Incorporation of observations with different residual error variances into existing complex test-day models

Automated milking systems (AMS) have become popular on dairy farms. Due to a different test-day recording scheme the variation of test-day observations differ from AMS differ from those of conventional milking system (CMS). An approach is presented for upgrading the genetic evaluation model for production traits milk, protein and fat yield by including residual covariance matrices for AMS and CMS test-day observations. Residual variances were found to be 16–37% smaller for milk and protein yields and 42–47% larger for fat yield when recorded under AMS herds compared to CMS herds. Daily heritability was higher for milk and protein yield and lower for fat yield when traits were recorded under AMS compared to recording under CMS. No difference was found between AMS and CMS in 305-day heritability for milk and protein yield except for second lactation milk yield. 305-day heritability for fat was lower for all lactations under AMS.     

Comparison of multiplicative heterogeneous variance adjustment models for genetic evaluations

Two heterogeneous variance adjustment methods and two variance models were compared in a simulation study. The method used for heterogeneous variance adjustment in the Nordic test‐day model, which is a multiplicative method based on Meuwissen (J. Dairy Sci., 79, 1996, 310), was compared with a restricted multiplicative method where the fixed effects were not scaled. Both methods were tested with two different variance models, one with a herd‐year and the other with a herd‐year‐month random effect. The simulation study was built on two field data sets from Swedish Red dairy cattle herds. For both data sets, 200 herds with test‐day observations over a 12‐year period were sampled. For one data set, herds were sampled randomly, while for the other, each herd was required to have at least 10 first‐calving cows per year. The simulations supported the applicability of both methods and models, but the multiplicative mixed model was more sensitive in the case of small strata sizes. Estimation of variance components for the variance models resulted in different parameter estimates, depending on the applied heterogeneous variance adjustment method and variance model combination. Our analyses showed that the assumption of a first‐order autoregressive correlation structure between random‐effect levels is reasonable when within‐herd heterogeneity is modelled by year classes, but less appropriate for within‐herd heterogeneity by month classes. Of the studied alternatives, the multiplicative method and a variance model with a random herd‐year effect were found most suitable for the Nordic test‐day model for dairy cattle evaluation.     

Multiple trait prediction for a type of model with heterogeneous genetic and residual covariance structures

A restricted set of models is defined that allows for heterogeneous genetic and residual covariance structures. Multiple trait models and models with multiple random factors are included. The restriction on the model is that the correlations among genetic effects in different classes are the same. Equivalently, the genetic covariance matrices are assumed to differ between classes due to scaling. This assumption greatly reduces the number of parameters that must be specified and does not adversely affect the computational burden of a mixed model analysis. An application of the model for genetic evaluation of beef cattle is described and illustrated numerically.     

Bayesian inference strategies for the prediction of genetic merit using threshold models with an application to calving ease scores in Italian Piemontese cattle

First parity calving difficulty scores from Italian Piemontese cattle were analysed using a threshold mixed effects model. The model included the fixed effects of age of dam and sex of calf and their interaction and the random effects of sire, maternal grandsire, and herd‐year‐season. Covariances between sire and maternal grandsire effects were modelled using a numerator relationship matrix based on male ancestors. Field data consisted of 23 953 records collected between 1989 and 1998 from 4741 herd‐year‐seasons. Variance and covariance components were estimated using two alternative approximate marginal maximum likelihood (MML) methods, one based on expectation‐maximization (EM) and the other based on Laplacian integration. Inferences were compared to those based on three separate runs or sequences of Markov Chain Monte Carlo (MCMC) sampling in order to assess the validity of approximate MML estimates derived from data with similar size and design structure. Point estimates of direct heritability were 0.24, 0.25 and 0.26 for EM, Laplacian and MCMC (posterior mean), respectively, whereas corresponding maternal heritability estimates were 0.10, 0.11 and 0.12, respectively. The covariance between additive direct and maternal effects was found to be not different from zero based on MCMC‐derived confidence sets. The conventional joint modal estimates of sire effects and associated standard errors based on MML estimates of variance and covariance components differed little from the respective posterior means and standard deviations derived from MCMC. Therefore, there may be little need to pursue computation‐intensive MCMC methods for inference on genetic parameters and genetic merits using conventional threshold sire and maternal grandsire models for large datasets on calving ease.     

