GGE technique using REML without A matrix by assuming homogeneous residual error variance, b) GGE technique using REML with A matrix by assuming homogeneous residual error variance, c) GGE technique using REML without A matrix by assuming heterogeneous residual error variance, and d) GGE technique using REML with A matrix by assuming heterogeneous residual error variance. The results showed that GGE technique using REML without A matrix by assuming heterogeneous residual error variance was more appropriate. Clones CMM 03038-7 (G8) had a wide adaptability and high yield potential, and its clone was closest to the ideal criteria for genotype compared with other genotypes. Clones CMM 03094-4 (G10) had specific adaptability in the environments S2 (Malang) and S5 (Mojokerto), and it had higher yield potential than the control varieties UJ5, Malang 6, and Adira 4. Environment Kediri (S1) had the highest yield among other environments and Kediri was a suitable environment for the growth and selection of cassava.<p align="center"> </p>

Combining different functions to describe milk, fat, and protein yield in goats using Bayesian multiple-trait random regression models.

We proposed multiple-trait random regression models (MTRRM) combining different functions to describe milk yield (MY) and fat (FP) and protein (PP) percentage in dairy goat genetic evaluation by using Bayesian inference. A total of 3,856 MY, FP, and PP test-day records, measured between 2000 and 2014, from 535 first lactations of Saanen and Alpine goats, including their cross, were used in this study. The initial analyses were performed using the following single-trait random regression models (STRRM): third- and fifth-order Legendre polynomials (Leg3 and Leg5), linear B-splines with 3 and 5 knots, the Ali and Schaeffer function (Ali), and Wilmink function. Heterogeneity of residual variances was modeled considering 3 classes. After the selection of the best STRRM to describe each trait on the basis of the deviance information criterion (DIC) and posterior model probabilities (PMP), the functions were combined to compose the MTRRM. All combined MTRRM presented lower DIC values and higher PMP, showing the superiority of these models when compared to other MTRRM based only on the same function assumed for all traits. Among the combined MTRRM, those considering Ali to describe MY and PP and Leg5 to describe FP (Ali_Leg5_Ali model) presented the best fit. From the Ali_Leg5_Ali model, heritability estimates over time for MY, FP. and PP ranged from 0.25 to 0.54, 0.27 to 0.48, and 0.35 to 0.51, respectively. Genetic correlation between MY and FP, MY and PP, and FP and PP ranged from -0.58 to 0.03, -0.46 to 0.12, and 0.37 to 0.64, respectively. We concluded that combining different functions under a MTRRM approach can be a plausible alternative for joint genetic evaluation of milk yield and milk constituents in goats.

An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models.

Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G:F relative to Trp:Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G:F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp:Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with the estimation process rendered results from the BLQ model questionable. Importantly, accounting for heterogeneous variance enhanced inferential precision as the breadth of the confidence interval for the mean breakpoint decreased by approximately 44%. In summary, the article illustrates the use of linear and nonlinear mixed models for dose-response relationships accounting for heterogeneous residual variances, discusses important diagnostics and their implications for inference, and provides practical recommendations for computational troubleshooting.

Genetic analysis of carcass traits in beef cattle using random regression models.

Livestock mature at different rates depending, in part, on their genetic merit; therefore, the optimal age at slaughter for progeny of certain sires may differ. The objective of the present study was to examine sire-level genetic profiles for carcass weight, carcass conformation, and carcass fat in cattle of multiple beef and dairy breeds, including crossbreeds. Slaughter records from 126,214 heifers and 124,641 steers aged between 360 and 1,200 d and from 86,089 young bulls aged between 360 and 720 d were used in the analysis; animals were from 15,127 sires. Variance components for each trait across age at slaughter were generated using sire random regression models that included quadratic polynomials for fixed and random effects; heterogeneous residual variances were assumed across ages. Heritability estimates across genders ranged from 0.08 (±0.02) to 0.34 (±0.02) for carcass weight, from 0.24 (±0.02) to 0.42 (±0.01) for conformation, and from 0.16 (±0.03) to 0.40 (±0.02) for fat score. Genetic correlations within each trait across ages weakened as the interval between ages compared lengthened but were all >0.64, suggesting a similar genetic background for each trait across different ages. Eigenvalues and eigenfunctions of the additive genetic covariance matrix revealed genetic variability among animals in their growth profiles for carcass traits, although most of the genetic variability was associated with the height of the growth profile. At the same age, a positive genetic correlation (0.60 to 0.78; SE ranged from 0.01 to 0.04) existed between carcass weight and conformation, whereas negative genetic correlations existed between fatness and both conformation (-0.46 to 0.08; SE ranged from 0.02 to 0.09) and carcass weight (-0.48 to -0.16; SE ranged from 0.02 to 0.14) at the same age. The estimated genetic parameters in the present study indicate genetic variability in the growth trajectory in cattle, which can be exploited through breeding programs and used in decision support tools.

