广义岭回归在家禽育种值估计中的应用

讨论了岭回归方法应用于混合线性模型方程组中估计家禽育种值的方法,其实质是将传统的混合线性模型方程组理解为一种广义岭回归估计,为确定遗传参数的估计提供了一种途径;同时,以番鸭为例,考虑了一个性状和两个固定效应,采用广义岭回归法对公番鸭育种值进行了估计,并与最佳线性无偏预测法(BLUP 法)进行了比较,结果表明,广义岭回归方法和BLUP 法估计的育种值及其排序非常接近,其相关系数和秩相关系数分别达到了0.998~(**)和0.986~(**),且采用广义岭回归法预测的误差率低(在±10%以内);表明在混合线性模型方程组中使用广义岭回归估计动物育种值的方法具有可行性,并可省去估计遗传参数的过程,使BLUP 法在动物选育中的应用更具实用性.     

动物模型及多性状BLUP在家禽遗传鉴定中的应用

利用最佳线性无偏预测法(BLUP)估计家畜的育种值,目前除家禽外已在其它各家畜中得到了广泛的应用。本文利用动物模型和多性状BLUP对“京白Ⅰ系”蛋鸡在1986—1987年24个家系的777个个体的系统分组资料进行了分析,估计出了所有个体的复合育种值。其中考虑了两个性状(40周产蛋数和36周蛋重)和两个固定效应(鸡舍-鸡笼效应和孵化批次效应)。同时还对混合模型方程组维数较大时如何在微机上实现进行了研究,即(1)利用磁盘存取系数矩阵的非零元素和中间计算结果;(2)简化了多性状BLUP的计算,利用乔列斯基(Cholesky)分解变换后,此法建立的方程数是常规算法方程数的1/q(q为性状数);(3)简化了方程组迭代求解的方法,即利用块迭代法,这样大大缩短了计算的机吋,节省了费用,使BLUP在家禽中的推广应用成为可能。     

动物模型的特征

动物模型是一系列具有不同结构的线性混合模型,共同特征是估测动物个体本身的育种值。在动物模型下,任一个体育种值的估计都能按最佳形式利用其所有可知亲属的记录资料。从统计学意义上看,动物模型在提供育种值的最佳线性无偏预测（BLUP）的同时,提供固定效应的最佳线性无偏估计（BLUE）,使固定环境效应易除得最为合理。对于由大量加性基因控制的性状,动物模型能反映选择、遗传漂为对群体遗传均值和方差的影响。近交和连锁不平衡的影响也可视为选择的结果。因此动物模型适用于存在选择、漂变、近交以及连锁不平衡的群体。     

畜禽遗传评定方法的研究进展

畜禽遗传评定是畜禽育种的重要内容。目前畜禽遗传评定方法中应用最广的是基于表型信息的BLUP动物模型。基因组学的发展和应用产生了大量分子遗传标记,结合分子遗传标记信息的遗传评定方法MBLUP随之产生。MBLUP将成为一种快速有效的畜禽遗传评定方法。本文主要介绍了畜禽遗传评定方法的研究进展和发展趋势。 Abstract:Genetic evaluation is one of the most important components in livestock breeding program.Best linear unbiased prediction (BLUP) Animal Model,which based on phenotypic information,has become the most widely accepted method for genetic evaluation of domestic livestock.Large numbers of molecular genetic markers have been discovered as the development and application of genomics.Some new methods (Marked Assisted BLUP,MBLUP) for genetic evaluation have being developed,which incorporating molecular genetic markers information into genetic evaluation.MBULP will be a rapid and efficient method for genetic evaluation of domestic livestock.The aim of the paper is to introduce the development and current situation of the methods for livestock genetic evaluation.     

贝叶斯方法估计阈性状育种值的原理和计算技术

本文介绍了估计阈性状育种值的贝叶斯方法的原理,演示了描述阈性状观察值、建立后验概率密度函数、以及导出非线性方程组的方法．并就这一估计方法的计算技术进行了讨论,针对动物遗传育种中方程组系数矩阵往往很大,超出计算机内存的情况,提出了不需要建立方程组,在数据上迭代求解的计算方法．本文还综述了这一非线性方法与线性方法在阈性状育种值估计上的比较．     

R法遗传参数估值置信区间的计算方法和重复估计次数的研究

探讨R法遗传参数估值置信区间的计算方法和重复估计次数(NORE)对参数估值的影响,利用4种模型通过模拟产生数据集。基础群中公、母畜数分别为200和2000头,BLUP育种值选择5个世代。利用多变量乘法迭代(MMI)法,结合先决条件的共扼梯度(PCG)法求解混合模型方程组估计方差组分。用经典方法、Box-Cox变换后的经典方法和自助法计算参数估值的均数、标准误和置信区间。结果表明,重复估计次数较多时,3种方法均可;重复估计次数较少时,建议使用自助法。简单模型下需要较少的重复估计,但对于复杂模型则需要较多的重复估计。随模型中随机效应数的增加,直接遗传力高估。随着PCG和MMI轮次的增大,参数估值表现出低估的趋势。     