Scaling to account for heterogeneous variances in a Bayesian analysis of broiler quantitative trait loci

A Bayesian method for QTL analysis that is capable of accounting for heterogeneity of variance between sexes, is introduced. The Bayesian method uses a parsimonious model that includes scaling parameters for polygenic and QTL allelic effects per sex. Furthermore, the method employs a reduced animal model to increase computational efficiency. Markov Chain Monte Carlo techniques were applied to obtain estimates of genetic parameters. In comparison with previous regression analyses, the Bayesian method 1) estimates dispersion parameters and polygenic effects, 2) uses individual observations instead of offspring averages, and 3) estimates fixed effect levels and covariates and heterogeneity of variance between sexes simultaneously with other parameters, taking uncertainties fully into account. Broiler data collected in a feed efficiency and a carcass experiment were used to illustrate QTL analysis based on the Bayesian method. The experiments were conducted in a population consisting of 10 full-sib families of a cross between two broiler lines. Microsatellite genotypes were determined on generation 1 and 2 animals and phenotypes were collected on third-generation offspring from mating members from different families. Chromosomal regions that seemed to contain a QTL in previous regression analyses and showed heterogeneity of variance were chosen. Traits analyzed in the feed efficiency experiment were BW at 48 d and growth, feed intake, and feed intake corrected for BW between 23 and 48 d. In the carcass experiment, carcass percentage was analyzed. The Bayesian method was successful in finding QTL in all regions previously detected.     

Bayesian inference for genetic parameter estimation on growth traits for Nelore cattle in Brazil,using the Gibbs sampler

This data set consisted of over 29 245 field records from 24 herds of registered Nelore cattle born between 1980 and 1993, with calves sires by 657 sires and 12 151 dams. The records were collected in south‐eastern and midwestern Brazil and animals were raised on pasture in a tropical climate. Three growth traits were included in these analyses: 205‐ (W205), 365‐ (W365) and 550‐day (W550) weight. The linear model included fixed effects for contemporary groups (herd‐year‐season‐sex) and age of dam at calving. The model also included random effects for direct genetic, maternal genetic and maternal permanent environmental (MPE) contributions to observations. The analyses were conducted using single‐trait and multiple‐trait animal models. Variance and covariance components were estimated by restricted maximum likelihood (REML) using a derivative‐free algorithm (DFREML) for multiple traits (MTDFREML). Bayesian inference was obtained by a multiple trait Gibbs sampling algorithm (GS) for (co)variance component inference in animal models (MTGSAM). Three different sets of prior distributions for the (co)variance components were used: flat, symmetric, and sharp. The shape parameters (ν) were 0, 5 and 9, respectively. The results suggested that the shape of the prior distributions did not affect the estimates of (co)variance components. From the REML analyses, for all traits, direct heritabilities obtained from single trait analyses were smaller than those obtained from bivariate analyses and by the GS method. Estimates of genetic correlations between direct and maternal effects obtained using REML were positive but very low, indicating that genetic selection programs should consider both components jointly. GS produced similar but slightly higher estimates of genetic parameters than REML, however, the greater robustness of GS makes it the method of choice for many applications.     

Estimation of genetic parameters for average daily gain using models with competition effects

Components of variance for ADG with models including competition effects were estimated from data provided by the Pig Improvement Company on 11,235 pigs from 4 selected lines of swine. Fifteen pigs with average age of 71 d were randomly assigned to a pen by line and sex and taken off test after approximately 89 d (off-test BW ranged from 61 to 158 kg). Models included fixed effects of line, sex, and contemporary group and initial test age as a covariate, with random direct genetic, competition (genetic and environmental), pen, litter, and residual effects. With the full model, variances attributable to direct, direct-competition, genetic competition, and litter (co)variance components could be partitioned; genetic competition variance was small but statistically significantly different from zero. Variances attributable to environmental competition, pen, and residual effects could not be partitioned, but combinations of these environmental variances were estimable. Variances could be partitioned with either pen effects or environmental competition effects in the model. Environmental competition effects seemed to be the source of variance associated with pens. With pen as a fixed effect and without environmental competition effects in the model, genetic components of variance could not be partitioned, but combinations of genetic (co)variances were estimable. With both pen and environmental competition effects ignored, estimates of direct-competition and genetic competition (co)variance components were greatly inflated. With competition (genetic and environmental) effects ignored, the estimate of pen variance increased by 39%, with little change in estimates of direct genetic or residual variance. When both pen and competition (genetic and environmental) effects were dropped from the model, variance attributable to direct genetic effects was inflated. Estimates of variance attributable to competition effects were small in this study. Including environmental competition effects as permanent environmental effects in the model did not change estimates of genetic (co)variances. We concluded that including either pen effects or environmental competition effects as random effects in the model avoids bias in estimates of genetic variances but that including pen effects is much easier.     

