Estimation Of Residual Variance Research Articles

Investigating the impact of non-additive genetic effects in the estimation of variance components and genomic predictions for heat tolerance and performance traits in crossbred and purebred pig populations

BackgroundNon-additive genetic effects are often ignored in livestock genetic evaluations. However, fitting them in the models could improve the accuracy of genomic breeding values. Furthermore, non-additive genetic effects contribute to heterosis, which could be optimized through mating designs. Traits related to fitness and adaptation, such as heat tolerance, tend to be more influenced by non-additive genetic effects. In this context, the primary objectives of this study were to estimate variance components and assess the predictive performance of genomic prediction of breeding values based on alternative models and two independent datasets, including performance records from a purebred pig population and heat tolerance indicators recorded in crossbred lactating sows.ResultsIncluding non-additive genetic effects when modelling performance traits in purebred pigs had no effect on the residual variance estimates for most of the traits, but lower additive genetic variances were observed, especially when additive-by-additive epistasis was included in the models. Furthermore, including non-additive genetic effects did not improve the prediction accuracy of genomic breeding values, but there was animal re-ranking across the models. For the heat tolerance indicators recorded in a crossbred population, most traits had small non-additive genetic variance with large standard error estimates. Nevertheless, panting score and hair density presented substantial additive-by-additive epistatic variance. Panting score had an epistatic variance estimate of 0.1379, which accounted for 82.22% of the total genetic variance. For hair density, the epistatic variance estimates ranged from 0.1745 to 0.1845, which represent 64.95–69.59% of the total genetic variance.ConclusionsIncluding non-additive genetic effects in the models did not improve the accuracy of genomic breeding values for performance traits in purebred pigs, but there was substantial re-ranking of selection candidates depending on the model fitted. Except for panting score and hair density, low non-additive genetic variance estimates were observed for heat tolerance indicators in crossbred pigs.

PSXII-3 Including Non-Additive Genetic Effects in Genomic Prediction and Estimation of Variance Components for Performance and Heat Stress Traits in Pigs

Abstract Non-additive genetic effects may have important roles in the phenotypic expression of performance and adaptation traits in livestock. Therefore, we aimed to evaluate the inclusion of non-additive genetic effects in genomic prediction models and variance component estimation of performance traits in a purebred pig population and heat tolerance indicators in a crossbred pig population. The first dataset consisted of 3,534 individuals with genotypes for 52,843 SNPs and five pre-adjusted phenotypes from a public database of a purebred pig line. Twelve models fitting or not dominance and/or epistasis effects (additive-by-additive, additive-by-dominance, and dominance-by-dominance) and inbreeding were used to estimate variance components. Prediction ability was assessed based on 10-fold cross-validation and the bias, dispersion, and accuracy estimates were computed based on the LR method. We also evaluated the impact of including non-additive genetic effects on the ranking of the animals’ breeding value and in the proportion of commonly selected individuals. The second dataset consisted of records from 1,645 lactating sows (Large White x Landrace cross) genotyped for 50,703 SNPs and traits related to heat stress response: skin temperature (ear, shoulder, rump, and tail), vaginal temperature measured every 10 minutes, and the average of the six records per hour corresponding to 08:00, 12:00, 16:00, and 20:00 hours during four days; respiration rate, panting score (PS; score scale from 0 to 3), and hair density (HD, score scale from 0 to 2). Four models including or not, inbreeding and the effect of dominance and additive-by-additive epistasis were used to estimate variance components. There was no effect on residual variance estimates due to the inclusion of non-additive genetic effects in the models for most traits. However, non-additive genetic effects reduced additive variance estimates, especially when additive-by-additive epistasis was fitted. Including non-additive genetic effects in the model did not improve the prediction accuracy of breeding values for purebreds, but there was a substantial change in the ranking of the animals and in the proportion of commonly selected individuals. For the crossbred traits, small non-additive genetic variance with large standard error estimates were obtained. Nevertheless, PS and HD presented notable additive-by-additive epistatic variance. PS presented h2aa estimates of 0.15 and additive-by-additive epistasis corresponding to 86.76% of the total genetic variance, while HD presented additive-by-additive epistatic heritability (h2aa) estimates from 0.46 to 0.49 and the proportion of total genetic variance explained by additive-by-additive epistasis ranged from 66.91% to 71.87%. In conclusion, including non-additive genetic effects did not improve the accuracy of prediction of breeding values for purebreds, but it changed the ranking of animals and selection decisions. Although PS and HD had large additive-by-additive epistasis effects, most of the traits related to heat stress in the crossbred population did not present relevant non-additive genetic effects.

