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1.
Rules for forming the mixed-model equations for the reduced animal model with all relationships and including maternal effects have been set out by Quaas and Pollak. They also have shown how to simplify the mixed-model equations when genetic group effects are included in the model with what has become known as the Q-P transformation. Westell has given rules for calculating the coefficients for the Q-P transformed equations that are associated with the inverse of the numerator relationship matrix and genetic group effects. Those rules can be extended to include maternal effects and genetic groups for maternal as well as direct effects. As with the rules of Quaas and Pollak for the equations for the reduced animal model, a similar set of rules can be obtained for the genetic groups model after the Q-P transformation. The rules are derived easily by examining the algebraic results of absorbing the direct and maternal breeding value equations for non-parents into the parent breeding value, group and fixed effects equations. These rules involve Westell's rules and the inverse elements of the genetic (co)variance matrix for direct and maternal additive genetic effects. The rules make calculation of breeding values for parents for models including direct and maternal genetic group effects nearly as easy as for models without genetic group effects. Back solution for direct and maternal breeding values of non-parents similarly is as simple as when genetic group effects are not in the model.  相似文献   

2.
Mixed-model equations for the reduced animal model with maternal effects and different genetic grouping of unknown parents for additive direct and maternal effects are derived. The matrices that relate the expected value and the variance of the breeding values of non-parents to the parents, as well as the different contributions of parental and non-parental breeding values, to the resulting mixed-model equations are presented. Mis-specification of additive maternal variance and the additive covariance between direct and maternal effects, arising from missing information on the dams of known individuals with records, is discussed. To avoid an incorrect specification of the variance-covariance matrix of the records without having to invert a nondiagonal variance of the residual terms, the breeding values of the unknown dams of individuals with records are included in the equations. Breeding values of non-parents are back-solved after the solutions for genetic groups and breeding values of parents are computed as simply as in cases in which maternal effects are absent. A numerical example is included to illustrate the derivations.  相似文献   

3.
We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left‐looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (yams ), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire–maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak , respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams . The yams package is freely available on request by contacting the corresponding author.  相似文献   

4.
For models with only additive direct genetic effects, the rules of Westell combined with the Q-P transformation can be used to calculate the coefficients of mixed-model equations corresponding to the inverse elements of the numerator relationship matrix and group effects that are used to account for selection on ancestors that do not have records. Groups generally can be assigned on the basis of most recent ancestors without records. When maternal effects are in the model, most recent female ancestors without records contribute maternal effects to their progeny. If the vectors for additive direct and maternal effects do not include the same animals, numerator relationship matrices for direct and maternal effects and between direct and maternal effects are different. Even if they are the same, the Q-P transformation and Westell's rules do not lead to simplification for calculation of the coefficient matrix unless group assignment is the same for direct and maternal effects. This result can be achieved by including each female ancestor with offspring having records in both vectors and by assigning both of her parents to the same group she would have been assigned for a model including only direct effects. This strategy is equivalent to assigning group effects similarly for both direct and maternal effects and allows making use of the computational efficiency available from the Q-P transformation and Westell's rules, which are similar to Henderson's rules for calculating the inverse of the numerator relationship matrix.  相似文献   

5.
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   

6.
Breeding value estimation procedures for two traits with moderate and high heritability were evaluated by using a single-trait animal model and computer-simulated data designs. Of interest were the effects of differing numbers of animals and degrees of relationships among animals within and across contemporary groups (tests). Test effects were assumed fixed and animal effects were assumed random. Family size, number of families per contemporary group, and degree of genetic relationships within and across contemporary groups were varied to determine interrelationships among the factors. Results were compared on the basis of accuracy by using both the correlation of true and estimated breeding values and the prediction error variance obtained from the inverse of the coefficient matrix of the mixed-model equations. Small contemporary groups in conjunction with evaluation of closely related families caused average accuracy to decrease relative to that obtained with the same number of unrelated animals because genetically related animals were less accurately evaluated relative to one another. Connecting contemporary groups with a genetic relationship matrix formed a large set of interdependent equations and improved the average accuracy of predicted breeding values. The slight decrease in accuracy for genetically related animals was more than offset by the increase in accuracy of evaluation for their unrelated test mates because the proportion of fixed effects to random effects was smaller. Care must be exercised in designing evaluation schemes involving small populations, and the decision of which fixed effects to include in the model is critical.  相似文献   

