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1.
Bayesian analysis via Gibbs sampling, restricted maximum likelihood (REML), and Method R were used to estimate variance components for several models of simulated data. Four simulated data sets that included direct genetic effects and different combinations of maternal, permanent environmental, and dominance effects were used. Parents were selected randomly, on phenotype across or within contemporary groups, or on BLUP of genetic value. Estimates by Bayesian analysis and REML were always empirically unbiased in large data sets. Estimates by Method R were biased only with phenotypic selection across contemporary groups; estimates of the additive variance were biased upward, and all the other estimates were biased downward. No empirical bias was observed for Method R under selection within contemporary groups or in data without contemporary group effects. The bias of Method R estimates in small data sets was evaluated using a simple direct additive model. Method R gave biased estimates in small data sets in all types of selection except BLUP. In populations where the selection is based on BLUP of genetic value or where phenotypic selection is practiced mostly within contemporary groups, estimates by Method R are likely to be unbiased. In this case, Method R is an alternative to single-trait REML and Bayesian analysis for analyses of large data sets when the other methods are too expensive to apply.  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.
Mixed model (co)variance component estimates by REML and Gibbs sampling for two traits were compared for base populations and control lines of Red Flour Beetle (Tribolium castaneum). Two base populations (1296 records in the first replication, 1292 in the second) were sampled from laboratory stock. Control lines were derived from corresponding base populations with random selection and mating for 16 generations. The REML estimate of each (co)variance component for both pupa weight and family size was compared with the mean and 95% central interval of the particular (co)variance estimated by Gibbs sampling with three different weights on the given priors: ‘flat’, smallest, and 3.7% degrees of belief. Results from Gibbs sampling showed that flat priors gave a wider and more skewed marginal posterior distribution than the other two weights on priors for all parameters. In contrast, the 3.7% degree of belief on priors provided reasonably narrow and symmetric marginal posterior distributions. Estimation by REML does not have the flexibility of changing the weight on prior information as does the Bayesian analysis implemented by Gibbs sampling. In general, the 95% central intervals from the three different weights on priors in the base populations were similar to those in control lines. Most REML estimates in base populations differed from REML estimates in control lines. Insufficient information from the data, and confounding of random effects contributed to the variability of REML estimates in base populations. Evidence is presented showing that some (co)variance components were estimated with less precision than others. Results also support the hypothesis that REML estimates were equivalent to the joint mode of posterior distribution obtained from a Bayesian analysis with flat priors, but only when there was sufficient information from data, and no confounding among random effects.  相似文献   

4.
The influence of selection and epistasis on inbreeding depression estimates   总被引：1，自引：0，他引：1  
Inbreeding depression estimates obtained by regression of the individual performance on the inbreeding were studied by stochastic simulation under various genetic models (solely additive, partial dominance, overdominance and epistasis), and mating strategies (random mating versus selection). In all models, inbreeding depression estimates based on the individual pedigree inbreeding coefficients were compared with estimates based on the true level of autozygosity. For the model with partial dominance and selection, the estimates of inbreeding depression from pedigree information were more negative (lower) than those based on true inbreeding coefficients whereas, in contrast, they were less negative (higher) for the models with overdominance and selection. The difference in the variation of true and pedigree individual inbreeding coefficient indicated that biased estimates might occur even in random mating populations. The estimation of inbreeding depression was further complicated when epistatic effects were present. The sign and the magnitude of the inbreeding effect (depression) estimates might be rather heterogeneous if additive by dominance effects are present because they are strongly dependent on the gene frequency. It was also shown that inbreeding depression is possible in models with negative additive by dominance effects. In models with dominance by dominance inheritance it was difficult to assess the non-linear relationship between performance and inbreeding, while at the same time, non-linear estimates based on pedigree information were extremely biased. The results obtained indicate that new or additional methodologies are required if reliable conclusions about consequences of inbreeding depression are needed.  相似文献   

5.
The purpose of this study is to present guidelines in selection of statistical and computing algorithms for variance components estimation when computing involves software packages. For this purpose two major methods are to be considered: residual maximal likelihood (REML) and Bayesian via Gibbs sampling. Expectation‐Maximization (EM) REML is regarded as a very stable algorithm that is able to converge when covariance matrices are close to singular, however it is slow. However, convergence problems can occur with random regression models, especially if the starting values are much lower than those at convergence. Average Information (AI) REML is much faster for common problems but it relies on heuristics for convergence, and it may be very slow or even diverge for complex models. REML algorithms for general models become unstable with larger number of traits. REML by canonical transformation is stable in such cases but can support only a limited class of models. In general, REML algorithms are difficult to program. Bayesian methods via Gibbs sampling are much easier to program than REML, especially for complex models, and they can support much larger datasets; however, the termination criterion can be hard to determine, and the quality of estimates depends on a number of details. Computing speed varies with computing optimizations, with which some large data sets and complex models can be supported in a reasonable time; however, optimizations increase complexity of programming and restrict the types of models applicable. Several examples from past research are discussed to illustrate the fact that different problems required different methods.  相似文献   