Optimal Fingerprinting with Estimating Equations

Abstract Climate change detection and attribution have played a central role in establishing the influence of human activities on climate. Optimal fingerprinting, a linear regression with errors in variables (EIVs), has been widely used in detection and attribution analyses of climate change. The method regresses observed climate variables on the expected climate responses to the external forcings, which are measured with EIVs. The reliability of the method depends critically on proper point and interval estimations of the regression coefficients. The confidence intervals constructed from the prevailing method, total least squares (TLS), have been reported to be too narrow to match their nominal confidence levels. We propose a novel framework to estimate the regression coefficients based on an efficient, bias-corrected estimating equations approach. The confidence intervals are constructed with a pseudo residual bootstrap variance estimator that takes advantage of the available control runs. Our regression coefficient estimator is unbiased, with a smaller variance than the TLS estimator. Our estimation of the sampling variability of the estimator has a low bias compared to that from TLS, which is substantially negatively biased. The resulting confidence intervals for the regression coefficients have coverage rates close to the nominal level, which ensures valid inferences in detection and attribution analyses. In applications to the annual mean near-surface air temperature at the global, continental, and subcontinental scales during 1951–2020, the proposed method led to shorter confidence intervals than those based on TLS in most of the analyses. Significance Statement Optimal fingerprinting is an important statistical tool for estimating human influences on the climate and for quantifying the associated uncertainty. Nonetheless, the estimators from the prevailing practice are not as optimal as believed, and their uncertainties are underestimated, both owing to the unreliable estimation of the optimal weight matrix that is critical to the method. Here we propose an estimation method based on the theory of estimating equations; to assess the uncertainty of the resulting estimator, we propose a pseudo bootstrap procedure. Through extensive numerical studies commonly used in statistical investigations, we demonstrate that the new estimator has a smaller mean-square error, and its uncertainty is estimated much closer to the true uncertainty than the prevailing total least squares method.

Automated tuning of denoising algorithms for noise removal in chromatograms

Different algorithms, such as the Savitzky-Golay filter and Whittaker smoother, have been proposed to improve the quality of experimental chromatograms. These approaches avoid excessive noise from hampering data analysis and as such allow an accurate detection and quantification of analytes. These algorithms require fine-tuning of their hyperparameters to regulate their roughness and flexibility. Traditionally, this fine-tuning is done manually until a signal is obtained that removes the noise while conserving valuable peak information. More objective and automated approaches are available, but these are usually method specific and/or require previous knowledge.In this work, the L-and V-curve, k-fold cross-validation, autocorrelation function and residual variance estimation approach are introduced as alternative automated and generally applicable parameter tuning methods. These methods do not require any previous information and are compatible with a multitude of denoising methods. Additionally, for k-fold cross-validation, autocorrelation function and residual variance estimation, a novel implementation based on median estimators is proposed to handle the specific shape of chromatograms, typically composed of alternating flat baselines and sharp peaks. These tuning methods are investigated in combination with four denoising methods; the Savitsky-Golay filter, Whittaker smoother, sparsity assisted signal smoother and baseline estimation and denoising using sparsity approach.It is demonstrated that the median estimators approach significantly improves the denoising and information conservation performance of relevant smoother-tuner combinations up to a factor 4 for simulated datasets and even up to a factor 10 for an experimental chromatogram. Moreover, the parameter tuning methods relying on residual variance estimation, k-fold cross-validation and autocorrelation function lead to similar small root-mean squared errors on the different simulated datasets and experimental chromatograms. The sparsity assisted signal smoother and baseline estimation and denoising using sparsity approach, which both rely on the use of sparsity, systematically outperform the two other methods and are hence most appropriate for chromatograms.

