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1.
Bayesian estimation via Gibbs sampling, REML, and Method R were compared for their empirical sampling properties in estimating genetic parameters from data subject to parental selection using an infinitesimal animal model. Models with and without contemporary groups, random or nonrandom parental selection, two levels of heritability, and none or 15% randomly missing pedigree information were considered. Nonrandom parental selection caused similar effects on estimates of variance components from all three methods. When pedigree information was complete, REML and Bayesian estimation were not biased by nonrandom parental selection for models with or without contemporary groups. Method R estimates, however, were strongly biased by nonrandom parental selection when contemporary groups were in the model. The bias was empirically shown to be a consequence of not fully accounting for gametic phase disequilibrium in the subsamples. The joint effects of nonrandom parental selection and missing pedigree information caused estimates from all methods to be highly biased. Missing pedigree information did not cause biased estimates in random mating populations. Method R estimates usually had greater mean square errors than did REML and Bayesian estimates.  相似文献   

2.
Method R and Restricted Maximum Likelihood (REML) were compared for estimating heritability (h2) and subsequent prediction of breeding values (a) with data subject to selection. A single-trait animal model was used to generate the data and to predict breeding values. The data originated from 10 sires and 100 dams and simulation progressed for 10 overlapping generations. In simulating the data, genetic evaluation used the underlying parameter values and sires and dams were chosen by truncation selection for greatest predicted breeding values. Four alternative pedigree structures were evaluated: complete pedigree information, 50% of phenotypes with sire identities missing, 50% of phenotypes with dam identities missing, and 50% of phenotypes with sire and dams identities missing. Under selection and with complete pedigree data, Method R was a slightly less consistent estimator of h2 than REML. Estimates of h2 by both methods were biased downward when there was selection and loss of pedigree information and were unbiased when no selection was practiced. The empirical mean square error (EMSE) of Method R was several times larger than the EMSE of REML. In a subsequent analysis, different combinations of generations selected and generations sampled were simulated in an effort to disentangle the effects of both factors on Method R estimates of h2. It was observed that Method R overestimated h2 when both the sampling that is intrinsic in the method and the selection occurred in generations 6 to 10. In a final experiment, BLUP(a) were predicted with h2 estimated by either Method R or REML. Subsequently, five more generations of selection were practiced, and the mean square error of prediction (MSEP) of BLUP(a) was calculated with estimated h2 by either method, or the true value of the parameter. The MSEP of empirical BLUP(a) using Method R was greater than the MSEP of empirical BLUP(a) using REML. The latter statistic was closer to prediction error variance of BLUP(a) than the MSEP of empirical BLUP(a) using Method R, indicating that empirical BLUP(a) calculated using REML produced accurate predictions of breeding values under selection. In conclusion, the variability of h2 estimates calculated with Method R was greater than the variability of h2 estimates calculated with REML, with or without selection. Also, the MSEP of EBLUP(a) calculated using estimates of h2 by Method R was larger than MSEP of EBLUP(a) calculated with REML estimates of h2.  相似文献   

3.
Summary Restricted maximum likelihood (REML) was used to determine the choice of statistical model, additive genetic maternal and common litter effects and consequences of ignoring these effects on estimates of variance–covariance components under random and phenotypic selection in swine using computer simulation. Two closed herds of different size and two traits, (i) pre‐weaning average daily gain and (ii) litter size at birth, were considered. Three levels of additive direct and maternal genetic correlations (rdm) were assumed to each trait. Four mixed models (denoted as GRM1 through GRM4) were used to generate data sets. Model GRM1 included only additive direct genetic effects, GRM2 included only additive direct genetic and common litter effects, GRM3 included only additive direct and maternal genetic effects and GRM4 included all the random effects. Four mixed animal models (defined as EPM1 through EPM4) were defined for estimating genetic parameters similar to GRM. Data from each GRM were fitted with EPM1 through EPM4. The largest biased estimates of additive genetic variance were obtained when EPM1 was fitted to data generated assuming the presence of either additive maternal genetic, common litter effects or a combination thereof. The bias of estimated additive direct genetic variance (VAd) increased and those of recidual variance (VE) decreased with an increase in level of rdm when GRM3 was used. EPM1, EPM2 and EPM3 resulted in biased estimation of the direct genetic variances. EPM4 was the most accurate in each GRM. Phenotypic selection substantially increased bias of estimated additive direct genetic effect and its mean square error in trait 1, but decreased those in trait 2 when ignored in the statistical model. For trait 2, estimates under phenotypic selection were more biased than those under random selection. It was concluded that statistical models for estimating variance components should include all random effects considered to avoid bias.  相似文献   