6.
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   

7.
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   

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.
Tying‐up is a condition that primarily affects the muscles of horses. In this study, the heritability of the Tying‐up syndrome in the Thoroughbred racehorse was estimated by Bayesian analysis with Gibbs sampling based on the threshold model for binary traits. The data used were the clinical data in racehorses diagnosed by veterinarians of the Racehorse Clinics of Japan Racing Association from 2000 to 2003. The health status of the Tying‐up was treated as a binary trait. In the genetic analysis, the effect of changing the amount of the pedigree or inbreeding information on the estimation of heritability was investigated, too. The heritability estimates with non‐zero probability in the posterior densities were approximately 0.16–0.18 in minimum, suggesting that the heritability of the Tying‐up is not zero at least. The posterior density distributions of the heritability estimates were generally more pointed and sharp with using inbreeding coefficients than without using it, suggesting that more stable estimations were obtained when inbreeding coefficients were used. Among the different amounts of pedigree and inbreeding information, the heritabilities obtained with three or four generations of pedigree using inbreeding coefficients seems to be preferable, i.e. heritability of 0.42 or 0.43 for Tying‐up.  相似文献   

10.
Monte Carlo (MC) methods have been found useful in estimation of variance parameters for large data and complex models with many variance components (VC), with respect to both computer memory and computing time. A disadvantage has been a fluctuation in round‐to‐round values of estimates that makes the estimation of convergence challenging. Furthermore, with Newton‐type algorithms, the approximate Hessian matrix might have sufficient accuracy, but the inaccuracy in the gradient vector exaggerates the round‐to‐round fluctuation to intolerable. In this study, the reuse of the same random numbers within each MC sample was used to remove the MC fluctuation. Simulated data with six VC parameters were analysed by four different MC REML methods: expectation‐maximization (EM), Newton–Raphson (NR), average information (AI) and Broyden's method (BM). In addition, field data with 96 VC parameters were analysed by MC EM REML. In all the analyses with reused samples, the MC fluctuations disappeared, but the final estimates by the MC REML methods differed from the analytically calculated values more than expected especially when the number of MC samples was small. The difference depended on the random numbers generated, and based on repeated MC AI REML analyses, the VC estimates were on average non‐biased. The advantage of reusing MC samples is more apparent in the NR‐type algorithms. Smooth convergence opens the possibility to use the fast converging Newton‐type algorithms. However, a disadvantage from reusing MC samples is a possible “bias” in the estimates. To attain acceptable accuracy, sufficient number of MC samples need to be generated.  相似文献   

11.
Estimation of genetic variance in populations under selection involves assumptions on base animals. Base animals are often considered unselected and it also has been proposed to treat selected base animals as fixed. The consequences of assumptions on base animals in the estimation of genetic variance in selected populations are not fully understood. Variance decompositions are introduced for simple designs to quantify the differences between models that treat base animals in different ways. Independent contrasts were constructed and REML estimates of variance components were compared for different designs and selection rules. The method shows how selection is accounted for in a complete model and why estimation of variance components can become biased when base animals are treated as fixed.  相似文献   

12.
Multiple‐trait and random regression models have multiplied the number of equations needed for the estimation of variance components. To avoid inversion or decomposition of a large coefficient matrix, we propose estimation of variance components by Monte Carlo expectation maximization restricted maximum likelihood (MC EM REML) for multiple‐trait linear mixed models. Implementation is based on full‐model sampling for calculating the prediction error variances required for EM REML. Performance of the analytical and the MC EM REML algorithm was compared using a simulated and a field data set. For field data, results from both algorithms corresponded well even with one MC sample within an MC EM REML round. The magnitude of the standard errors of estimated prediction error variances depended on the formula used to calculate them and on the MC sample size within an MC EM REML round. Sampling variation in MC EM REML did not impair the convergence behaviour of the solutions compared with analytical EM REML analysis. A convergence criterion that takes into account the sampling variation was developed to monitor convergence for the MC EM REML algorithm. For the field data set, MC EM REML proved far superior to analytical EM REML both in computing time and in memory need.  相似文献   

13.
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   

14.
Volumes of official data sets have been increasing rapidly in the genetic evaluation using the Japanese Black routine carcass field data. Therefore, an alternative approach with smaller memory requirement to the current one using the restricted maximum likelihood (REML) and the empirical best linear unbiased prediction (EBLUP) is desired. This study applied a Bayesian analysis using Gibbs sampling (GS) to a large data set of the routine carcass field data and practically verified its validity in the estimation of breeding values. A Bayesian analysis like REML‐EBLUP was implemented, and the posterior means were calculated using every 10th sample from 90 000 of samples after 10 000 samples discarded. Moment and rank correlations between breeding values estimated by GS and REML‐EBLUP were very close to one, and the linear regression coefficients and the intercepts of the GS on the REML‐EBLUP estimates were substantially one and zero, respectively, showing a very good agreement between breeding value estimation by the current GS and the REML‐EBLUP. The current GS required only one‐sixth of the memory space with REML‐EBLUP. It is confirmed that the current GS approach with relatively small memory requirement is valid as a genetic evaluation procedure using large routine carcass data.  相似文献   