Estimates of Genetic Parameters for Milk, the Occurrence of and Susceptibility to Clinical Lameness and Claw Disorders in Dairy Goats.

The New Zealand goat industry accesses niche markets for high-value products, mainly formula for infants and young children. This study aimed to estimate the genetic parameters of occurrence and susceptibility of clinical lameness and selected claw disorders and establish their genetic associations with milk production traits. Information on pedigree, lameness, claw disorders, and milk production was collected on three farms between June 2019 and July 2020. The dataset contained 1637 does from 174 sires and 1231 dams. Estimates of genetic and residual (co)variances, heritabilities, and genetic and phenotypic correlations were obtained with uni- and bi-variate animal models. The models included the fixed effects of farm and parity, deviation from the median kidding date as a covariate, and the random effects of animal and residual error. The heritability (h2) estimates for lameness occurrence and susceptibility were 0.07 and 0.13, respectively. The h2 estimates for claw disorder susceptibilities ranged from 0.02 to 0.23. The genotypic correlations ranged from weak to very strong between lameness and milk production traits (-0.94 to 0.84) and weak to moderate (0.23 to 0.84) between claw disorder and milk production traits.

Detecting and correcting for heteroscedasticity in the presence of measurement error

The problem of measurement error in predictors has received a vast amount of attention for both linear and non-linear models. The major focus has generally been on inference for regression coefficients, while residual analysis, variance estimation and heteroscedasticity assessment have received limited attention. In this paper we propose and evaluate new methods, based on reconstructed predictors, to address these problems in the context of linear regression. Methods using moment reconstructed predictors are found to perform well, including a new model-based bootstrapping technique for testing heteroscedasticity. Motivated by an example where the predictor is methylation rate and the measurement error model is based on the binomial distribution, particular attention is given to being able to handle the situation where both the measurement error variances and the variance of the error in the equation may be changing as a quadratic function of the unobserved predictor.

Estimation of Heritability of Karan Fries Cattle using Bayesian Procedure

  The Bayesian model was applied for analyzing the first lactation in Karan Fries cattle. First lactation data of production (305-day or less milk yield and daily milk yield) were collected from the history-cum pedigree sheet and daily milk yield registers of the division of Dairy Cattle Breeding (DCB), National Dairy Research Institute (NDRI), Karnal. In the Bayesian paradigm, MCMC methods are applied to solve complex mathematical problems to estimate a large number of unknown parameters. Assuming linear mixed model and using the different prior set up, diagnostic of MCMC (Markov Chain Monte Carlo) was carried out graphically as well as by Heidelberg stationarity test. Variance estimates of the random effects (VA) and residual variance estimation (VR) and Variance estimate location effects i.e. fixed effects were calculated along with effective sample size. Finally, heritability (h2) estimates for First lactation 305 days or less milk yield (FL305DMY) was estimated along with its credible interval.

PSXIV-19 Heritability for growth and resistance to gastrointestinal parasitism in meat goats and hair sheep