4.
Simulated horse data were used to compare multivariate estimation of genetic parameters and prediction of breeding values (BV) for categorical, continuous and molecular genetic data using linear animal models via residual maximum likelihood (REML) and best linear unbiased prediction (BLUP) and mixed linear-threshold animal models via Gibbs sampling (GS). Simulation included additive genetic values, residuals and fixed effects for one continuous trait, liabilities of four binary traits, and quantitative trait locus (QTL) effects and genetic markers with different recombination rates and polymorphism information content for one of the liabilities. Analysed data sets differed in the number of animals with trait records and availability of genetic marker information. Consideration of genetic marker information in the model resulted in marked overestimation of the heritability of the QTL trait. If information on 10,000 or 5,000 animals was used, bias of heritabilities and additive genetic correlations was mostly smaller, correlation between true and predicted BV was always higher and identification of genetically superior and inferior animals was - with regard to the moderately heritable traits, in many cases - more reliable with GS than with REML/BLUP. If information on only 1,000 animals was used, neither GS nor REML/BLUP produced genetic parameter estimates with relative bias 50% for all traits. Selection decisions for binary traits should rather be based on GS than on REML/BLUP breeding values.  相似文献   

5.
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.  相似文献   

6.
A simulation study was conducted to assess the influence of differences in the length of individual testing periods on estimates of (co)variance components of a random regression model for daily feed intake of growing pigs performance tested between 30 and 100 kg live weight. A quadratic polynomial in days on test with fixed regressions for sex, random regressions for additive genetic and permanent environmental effects and a constant residual variance was used for a bivariate simulation of feed intake and daily gain. (Co)variance components were estimated for feed intake only by means of a Bayesian analysis using Gibbs sampling and restricted maximum likelihood (REML). A single trait random regression model analogous to the one used for data simulation was used to analyse two versions of the data: full data sets with 18 weekly means of feed intake per animal and reduced data sets with the individual length of testing periods determined when tested animals reached 100 kg live weight. Only one significant difference between estimates from full and reduced data (REML estimate of genetic covariance between linear and quadratic regression parameters) and two significant differences from expected values (Gibbs estimates of permanent environmental variance of quadratic regression parameters) occurred. These differences are believed to be negligible, as the number lies within the expected range of type I error when testing at the 5% level. The course of test day variances calculated from estimates of additive genetic and permanent environmental covariance matrices also supports the conclusion that no bias in estimates of (co)variance components occurs due to the individual length of testing periods of performance‐tested growing pigs. A lower number of records per tested animal only results in more variation among estimates of (co)variance components from reduced compared with full data sets. Compared with the full data, the effective sample size of Gibbs samples from the reduced data decreased to 18% for residual variance and increased up to five times for other (co)variances. The data structure seems to influence the mixing of Gibbs chains.  相似文献   

7.
We investigated the effects of different strategies for genotyping populations on variance components and heritabilities estimated with an animal model under restricted maximum likelihood (REML), genomic REML (GREML), and single‐step GREML (ssGREML). A population with 10 generations was simulated. Animals from the last one, two or three generations were genotyped with 45,116 SNP evenly distributed on 27 chromosomes. Animals to be genotyped were chosen randomly or based on EBV. Each scenario was replicated five times. A single trait was simulated with three heritability levels (low, moderate, high). Phenotypes were simulated for only females to mimic dairy sheep and also for both sexes to mimic meat sheep. Variance component estimates from genomic data and phenotypes for one or two generations were more biased than from three generations. Estimates in the scenario without selection were the most accurate across heritability levels and methods. When selection was present in the simulations, the best option was to use genotypes of randomly selected animals. For selective genotyping, heritabilities from GREML were more biased compared to those estimated by ssGREML, because ssGREML was less affected by selective or limited genotyping.  相似文献   