15.
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   

16.
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   

17.
The multiple-trait derivative-free REML set of programs was written to handle partially missing data for multiple-trait analyses as well as single-trait models. Standard errors of genetic parameters were reported for univariate models and for multiple-trait analyses only when all traits were measured on animals with records. In addition to estimating (co)variance components for multiple-trait models with partially missing data, this paper shows how the multiple-trait derivative-free REML set of programs can also estimate SE by augmenting the data file when not all animals have all traits measured. Although the standard practice has been to eliminate records with partially missing data, that practice uses only a subset of the available data. In some situations, the elimination of partial records can result in elimination of all the records, such as one trait measured in one environment and a second trait measured in a different environment. An alternative approach requiring minor modifications of the original data and model was developed that provides estimates of the SE using an augmented data set that gives the same residual log likelihood as the original data for multiple-trait analyses when not all traits are measured. Because the same residual vector is used for the original data and the augmented data, the resulting REML estimators along with their sampling properties are identical for the original and augmented data, so that SE for estimates of genetic parameters can be calculated.  相似文献   

18.
The amount of variance captured in genetic estimations may depend on whether a pedigree‐based or genomic relationship matrix is used. The purpose of this study was to investigate the genetic variance as well as the variance of predicted genetic merits (PGM) using pedigree‐based or genomic relationship matrices in Brown Swiss cattle. We examined a range of traits in six populations amounting to 173 population‐trait combinations. A main aim was to determine how using different relationship matrices affect variance estimation. We calculated ratios between different types of estimates and analysed the impact of trait heritability and population size. The genetic variances estimated by REML using a genomic relationship matrix were always smaller than the variances that were similarly estimated using a pedigree‐based relationship matrix. The variances from the genomic relationship matrix became closer to estimates from a pedigree relationship matrix as heritability and population size increased. In contrast, variances of predicted genetic merits obtained using a genomic relationship matrix were mostly larger than variances of genetic merit predicted using pedigree‐based relationship matrix. The ratio of the genomic to pedigree‐based PGM variances decreased as heritability and population size rose. The increased variance among predicted genetic merits is important for animal breeding because this is one of the factors influencing genetic progress.  相似文献   

19.
Multivariate estimation of genetic parameters involving more than a handful of traits can be afflicted by problems arising through substantial sampling variation. We present a review of underlying causes and proposals to improve estimates, focusing on linear mixed model‐based estimation via restricted maximum likelihood (REML). Both full multivariate analyses and pooling of results from overlapping subsets of traits are considered. It is suggested to impose a penalty on the likelihood designed to reduce sampling variances at the expense of a little additional bias. Simulation results are discussed which demonstrate that this can yield REML estimates that are on average closer to the population values than their unpenalized counterparts. Suitable penalties can be obtained based on assumed prior distributions of selected parameters. Necessary choices of penalty functions and of the stringency of penalization are examined. We argue that scale‐free penalty functions lend themselves to a simple scheme imposing a mild, default penalty which can yield “better” estimates without being likely to incur detrimental effects.  相似文献   

20.
The selection of genetically superior individuals is conditional upon accurate breeding value predictions which, in turn, are highly depend on how precisely relationship is represented by pedigree. For that purpose, the numerator relationship matrix is essential as a priori information in mixed model equations. The presence of pedigree errors and/or the lack of relationship information affect the genetic gain because it reduces the correlation between the true and estimated breeding values. Thus, this study aimed to evaluate the effects of correcting the pedigree relationships using single‐nucleotide polymorphism (SNP) markers on genetic evaluation accuracies for resistance of beef cattle to ticks. Tick count data from Hereford and Braford cattle breeds were used as phenotype. Genotyping was carried out using a high‐density panel (BovineHD ‐ Illumina® bead chip with 777 962 SNPs) for sires and the Illumina BovineSNP50 panel (54 609 SNPs) for their progenies. The relationship between the parents and progenies of genotyped animals was evaluated, and mismatches were based on the Mendelian conflicts counts. Variance components and genetic parameters estimates were obtained using a Bayesian approach via Gibbs sampling, and the breeding values were predicted assuming a repeatability model. A total of 460 corrections in relationship definitions were made (Table 1) corresponding to 1018 (9.5%) tick count records. Among these changes, 97.17% (447) were related to the sire's information, and 2.8% (13) were related to the dam's information. We observed 27.2% (236/868) of Mendelian conflicts for sire–progeny genotyped pairs and 14.3% (13/91) for dam–progeny genotyped pairs. We performed 2174 new definitions of half‐siblings according to the correlation coefficient between the coancestry and molecular coancestry matrices. It was observed that higher‐quality genetic relationships did not result in significant differences of variance components estimates; however, they resulted in more accurate breeding values predictions. Using SNPs to assess conflicts between parents and progenies increases certainty in relationships and consequently the accuracy of breeding value predictions of candidate animals for selection. Thus, higher genetic gains are expected when compared to the traditional non‐corrected relationship matrix.  相似文献   

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