042 An update on modeling dose–response relationships: Accounting for correlated data structures and heterogeneous variance in linear and nonlinear mixed models

Advanced methods for dose–response assessments are used to estimate concentrations of a nutrient that optimize a given outcome of interest, thereby determining nutritional requirements for optimal performance. Traditionally, many dose–response methods use a fixed-effects framework that assumes mutually independent observations with homogeneous variances. Yet experimental data often present a design structure that includes correlations between observations (e.g., blocking, nesting, etc.) as well as heterogeneity of variances that can mislead inference if disregarded. Our objective is to demonstrate practical implementation of computationally intensive linear and nonlinear mixed models methodology to describe dose–response relationships accounting for correlated data structure and heterogeneous variances. To illustrate, we model data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys dose–response on G:F of nursery pigs. A base linear mixed model was fit to explore the functional form of G:F relative to Trp:Lys and assess model assumptions, in particular residual homoscedasticity. Next, we fitted 3 competing dose–response mixed models to G:F, namely a quadratic polynomial (QP), a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model, and used parameter estimates from the base model as initial values. The GLIMMIX procedure of SAS (version 9.4; SAS Inst. Inc., Cary, NC) was used to fit the base and QP models and the NLMIXED procedure was used to fit the nonlinear models. We further illustrate the use of a grid-search approach to facilitate convergence and parameter estimation in nonlinear mixed models, as this seemed to be the most common implementation problem. Model fit between competing dose–response models was compared using maximum likelihood–based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, indicating a better fit of BLL followed closely by BLQ. The BLL breakpoint estimate of the SID Trp:Lys was 16.5% (95% confidence interval [CI] 16.1–17.0), whereas the BLQ estimate was 16.0% (95% CI 15.5–16.6). Importantly, accounting for heterogeneous variance enhanced inferential precision as the breadth of the CI for mean breakpoint decreased by approximately 44%, from 95% CI 15.8 to 17.4 to 95% CI 16.1 to 17.0 SID Trp:Lys. In summary, we illustrate the use of linear and nonlinear mixed models for dose–response relationships accounting for heterogeneous residual variances, discuss important diagnostics and their implications for inference, and provide practical recommendations for computational troubleshooting.

Evaluation of sire by environment interactions for growth rate and backfat depth using reaction norm models in pigs.

Reaction norm models for sires were used to evaluate genotype by environment interactions for lifetime average daily gain (ADG) and backfat depth (BF) in pigs recorded at 143days. Data for ADG and BF were available for 265103 pigs recorded in Australia between 2000 and 2010 in nine herds. The full data set and two subsets based on minimum numbers of progeny per sire of 50 and 100 were analysed. The environmental descriptor was quantified as least square means of herd-by-birth month (HBM) contemporary groups which varied from 540 to 738g/day for ADG and from 8.2 to 13.8mm for BF. Several models were evaluated for estimation of variance components in terms of predictive ability for sire intercepts and slopes. The accuracy of genetic parameter estimates was improved by increasing family size, fitting models with a fixed regression coefficient on the environmental descriptor instead of fixed HBM effects and heterogeneous residual variances. Significant sire by environment interactions were found for ADG but not for BF. Heritability estimates for ADG ranged from approximately 0.21 in average environments to approximately 0.30 in the most unfavourable environments. Estimates of sire intercepts and slopes varied by 98.5g/day and 0.253g/day per g/day for ADG, respectively. Lowly negative correlations between sire intercept and slope do not support the hypothesis that high growth is associated with larger environmental sensitivity.