8.
Two methods are presented for estimating variances and covariances from beef cattle field data using multiple-trait sire models. Both methods require that the first trait have no missing records and that the contemporary groups for the second trait be subsets of the contemporary groups for the first trait; however, the second trait may have missing records. One method uses pseudo expectations involving quadratics composed of the solutions and the right-hand sides of the mixed model equations. The other method is an extension of Henderson's Simple Method to the multiple trait case. Neither of these methods requires any inversions of large matrices in the computation of the parameters; therefore, both methods can handle very large sets of data. Four simulated data sets were generated to evaluate the methods. In general, both methods estimated genetic correlations and heritabilities that were close to the Restricted Maximum Likelihood estimates and the true data set values, even when selection within contemporary groups was practiced. The estimates of residual correlations by both methods, however, were biased by selection. These two methods can be useful in estimating variances and covariances from multiple-trait models in large populations that have undergone a minimal amount of selection within contemporary groups.  相似文献   

9.
Fixed effects of age at first litter and of season of lambing as well as variance components for additive genetic, flock × year and sire of litter effects on size of first litter were estimated for an animal model by a derivative-free REML procedure. Data of the four Swiss sheep breeds White Alpine (WAS), Brown-headed Meat (BFS), Black-Brown Mountain (SBS) and Valais Black Nose (SN) were available. Number of first litters used were 21 384, 21 607, 15 013, 12 394 and 18 110 the WAS (two data sets, WAS1, WAS2), BFS, SBS and SN, respectively. Litter size of ewes lambing the first time at 2 years of age was 0.27, 0.31, 0.41, 0.46 and 0.26 lambs larger than of ewes lambing the first time at 1 year of age. The largest increase occurred for the two breeds (BFS, SBS) with the lowest average age at first litter. The largest difference between any two lambing seasons within breed were 0.16, 0.16, 0.29, 0.22 and 0.07 lambs. Estimates of additive genetic variance of size of first litter were between 0.0269 (SN) and 0.0765 (SBS). Heritability estimates for this trait were 0.171, 0.156, 0.114, 0.225 and 0.122 for WAS1, WAS2, BFS, SBS and SN, respectively. A large flock × year component (relative to phenotypic variance) of 0.148 was found for SN, compared with estimates between 0.042 and 0.067 for the other breeds. A sire of litter component (relative to phenotypic variance) of 0.066 was found for SN, compared with estimates between 0.016 and 0.039 for the other breeds. It can be concluded that all nongenetic effects investigated should be taken into account for the estimation of additive genetic variance and breeding values for size of first litter, and that considerable variation in size of genetic and nongenetic effects exists in the sheep breeds under consideration.  相似文献   

10.
The purpose of this study was to compare estimates of genetic parameters for sequential growth of beef cattle using two models and two data sets. Growth curves of Nellore cattle were analyzed using body weights measured at ages 1 (birth weight) to 733 d. Two data samples were created, one with 71,867 records sampled from all herds (MISS), and the other with 74,601 records sampled from herds with no missing traits (NMISS). Records preadjusted to a fixed age were analyzed by a multiple-trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were by REML, with five traits at a time. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, additive maternal, permanent environment, and maternal permanent environment. All effects were modeled as cubic Legendre polynomials. These analyses were also by REML. Shapes of estimates of variances by MTM were mostly similar for both data sets for all except late ages, where estimates for MISS were less regular, and for birth weight with MISS. Genetic correlations among ages for the direct and maternal effects were less smooth with MISS. Genetic correlations between direct and maternal effects were more negative for NMISS, where few sires were maternal grandsires. Parameter estimates with RRM were similar to MTM cept that estimates of variances showed more artifacts for MISS; the estimates of additive direct-maternal correlations were more negative with both data sets and approached -1.0 for some ages with NMISS. When parameters of a growth model obtained by used for genetic evaluation, these parameters should be examined for consistency with parameters from MTM and prior information, and adjustments may be required to eliminate artifacts.  相似文献   