Abstract Genetic selection for resistance to internal parasitism is of great research interest. Heritabilities were determined for average daily gain (ADG), logarithmic transformed fecal egg count (FEC), packed cell volume (PCV), and serum immunoglobin (Ig) levels of growing male meat goats and hair sheep from different farms in the southcentral USA during three consecutive central performance tests (CPT). Tests entailed 7–10 wk of data collection after artificial infection with Haemonchus contortus. In year 1, animals evaluated were selected randomly and in years 2 and 3 progeny of CPT sires classified as highly or moderately resistant, which included 46, 50, and 51 Boer, Kiko, and Spanish and 59, 61, 34, and 46 Dorper, Katahdin-farm A, Katahdin-farm B, and St. Croix, respectively. Females were classified accordingly on-farm based on FEC and FAMACHA. Pedigree records consisted of 32 and 57 known sires, 95 and 152 known dams including 4 and 10 full-sibs and 97 and 149 half-sibs for goats and sheep, respectively. Variance components and heritabilities were estimated by AIREML using WOMBAT with a multivariate animal model. Heritability estimates were 0.48 ± 0.214 and 0.85 ± 0.157 of ADG, 0.31 ± 0.237 and 0.20 ± 0.172 of FEC, 0.60 ± 0.206 and 0.24 ± 0.185 of PCV, 0.26 ± 0.172 and 0.51 ± 0.167 of IgA, 0.335 and 0.543 of IgM, and 0.14 ± 0.192 and 0.31 ± 0.190 of IgG for goats and sheep, respectively. Reasons for relatively high heritabilities for all traits include the low residual variance estimates due primarily to a standardized environment in the performance test. In conclusion, moderate to high heritabilities were found for growth performance and response to parasite infection for growing meat goat and hair sheep males under a standardized environment that suggests considerable for genetic improvement through selection.

Estimation of genetic parameters for sexual dimorphism in body weight of Baluchi sheep

The objective of this study was to estimate genetic parameters for sexual dimorphism (SD) in birth weights (BW), weaning weights (WW), 6-month weight (W6), 9-month weight (W9) and 12-month weight (W12) of Baluchi sheep. Data were collected during 1981-2015 from Baluchi sheep flock (flock no 1) of Abbas Abad sheep breeding station located in Mashhad, Iran. Data were included 7339, 7303, 5884, 5162 and 4691 records of birth weight, weaning weight, 6-month weight, 9-month weight and 12-month weight, respectively. Six bivariate animal models were used to estimate variance components and corresponding genetic parameters in male and female lambs separately. The SD levels (ratio of Male/Female) increased from 1.06 at birth to 1.13 at yearling age. Except for W9 in which additive genetic variance and direct heritability (h_a^2) were greater in males, for the other studied traits, females experienced higher additive genetic variance and h_a^2. In both sex, maternal effects contributed significantly in phenotypic variation of body weights with greater contribution to body weights measured early in life. While in females, maternal genetic effect was greater than males, in males, maternal permanent environmental effect was greater which together with higher estimates of residual variances revealed greater sensitivity of male lambs to environmental conditions. Cross-sex additive genetic correlation (ra) was 0.86 for BW and 1.00 for the other studied traits. Maternal correlations between sexes were close to 1.00 indicating lack of sexual dimorphism for maternal effects on body weights of Baluchi lambs. Based on an approximate 95% confidence interval, the difference between sexes regarding direct heritability were not significant, indicating no need or opportunity for different selection strategies in two sexes. Therefore, a model including lambs of both sexes and with sex effects included in the model can be used for genetic evaluation.

Joint Modeling of Genetics and Field Variation in Plant Breeding Trials Using Relationship and Different Spatial Methods: A Simulation Study of Accuracy and Bias

