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。     

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。     

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。     

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．     

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。     

基因组选择及其应用

品种选育在农业生产中占有十分重要的地位,育种值估计是品种选育的核心。随着遗传标记的发展,尤其是高通量的基因分型技术,使得从基因组水平估计育种值成为可能,即基因组选择。文章将基因组选择的方法分为两类:一是基于估计等位基因效应来预测基因组估计育种值(GEBV),如最小二乘法,随机回归-最佳线性无偏预测(RR-BLUP)、Bayes、主成分分析等方法;二是基于遗传关系矩阵来预测GEBV,通过采用高通量标记构建个体间的遗传关系矩阵,然后用线性混合模型来预测育种值,即GBLUP法,并以这两种分类简要介绍了基因组选择各种方法的大致原理。影响基因组选择准确性的因素主要有标记类型和密度、单倍型长度、参考群体大小和标记-数量性状基因座(QTL)连锁不平衡(LD)大小等;在基因组选择的各种方法中,一般说来Bayes方法和GBLUP方法具有较高的准确性,最小二乘法最差;GBLUP计算速度快,能够将标记和系谱结合起来,因而比其他方法更具优势。尽管基因组选择取得了很大进展,但在理论方面还面临着一些挑战,如联合育种、长期选择的遗传进展及如何解析与性状有关和无关的标记等。基因组选择在一些动植物育种上已经开始应用,在人类遗传倾向预测和进化动力学研究中也有潜在的应用前景。基因组选择在个体间亲缘关系的量化上有了突破,比传统方法更加精确,因此,基因组选择将会是动植物育种史上革命性的事件。     

远交群体动态性状基因定位的似然分析Ⅰ.理论方法

受动物遗传育种中用来估计动态性状育种值的随机回归测定日模型思想的启发 ,将关于时间 (测定日期 )的Legendre多项式镶嵌在遗传模型的每个遗传效应中 ,以刻画QTL对动态性状变化过程的作用 ,从而建立起动态性状基因定位的数学模型。利用远交设计群体 ,阐述了动态性状基因定位的似然分析原理 ,推导了定位参数似然估计的EM法两步求解过程。结合动态性状遗传分析的特点和普通数量性状基因定位研究进展 ,还提出了有关动态性状基因定位进一步研究的设想     

远交群体动态性状基因定位的似然分析 I．理论方法

受动物遗传育种中用来估计动态性状育种值的随机回归测定日模型思想的启发,将关于时间(测定日期)的Legendre多项式镶嵌在遗传模型的每个遗传效应中,以刻画QTL对动态性状变化过程的作用,从而建立起动态性状基因定位的数学模型。利用远交设计群体,阐述了动态性状基因定位的似然分析原理,推导了定位参数似然估计的EM法两步求解过程。结合动态性状遗传分析的特点和普通数量性状基因定位研究进展,还提出了有关动态性状基因定位进一步研究的设想。     

农药残留预测模型可靠性的检验与改良

对农药残留预测模型可靠性问题进行了分析。根据矩阵的条件数理论,提供了检验预测模型可靠性的方法,基于岭回归和广义岭回归估计理论,建立了对不可靠预测模型改良的方法。最后通过氰戊菊酯在甘篮上的残留动态预测,对所建改良方法进行了检验,结果表明,预测模型的精度得到了大幅度提高.     

Comparison of statistical models to analyse the genetic effect on within-litter variance in pigs

Genetics affects not only the weight of piglets at birth but also the variability of birth weight within litter. Previous studies on this topic assigned the sample standard deviation of piglet birth weights within litter as an observation to the sow. However, the contribution of the difference in mean birth weight per sex on the within-litter variance has been neglected so far. This work deals with the genetic effect on within-litter variance when different statistical models with different distributional assumptions are used and considers the sex effect and appropriate weights per trait. Traits were formed from the pooled sample variance of male and female birth weights within litter. A linear model approach was fitted to the logarithmized within-litter variance and the sample standard deviation. A generalized linear model with gamma-distributed residuals and log-link function was applied to the untransformed sample variance. Models were compared by analysing data from 9439 litters from Landrace and Large White of a commercial breeding programme. The estimates of heritability for different traits ranged from 7% to 11%. Although the generalized linear mixed model is preferred from a mathematical view, the rank correlations between breeding values of the linear mixed models and the generalized linear mixed model were relatively high, i.e. 94% to 98%. By residual diagnostics, a linear mixed model using the weighted and pooled within-litter standard deviation was identified as most suitable.     

