Average information residual maximum likelihood in practice

Gilmour, Thompson, and Cullis (Biometrics, 1995, 51, 1440) presented the average information residual maximum likelihood (REML) algorithm for efficient variance parameter estimation in the linear mixed model. That paper dealt specifically with traditional variance component models, but the algorithm was quickly applied to more general models and implemented in several REML packages including ASReml (Gilmour et al., Biometrics, 2015, 51, 1440). This paper outlines the theory with respect to these more general models, describes the main issues encountered in fitting these models and how they have been addressed in the ASReml software. The issues covered are the basics steps in the implementation of the algorithm, keeping parameters within the parameter space, maximizing sparsity, avoiding issues associated with unstructured variance matrices by using the factor‐analytic structure and handling singularities in marker‐based relationship matrices and current work.     

Utilization of F1 information in estimating QTL effects in F2 crosses between outbred lines

Quantitative trait loci (QTL) analysis in designed experiments is investigated using a mixed model framework through the modification of segment mapping techniques. Allele effects are modelled in the F₁ generation allowing the estimation of additive substitution effects while accounting for QTL segregation within lines and differences in mean QTL effects between lines. The resulting approach is called F₁ segment mapping. Simulation is used to illustrate the method and its properties. F₁ segment mapping has advantages over F₂ segment mapping in the derivation of exact additive genetic covariances and in the computation time for variance component estimation.     

基于约束最大似然法对虹鳟生长性状遗传参数的估计

文章以黑龙江水产研究所渤海冷水性鱼类试验站5个品系虹鳟为材料,建立300家系,养殖到2龄时,对约5000尾鱼的生长数据,采用单性状约束最大似然法(Restricted Maximum Likelihood Method,REML)对其生长性状进行遗传参数的估计。结果表明,体重的遗传力为范围为0.20～0.45、体长的遗传力范围为0.17～0.43、肥满度的遗传力范围为0.47～0.65。其中肥满度的遗传性能稍高于体重和全长的遗传性能。另外,从性状的表型相关来看,体重和体长之间存在较大的正相关。     

基于空间效应与竞争效应的林木遗传分析模型

【目的】建立空间效应与竞争效应的分析模型,以提高林木遗传评估的准确性.【方法】利用R软件及其程序包breed R模拟数据,结合实测数据,采用XFA1结构拟合加性效应、近邻竞争效应和AR1结构拟合空间效应,建立随机区组设计模型(RCBM)、空间模型(SM)、空间与测量误差模型(SUM)和空间与竞争模型(SCM),运行ASReml估算遗传参数,进行模型比较。【结果】对于模拟数据,估计的参数结果均显示SCM是最优模型,其大大降低了随机误差方差,随机误差方差分别由7.56(RCBM)、5.72(SUM)降低到3.13(SCM),分别降低了58.6%、45.3%,并估算到四周近邻竞争方差;SCM模型估算的单株狭义遗传力在0.40左右,高于RCBM(0.24)和SUM模型(0.30);设置参数的不同初始值,SCM估计的参数结果均较为稳定;对于实测数据,估算结果与模拟结果比较一致。【结论】SCM模型是新的单株混合模型,可用于林木遗传分析。     

Utilization of F1 information in estimating QTL effects in F2 crosses between outbred lines.

Quantitative trait loci (QTL) analysis in designed experiments is investigated using a mixed model framework through the modification of segment mapping techniques. Allele effects are modelled in the F1 generation allowing the estimation of additive substitution effects while accounting for QTL segregation within lines and differences in mean QTL effects between lines. The resulting approach is called F1 segment mapping. Simulation is used to illustrate the method and its properties. F1 segment mapping has advantages over F2 segment mapping in the derivation of exact additive genetic covariances and in the computation time for variance component estimation.     

基于线性混合模型的滨海盐碱土盐分空间变异性研究

准确的土壤盐分空间变异信息是防治土壤盐碱化和制定科学种植规划的重要依据。本文根据电磁型近地传感器EM38测定的土壤表征电导率(EC_a),研究有限最大似然法(REML)在地统计建模趋势去除中的应用,基于线性混合模型将趋势与残差分离,然后利用泛克立格开展海涂围垦区水稻田土壤盐分的空间变异性研究。结果表明,本研究区土壤盐分存在强烈的空间变异性且呈一定的空间分布趋势;REML方法拟合的二次多项式模型可较好的表征土壤盐分的空间分布趋势,在去除趋势的同时,选用指数模型对残差的半方差函数进行拟合;基于泛克立格插值的交叉检验结果可见,该方法可得到较小的预测误差,且标准离差比平均值参数接近理想值,REML方法大大提高了模型的精度;就地统计空间插值结果可看出,土壤盐分呈出从西北角向东北角、从周边向中心渐变的空间分布特征,且与土壤排水条件表现出较好的耦合性。     