动物模型BLUP法评定内蒙古白绒山羊的遗传趋势

本研究应用动物模型BLUP法估计了1989～1998年内蒙古鄂托克旗阿尔巴斯白绒山羊种羊场抓绒量和抓绒后体重的遗传进展。结果为抓绒量的遗传进展呈上升趋势,抓绒后体重的遗传进展基本平稳。研究表明,内蒙古白绒山羊根据个体表型值选种,存在准确性较差和难以同时兼顾两个性状的缺点。本文认为今后内蒙古白绒山羊选种方法应该采用动物模型BLUP法。 Abstract:In this study,animal model BLUP method was used to estimate genetic trend for cashmere yield and bodyweight during 1989～1998 at Albas goats farm,Etuoke Banner,Inner Mongolia.The results were that genetic trend for cashmere yield had a rising trend and for bodyweight showed smooth.The study indicated selecting Inner Mongolia cashmere goats based on phenotypic value had a low accuracy and was difficult to give consideration to the two traits at the same time.The article raised animal model BLUP method should be used to select Inner Mongolia white cashmere goats in future.     

具有亲缘关系矩阵的混合模型的方差组分迭代估计——应用于计算BLUP的方差比值和遗传参数

论述的是来自非均街资料的混合模型中具有亲缘关系矩阵时利用迭代法估计方差组分问题。这篇文章表明计算程序是可行的,只要能够按照混合模型中固定效应的结构矩阵和Henderson方法3的固定效应的假设条件正确地计算二次型约化平方和,就可获得较为精确的方差组分估计值;而且表明方差初始比值k偏高或偏低,不影响迭代求解的最后结果,这是因为在迭代过程中可以通过结构矩阵x'x和x'x的控制而自行调整。这些方差组分不仅可应用于选种种畜用的BLUP计算,还可用来估计遗传参数。     

基因组育种值估计的贝叶斯方法

基因组育种值估计是基因组选择的重要环节,基因组育种值的准确性是基因组选择成功应用的关键,而其准确性在很大程度上取决于估计方法。目前研究和应用最多的基因组育种值估计方法是贝叶斯(Bayes)和最佳线性无偏预测(BLUP)两大类方法。文章系统介绍了目前已提出的各种Bayes方法,并总结了该类方法的估计效果和各方面的改进。模拟数据和实际数据研究结果都表明,Bayes类方法估计基因组育种值的准确性优于BLUP类方法,特别对于存在较大效应QTL的性状其优势更明显。由于Bayes方法的理论和计算过程相对复杂,目前其在实际育种中的运用不如BLUP类方法普遍,但随着快速算法的开发和计算机硬件的改进,计算问题有望得到解决;另外,随着对基因组和性状遗传结构研究的深入开展,能为Bayes方法提供更为准确的先验信息,从而使Bayes方法估计基因组育种值准确性的优势更加突出,应用将会更加广泛。     

在BLUP中亲属多次记录利用研究

一般的最优线性无偏预测(BLUP)法由于微机功能不足或出于成本的考虑,常常只能利用一次记录,而且仅仅用于种公畜的选择,多次记录所提供的大量遗传信息白白地丢失,无疑是一重大损失。本文推导了利用多次记录预测公、母畜育种值的简化BLUP法,其特点是省去了母体效应方程,从而大大简化了矩阵,使整个运算在微机甚至类似夏普PC-1500袖珍机上就可迅速完成,其准确度无疑要高于一次记录法。本法不仅适用于羊、猪业,对于世代间距长、后裔数目少的奶牛育种同样有应用价值。     

Validation of an approximate approach to compute genetic correlations between longevity and linear traits

The estimation of genetic correlations between a nonlinear trait such as longevity and linear traits is computationally difficult on large datasets. A two-step approach was proposed and was checked via simulation. First, univariate analyses were performed to get genetic variance estimates and to compute pseudo-records and their associated weights. These pseudo-records were virtual performances free of all environmental effects that can be used in a BLUP animal model, leading to the same breeding values as in the (possibly nonlinear) initial analyses. By combining these pseudo-records in a multiple trait model and fixing the genetic and residual variances to their values computed during the first step, we obtained correlation estimates by AI-REML and approximate MT-BLUP predicted breeding values that blend direct and indirect information on longevity. Mean genetic correlations and reliabilities obtained on simulated data confirmed the suitability of this approach in a wide range of situations. When nonzero residual correlations exist between traits, a sire model gave nearly unbiased estimates of genetic correlations, while the animal model estimates were biased upwards. Finally, when an incorrect genetic trend was simulated to lead to biased pseudo-records, a joint analysis including a time effect could adequately correct for this bias.     