Computing simplifications for non-additive genetic models

A limiting factor in the analysis of non‐additive genetic models has been the ability to compute the inverses of non‐additive genetic covariance matrices for large populations. Also, the order of the equations was equal to the number of animals times the number of non‐additive genetic effects that were included in the model. This paper describes a computing algorithm that avoids the inverses of the non‐additive genetic covariance matrices and keeps the size of the equations to be the same as any animal model with only additive genetic effects. Quadratic forms for the non‐additive genetic variances could also be computed without the inverses of the non‐additive genetic covariance matrices.     

Estimation of dominance genetic variances for reproductive traits and growth traits of calves in Japanese Black cattle

The dominance genetic effects for reproductive and calf growth abilities in the practical Japanese Black populations were examined using average information (AI) algorithm restricted maximum likelihood (REML) under animal models. The reproductive traits were observed in Japanese Black cattle maintained at Tottori and Okinawa prefectures, and growth traits of calves were observed in cattle at Okinawa. The average of dominance relationships in Tottori ranged from 0.2 to 0.4%, while the level in Okinawa was lower and sparse compared with Tottori. The proportions of the dominance variances to sum of additive and dominance variances () were all 0.02 for reproductive traits in Tottori. In contrast, the proportion was 0.02–0.64 in Okinawa regardless of the level of dominance relationships. These proportions suggested that the dominance might affect the expression of calving interval, days open and gestation length in Okinawa, where breeding units were spread over many islands. Although the dominance variances could not estimate birthweight, w as 0.34 for calf market weight and 0.27 for average daily gain from birth to calf market in Okinawa. These values also suggested that the dominance might affect the early growth of calves. In the near future, genetic relationships will become more complicated with continuation of the current selection and mating systems. Therefore, genetic evaluation accounting for dominance effects would be necessary for particular traits and populations.     

Estimation of genetic parameters related to eggshell strength using random regression models

1. This study examined the changes in eggshell strength and the genetic parameters related to this trait throughout a hen’s laying life using random regression.

2. The data were collected from a crossbred population between 2011 and 2014, where the eggshell strength was determined repeatedly for 2260 hens.

3. Using random regression models (RRMs), several Legendre polynomials were employed to estimate the fixed, direct genetic and permanent environment effects. The residual effects were treated as independently distributed with heterogeneous variance for each test week.

4. The direct genetic variance was included with second-order Legendre polynomials and the permanent environment with third-order Legendre polynomials.

5. The heritability of eggshell strength ranged from 0.26 to 0.43, the repeatability ranged between 0.47 and 0.69, and the estimated genetic correlations between test weeks was high at > 0.67.

6. The first eigenvalue of the genetic covariance matrix accounted for about 97% of the sum of all the eigenvalues.

7. The flexibility and statistical power of RRM suggest that this model could be an effective method to improve eggshell quality and to reduce losses due to cracked eggs in a breeding plan.

     

Comparison of homogeneity and heterogeneity of residual variance using random regression test-day models for first lactation Japanese Holstein cows

Using a large‐scale data set that included first lactation test day records from 1975 to 2000 for Japanese Holsteins, genetic parameters for milk yield were estimated by using random regression (RR) test‐day models (TDM) with heterogeneous and homogeneous residual variances. It is necessary for the RR‐TDM to include a function that explains the shape of the lactation curve. The RR‐TDM with the LW curve, which combined Wilmink's curve and a Legendre polynomial, was used for fitting the model for milk yield. In recent years, increases in residual variance have been noted for Japanese dairy cattle. Thus, three kinds of heterogeneous residual variance over the calving year were considered: H1, H2 and HG. Linear and quadratic exponential functions for the calving year were used in H1 and H2, respectively. Residual variance of HG was divided into five groups according to calving year. Homogeneous residual variance was HO. All heterogeneous residual variances increased with calving year in an almost linear fashion. Residual variance increased over the study period. However, there is no need to consider heterogeneous residual variances in genetic evaluations, because the heterogeneity of residual variance over the years did not affect the ranking of top sires and cows.     