11.
Records of on-test ADG of Large White gilts were analyzed to estimate variance components of direct and associative genetic effects. Models included the effects of contemporary group (farm-barn-batch), birth litter, pen group, and direct and associative additive genetic effects. The area of each pen was 14 m2. The additive genetic variance was a function of the number of competitors in a group, the additive relationships between the animal performing the record and its pen mates, and the additive relationships between pen mates. To partially account for differences in the number of pen mates, a covariable (qi = 1, 1/n, or 1/n(1/2)) was added to the associative genetic effect. There were 4,946 records from 2,409 litters and 362 pen groups. Pen group size ranged from 12 to 16 gilts. Analyses by REML converged very slowly. A grid search showed that the likelihood function was almost flat when the additive genetic associative effect was fitted. Estimates of direct and associative heritability were 0.15 and 0.03, respectively. Within the BLUPF90 family of programs, the mixed-model equations can be set up directly. For variance component estimation, simple programs (REMLF90 and GIBBSF90) worked without modifications, but more optimized programs did not. Estimates obtained using the three values of qi were similar. With the data structure available for this study and under an environment with relative low competition among animals, accurate estimation of associative genetic effects was not possible. Estimation of competitive effects with large pen size is difficult. The magnitude of competition effects may be larger in commercial populations, where housing is denser and food is limited.  相似文献   

12.
方差组分估计方法的比较   总被引：2，自引：0，他引：2  
本文通过蒙特卡罗模拟产生的八个模拟资料比较了我国常用的方差分析法(不考虑场年季效应)、Henderson方法1、Henderson方法3、最大似然法、改进最大似然法与约束最大似然法。结果表明:方差分析法估计值偏差最大,而约束最大似然法的估计值最准确。  相似文献   

13.
A Markov Chain Monte Carlo Bayesian method and BLUP analyses were used on Tunisian dairy cattle data. Data included 92,106 lactation records collected on 37,536 animals over 19 freshening years, from 1983 to 2001. Each record was partitioned into the fixed effects of herd-year, month of calving, and age-parity, a permanent environmental effect, an additive genetic effect, and a residual effect.

Posterior conditional distributions were determined for variance components and model effects. Solutions (BLUE) and posterior means for levels of herd-year, month of calving, and age-parity showed similar patterns. Posterior means of heritability and repeatability were 0.17 ± 18 × 10− 5 and 0.39 ± 8 × 10− 5, respectively. Posterior means of bull's breeding values were compared to bull's BLUP solutions. BLUP solutions were obtained using 0.17 and 0.39, estimated from the data, and 0.25 and 0.40 estimates for heritability and repeatability, respectively. Rank correlations between bull's posterior means and BLUP breeding values were 0.998 and 0.994 using genetic parameters estimated from the data and from the literature, respectively. This correlation coefficient was 0.995 between bull's BLUP solutions using either of the two sets of genetic parameters.  相似文献   


14.
We developed a Bayesian analysis approach by using a variational inference method, a so‐called variational Bayesian method, to determine the posterior distributions of variance components. This variational Bayesian method and an alternative Bayesian method using Gibbs sampling were compared in estimating genetic and residual variance components from both simulated data and publically available real pig data. In the simulated data set, we observed strong bias toward overestimation of genetic variance for the variational Bayesian method in the case of low heritability and low population size, and less bias was detected with larger population sizes in both methods examined. The differences in the estimates of variance components between the variational Bayesian and the Gibbs sampling were not found in the real pig data. However, the posterior distributions of the variance components obtained with the variational Bayesian method had shorter tails than those obtained with the Gibbs sampling. Consequently, the posterior standard deviations of the genetic and residual variances of the variational Bayesian method were lower than those of the method using Gibbs sampling. The computing time required was much shorter with the variational Bayesian method than with the method using Gibbs sampling.  相似文献   