Modelling field spatial patterns is standard practice for the analysis of plant breeding. Jointly fitting the genetic relationship among individuals and spatial information enables better separability between the variance due to genetics and field variation. This study aims to quantify the accuracy and bias of estimative parameters using different approaches. We contrasted three settings for the genetic term: no relationship (I), pedigree relationship (A), and genomic relationship (G); and a set of approaches for the spatial variation: no-spatial (NS), moving average covariate (MA), row-column adjustment (RC), autoregressive AR1 × AR1 (AR), spatial stochastic partial differential equations, or SPDE (SD), nearest neighbor graph (NG), and Gaussian kernel (GK). Simulations were set to represent soybean field trials at F2:4 generation. Heritability was sampled from a uniform distribution U(0,1). The simulated residual-to-spatial ratio between residual variance and spatial variance (Ve:Vs) ranged from 9:1 to 1:9. Experimental settings were conducted under an augmented block design with the systematic distribution of checks accounting for 10% of the plots. Relationship information had a substantial impact on the accuracy of the genetic values (G > A > I) and contributed to the accuracy of spatial effects (30.63–42.27% improvement). Spatial models were ranked based on an improvement to the accuracy of estimative of genetic effects as SD ≥ GK ≥ AR ≥ NG ≥ MA > RC ≥ NS, and to the accuracy of estimative of spatial effects as GK ≥ SD ≥ NG > AR ≥ MA > RC. Estimates of genetic and spatial variance were generally biased downwards, whereas residual variances were biased upwards. The advent of relationship information reduced the bias of all variance components. Spatial methods SD, AR, and GK provided the least biased estimates of spatial and residual variance.

The Estimation of Residual Variance in Nonparametric Regression

Given a nonparametric regression model
 Yi = g(xi) + ei, i = 1, 2, …, n,
 where Y is a dependent variable, x is an independent variable, g is an unknown function and e is an error assumed to be an independent, identical, and is distributed with mean 0 and variance σ2. In this research Rice estimator is used to determine the biased value of a residual variance estimator. The Rice estimator is given as follows:
 .
 The biased value of residual variance estimator of the Rice method is:
 , where and.
 Using the Rice estimator, the Tong-Wang residual variance estimator is obtained, that is:
 ,
 Where , , ,
 , , k = 1, 2, … , m.
 Based upon the data simulation by considering the exponential, arithmetical, and trigonometrical models, it is found that the MSE value of the Tong-Wang estimator tends to be less compared to those of the Rice estimator as well as the GSJ (Gasser, Sroka, and Jennen) estimator.

Exploring the use of residual variance for uniformity of body weight in meat quail lines using Bayesian inference

ABSTRACT 1. Uniformity in animal products is an important aspect of the production system. Several studies have reported estimates of genetics on residual variance in different species, indicating that it could be exploited to improve uniformity by selection. Nevertheless, there are no reports about the possibilities of such a selection strategy in meat quail. 2. Records of hatching weight (HW) and body weight at 42 days (W42) of female and male birds from two meat quail lines (UFV1 and UFV2) were analysed. A three-step genetic evaluation was used to investigate the effect of genetic variation on residual variance of HW and W42 in both lines. In Step 1, a single-trait model was fitted to the data. In Step 2, log-transformed squared estimated residuals (ln(ê2)) were evaluated for these traits. In Step 3, a multi-trait analysis was performed to estimate the genetic correlation between the additive genetic effects for HW, W42, and their respective ln(ê2). 3. The heritability estimates ranged from 0.12 to 0.23 for HW and from 0.22 to 0.35 for W42. The estimated heritabilities for the residual part were low and ranged from 0.0003 to 0.02 for both traits, and the genetic coefficient of variation residual variance estimates ranged from 0.31 to 0.42 for HW and from 0.09 to 0.25 for W42. Genetic correlations between the means (HW and W42) and ln(ê2) values were both positive and did not differ from zero, indicating no association between mean and ln(ê2). 4. In conclusion, the uniformity of HW and W42 could be improved by selecting for lower residual variance in both meat quail lines, but the accuracy of selection may be low due to low heritability for uniformity, mainly for W42.

Accuracy of breeding values for production traits in turkeys (Meleagris gallopavo) using recursive models with or without genomics