Estimation of genetic parameters for ultrasound-predicted percentage of intramuscular fat in Angus cattle using random regression models

The present study included 3,358 observations of 675 bulls and heifers from the Iowa State University beef cattle breeding project. Data were collected over a 3-yr period between 1998 and 2000. Each year, cattle were scanned four to six times for ultrasound-predicted percentage of intramuscular fat (UPFAT) and other ultrasound traits, starting at a minimum age of 28 wk. The objective of the current study was to estimate variance components, heritability, and repeatability of UPFAT in young bulls and heifers. Data were subjected to random-regression animal models that included fixed effects of contemporary group, fixed Legendre polynomial of age at measurement, and random regression coefficients on Legendre polynomial of age at measurement for animals' direct genetic and direct permanent environmental effects. Phenotypic and genetic models involving different levels of polynomial fit for the animal component were considered. A model fitting a linear effect of Legendre polynomial of age at a measurement for animal direct genetic and direct permanent environmental effects and a homogeneous error variance described the present data adequately. Heritability of UPFAT ranged from 0.32 at 28 wk of age to a maximum of 0.53 at 63 wk. Repeatability of UPFAT increased from a minimum of 0.60 at ages of 28 to 39 wk to a maximum of 0.80 at ages 61 to 63 wk. Heritability and repeatability of yearling UPFAT were 0.50 and 0.71, respectively. With the exception of minor differences at earlier ages, fitting heterogeneous error variances did not have an effect on genetic parameter estimates for most ages of measurement. The present results showed an optimal heritability and repeatability of UPFAT measures around 52 wk and through at least 63 wk of age. This suggested that differences in UPFAT measures during this period also are good measures of differences in marbling genetic potential of Angus cattle.     

Variation in autosomal and sex-linked genetic effects for growth traits in Markhoz goat using multivariate animal models

Tropical Animal Health and Production - The present study was conducted to estimate autosomal and sex-linked genetic parameters by restricted maximum likelihood method using four different...     

Selection response and genetic parameters for residual feed intake in Yorkshire swine

Residual feed intake (RFI) is a measure of feed efficiency defined as the difference between the observed feed intake and that predicted from the average requirements for growth and maintenance. The objective of this study was to evaluate the response in a selection experiment consisting of a line selected for low RFI and a random control line and to estimate the genetic parameters for RFI and related production and carcass traits. Beginning with random allocation of purebred Yorkshire littermates, in each generation, electronically measured ADFI, ADG, and ultrasound backfat (BF) were evaluated during a approximately 40- to approximately 115-kg of BW test period on approximately 90 boars from first parity and approximately 90 gilts from second parity sows of the low RFI line. After evaluation of first parity boars, approximately 12 boars and approximately 70 gilts from the low RFI line were selected to produce approximately 50 litters for the next generation. Approximately 30 control line litters were produced by random selection and mating. Selection was on EBV for RFI from an animal model analysis of ADFI, with on-test group and sex (fixed), pen within group and litter (random), and covariates for interactions of on- and off-test BW, on-test age, ADG, and BF with generations. The RFI explained 34% of phenotypic variation in ADFI. After 4 generations of selection, estimates of heritability for RFI, ADFI, ADG, feed efficiency (FE, which is the reciprocal of the feed conversion ratio and equals ADG/ ADFI), and ultrasound-predicted BF, LM area (LMA), and intramuscular fat (IMF) were 0.29, 0.51, 0.42, 0.17, 0.68, 0.57, and 0.28, respectively; predicted responses based on average EBV in the low RFI line were -114, -202, and -39 g/d for RFI (= 0.9 phenotypic SD), ADFI (0.9 SD), and ADG (0.4 SD), respectively, and 1.56% for FE (0.5 SD), -0.37 mm for BF (0.1 SD), 0.35 cm(2) for LMA (0.1 SD), and -0.10% for IMF (0.3 SD). Direct phenotypic comparison of the low RFI and control lines based on 92 low RFI and 76 control gilts from the second parity of generation 4 showed that selection had significantly decreased RFI by 96 g/d (P = 0.002) and ADFI by 165 g/d (P < 0.0001). The low RFI line also had 33 g/d lower ADG (P = 0.022), 1.36% greater FE (P = 0.09), and 1.99 mm less BF (P = 0.013). There was not a significant difference in LMA and other carcass traits, including subjective marbling score, despite a large observed difference in ultrasound-predicted IMF (-1.05% with P < 0.0001). In conclusion, RFI is a heritable trait, and selection for low RFI has significantly decreased the feed required for a given rate of growth and backfat.     