Two-Variance-Component Model Improves Genetic Prediction in Family Datasets

Genetic prediction based on either identity by state (IBS) sharing or pedigree information has been investigated extensively with best linear unbiased prediction (BLUP) methods. Such methods were pioneered in plant and animal-breeding literature and have since been applied to predict human traits, with the aim of eventual clinical utility. However, methods to combine IBS sharing and pedigree information for genetic prediction in humans have not been explored. We introduce a two-variance-component model for genetic prediction: one component for IBS sharing and one for approximate pedigree structure, both estimated with genetic markers. In simulations using real genotypes from the Candidate-gene Association Resource (CARe) and Framingham Heart Study (FHS) family cohorts, we demonstrate that the two-variance-component model achieves gains in prediction r² over standard BLUP at current sample sizes, and we project, based on simulations, that these gains will continue to hold at larger sample sizes. Accordingly, in analyses of four quantitative phenotypes from CARe and two quantitative phenotypes from FHS, the two-variance-component model significantly improves prediction r² in each case, with up to a 20% relative improvement. We also find that standard mixed-model association tests can produce inflated test statistics in datasets with related individuals, whereas the two-variance-component model corrects for inflation.     

Variance components for survival of piglets at farrowing using a reduced animal model

Farrowing survival is usually analysed as a trait of the sow, but this precludes estimation of any direct genetic effects associated with individual piglets. In order to estimate these effects, which are particularly important for sire lines, it is necessary to fit an animal model. However this can be computationally very demanding. We show how direct and maternal genetic effects can be estimated with a simpler analysis based on the reduced animal model and we illustrate the method using farrowing survival information on 118 193 piglets in 10 314 litters. We achieve a 30% reduction in computing time and a 70% reduction in memory use, with no important loss of accuracy. This use of the reduced animal model is not only of interest for pig breeding but also for poultry and fish breeding where large full-sib families are performance tested.     

Estimation of dominance components in noninbred populations by using additive animal model residuals

In the case of noninbred and unselected populations with linkage equilibrium, the additive and dominance genetic effects are uncorrelated and the variance-covariance matrix of the second component is simply a product of its variance by a matrix that can be computed from the numerator relationship matrix A. The aim of this study is to present a new approach to estimate the dominance part with a reduced set of equations and hence a lower computing cost. The method proposed is based on the processing of the residual terms resulting from the BLUP methodology applied to an additive animal model. Best linear unbiased prediction of the dominance component d is almost identical to the one given by the full mixed model equations. Based on this approach, an algorithm for restricted maximum likelihood (REML) estimation of the variance components is also presented. By way of illustration, two numerical examples are given and a comparison between the parameters estimated with the expectation maximization (EM) algorithm and those obtained by the proposed algorithm is made. The proposed algorithm is iterative and yields estimates that are close to those obtained by EM, which is also iterative.     

Multiple-trait BLUP: a suitable strategy for genetic selection of <Emphasis Type="Italic">Eucalyptus</Emphasis>

Usually, genetic selection is carried out based on several traits, which can be genetically correlated. In this case, selection bias may occur if these traits are analyzed individually. Thus, the present work aimed to evaluate the applicability and efficiency of multiple-trait best linear unbiased prediction (BLUP) in the genetic selection of Eucalyptus. The data used in this work refer to the evaluation of a partial diallel of Eucalyptus spp. in relation to height, diameter at breast height (DBH), and volume. Variance components and genetic and non-genetic parameters were estimated via residual maximum likelihood (REML). Multiple-trait BLUP led to estimates of mean additive genetic variance higher than the estimates obtained via single-trait BLUP and, consequently, led to higher estimates of narrow-sense individual interpopulational heritabilities and mean accuracies. Partial genetic correlations obtained via multiple-trait BLUP allowed a real understanding of the association between traits, differently from those obtained via single-trait BLUP. Multiple-trait BLUP led to higher gains predicted with the selection for height, DBH, and volume and can be efficiently applied in the genetic selection of Eucalyptus.     