Genotype by environment interaction for tick resistance of Hereford and Braford beef cattle using reaction norm models.

Background The cattle tick is a parasite that adversely affects livestock performance in tropical areas. Although countries such as Australia and Brazil have developed genetic evaluations for tick resistance, these evaluations have not considered genotype by environment (G*E) interactions. Genetic gains could be adversely affected, since breedstock comparisons are environmentally dependent on the presence of G*E interactions, particularly if residual variability is also heterogeneous across environments. The objective of this study was to infer upon the existence of G*E interactions for tick resistance of cattle based on various models with different assumptions of genetic and residual variability.MethodsData were collected by the Delta G Connection Improvement program and included 10,673 records of tick counts on 4363 animals. Twelve models, including three traditional animal models (AM) and nine different hierarchical Bayesian reaction norm models (HBRNM), were investigated. One-step models that jointly estimate environmental covariates and reaction norms and two-step models based on previously estimated environmental covariates were used to infer upon G*E interactions. Model choice was based on the deviance criterion information.ResultsThe best-fitting model specified heterogeneous residual variances across 10 subclasses that were bounded by every decile of the contemporary group (CG) estimates of tick count effects. One-step models generally had the highest estimated genetic variances. Heritability estimates were normally higher for HBRNM than for AM. One-step models based on heterogeneous residual variances also usually led to higher heritability estimates. Estimates of repeatability varied along the environmental gradient (ranging from 0.18 to 0.45), which implies that the relative importance of additive and permanent environmental effects for tick resistance is influenced by the environment. Estimated genetic correlations decreased as the tick infestation level increased, with negative correlations between extreme environmental levels, i.e., between more favorable (low infestation) and harsh environments (high infestation).ConclusionsHBRNM can be used to describe the presence of G*E interactions for tick resistance in Hereford and Braford beef cattle. The preferred model for the genetic evaluation of this population for tick counts in Brazilian climates was a one-step model that considered heteroscedastic residual variance. Reaction norm models are a powerful tool to identify and quantify G*E interactions and represent a promising alternative for genetic evaluation of tick resistance, since they are expected to lead to greater selection efficiency and genetic progress.

Genomic Prediction Accounting for Residual Heteroskedasticity.

Whole-genome prediction (WGP) models that use single-nucleotide polymorphism marker information to predict genetic merit of animals and plants typically assume homogeneous residual variance. However, variability is often heterogeneous across agricultural production systems and may subsequently bias WGP-based inferences. This study extends classical WGP models based on normality, heavy-tailed specifications and variable selection to explicitly account for environmentally-driven residual heteroskedasticity under a hierarchical Bayesian mixed-models framework. WGP models assuming homogeneous or heterogeneous residual variances were fitted to training data generated under simulation scenarios reflecting a gradient of increasing heteroskedasticity. Model fit was based on pseudo-Bayes factors and also on prediction accuracy of genomic breeding values computed on a validation data subset one generation removed from the simulated training dataset. Homogeneous vs. heterogeneous residual variance WGP models were also fitted to two quantitative traits, namely 45-min postmortem carcass temperature and loin muscle pH, recorded in a swine resource population dataset prescreened for high and mild residual heteroskedasticity, respectively. Fit of competing WGP models was compared using pseudo-Bayes factors. Predictive ability, defined as the correlation between predicted and observed phenotypes in validation sets of a five-fold cross-validation was also computed. Heteroskedastic error WGP models showed improved model fit and enhanced prediction accuracy compared to homoskedastic error WGP models although the magnitude of the improvement was small (less than two percentage points net gain in prediction accuracy). Nevertheless, accounting for residual heteroskedasticity did improve accuracy of selection, especially on individuals of extreme genetic merit.