Model Selection in Estimating Equations

Model selection is a necessary step in many practical regression analyses. But for methods based on estimating equations, such as the quasi-likelihood and generalized estimating equation (GEE) approaches, there seem to be few well-studied model selection techniques. In this article, we propose a new model selection criterion that minimizes the expected predictive bias (EPB) of estimating equations. A bootstrap smoothed cross-validation (BCV) estimate of EPB is presented and its performance is assessed via simulation for overdispersed generalized linear models. For illustration, the method is applied to a real data set taken from a study of the development of ewe embryos.     

Genome-based prediction of test cross performance in two subsequent breeding cycles

Genome-based prediction of genetic values is expected to overcome shortcomings that limit the application of QTL mapping and marker-assisted selection in plant breeding. Our goal was to study the genome-based prediction of test cross performance with genetic effects that were estimated using genotypes from the preceding breeding cycle. In particular, our objectives were to employ a ridge regression approach that approximates best linear unbiased prediction of genetic effects, compare cross validation with validation using genetic material of the subsequent breeding cycle, and investigate the prospects of genome-based prediction in sugar beet breeding. We focused on the traits sugar content and standard molasses loss (ML) and used a set of 310 sugar beet lines to estimate genetic effects at 384 SNP markers. In cross validation, correlations >0.8 between observed and predicted test cross performance were observed for both traits. However, in validation with 56 lines from the next breeding cycle, a correlation of 0.8 could only be observed for sugar content, for standard ML the correlation reduced to 0.4. We found that ridge regression based on preliminary estimates of the heritability provided a very good approximation of best linear unbiased prediction and was not accompanied with a loss in prediction accuracy. We conclude that prediction accuracy assessed with cross validation within one cycle of a breeding program can not be used as an indicator for the accuracy of predicting lines of the next cycle. Prediction of lines of the next cycle seems promising for traits with high heritabilities.     

Low-rank scale-invariant tensor product smooths for generalized additive mixed models

A general method for constructing low-rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented. A penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately, these "marginal" smooths being represented using a low-rank basis with an associated quadratic wiggliness penalty. The smooths offer several advantages: (i) they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no "natural" way to scale covariates relative to each other; (ii) they have a useful tuneable range of smoothness, unlike single-penalty tensor product smooths that are scale invariant; (iii) the relatively low rank of the smooths means that they are computationally efficient; (iv) the penalties on the smooths are easily interpretable in terms of function shape; (v) the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties, giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task; and (vi) the smooths can easily be written as components of a standard linear or generalized linear mixed model, allowing them to be used as components of the rich family of such models implemented in standard software, and to take advantage of the efficient and stable computational methods that have been developed for such models. A small simulation study shows that the methods can compare favorably with recently developed smoothing spline ANOVA methods.     

Joint regression analysis of correlated data using Gaussian copulas

Summary .  This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.     

Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture–recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture–recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi‐likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture–recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods.     

A Ranking Approach to Genomic Selection

Background

Genomic selection (GS) is a recent selective breeding method which uses predictive models based on whole-genome molecular markers. Until now, existing studies formulated GS as the problem of modeling an individual’s breeding value for a particular trait of interest, i.e., as a regression problem. To assess predictive accuracy of the model, the Pearson correlation between observed and predicted trait values was used.

Contributions

In this paper, we propose to formulate GS as the problem of ranking individuals according to their breeding value. Our proposed framework allows us to employ machine learning methods for ranking which had previously not been considered in the GS literature. To assess ranking accuracy of a model, we introduce a new measure originating from the information retrieval literature called normalized discounted cumulative gain (NDCG). NDCG rewards more strongly models which assign a high rank to individuals with high breeding value. Therefore, NDCG reflects a prerequisite objective in selective breeding: accurate selection of individuals with high breeding value.

Results

We conducted a comparison of 10 existing regression methods and 3 new ranking methods on 6 datasets, consisting of 4 plant species and 25 traits. Our experimental results suggest that tree-based ensemble methods including McRank, Random Forests and Gradient Boosting Regression Trees achieve excellent ranking accuracy. RKHS regression and RankSVM also achieve good accuracy when used with an RBF kernel. Traditional regression methods such as Bayesian lasso, wBSR and BayesC were found less suitable for ranking. Pearson correlation was found to correlate poorly with NDCG. Our study suggests two important messages. First, ranking methods are a promising research direction in GS. Second, NDCG can be a useful evaluation measure for GS.     

Unbiasedness of the Estimator of the Function of Expected Value in the Mixed Linear Model

The traditional method for estimating the linear function of fixed parameters in mixed linear model is a two-stage procedure. In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance components to estimating the linear function of fixed parameters according to generalized least squares method. In this paper the general mixed linear model is considered in which a matrix related to fixed parameters and or/a dispersion matrix of observation vector may be deficient in rank. It is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value and the estimators of variance components from first stage are translation-invariant and are even functions of the observation vector.