Method for the estimation of genetic merit of animals with uncertain paternity under Bayesian inference

The use of controlled mating or artificial insemination is impracticable in the case of large herds, mainly because of labour costs and the need to delimit areas during the breeding period. However, the exclusion of information from animals with uncertain paternity reduces genetic progress. The objectives of this study were as follows: (i) propose an iterative empirical Bayesian procedure to implement the hierarchical animal model (ITER); (ii) calculate the posterior probabilities of paternity by the maximum likelihood method following the concepts; (iii) compare an average numerator relationship matrix (ANRM), Bayesian hierarchical (HIER) models and ITER. Records of Nellore animals born between 1984 and 2006 from the zootechnical archive of Agropecuária Jacarezinho Ltda were used. For data consistency, records of contemporary groups (CGs) with fewer than three animals and animals whose records were 3.5 standard deviations above or below the mean of their CG were eliminated. After editing the data, 62,212 animals in the file and 12,876 animals in pedigree file were maintained, respectively. Spearman and Pearson correlations between the posterior mean of the genetic effects of animals were calculated to compare the ranking of animals for selection. Simulated data were used to confirm the veracity of the model. The correlations between ITER and HIER and between ITER and ANRM were similar evaluating different files, which decreased at the same proportion when only high‐ranked animals were evaluated. In conclusion, the model proposed herein is a suitable computational alternative to improve the prediction of breeding values of animals in genetic evaluations using large databases, including animals with uncertain paternity.     

Risk ratio as parameter for the genetic characterization of complex binary traits in cattle. A simulation study under various genetic models using halfsib families

The risk ratio (λ_R) is defined as ‘the recurrence risk for a relative of an affected individual divided by the prevalence in the general population’ and is considered as the most important parameter when designing mapping experiments for diseases in humans. In this paper, the risk ratio was introduced as a parameter to genetically characterize complex binary traits such as mastitis in cattle. Simulations were applied to evaluate the properties of λ_R under different genetic models (monogenic, digenic, polygenic and mixed models) and in dependency of their parameters for a design consisting of unbalanced halfsib families typically found in dairy cattle. Population prevalences of the simulated data ranged from 5 to 40% and λ_R was estimated on a phenotypic level. In the discrete loci models complexity of the traits was introduced through different levels of penetrance and the proportions of phenocopies within each genetic background. The risk ratio and the power to reject the null hypothesis of independent halfsibs (λ_R=1) were influenced by the prevalence in all genetic models chosen. Absolute values for λ_R were higher for lower prevalences, for example, λ_R=2.77 and 1.62 for a pure monogenic recessive model with 5 and 20% prevalence, respectively, whereas the power decreases in the case of lower prevalences. For all the prevalences investigated, higher risk ratios were found for discrete loci models compared with the polygenic models, with higher values for the monogenic relative to the digenic models in general. For the mixed models, λ_R was intermediate between the polygenic and discrete loci models. Genes with dominant relative to recessive inheritance for susceptibility caused higher risk ratios in monogenic and mixed models, for example, λ_R=5.16 and 2.77 for a pure monogenic model with 5% prevalence. In the discrete loci models, λ_R decreased with lower penetrance and a higher proportion of phenocopies. Risk ratios increased with the heritability in the polygenic and in addition with the effect of the major gene in mixed models. Consistent patterns of risk ratios were observed under the analysed genetic models and parameters, which indicate that the risk ratio is a parameter well suited to genetically characterize binary traits in unbalanced halfsib families.     