Genetic Diversity and Association Studies in US Hispanic/Latino Populations: Applications in the Hispanic Community Health Study/Study of Latinos

US Hispanic/Latino individuals are diverse in genetic ancestry, culture, and environmental exposures. Here, we characterized and controlled for this diversity in genome-wide association studies (GWASs) for the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). We simultaneously estimated population-structure principal components (PCs) robust to familial relatedness and pairwise kinship coefficients (KCs) robust to population structure, admixture, and Hardy-Weinberg departures. The PCs revealed substantial genetic differentiation within and among six self-identified background groups (Cuban, Dominican, Puerto Rican, Mexican, and Central and South American). To control for variation among groups, we developed a multi-dimensional clustering method to define a "genetic-analysis group" variable that retains many properties of self-identified background while achieving substantially greater genetic homogeneity within groups and including participants with non-specific self-identification. In GWASs of 22 biomedical traits, we used a linear mixed model (LMM) including pairwise empirical KCs to account for familial relatedness, PCs for ancestry, and genetic-analysis groups for additional group-associated effects. Including the genetic-analysis group as a covariate accounted for significant trait variation in 8 of 22 traits, even after we fit 20 PCs. Additionally, genetic-analysis groups had significant heterogeneity of residual variance for 20 of 22traits, and modeling this heteroscedasticity within the LMM reduced genomic inflation for 19 traits. Furthermore, fitting an LMMthat utilized a genetic-analysis group rather than a self-identified background group achieved higher power to detect previously reported associations. We expect that the methods applied here will be useful in other studies with multiple ethnic groups, admixture, and relatedness.

Multiple-breed reaction norm animal model accounting for robustness and heteroskedastic in a Nelore–Angus crossed population

Our objective was to genetically characterize post-weaning weight gain (PWG), over a 345-day period after weaning, of Brangus-Ibagé (Nelore×Angus) cattle. Records (n=4016) were from the foundation herd of the Embrapa South Livestock Center. A Bayesian approach was used to assess genotype by environment (G×E) interaction and to identify a suitable model for the estimation of genetic parameters and use in genetic evaluation. A robust and heteroscedastic reaction norm multiple-breed animal model was proposed. The model accounted for heterogeneity of residual variance associated with effects of breed, heterozygosity, sex and contemporary group; and was robust with respect to outliers. Additive genetic effects were modeled for the intercept and slope of a reaction norm to changes in the environmental gradient. Inference was based on Monte Carlo Markov Chain of 110 000 cycles, after 10 000 cycles of burn-in. Bayesian model choice criteria indicated the proposed model was superior to simpler sub-models that did not account for G×E interaction, multiple-breed structure, robustness and heteroscedasticity. We conclude that, for the Brangus-Ibagé population, these factors should be jointly accounted for in genetic evaluation of PWG. Heritability estimates increased proportionally with improvement in the environmental conditions gradient. Therefore, an increased proportion of differences in performance among animals were explained by genetic factors rather than environmental factors as rearing conditions improved. As a consequence response to selection may be increased in favorable environments.

Egg numbers, weight, and egg mass production in meat-type quail through 58 weeks old

Egg production was evaluated in a line of meat-type quail undergoing selection for increased 21-day body weight, using random regression and compares the influence of heterogeneity of residual variance on estimated genetic parameters to the growth curve of meat quails. Six models were estimated, one for homogeneous residual variance and five for heterogeneous residual variance structures, established at intervals of 182, 112, 91, 56, or 28 days. An increase (P < 0.01) of the natural logarithm of the likelihood function, by increasing the number of heterogeneous classes was observed. The model that considered homogeneity of residual variances was inadequate. Genetic variability was observed for egg weight with homogeneity of residual variance varying from .15 to .32 and with heterogeneity varying from .16 to .38 in 13 partial (4-wk long) laying periods. Heritabilities for number of eggs laid and egg mass varied from .03 to .10 and .03 to .15, and from 0.01 to 0.15 and .01 to .20, respectively, with homogeneity and heterogeneity of residual variances. It is justifiable to include egg weight in the selection goals for meat-type quail. Low heritabilities values were found for egg number and egg mass but there are particular periods, especially from 99-126 days old and from 211-238 days old where selection could be effective. Peak production values for the three traits occurred between these periods.

Models for Estimating Genetic Parameters of Milk Production Traits Using Random Regression Models in Korean Holstein Cattle.

