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.     

种畜生产性能测验的评定中采用简化动物模型的BLUP法研究

本文是探讨采用简化动物模型计算最优线性无偏预测值(BLUP)的方法。BLUP是一种评定种畜遗传价值的有效方法,但是如果涉及的动物很多,则需要解较大系列的方程,常使计算代价很大,而采用一种减少评定种畜育种值的元素数的等价线性模型,可以大大简化计算。这里利用普通动物模型和简化动物模型,以包括父亲和外祖父后裔测验资料的一组简单数据为例,对比说明这两种解法计算的BLUP值的恒等性。一般采用包括父亲和外祖父的简化模型与普通模型比较,方程组的阶数可缩小30—50％左右,解亲缘系数矩阵的逆阵和混合模型方程组所需时间减少到10％左右,计算机的存储记忆也大大减少。     

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。     

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。     

植物全基因组选择技术的研究进展及其在玉米育种上的应用（英文）

全基因组选择技术通过全基因组中大量的单核苷酸多态性标记(SNP)和参照群体的表型数据建立BLUP模型估计出每一标记的育种值,称为估计育种值(GEBV),然后仅利用同样的分子标记估计出后代个体育种值并进行选择。该文就近年来国内外有关影响基因组选择效率的主要因素——参考群体的类型与大小、模型的建立方法、标记的类型及其数目、性状遗传力,以及对基因组选择效率的影响等方面的研究进展进行综述,并介绍了全基因组选择技术在玉米育种上应用概况以及对未来的展望。     

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．     

肉兔配套系的选育研究进展

配套系在动物育种中能最大程度地利用品系的杂种优势,以获得最大的经济效益,配套系的选育是今后肉兔遗传改良的发展趋势。肉兔父系以选择平均日增重和上市体重为主,断奶后生长性状一般与料肉比呈有利的负遗传相关,可作为料肉比的间接选择标准。而母系以选择断奶数和产仔数为主。大多数繁殖性状的遗传力较低,在进行遗传评估时应当尽可能全面地收集个体和相关亲缘关系个体的记录。重复观测值动物模型下的BLUP估计是进行肉兔专门化品系选育的主要方法。虽然窝内个体数性状的直接选择效率低于生长性状,但其杂种优势一般高于生长性状。通过计算杂交参数和比较同代杂种与纯种间的生产性能可以进行杂种优势的估计。文章对肉兔专门化品系的选育、杂种优势的利用和良种繁育体系的建立进行了综述,总结了肉兔专门化品系的培育方法,性状选择的标准以及杂种优势的估计结果。     

植物全基因组选择技术的研究进展及其在玉米育种上的应用

全基因组选择技术通过全基因组中大量的单核苷酸多态性标记（SNP）和参照群体的表型数据建立 BLUP 模型估计出每一标记的育种值,称为估计育种值（GEBV）,然后仅利用同样的分子标记估计出后代个体育种值并进行选择。该文就近年来国内外有关影响基因组选择效率的主要因素——参考群体的类型与大小、模型的建立方法、标记的类型及其数目、性状遗传力,以及对基因组选择效率的影响等方面的研究进展进行综述,并介绍了全基因组选择技术在玉米育种上应用概况以及对未来的展望。     

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。     

动物模型BLUP法估计内蒙古白绒山羊育种值的研究

应用动物模型ＢＬＵＰ法估计了阿尔巴斯白绒山羊种羊场１９８９－１９９８年共１０个年度３９８１只个体的抓绒量和体重的单性状育种值,以及这两个性状的综合育种值。在模型中考虑的固定效应有年龄效应和性别－群体－年度效应、随机效应有个体的加性效应和个体永久性环境效应。比较育种值选择与表型值选择的结果表明：⑴公羔依据断乳重选择与依据育咱值选择的结果差异较大;⑵育成母羊依据表型值选择与依据综合育种值选择的结果差异     

Response to genomic selection: The Bulmer effect and the potential of genomic selection when the number of phenotypic records is limiting

Background

Over the last ten years, genomic selection has developed enormously. Simulations and results on real data suggest that breeding values can be predicted with high accuracy using genetic markers alone. However, to reach high accuracies, large reference populations are needed. In many livestock populations or even species, such populations cannot be established when traits are difficult or expensive to record, or when the population size is small. The value of genomic selection is then questionable.