7.
基因组选择常用的评估方法GBLUP和ssGBLUP都涉及到基因组亲缘矩阵的求逆,而大规模矩阵求逆运算非常耗时。本研究以提高大型基因组亲缘矩阵求逆运算的效率为目的。本研究通过真实数据和模拟数据构建基因组亲缘矩阵,引入Intel MKL矩阵函数,以减少迭代次数（方法1）和重复分块（方法2）两种方式改良分块迭代求逆算法,编程实现算法并在台式电脑和服务器上测试计算时间。结果表明,利用方法1计算4 000×4 000的基因组亲缘矩阵逆矩阵时,与MKL库函数的加速比为0.898。而16 000×16 000矩阵的计算速度为MKL库函数的1.006倍。利用方法2计算4 000×4 000矩阵的运算速度是MKL库函数的1.084倍;而在更大型的128 000×128 000基因组亲缘矩阵求逆运算时,该方法与MKL直接求逆函数的加速比为1.805倍。相比于MKL直接求逆函数,改进后的两种方法在效率上有一定程度的提升。  相似文献   

8.
There is an increased interest in estimating the (co)variance components of additive animal models with direct and competition effects (AMC). However, some attempts to estimate the dispersion parameters in different animal species faced problems of convergence or inaccurate estimates when pen effects entered the model. We argue that the problem relates to lack of identifiability of the (co)variance components in some AMC. The check for identifiability of the dispersion parameters in mixed models with linear (co)variance structure requires that all the eigenvalues of the restricted maximum likelyhood information matrix ( I ( θ )) be positive. We show, by way of simple numerical examples, that the singularity of I ( θ ) is due to confounding between fixed pen effects and the additive competition effects (SBVs). It is also observed that setting pen effects as random does not always remedy the collinearity with SBVs. An alternative AMC is presented in which the incidence matrix of the SBVs can be written as a function of the ‘intensity of competition’ (IC) among animals in the same pen. Examples are presented in which the ICs are related to time. The distribution of families of full and half sibs across pens also plays a role in the identifiability and asymptotic variances of the (co)variance components.  相似文献   

9.
Effects of foster dams can be included in genetic evaluations using animal models with maternal effects in several ways. The alternatives discussed involve minor changes in computing strategies from strategies used with reduced animal models that predict breeding values for direct and maternal effects. The easiest alternative is to assign foster dams to groups by breed and time period and add equations for fixed effects of breed-period. Random and, assumed, independent effects of foster dams can be nested in breed-period groups. If foster dams do not repeat, then those effects can be absorbed into equations for other fixed effects, additive direct breeding value and breed-period effects by slightly modifying least squares contributions to coefficients of those equations. A third alternative for foster dams of the same breed is to add breeding values for foster dams for direct and maternal effects to solution vectors for breeding values. Equations are similar to those without foster dams, except that least squares contributions to coefficient matrix and right-hand sides are to equations for maternal breeding values and nongenetic maternal effects of foster dams rather than biological dams. Relationships and covariance between direct and maternal effects contribute mixed-model coefficients to direct and maternal breeding value equations of biological dams. This alternative basically requires only larger solution vectors for direct and maternal breeding values to accommodate foster dams that might not be included. The fourth alternative includes a vector of maternal breeding values for foster dams of each breed of foster dams and would require using rules of Westell to calculate coefficients due to relationships and fixed maternal genetic groups within each breed of foster dam. These alternatives do not require much additional computational effort compared with full or reduced animal model equations when the transformation to predict breeding values is used with Westell's rules to calculate coefficients due to relationships and genetic group effects due to prior genetic selection.  相似文献   