The objectives of the study were to estimate genetic parameters for milk production traits of Holstein cattle using random regression models (RRMs), and to compare the goodness of fit of various RRMs with homogeneous and heterogeneous residual variances. A total of 126,980 test-day milk production records of the first parity Holstein cows between 2007 and 2014 from the Dairy Cattle Improvement Center of National Agricultural Cooperative Federation in South Korea were used. These records included milk yield (MILK), fat yield (FAT), protein yield (PROT), and solids-not-fat yield (SNF). The statistical models included random effects of genetic and permanent environments using Legendre polynomials (LP) of the third to fifth order (L3–L5), fixed effects of herd-test day, year-season at calving, and a fixed regression for the test-day record (third to fifth order). The residual variances in the models were either homogeneous (HOM) or heterogeneous (15 classes, HET15; 60 classes, HET60). A total of nine models (3 orders of polynomials×3 types of residual variance) including L3-HOM, L3-HET15, L3-HET60, L4-HOM, L4-HET15, L4-HET60, L5-HOM, L5-HET15, and L5-HET60 were compared using Akaike information criteria (AIC) and/or Schwarz Bayesian information criteria (BIC) statistics to identify the model(s) of best fit for their respective traits. The lowest BIC value was observed for the models L5-HET15 (MILK; PROT; SNF) and L4-HET15 (FAT), which fit the best. In general, the BIC values of HET15 models for a particular polynomial order was lower than that of the HET60 model in most cases. This implies that the orders of LP and types of residual variances affect the goodness of models. Also, the heterogeneity of residual variances should be considered for the test-day analysis. The heritability estimates of from the best fitted models ranged from 0.08 to 0.15 for MILK, 0.06 to 0.14 for FAT, 0.08 to 0.12 for PROT, and 0.07 to 0.13 for SNF according to days in milk of first lactation. Genetic variances for studied traits tended to decrease during the earlier stages of lactation, which were followed by increases in the middle and decreases further at the end of lactation. With regards to the fitness of the models and the differential genetic parameters across the lactation stages, we could estimate genetic parameters more accurately from RRMs than from lactation models. Therefore, we suggest using RRMs in place of lactation models to make national dairy cattle genetic evaluations for milk production traits in Korea.

Effects of standardized ileal digestible tryptophan: lysine ratio on growth performance of nursery pigs.

Two experiments were conducted to estimate the standardized ileal digestible (SID) Trp:Lys ratio requirement for growth performance of nursery pigs. Experimental diets were formulated to ensure that lysine was the second limiting AA throughout the experiments. In Exp. 1 (6 to 10 kg BW), 255 nursery pigs (PIC 327 × 1050, initially 6.3 ± 0.15 kg, mean ± SD) arranged in pens of 6 or 7 pigs were blocked by pen weight and assigned to experimental diets (7 pens/diet) consisting of SID Trp:Lys ratios of 14.7%, 16.5%, 18.4%, 20.3%, 22.1%, and 24.0% for 14 d with 1.30% SID Lys. In Exp. 2 (11 to 20 kg BW), 1,088 pigs (PIC 337 × 1050, initially 11.2 kg ± 1.35 BW, mean ± SD) arranged in pens of 24 to 27 pigs were blocked by average pig weight and assigned to experimental diets (6 pens/diet) consisting of SID Trp:Lys ratios of 14.5%, 16.5%, 18.0%, 19.5%, 21.0%, 22.5%, and 24.5% for 21 d with 30% dried distillers grains with solubles and 0.97% SID Lys. Each experiment was analyzed using general linear mixed models with heterogeneous residual variances. Competing heteroskedastic models included broken-line linear (BLL), broken-line quadratic (BLQ), and quadratic polynomial (QP). For each response, the best-fitting model was selected using Bayesian information criterion. In Exp. 1 (6 to 10 kg BW), increasing SID Trp:Lys ratio linearly increased ( 0.05) ADG and G:F. For ADG, the best-fitting model was a QP in which the maximum ADG was estimated at 23.9% (95% confidence interval [CI]: [<14.7%, >24.0%]) SID Trp:Lys ratio. For G:F, the best-fitting model was a BLL in which the maximum G:F was estimated at 20.4% (95% CI: [14.3%, 26.5%]) SID Trp:Lys. In Exp. 2 (11 to 20 kg BW), increasing SID Trp:Lys ratio increased ( 0.05) ADG and G:F in a quadratic manner. For ADG, the best-fitting model was a QP in which the maximum ADG was estimated at 21.2% (95% CI: [20.5%, 21.9%]) SID Trp:Lys. For G:F, BLL and BLQ models had comparable fit and estimated SID Trp:Lys requirements at 16.6% (95% CI: [16.0%, 17.3%]) and 17.1% (95% CI: [16.6%, 17.7%]), respectively. In conclusion, the estimated SID Trp:Lys requirement in Exp. 1 ranged from 20.4% for maximum G:F to 23.9% for maximum ADG, whereas in Exp. 2 it ranged from 16.6% for maximum G:F to 21.2% for maximum ADG. These results suggest that standard recommendations may underestimate the SID Trp:Lys requirement for nursery pigs from 11 to 20 kg BW.