Methods

In this study, we compare traditional breeding schemes based on own performance or progeny information to genomic selection schemes, for which the number of phenotypic records is limiting. Deterministic simulations were performed using selection index theory. Our focus was on the equilibrium response obtained after a few generations of selection. Therefore, we first investigated the magnitude of the Bulmer effect with genomic selection.

Results

Results showed that the reduction in response due to the Bulmer effect is the same for genomic selection as for selection based on traditional BLUP estimated breeding values, and is independent of the accuracy of selection. The reduction in response with genomic selection is greater than with selection based directly on phenotypes without the use of pedigree information, such as mass selection. To maximize the accuracy of genomic estimated breeding values when the number of phenotypic records is limiting, the same individuals should be phenotyped and genotyped, rather than genotyping parents and phenotyping their progeny. When the generation interval cannot be reduced with genomic selection, large reference populations are required to obtain a similar response to that with selection based on BLUP estimated breeding values based on own performance or progeny information. However, when a genomic selection scheme has a moderate decrease in generation interval, relatively small reference population sizes are needed to obtain a similar response to that with selection on traditional BLUP estimated breeding values.

Conclusions

When the trait of interest cannot be recorded on the selection candidate, genomic selection schemes are very attractive even when the number of phenotypic records is limited, because traditional breeding requires progeny testing schemes with long generation intervals in those cases.     

Best linear prediction of breeding values in a forest tree improvement program

Summary Best Linear Prediction (BLP) was used to predict breeding values for 1,396 parents from progeny test data in an operational slash pine breeding program. BLP rankings of parents were compared to rankings of averaged standard scores, a common approach in forestry. Using BLP rankings, selection of higher ranking parents tends to choose parents in a larger number of more precise progeny tests. The trend is the opposite with standard scores; higher ranking parents tend to be those in fewer, less precise tests. BLP and a related methodology, Best Linear Unbiased Prediction (BLUP), were developed by dairy cattle breeders and have not been used widely outside of animal breeding for predicting breeding values from messy progeny test data. Application of either of these techniques usually requires simplifying assumptions to keep the problem computationally tractable. The more appropriate technique for a given application depends upon which set of assumptions are better for the given problem. An assumption of homogeneous genetic and error variances and covariances, generally made by animal breeders when applying BLUP, was inappropriate for our data. We employed an approach that treated fixed effects as known and treated the same trait measured in different environments as different traits with heterogeneous variance structures. As tree improvement programs become more complex, the ease with which BLP and BLUP handle messy data and incorporate diverse sources of information should make these techniques appealing to forest tree breeders.     

Evaluation of the best linear unbiased prediction method for breeding values of fruit-quality traits in citrus

Fruit-quality trait improvement is an important objective in citrus breeding; however, fruit breeding programs often accumulate highly unbalanced phenotypic records, which are a serious obstacle in comparing and selecting genotypes. The best linear unbiased prediction (BLUP) method can be used to overcome these difficulties, but few fruit breeding programs have adopted the method, and to our knowledge, the method has not yet been used to predict breeding values of traits based on pedigree information and genetic correlations between traits in citrus. Accordingly, we used the BLUP method to predict the breeding values of nine fruit-quality traits (fruit weight, fruit skin color, fruit surface texture, peelability, flesh color, pulp firmness, segment firmness, sugar content, and acid content) utilizing phenotypic records collected over several years as part of the citrus breeding program conducted at the Kuchinotsu branch of the National Institute of Fruit Tree Science in Japan. Although the accumulated phenotypic records were highly unbalanced, the BLUP method was able to predict the breeding values of all 2122 genotypes (111 parental cultivars and 2011 F₁ offspring from 126 pair-cross families), as well as estimates of several genetic parameters, including narrow-sense heritability and phenotypic and genotypic correlations. These findings demonstrate the utility of the BLUP method in citrus crossbreeding and provide predicted breeding values, which can be used to select superior genotypes in the Kuchinotsu Citrus Breeding Program and related genetic selection endeavors.     