Genomic prediction of reproduction traits for Merino sheep

Economically important reproduction traits in sheep, such as number of lambs weaned and litter size, are expressed only in females and later in life after most selection decisions are made, which makes them ideal candidates for genomic selection. Accurate genomic predictions would lead to greater genetic gain for these traits by enabling accurate selection of young rams with high genetic merit. The aim of this study was to design and evaluate the accuracy of a genomic prediction method for female reproduction in sheep using daughter trait deviations (DTD) for sires and ewe phenotypes (when individual ewes were genotyped) for three reproduction traits: number of lambs born (NLB), litter size (LSIZE) and number of lambs weaned. Genomic best linear unbiased prediction (GBLUP), BayesR and pedigree BLUP analyses of the three reproduction traits measured on 5340 sheep (4503 ewes and 837 sires) with real and imputed genotypes for 510 174 SNPs were performed. The prediction of breeding values using both sire and ewe trait records was validated in Merino sheep. Prediction accuracy was evaluated by across sire family and random cross‐validations. Accuracies of genomic estimated breeding values (GEBVs) were assessed as the mean Pearson correlation adjusted by the accuracy of the input phenotypes. The addition of sire DTD into the prediction analysis resulted in higher accuracies compared with using only ewe records in genomic predictions or pedigree BLUP. Using GBLUP, the average accuracy based on the combined records (ewes and sire DTD) was 0.43 across traits, but the accuracies varied by trait and type of cross‐validations. The accuracies of GEBVs from random cross‐validations (range 0.17–0.61) were higher than were those from sire family cross‐validations (range 0.00–0.51). The GEBV accuracies of 0.41–0.54 for NLB and LSIZE based on the combined records were amongst the highest in the study. Although BayesR was not significantly different from GBLUP in prediction accuracy, it identified several candidate genes which are known to be associated with NLB and LSIZE. The approach provides a way to make use of all data available in genomic prediction for traits that have limited recording.     

Should genetic groups be fitted in BLUP evaluation? Practical answer for the French AI beef sire evaluation

Some analytical and simulated criteria were used to determine whether a priori genetic differences among groups, which are not accounted for by the relationship matrix, ought to be fitted in models for genetic evaluation, depending on the data structure and the accuracy of the evaluation. These criteria were the mean square error of some extreme contrasts between animals, the true genetic superiority of animals selected across groups, i.e. the selection response, and the magnitude of selection bias (difference between true and predicted selection responses). The different statistical models studied considered either fixed or random genetic groups (based on six different years of birth) versus ignoring the genetic group effects in a sire model. Including fixed genetic groups led to an overestimation of selection response under BLUP selection across groups despite the unbiasedness of the estimation, i.e. despite the correct estimation of differences between genetic groups. This overestimation was extremely important in numerical applications which considered two kinds of within-station progeny test designs for French purebred beef cattle AI sire evaluation across years: the reference sire design and the repeater sire design. When assuming a priori genetic differences due to the existence of a genetic trend of around 20% of genetic standard deviation for a trait with h² = 0.4, in a repeater sire design, the overestimation of the genetic superiority of bulls selected across groups varied from about 10% for an across-year selection rate p = 1/6 and an accurate selection index (100 progeny records per sire) to 75% for p = 1/2 and a less accurate selection index (20 progeny records per sire). This overestimation decreased when the genetic trend, the heritability of the trait, the accuracy of the evaluation or the connectedness of the design increased. Whatever the data design, a model of genetic evaluation without groups was preferred to a model with genetic groups when the genetic trend was in the range of likely values in cattle breeding programs (0 to 20% of genetic standard deviation). In such a case, including random groups was pointless and including fixed groups led to a large overestimation of selection response, smaller true selection response across groups and larger variance of estimation of the differences between groups. Although the genetic trend was correctly predicted by a model fitting fixed genetic groups, important errors in predicting individual breeding values led to incorrect ranking of animals across groups and, consequently, led to lower selection response.     

A comparison of experimental designs for selection in breeding trials with nested treatment structure

Plant breeders frequently evaluate large numbers of entries in field trials for selection. Generally, the tested entries are related by pedigree. The simplest case is a nested treatment structure, where entries fall into groups or families such that entries within groups are more closely related than between groups. We found that some plant breeders prefer to plant close relatives next to each other in the field. This contrasts with common experimental designs such as the α-design, where entries are fully randomized. A third design option is to randomize in such a way that entries of the same group are separated as much as possible. The present paper compares these design options by simulation. Another important consideration is the type of model used for analysis. Most of the common experimental designs were optimized assuming that the model used for analysis has fixed treatment effects. With many entries that are related by pedigree, analysis based on a model with random treatment effects becomes a competitive alternative. In simulations, we therefore study the properties of best linear unbiased predictions (BLUP) of genetic effects based on a nested treatment structure under these design options for a range of genetic parameters. It is concluded that BLUP provides efficient estimates of genetic effects and that resolvable incomplete block designs such as the α-design with restricted or unrestricted randomization can be recommended.