BackgroundKnowledge about potential functional relationships among traits of interest offers a unique opportunity to understand causal mechanisms and to optimize breeding goals, management practices, and prediction accuracy. In this study, we inferred the phenotypic causal networks among five traits in a turkey population and assessed the effect of the use of such causal structures on the accuracy of predictions of breeding values.MethodsPhenotypic data on feed conversion ratio, residual feed intake, body weight, breast meat yield, and walking score in addition to genotype data from a commercial breeding population were used. Causal links between the traits were detected using the inductive causation algorithm based on the joint distribution of genetic effects obtained from a standard Bayesian multiple trait model. Then, a structural equation model was implemented to infer the magnitude of causal structure coefficients among the phenotypes. Accuracies of predictions of breeding values derived using pedigree- and blending-based multiple trait models were compared to those obtained with the pedigree- and blending-based structural equation models.ResultsIn contrast to the two unconditioned traits (i.e., feed conversion ratio and breast meat yield) in the causal structures, the three conditioned traits (i.e., residual feed intake, body weight, and walking score) showed noticeable changes in estimates of genetic and residual variances between the structural equation model and the multiple trait model. The analysis revealed interesting functional associations and indirect genetic effects. For example, the structural coefficient for the path from body weight to walking score indicated that a 1-unit genetic improvement in body weight is expected to result in a 0.27-unit decline in walking score. Both structural equation models outperformed their counterpart multiple trait models for the conditioned traits. Applying the causal structures led to an increase in accuracy of estimated breeding values of approximately 7, 6, and 20% for residual feed intake, body weight, and walking score, respectively, and different rankings of selection candidates for the conditioned traits.ConclusionsOur results suggest that structural equation models can improve genetic selection decisions and increase the prediction accuracy of breeding values of selection candidates. The identified causal relationships between the studied traits should be carefully considered in future turkey breeding programs.

Partitioning variation in measurements of beef carcass traits using ultrasound.

Ultrasound technology provides cattle breeders with a quick, noninvasive, and inexpensive way to measure carcass data on live animals. Ultrasound data are used as indicator traits in cattle genetic evaluations for economically relevant carcass traits. Ultrasound cattle genetic evaluations assume homogeneous additive genetic and residual variance. Thus, the objective was to partition phenotypic variance in ultrasound carcass measurements into components for additive genetic effects, technicians, contemporary groups within technicians, and residual and to examine the homogeneity of these variances among image interpretation laboratories. Records of longissimus muscle area (LMA), percentage of intramuscular fat (IMF), and subcutaneous fat depth (SFD), measured using ultrasound, were provided by the American Angus Association (n = 65,967), American Hereford Association (n = 43,182), and American Simmental Association (n = 48,298). The data also included contemporary group, technician, imaging lab, and a three-generation pedigree for each animal. Variance components for ultrasound carcass measurements were first estimated with univariate animal models for each breed and imaging laboratory using derivative-free restricted maximum likelihood. Then, treating data from each imaging laboratory as separate traits, genetic correlations between laboratories for LMA, percentage of IMF, and subcutaneous fat were estimated with trivariate animal models. The technician explained 12–27%, 5–23%, and 4–26% of the variance for IMF, SFD, and LMA, respectively, across all three breeds. Variance due to technician was often greater than variance due to additive genetic effects but almost always less than that explained by the contemporary group. Within breeds, estimates of additive genetic variance for LMA, SFD, and IMF differed (range divided by mean) among laboratories by 4.5%, 21.5%, and 39.4 % (Angus); 31.6%, 15.0%, and 49.1% (Hereford); and 19.9%, 46.6%, and 55.3% (Simmental), respectively. Likewise, estimates of residual variance for LMA, SFD, and IMF differed among laboratories by 43.4%, 22.9%, and 43.3% (Angus); 24.9%, 15.2%, and 79.2% (Hereford); and 26.4%, 32.5%, and 46.2% (Simmental), respectively. Genetic correlations between labs across breeds ranged from 0.79 to 0.95 for IMF, 0.26 to 0.94 for SFD, and 0.78 to 0.98 for LMA. The impact of the observed heterogeneity of variance between labs on genetic evaluation requires further study.

Contextual and Individual Determinants of Mental Health: A Cross-sectional Multilevel Study in Tehran, Iran.