10.
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   

11.
Treating gametes as homozygous diploid individuals, TIER and SÖLKNER (Theor. Appl. Genet. 85: 868–872, 1993) proposed a method which manages the use of available computer programs with a common animal model to estimate variance components caused by imprinting effects. Despite some relevant model restrictions, this approach has already been used in some field data analyses by an adapted version of the widely used DFREML computer program, subsequently indicated by DFREML a. The main objective of this study was to ascertain the properties of DFREML a by computer simulation and to examine other alternative estimation approaches. The most important results may be summarized as follows: (1) Treating gametes as homozygous diploid individuals has the consequence that one‐half of the actually realized gametic effect is totally abstracted in variance component estimation. Thus, an additional adjustment of the phenotypic variance calculated by DFREML a is necessary to get correct values of estimated variance component ratios. (2) Adjusted DFREML a estimates yielded correct results when animals were unselected and only maternal or paternal imprinting (not both simultaneously) occurred. (3) When the model did not adequately account for the additive genetic component within a maternal lineage, significant upward biases for the cytoplasmic component were observed. (4) The use of a simple dam and sire model with appropriate relationship matrices can be recommended when only the difference of maternal and paternal imprinting effects is of primary interest and the covariance between maternal halfsibs is not substantially increased by common environmental effects. (5) An adequate estimation of variance components for all possible imprinting situations requires the use of an animal model augmented by both maternal and paternal gametic effects. Unfortunately, a computer program on the basis of such a model does not yet exist.  相似文献   

12.
Reliabilities for a multiple-trait maternal model were obtained by combining reliabilities obtained from single-trait models. Single-trait reliabilities were obtained using an approximation that supported models with additive and permanent environmental effects. For the direct effect, the maternal and permanent environmental variances were assigned to the residual. For the maternal effect, variance of the direct effect was assigned to the residual. Data included 10,550 birth weight, 11,819 weaning weight, and 3,617 postweaning gain records of Senepol cattle. Reliabilities were obtained by generalized inversion and by using single-trait and multiple-trait approximation methods. Some reliabilities obtained by inversion were negative because inbreeding was ignored in calculating the inverse of the relationship matrix. The multiple-trait approximation method reduced the bias of approximation when compared with the single-trait method. The correlations between reliabilities obtained by inversion and by multiple-trait procedures for the direct effect were 0.85 for birth weight, 0.94 for weaning weight, and 0.96 for postweaning gain. Correlations for maternal effects for birth weight and weaning weight were 0.96 to 0.98 for both approximations. Further improvements can be achieved by refining the single-trait procedures.  相似文献   

13.
Preconditioned conjugate gradient method can be used to solve large mixed model equations quickly. Convergence of the method depends on the quality of the preconditioner. Here, the effect of simple preconditioners on the number of iterations until convergence was studied by solving breeding values for several test day models. The test day records were from a field data set, and several simulated data sets with low and high correlations among regression coefficients. The preconditioner matrices had diagonal or block diagonal parts. Transformation of the mixed model equations by diagonalization of the genetic covariance matrix was studied as well. Preconditioner having the whole block of the fixed effects was found to be advantageous. A block diagonal preconditioner for the animal effects reduced the number of iterations the higher the correlations among animal effects, but increased memory usage of the preconditioner. Diagonalization of the animal genetic covariance matrix often reduced the number of iterations considerably without increased memory usage.  相似文献   

14.
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   

15.
Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is essential.  相似文献   

16.
草地遥感估产中不同尺度信息源关联方法对比及评价   总被引：2，自引：0，他引：2  
选用NDVI、EVI、MSAVI、OSAVI、AFRI五种植被指数分析比较了样点法、纯光谱法、绿度分层法三种关联方法,研究表明:(1)绿度分层法是最好的关联方法,得到的决定系数超过了0.9,但还需要进一步的生态分区才能更多的表达产量的局部空间特征;(2)对分辨率为1000m的MODIS影像来说,样点法中的“点-点“关联与“点-面“关联经统计检验没有显著差别,植被指数之间拟合程度差别不大;(3)在纯光谱法中,计算出了基于MODIS数据的K-T变换系数阵,但没得到预期的结果;(4)植被指数中EVI、MSAVI、OSAVI是比较好的估产指标.  相似文献   