Improving the analysis of low heritability complex traits for enhanced genetic gain in potato

Key message

Best linear unbiased prediction (BLUP), which uses pedigree to estimate breeding values, can result in increased genetic gains for low heritability traits in autotetraploid potato.

Abstract

Conventional potato breeding strategies, based on outcrossing followed by phenotypic recurrent selection over a number of generations, can result in slow but steady improvements of traits with moderate to high heritability. However, faster gains, particularly for low heritability traits, could be made by selection on estimated breeding values (EBVs) calculated using more complete pedigree information in best linear unbiased prediction (BLUP) analysis. One complication in applying BLUP predictions of breeding value to potato breeding programs is the autotetraploid inheritance pattern of this species. Here we have used a large pedigree, dating back to 1908, to estimate heritability for nine key traits for potato breeding, modelling autotetraploid inheritance. We estimate the proportion of double reduction in potatoes from our data, and across traits, to be in the order of 10 %. Estimates of heritability ranged from 0.21 for breeder’s visual preference, 0.58 for tuber yield, to 0.83 for plant maturity. Using the accuracies of the EBVs determined by cross generational validation, we model the genetic gain that could be achieved by selection of genotypes for breeding on BLUP EBVs and demonstrate that gains can be greater than in conventional schemes.     

Accuracy of pedigree and genomic predictions of carcass and novel meat quality traits in multi-breed sheep data assessed by cross-validation

Background

Genomic predictions can be applied early in life without impacting selection candidates. This is especially useful for meat quality traits in sheep. Carcass and novel meat quality traits were predicted in a multi-breed sheep population that included Merino, Border Leicester, Polled Dorset and White Suffolk sheep and their crosses.

Methods

Prediction of breeding values by best linear unbiased prediction (BLUP) based on pedigree information was compared to prediction based on genomic BLUP (GBLUP) and a Bayesian prediction method (BayesR). Cross-validation of predictions across sire families was used to evaluate the accuracy of predictions based on the correlation of predicted and observed values and the regression of observed on predicted values was used to evaluate bias of methods. Accuracies and regression coefficients were calculated using either phenotypes or adjusted phenotypes as observed variables.

Results and conclusions

Genomic methods increased the accuracy of predicted breeding values to on average 0.2 across traits (range 0.07 to 0.31), compared to an average accuracy of 0.09 for pedigree-based BLUP. However, for some traits with smaller reference population size, there was no increase in accuracy or it was small. No clear differences in accuracy were observed between GBLUP and BayesR. The regression of phenotypes on breeding values was close to 1 for all methods, indicating little bias, except for GBLUP and adjusted phenotypes (regression = 0.78). Accuracies calculated with adjusted (for fixed effects) phenotypes were less variable than accuracies based on unadjusted phenotypes, indicating that fixed effects influence the latter. Increasing the reference population size increased accuracy, indicating that adding more records will be beneficial. For the Merino, Polled Dorset and White Suffolk breeds, accuracies were greater than for the Border Leicester breed due to the smaller sample size and limited across-breed prediction. BayesR detected only a few large marker effects but one region on chromosome 6 was associated with large effects for several traits. Cross-validation produced very similar variability of accuracy and regression coefficients for BLUP, GBLUP and BayesR, showing that this variability is not a property of genomic methods alone. Our results show that genomic selection for novel difficult-to-measure traits is a feasible strategy to achieve increased genetic gain.     