Estimates of genetic parameters for growth traits in Brahman cattle using random regression and multitrait models.

Random regression models (RRM) and multitrait models (MTM) were used to estimate genetic parameters for growth traits in Brazilian Brahman cattle and to compare the estimated breeding values obtained by these 2 methodologies. For RRM, 78,641 weight records taken between 60 and 550 d of age from 16,204 cattle were analyzed, and for MTM, the analysis consisted of 17,385 weight records taken at the same ages from 12,925 cattle. All models included the fixed effects of contemporary group and the additive genetic, maternal genetic, and animal permanent environmental effects and the quadratic effect of age at calving (AAC) as covariate. For RRM, the AAC was nested in the animal's age class. The best RRM considered cubic polynomials and the residual variance heterogeneity (5 levels). For MTM, the weights were adjusted for standard ages. For RRM, additive heritability estimates ranged from 0.42 to 0.75, and for MTM, the estimates ranged from 0.44 to 0.72 for both models at 60, 120, 205, 365, and 550 d of age. The maximum maternal heritability estimate (0.08) was at 140 d for RRM, but for MTM, it was highest at weaning (0.09). The magnitude of the genetic correlations was generally from moderate to high. The RRM adequately modeled changes in variance or covariance with age, and provided there was sufficient number of samples, increased accuracy in the estimation of the genetic parameters can be expected. Correlation of bull classifications were different in both methods and at all the ages evaluated, especially at high selection intensities, which could affect the response to selection.

Genetic analysis of live weight of Sardi sheep using random regression and multi-trait animal models

Genetic parameters and breeding values for live weight from birth to weaning (85 days) of Sardi sheep were estimated using random regression (RR) and multi-trait (MT) animal models. A longitudinal data set for live weight of 44,509 lamb progeny of 605 sires and 18,569 dams were used to describe variance components along growth curve trajectory using RR model. This data set was collected in 89 flocks between 2001 and 2012, with a total of 45,941 animals in the pedigree. Eleven RR models were compared based on the log likelihood and Akaike information criterion. The model with the best fit was found to include quadratic Legendre polynomials for direct and maternal genetic effects and direct permanent environment effects and a linear polynomial for maternal permanent environment effects, including covariance between direct and maternal genetic effects and a heterogeneous residual variance. Direct and maternal heritabilities were 0.11 and 0.03, respectively, at the first day of age, and 0.37 and 0.10, respectively, at 85 days of age. The increase of heritability and genetic variance indicated that there was a large potential for selection of Sardi sheep and suggested that selection during the study period would be more effective if it was done on weaning weight. The low genetic correlation between early weight and weaning weight suggests that these traits are controlled by different genes. Genetic parameters obtained at the selected ages (i.e. 10, 30, 70 days) using MT and RR models were generally similar, but the two methods produced different ranking of genetic merit. This study has demonstrated the possibility of applying RR model for routine genetic evaluation of Sardi sheep.

Longitudinal analysis of residual feed intake and BW in mink using random regression with heterogeneous residual variance