15.
Weaning weights from nine parental breeds and three composites were analyzed to estimate variance due to grandmaternal genetic effects and to compare estimates for variance due to maternal genetic effects from two different models. Number of observations ranged from 794 to 3,465 per population. Number of animals in the pedigree file ranged from 1,244 to 4,326 per population. Two single-trait animal models were used to obtain estimates of covariance components by REML using an average information method. Model 1 included random direct and maternal genetic, permanent maternal environmental, and residual environmental effects as well as fixed sex x year and age of dam effects. Model 2 in addition included random grandmaternal genetic and permanent grandmaternal environmental effects to account for maternal effects of a cow on her daughter's maternal ability. Non-zero estimates of proportion of variance due to grandmaternal effects were obtained for 7 of the 12 populations and ranged from .03 to .06. Direct heritability estimates in these populations were similar with both models. Existence of variance due to grandmaternal effects did not affect the estimates of maternal heritability (m2) or the correlation between direct and maternal genetic effects (r(am)) for Angus and Gelbvieh. For the other five populations, magnitude of estimates increased for both m2 and r(am) when estimates of variance due to grandmaternal effects were not zero. Estimates of the correlation between maternal and grandmaternal genetic effects were large and negative. These results suggest that grand-maternal effects exist in some populations, that when such effects are ignored in analyses maternal heritability may be underestimated, and that the correlation between direct and maternal genetic effects may be biased downward if grandmaternal effects are not included in the model for weaning weight of beef cattle.  相似文献   

16.
Components of (co)variance for weaning weight were estimated from field data provided by the American Simmental Association. These components were obtained for the observational components of variance corresponding to a sire, maternal grandsire, and dam within maternal grandsire model. From these estimates, direct additive genetic variance (Sigma2A), maternal additive genetic variance (Sigma2M), covariance between direct and maternal additive genetic effects (SigmaAM), variance of permanent environment(Sigma2pe) and temporary environment variance(Sigma2te) were determined. A procedure to approximate restricted maximum likelihood (REML) estimates of the observational components of variance based on the expectation-maximization (EM) algorithm is described. From these results, phenotypic variance ( ) of weaning weight was 667.88 kg2. Values forSigma2A, Sigma2M, Sigma2pe and Sigma2te were 79,30,58,38,49.45, and 469.97 kg2, respectively. Genetic correlation between direct and maternal additive genetic effects was .16.  相似文献   

17.
The aim of the present study was to estimate genetic parameters for flight speed and its association with growth traits in Nellore beef cattle. The flight speed (FS) of 7,402 yearling animals was measured, using a device composed of a pair of photoelectric cells. Time interval data (s) were converted to speed (m/s) and faster animals were regarded as more reactive. The growth traits analyzed were weaning weight (WW), ADG from weaning to yearling age, and yearling scrotal circumference (SC). The (co)variance components were estimated using REML in a multitrait analysis applying an animal model. The model included random direct additive genetic and residual effects, fixed effects of contemporary groups, age of dam (classes), and age of animal as covariable. For WW, the model also included maternal genetic and permanent environmental random effects. The direct heritability estimate for FS was 0.26 ± 0.05 and direct heritability estimates for WW, SC, and ADG were 0.30 ± 0.01, 0.48 ± 0.02, and 0.19 ± 0.01, respectively. Estimates of the genetic correlation between FS and the growth traits were -0.12 ± 0.07 (WW), -0.13 ± 0.08 (ADG), and -0.11 ± 0.07 (SC). Although the values were low, these correlations showed that animals with better temperaments (slower FS) tended to present better performance. It is possible to infer that longterm selection for weight and scrotal circumference can promote a positive genetic response in the temperament of animals. Nevertheless, to obtain faster genetic progress in temperament, it would be necessary to perform direct selection for such trait. Flight speed is an easily measured indicator of temperament and can be included as a selection criterion in breeding programs for Nellore cattle.  相似文献   