ObjectivesOur aim was to answer the following questions: (1) Can mental health variance be partitioned to individual and higher levels (e.g., neighborhood and district); (2) How much (as a percentage) do individual-level determinants explain the variability of mental health at the individual-level; and (3) How much do determinants at the neighborhood- or district-level explain the variability of mental health at the neighborhood- or district-level?MethodsWe used raw data from the second round of the Urban Health Equity Assessment and Response Tool in Tehran (in 2012-2013, n=34 700 samples nested in 368 neighborhoods nested in 22 districts) and the results of the official report of Tehran’s Center of Studies and Planning (in 2012-2013, n=22 districts). Multilevel linear regression models were used to answer the study questions.ResultsApproximately 40% of Tehran residents provided responses suggestive of having mental health disorders (30-52%). According to estimates of residual variance, 7% of mental health variance was determined to be at the neighborhood-level and 93% at the individual-level. Approximately 21% of mental health variance at the individual-level and 49% of the remaining mental health variance at the neighborhood-level were determined by determinants at the individual-level and neighborhood-level, respectively.ConclusionsIf we want to make the most effective decisions about the determinants of mental health, in addition to considering the therapeutic perspective, we should have a systemic or contextual view of the determinants of mental health.

Estimation of litter size variability phenotypes in Large White sows.

The objective of this study was to obtain new phenotypes of phenotypic variability for the total number born (TNB) in pigs using the residual variance of TNB. The analysis was based on 246,799 Large White litter observations provided by Topigs Norsvin. Three animal models were used to obtain estimates of residual variance for TNB: the basic model (BM) containing fixed effects of farm-year and season and random effects of animal and permanent environmental sow, the basic model with an additional fixed effect of parity (BMP) and a random regression model (RRM). The within-individual variance of the residuals was calculated and log-transformed to obtain three new variability traits: LnVarBM, LnVarBMP and LnVarRRM. Then, (co)variance components, heritability, the genetic coefficient of variation at the standard deviation level (GCVSDe ) and genetic correlations between the three LnVar's and between the LnVar's and mean total number born (mTNB) were estimated with uni-, bi- and trivariate models. Results indicated that genetically LnVar's are the same trait and are positively correlated with the mTNB (~0.60). Thus, both traits should be included in breeding programmes to avoid an increase in TNB variability while selecting for increased TNB. Heritability of the LnVar's was estimated at 0.021. The GCVSDe for LnVar's showed that a change of 8% in residual standard deviation of TNB could be obtained per generation. Those results indicate that phenotypic variability of litter size is under genetic control, thus it may be improved by selection.

Fully moderated t-statistic in linear modeling of mixed effects for differential expression analysis

BackgroundGene expression profiling experiments with few replicates lead to great variability in the estimates of gene variances. Toward this end, several moderated t-test methods have been developed to reduce this variability and to increase power for testing differential expression. Most of these moderated methods are based on linear models with fixed effects where residual variances are smoothed under a hierarchical Bayes framework. However, they are inadequate for designs with complex correlation structures, therefore application of moderated methods to linear models with mixed effects are needed for differential expression analysis.ResultsWe demonstrated the implementation of the fully moderated t-statistic method for linear models with mixed effects, where both residual variances and variance estimates of random effects are smoothed under a hierarchical Bayes framework. We compared the proposed method with two current moderated methods and show that the proposed method can control the expected number of false positives at the nominal level, while the two current moderated methods fail.ConclusionsWe proposed an approach for testing differential expression under complex correlation structures while providing variance shrinkage. The proposed method is able to improve power by moderation and controls the expected number of false positives properly at the nominal level.

Genetic parameters for total lactation yields of milk, fat, protein, and somatic cell score in New Zealand dairy goats.