The aim of this study was to determine the genetic background of longitudinal residual feed intake (RFI) and BW gain in farmed mink using random regression methods considering heterogeneous residual variances. The individual BW was measured every 3 weeks from 63 to 210 days of age for 2139 male+female pairs of juvenile mink during the growing-furring period. Cumulative feed intake was calculated six times with 3-week intervals based on daily feed consumption between weighing’s from 105 to 210 days of age. Genetic parameters for RFI and BW gain in males and females were obtained using univariate random regression with Legendre polynomials containing an animal genetic effect and permanent environmental effect of litter along with heterogeneous residual variances. Heritability estimates for RFI increased with age from 0.18 (0.03, posterior standard deviation (PSD)) at 105 days of age to 0.49 (0.03, PSD) and 0.46 (0.03, PSD) at 210 days of age in male and female mink, respectively. The heritability estimates for BW gain increased with age and had moderate to high range for males (0.33 (0.02, PSD) to 0.84 (0.02, PSD)) and females (0.35 (0.03, PSD) to 0.85 (0.02, PSD)). RFI estimates during the growing period (105 to 126 days of age) showed high positive genetic correlations with the pelting RFI (210 days of age) in male (0.86 to 0.97) and female (0.92 to 0.98). However, phenotypic correlations were lower from 0.47 to 0.76 in males and 0.61 to 0.75 in females. Furthermore, BW records in the growing period (63 to 126 days of age) had moderate (male: 0.39, female: 0.53) to high (male: 0.87, female: 0.94) genetic correlations with pelting BW (210 days of age). The result of current study showed that RFI and BW in mink are highly heritable, especially at the late furring period, suggesting potential for large genetic gains for these traits. The genetic correlations suggested that substantial genetic gain can be obtained by only considering the RFI estimate and BW at pelting, however, lower genetic correlations than unity indicate that extra genetic gain can be obtained by including estimates of these traits during the growing period. This study suggests random regression methods are suitable for analysing feed efficiency and BW gain; and genetic selection for RFI in mink is promising.

Estimation of Breeding Values with Heterogeneous Residual Variances by Random Regression Models

Estimation of Breeding Values with Heterogeneous Residual Variances by Random Regression Models

Generalized linear model for mapping discrete trait loci implemented with LASSO algorithm.

Generalized estimating equation (GEE) algorithm under a heterogeneous residual variance model is an extension of the iteratively reweighted least squares (IRLS) method for continuous traits to discrete traits. In contrast to mixture model-based expectation–maximization (EM) algorithm, the GEE algorithm can well detect quantitative trait locus (QTL), especially large effect QTLs located in large marker intervals in the manner of high computing speed. Based on a single QTL model, however, the GEE algorithm has very limited statistical power to detect multiple QTLs because of ignoring other linked QTLs. In this study, the fast least absolute shrinkage and selection operator (LASSO) is derived for generalized linear model (GLM) with all possible link functions. Under a heterogeneous residual variance model, the LASSO for GLM is used to iteratively estimate the non-zero genetic effects of those loci over entire genome. The iteratively reweighted LASSO is therefore extended to mapping QTL for discrete traits, such as ordinal, binary, and Poisson traits. The simulated and real data analyses are conducted to demonstrate the efficiency of the proposed method to simultaneously identify multiple QTLs for binary and Poisson traits as examples.

Interaction between genotype and geographical region for milk production traits of Iranian Holstein dairy cattle

In order to investigate the presence of genotype by environment (G×E) interactions, first lactation milk production traits of Iranian Holstein cows were used. The data were collected by the National Animal Breeding Center of Iran, Karaj. The records were classified by herds in cold, semi-cold, moderate or warm regions based on climatic data of weather stations. The edited data that were collected between 2004 and 2010, included 618,343, 472,597 and 243,792 test day records for milk, fat and protein yields, respectively. Variance components were estimated using Bayesian׳s Gibbs sampling method in a random regression model (RRM). For all traits, after examining models according to DIC, better fitting RRM was the model with heterogeneous residual variances. Genetic parameters estimate for milk production traits were different in the four regions. The highest genetic variances were obtained for cold climate regions; and the highest residual variances across the lactation were obtained for warm climate. Genetic variances and heritability estimates revealed unequal genetic expression of Holstein genes under different climates. Generally, for fat and protein yields, the genetic correlation between different regions was lower than that for milk yield, especially for genetic correlations of protein yield between cold and warm regions (ranged from 0.22 to 0.48). The lower correlations between warm and other regions, especially at the beginning and the end of lactation, showed that a trait in different environments was genetically different traits. For milk and fat yields, the high genetic correlations for 305-d yield (>0.84) between cold, semi-cold and moderate regions indicated a few rank changes of animals over these climates. The results indicated that superior sires in one of regions have their genetic expression for yield limited under other climate conditions and indicated the existence of G×E interaction which may have several implications for the genetic improvement of Holstein cows in Iran.