18.
The genetic evaluation using the carcass field data in Japanese Black cattle has been carried out employing an animal model, implementing the restricted maximum likelihood (REML) estimation of additive genetic and residual variances. Because of rapidly increasing volumes of the official data sets and therefore larger memory spaces required, an alternative approach like the REML estimation could be useful. The purpose of this study was to investigate Gibbs sampling conditions for the single-trait variance component estimation using the carcass field data. As prior distributions, uniform and normal distributions and independent scaled inverted chi-square distributions were used for macro-environmental effects, breeding values, and the variance components, respectively. Using the data sets of different sizes, the influences of Gibbs chain length and thinning interval were investigated, after the burn-in period was determined using the coupling method. As would be expected, the chain lengths had obviously larger effects on the posterior means than those of thinning intervals. The posterior means calculated using every 10th sample from 90 000 of samples after 10 000 samples discarded as burn-in period were all considered to be reasonably comparable to the corresponding estimates by REML.  相似文献   

19.
Estimates of direct and maternal variance and heritability for weights at each week (up to 280 days of age) and month of age (up to 600 days of age) in Zebu cattle are presented. More than one million records on 200 000 animals, weighed every 90 days from birth to 2 years of age, were available. Data were split according to week (data sets 1) or month (data sets 2) of age at recording, creating 54 and 21 data sets, respectively. The model of analysis included contemporary groups as fixed effects, and age of dam (linear and quadratic) and age of calf (linear) effects as covariables. Random effects fitted were additive direct and maternal genetic effects, and maternal permanent environmental effect. Direct heritability estimates decreased from 0.28 at birth, to 0.12–0.13 at about 150 days of age, stayed more or less constant at 0.14–0.16 until 270 days of age and increased with age after that, up to 0.25–0.26. Maternal heritability estimates increased from birth (0.01) to a peak of 0.14 for data sets 1 and 0.07–0.08 for data sets 2 at about 180–210 days of age, before decreasing slowly to 0.07 and 0.05, respectively, at 300 days, and then rapidly diminished after 300 days of age. Permanent environmental effects were 1.5 to four times higher than genetic maternal effects and showed a similar trend.  相似文献   

20.
Performance of the "quasi-REML" method for estimating correlations between a continuous trait and a categorical trait, and between two categorical traits, was studied with Monte Carlo simulations. Three continuous, correlated traits were simulated for identical populations and three scenarios with either no selection, selection for one moderately heritable trait (Trait 1, h2 = .25), and selection for the same trait plus confounding between sires and management groups. The "true" environmental correlations between Traits 2 (h2 = .10) and 3 (h2 = .05) were always of the same absolute size (.20), but further data scenarios were generated by setting the sign of environmental correlation to either positive or negative. Observations for Traits 2 and 3 were then reassigned to binomial categories to simulate health or reproductive traits with incidences of 15 and 5%, respectively. Genetic correlations (r(g12), r(g13), and r(g23) and environmental correlations (r(e12), r(e13), and r(e23)) were estimated for the underlying continuous scale (REML) and the visible categorical scales ("quasi-REML") with linear multiple-trait sire and animal models. Contrary to theory, practically all "quasi-REML" genetic correlations were underestimated to some extent with the sire and animal models. Selection inflated this negative bias for sire model estimates, and the sign of r(e23) noticeably affected r(g23) estimates for the animal model, with greater bias and SD for estimates when the "true" r(e23) was positive. Transformed "quasi-REML" environmental correlations between a continuous and a categorical trait were estimated with good efficiency and little bias, and corresponding correlations between two categorical traits were systematically overestimated. Confounding between sires and contemporary groups negatively affected all correlation estimates on the underlying and the visible scales, especially for sire model "quasi-REML" estimates of genetic correlation. Selection, data structure, and the (co)variance structure influences how well correlations involving categorical traits are estimated with "quasi-REML" methods.  相似文献   

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