17.
Data structure designs for breeding value estimation of performance-tested boars using mixed-model methodology were compared. Computer models were based on estimates of parameters from the literature and from results of a survey of test station managers. Results were compared using accuracy (the correlation of true and estimated breeding values) and prediction error variance (PEV). The single-trait animal model included a fixed effect due to station-season, a random effect due to breeding value for ADG or backfat, and a random error term. Family size, number of families per test, and relationships among animals within and across tests were varied. Prediction error variance decreased faster for small families than for large ones as number of families increased, but increasing numbers of animals per pen was most important, especially if test size was optimized. With no other genetic ties, full-sibs were much more accurately evaluated than half-sibs. Designs that included sire ties among families within a station-season resulted in increased PEV. Increasing the number of full-sibs and(or) increasing the number of families per test would help to optimize PEV and correct this problem. Tying station-seasons with the relationship matrix improved the average accuracy of predicted breeding values. Placing full-sibs in different stations resulted in the greatest accuracy of evaluation, but a large number of half-sib (sire) ties resulted in comparable accuracies. Half-cousin ties did not improve accuracy of evaluation but could result in significant genetic progress by increasing the selection differential.  相似文献   

18.
Milk performance traits are likely influenced by both additive and non‐additive (e.g. dominance) genetic effects. Genetic variation can be partitioned using genomic information. The objective of this study was to estimate genetic variance components of production and milk component traits (e.g. acetone, fatty acids), which are particularly important for milk processing or which can provide information on the health status of cows. A genomic relationship approach was applied to phenotypic and genetic information of 1295 Holstein cows for estimating additive genetic and dominance variance components. Most of the 17 investigated traits were mainly affected by additive genetic effects, but protein content and casein content also showed a significant contribution of dominance. The ratio of dominance to additive variance was estimated as 0.64 for protein content and 0.56 for casein content. This ratio was highest for SCS (1.36) although dominance was not significant. Dominance effects were negligible in other moderately heritable milk traits.  相似文献   

19.
Estimated breeding values (EBVs) using data from genetic markers can be predicted using a genomic relationship matrix, derived from animal's genotypes, and best linear unbiased prediction. However, if the accuracy of the EBVs is calculated in the usual manner (from the inverse element of the coefficient matrix), it is likely to be overestimated owing to sampling errors in elements of the genomic relationship matrix. We show here that the correct accuracy can be obtained by regressing the relationship matrix towards the pedigree relationship matrix so that it is an unbiased estimate of the relationships at the QTL controlling the trait. This method shows how the accuracy increases as the number of markers used increases because the regression coefficient (of genomic relationship towards pedigree relationship) increases. We also present a deterministic method for predicting the accuracy of such genomic EBVs before data on individual animals are collected. This method estimates the proportion of genetic variance explained by the markers, which is equal to the regression coefficient described above, and the accuracy with which marker effects are estimated. The latter depends on the variance in relationship between pairs of animals, which equals the mean linkage disequilibrium over all pairs of loci. The theory was validated using simulated data and data on fat concentration in the milk of Holstein cattle.  相似文献   

20.
Coefficients of inbreeding are commonly used in mixed-model methods for forming inverses of Wright's numerator relationship matrix and transformation matrices used in variance component estimation and national cattle evaluation. Computation of exact coefficients of inbreeding from very large data sets has been believed to be too expensive or too difficult a task to perform. Approximate methods have been used instead. The effects of using approximation methods for inbred data that appear in national cattle data sets are demonstrated. An algorithm is given for the computation of inbreeding coefficients for large data sets. The algorithm feasibly computes inbreeding coefficients for large data sets even on small computing architectures.  相似文献   

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