The aim of this study was to estimate genetic parameters for lactation yields of milk (MY), fat (FY), protein (PY), and somatic cell score (SCS) of New Zealand dairy goats. The analysis used 64,604 lactation records from 23,583 does, kidding between 2004 and 2017, distributed in 21 flocks and representing 915 bucks. Estimates of genetic and residual (co) variances, heritabilities, and repeatabilities were obtained using a multiple-trait repeatability animal model. The model included the fixed effects of contemporary group (does kidding in the same flock and year), age of the doe (in years), and as covariates, kidding day, proportion of Alpine, Nubian, Toggenburg, and "unknown" breeds (Saanen was used as the base breed), and heterosis. Random effects included additive animal genetic and doe permanent environmental effects. Estimates of heritabilities were 0.25 for MY, 0.24 for FY, 0.24 for PY, and 0.21 for SCS. The phenotypic correlations between MY, FY, and PY ranged from 0.90 to 0.96, and the genetic correlations ranged from 0.81 to 0.93. These results indicate lactation yield traits exhibit useful heritable variation and that multiple trait selection for these traits could improve milk revenue produced from successive generations of New Zealand dairy goats.

Statistical models for the analysis of longitudinal traits in beef cattle under sequential selection

The comprehensive analyses of longitudinal traits under sequential selection could improve genetic parameters estimates and lead to more accurate selection decisions. The objective of this study was to evaluate statistical models for analyzing longitudinal traits under sequential selection. We used single trait (STM), multiple trait (MTM) and random regression model with linear splines polynomials (RRM) to estimate genetic parameters for body weight records of Nellore young bulls. First, we used a complete dataset (DS100) with 60,550 body weight records of 12,110 young bulls. Two additional datasets were also obtained from DS100. They were obtained with a sequential selection of 85% (DS85) and 70% (DS70) of heaviest animals. In addition, some datasets with the same number of records as DS85 and DS70 were also obtained with random sampling of 85% (RS85) and 70% (RS70) of body weight records at each age. Body weights were standardized at 330, 385, 440, 495 and 550 days of age for STM and MTM analysis. In RRM, the knots of linear splines were fitted at 250, 330, 385, 440, 495, 550 and 597 days of age. The estimates of additive genetic, residual and phenotypic variances from STM analysis of DS85 and DS70 were lower than the corresponding estimates from STM analysis of DS100. However, the estimates of genetic and environmental parameters from MTM and RRM analysis of DS100, DS85 and DS70 were similar. The reduction of dataset size with random sampling (RS85 and RS70) did not affect the estimates of genetic and environmental parameters from STM, MTM and RRM analysis. MTM and RRM are adequate for genetic evaluation of the longitudinal traits under sequential selection, but RRM presents some advantages over MTM. RRM with linear splines does not need previous adjustments of the body weights for standard ages and it also provides estimates of genetic and environmental parameters directly at the same points as the corresponding traits in MTM.

Genetic heterogeneity of residual variance of hatch weight in Mazandaran native chicken

ABSTRACT1. In current breeding programmes, uniformity of end products and producing animals that are robust to environmental challenges are desirable. Several studies have provided evidence of the presence of genetic heterogeneity of residual variance and proposed that it could be possible to increase uniformity of livestock productions by selection. The present study aimed to define the micro environmental sensitivity of dual-purpose chickens for body weight at hatch.2. The data set consisted of 24,321 female and 21,547 male chickens’ records of hatch weight from 19 consecutive generations of Mazandaran fowl. The statistical analysis was carried out in a two-step approach: first, an animal model was fitted to the data and then, the impact of additive genetic effects on the residual variance of the studied trait was investigated.3. The estimate of heritability for body weight at hatch was in the range of 0.23–0.25 for female and 0.14–0.16 for male offspring, respectively. The proportion of maternal environmental variance to phenotypic variance ranged from 0.24 to 0.27 for female and 0.17 to 0.24 for male offspring. Heritabilities in females were higher than males. Estimates of the heritability of residual variance ranged between 0.067 and 0.090. The genetic coefficients of variation were high ranging between 0.83 and 0.86. Genetic correlations between hatch weight and its residual variance estimates from bivariate analysis were −0.39 and −0.44 in females and males, respectively.4. The results suggest that there is an opportunity to simultaneously improve body weight and the uniformity of body weight by selecting for lower residual variance in native chickens.