Inclusion of sire by herd interaction effect in the genomic evaluation for weaning weight of American Angus

A spurious negative genetic correlation between direct and maternal effects of weaning weight (WW) in beef cattle has historically been problematic for researchers and industry. Previous research has suggested the covariance between sires and herds may be contributing to this relationship. The objective of this study was to estimate the variance components (VC) for WW in American Angus with and without sire by herd (S×H) interaction effect when genomic information is used or not. Five subsets of ~100k animals for each subset were used. When genomic information was included, genotypes were added for 15,637 animals. Five replicates were performed. Four different models were tested, namely, M1: without S×H interaction effect and with covariance between direct and maternal effect (σam) ≠ 0; M2: with S×H interaction effect and σam ≠ 0; M3: without S×H interaction effect and with σam = 0; M4: with S×H interaction effect and σam = 0. VC were estimated using the restricted maximum likelihood (REML) and single-step genomic REML (ssGREML) with the average information algorithm. Breeding values were computed using single-step genomic BLUP for the models above and one additional model, which had the covariance zeroed after the estimation of VC (M5). The ability of each model to predict future breeding values was investigated with the linear regression method. Under REML, when the S×H interaction effect was added to the model, both direct and maternal genetic variances were greatly reduced, and the negative covariance became positive (i.e., when moving from M1 to M2). Similar patterns were observed under ssGREML, but with less reduction in the direct and maternal genetic variances and still a negative covariance. Models with the S×H interaction effect (M2 and M4) had a better fit according to the Akaike information criteria. Breeding values from those models were more accurate and had less bias than the other three models. The rankings and breeding values of artificial insemination sires (N = 1,977) greatly changed when the S×H interaction effect was fit in the model. Although the S×H interaction effect accounted for 3% to 5% of the total phenotypic variance and improved the model fit, this change in the evaluation model will cause severe reranking among animals.     

混合模型且亲本间存在相关时的遗传力的估测

现实中的同胞资料大多同时具有两个特点:一是所有个体并非处于同一环境,二是亲本之间也非一概没有相关。据此资料估计遗传力,常规方法难免偏差。本文通过试验模型分析并运用约束最大似然法的思想,给出了解决这一问题的方法,并用实例作了应用说明。这种方法具有更广泛的适用范围。其估测值的准确程度也有很大提高,尤其是较对亲本间相关不加考虑而言。为了便于推广应用,本文还编制了两个相应的程序。     

北京市荷斯坦牛头胎产奶量的遗传统计分析

本研究对北京市47头公牛的约13000个女儿的头胎产奶量记录进行了系统的遗传统计分析。首先进行了305 d 奶量校正方法的研究。提出了用于从306～420 d 不同阶段的305 d 奶量校正的线性回归方程。同时分析了影响305 d 奶量的季节效应,根据305 d 奶量在各产犊月份的最小二乘均数和育种值估计及遗传参数估计的特点,建议将12个产犊月份划分为3个产犊季节。利用一公畜模型(考虑公畜间的血缘关系)和 REML 估计法的 EM 算法对遗传力进行了估计,估计值为0.11,低于文献中常见的报道。在取遗传力真值为0.10～0.35时,这个估计值的大样本标准误为0.03～0.08,说明估计值的精确性较低,亦即本资料样本对遗传力估计来说仍然偏小。     

Estimation of Variances and Covariances of Milk Traits by REML with an Individual Animal Model

Abstract

Records form Finnish Ayrshire cattle were used to estimate variances and covariances of milk traits by the restricted maximum likelihood (REML) method using the individual animal model (IAM). Two data sets were analyzed. The first data set consisted of 1423 sires and 16363 cows, of which 11911 had records on first lactation. The heritabilities estimated from this data set for milk yield, protein yield, protein content and fat content were 0.40, 0.31, 0.63 and 0.68, respectively. The second data set was a subset of first data set with herds with less than ten observations excluded and consisted of 1335 sires and 11262 cows with 8140 first, 5688 second and 3717 third lactation records. The heritability estimates from the second data set under a repeatability model for milk yield, protein yield, protein content and fat content were 0.30, 0.26, 0.59 and 0.66, respectively. The repeatability estimates for the same traits were 0.53, 0.51, 0.67 and 0.76, respectively. The second data set was also used to estimate genetic and phenotypic correlations among milk traits in first lactation. Both genetic and phenotypic correlations among protein yield and protein and fat content traits were small. The genetic correlation between milk yield and protein content was -0.61, between milk yield and fat content -0.50 and between protein content and fat content 0.67. Absolute values of phenotypic correlations for the same pairs of traits were somewhat smaller than respective genetic correlations.