Comparison between estimation of breeding values and fixed effects using Bayesian and empirical BLUP estimation under selection on parents and missing pedigree information

Bayesian (via Gibbs sampling) and empirical BLUP (EBLUP) estimation of fixed effects and breeding values were compared by simulation. Combinations of two simulation models (with or without effect of contemporary group (CG)), three selection schemes (random, phenotypic and BLUP selection), two levels of heritability (0.20 and 0.50) and two levels of pedigree information (0% and 15% randomly missing) were considered. Populations consisted of 450 animals spread over six discrete generations. An infinitesimal additive genetic animal model was assumed while simulating data. EBLUP and Bayesian estimates of CG effects and breeding values were, in all situations, essentially the same with respect to Spearman''s rank correlation between true and estimated values. Bias and mean square error (MSE) of EBLUP and Bayesian estimates of CG effects and breeding values showed the same pattern over the range of simulated scenarios. Methods were not biased by phenotypic and BLUP selection when pedigree information was complete, albeit MSE of estimated breeding values increased for situations where CG effects were present. Estimation of breeding values by Bayesian and EBLUP was similarly affected by joint effect of phenotypic or BLUP selection and randomly missing pedigree information. For both methods, bias and MSE of estimated breeding values and CG effects substantially increased across generations.     

Turning science on robust cattle into improved genetic selection decisions

More robust cattle have the potential to increase farm profitability, improve animal welfare, reduce the contribution of ruminant livestock to greenhouse gas emissions and decrease the risk of food shortages in the face of increased variability in the farm environment. Breeding is a powerful tool for changing the robustness of cattle; however, insufficient recording of breeding goal traits and selection of animals at younger ages tend to favour genetic change in productivity traits relative to robustness traits. This paper has extended a previously proposed theory of artificial evolution to demonstrate, using deterministic simulation, how choice of breeding scheme design can be used as a tool to manipulate the direction of genetic progress, whereas the breeding goal remains focussed on the factors motivating individual farm decision makers. Particular focus was placed on the transition from progeny testing or mass selection to genomic selection breeding strategies. Transition to genomic selection from a breeding strategy where candidates are selected before records from progeny being available was shown to be highly likely to favour genetic progress in robustness traits relative to productivity traits. This was shown even with modest numbers of animals available for training and when heritability for robustness traits was only slightly lower than that for productivity traits. When transitioning from progeny testing to a genomic selection strategy without progeny testing, it was shown that there is a significant risk that robustness traits could become less influential in selection relative to productivity traits. Augmentations of training populations using genotyped cows and support for industry-wide improvements in phenotypic recording of robustness traits were put forward as investment opportunities for stakeholders wishing to facilitate the application of science on robust cattle into improved genetic selection schemes.     

Selecting an appropriate genetic evaluation model for selection in a developing dairy sector

This study aimed to identify genetic evaluation models (GEM) to accurately select cattle for milk production when only limited data are available. It is based on a data set from the Pakistani Sahiwal progeny testing programme which includes records from five government herds, each consisting of 100 to 350 animals, with lactation records dating back to 1968. Different types of GEM were compared, namely: (1) multivariate v. repeatability model when using the first three lactations, (2) an animal v. a sire model, (3) different fixed effects models to account for effects such as herd, year and season; and (4) fitting a model with genetic parameters fixed v. estimating the genetic parameters as part of the model fitting process. Two methods were used for the comparison of models. The first method used simulated data based on the Pakistani progeny testing system and compared estimated breeding values with true breeding values. The second method used cross-validation to determine the best model in subsets of actual Australian herd-recorded data. Subsets were chosen to reflect the Pakistani data in terms of herd size and number of herds. Based on the simulation and the cross-validation method, the multivariate animal model using fixed genetic parameters was generally the superior GEM, but problems arise in determining suitable values for fixing the parameters. Using mean square error of prediction, the best fixed effects structure could not be conclusively determined. The simulation method indicated the simplest fixed effects structure to be superior whereas in contrast, the cross-validation method on actual data concluded that the most complex one was the best. In conclusion it is difficult to propose a universally best GEM that can be used in any data set of this size. However, some general recommendations are that it is more appropriate to estimate the genetic parameters when evaluating for selection purposes, the animal model was superior to the sire model and that in the Pakistani situation the repeatability model is more suitable than a multivariate.