Characterization of feline hereditary retinal dystrophies using clinical, functional, structural and molecular genetic studies

Only in recent years have specific mutations been elucidated for feline hereditary retinal dystrophies. Molecular genetic characterization of feline diseases has so far been a slow process but with a full genome sequence for the cat recently completed and the development of a feline single nucleotide polymorphism chip, the characterization of feline monogenic disorders will be significantly simplified. This review summarizes current knowledge with regard to specific hereditary retinal dystrophies in cats and gives an overview of how cats can be used as models in translational research.     

Evaluation models and genetic parameters for calving difficulty in beef cattle

Calving difficulty was analyzed under threshold and linear models considering either a fixed or random herd-year effect. The aim of the study was to compare models for predicting breeding values according to the size of herd-year groups. When simulating data sets with small herds, in order to obtain an unbiased evaluation under a nonrandom and negative association of sire and herd effects, the best model for a practical evaluation was the fixed linear model. Field data included 246,576 records of the largest Charolais herds in France. Models were compared using the correlations of estimated breeding values between the different models. Although the best model from a theoretical point of view was a threshold model with a fixed herd-year effect, a linear model with a fixed herd-year effect was the best choice from a practical point of view for predicting direct effects for calving difficulty in beef cattle and was a sufficient choice for predicting the associated maternal effects for data set with large herds. Correlations between direct estimated breeding values under the reference model and the fixed linear model and the random threshold model were 0.94 and 0.91, respectively. Correlations between the corresponding maternal estimated breeding values were 0.94 and 0.98. Heritabilities of direct effects were 0.27 and 0.14 under fixed threshold and fixed linear models, respectively. The corresponding heritabilities of maternal effects were 0.18 and 0.13, and the genetic correlation between direct and maternal effects were -0.36 and -0.34, respectively.     

Predictive ability of alternative models for genetic analysis of clinical mastitis

Mastitis in cows can be defined as a binary trait, reflecting presence or absence of clinical mastitis (CM), or as a count variable, number of mastitis cases (NCM), within a defined time interval. Many different models have been proposed for genetic analyses of mastitis, and the objective of this study was to evaluate the predictive ability and sire predictions of a set of models for genetic evaluation of CM or NCM. Linear- and threshold liability models for CM, and linear, censored ordinal threshold, and zero-inflated Poisson (ZIP) models for NCM were compared in a cross-validation study. To assess the ability of these models to predict future data, records from 620492 first-lactation Norwegian Red cows, which were daughters of 3064 sires, were evaluated in a fourfold cross-validation scheme. The mean squared error of prediction was used for model comparison. All models but ordinal threshold model equally performed when comparing the overall predictive ability. This result was on average, across sick and healthy cows; however, the models behaved differently for each category of animals. For example, healthy cows were predicted better by the threshold and linear models for binary data and ZIP model, whereas for mastitic cows, the ordinal threshold model was by far the best model. Predicted sire effects and rankings of sires were highly correlated across all models. For practical purposes, the linear models are very competitive with the nonlinear models.     

Multiplicative random regression model for heterogeneous variance adjustment in genetic evaluation for milk yield in Simmental.

A multiplicative random regression (M-RRM) test-day (TD) model was used to analyse daily milk yields from all available parities of German and Austrian Simmental dairy cattle. The method to account for heterogeneous variance (HV) was based on the multiplicative mixed model approach of Meuwissen. The variance model for the heterogeneity parameters included a fixed region x year x month x parity effect and a random herd x test-month effect with a within-herd first-order autocorrelation between test-months. Acceleration of variance model solutions after each multiplicative model cycle enabled fast convergence of adjustment factors and reduced total computing time significantly. Maximum Likelihood estimation of within-strata residual variances was enhanced by inclusion of approximated information on loss in degrees of freedom due to estimation of location parameters. This improved heterogeneity estimates for very small herds. The multiplicative model was compared with a model that assumed homogeneous variance. Re-estimated genetic variances, based on Mendelian sampling deviations, were homogeneous for the M-RRM TD model but heterogeneous for the homogeneous random regression TD model. Accounting for HV had large effect on cow ranking but moderate effect on bull ranking.