MIXED MODEL APPROACHES FOR ESTIMATING GENETIC VARIANCES AND COVARIANCES

The limitations of methods for analysis of variance(ANOVA)in estimating genetic variances are discussed. Among the three methods(maximum likelihood ML, restricted maximum likelihood REML, and minimum norm quadratic unbiased estimation MINQUE)for mixed linear models, MINQUE method is presented with formulae for estimating variance components and covariances components and for predicting genetic effects. Several genetic models, which cannot be appropriately analyzed by ANOVA methods, are introduced in forms of mixed linear models. Genetic models with independent random effects can be analyzed by MINQUE(1)method whieh is a MINQUE method with all prior values setting 1. MINQUE(1)method can give unbiased estimation for variance components and covariance components, and linear unbiased prediction (LUP) for genetic effects. There are more complicate genetic models for plant seeds which involve correlated random effects. MINQUE(0/1)method, which is a MINQUE method with all prior covariances setting 0 and all prior variances setting 1, is suitable for estimating variance and covariance components in these models. Mixed model approaches have advantage over ANOVA methods for the capacity of analyzing unbalanced data and complicated models. Some problems about estimation and hypothesis test by MINQUE method are discussed.     

METHODS FOR DETECTION AND ESTIMATION OF LINKAGE BETWEEN A MARKER LOCUS AND QUANTITATIVE TRAIT LOCI Ⅰ. USING F_2 FAMILY SUBPOPULATION

Several methods heve been proposed over the years to detect linkage between a marker gene and a quantitative trait locus (QTL). Use of isozymes and restriction fragment length polymorphisms (RFLPs) as genetic markers has encouraged the development of new methods to detect linkage. In the paper authors present three methods to detect linkage and two methods to measure recombination frequency (r). The three methods that detect linkage are fit for the test of one or several QTLs of quantitative trait considered as long as the net gene effect vaIue of all loci belonging to a linkage cluster is greater significantly than zero, irrespective of their linkage relationship among the several QTLs.     

植物数量性状遗传体系检测中回交或自交家系重复试验数据的分析方法

为提高主基因+多基因混合遗传分析的精度,降低试验误差,采用重复内分组随机区组设计,对低遗传力性状的B1:2和B2:2或F2:3家系平均数资料进行遗传分析.通过AIC准则和适合性检验比较无主基因(A-0)、1对主基因(A)、2对主基因(B)、多基因(C)、1对主基因+多基因(D)和2对主基因+多基因(E)模型以鉴定其遗传模式.采用IECM算法估计混合模型参数.通过油菜HSTC14×宁油7号初花期F2:3家系平均数资料阐明该方法。 abstract:To improve the precision in the genetic analysis of quantitative traits,the B1:2 and 132:2,or F2:3 families in a randomized blocks design were used to identify the mixed major gene plus polygene inheritance model while error variance was estimated from the analysis of variance.Five kinds of genetic models were established,including:one-major-gene model,two-major-gene model,polygene model,mixed one-major-gene plus polygene model,and mixed two-major-gene plus polygene model.The AIC value and a set of tests of goodness-of-fit were used to identify the most fitted model among the possible ones.The iterated ECM (IECM) algorithm was used to obtain maximum likelihood estimates of the parameters in sample likelihood function.An example of the genetic analysis of days from planting to flowering of a rape cross was used to illuminate the above procedure.     

数量性状发育遗传模型及其分析方法的研究进展

发育遗传模型是同时反映性状遗传和发育本质、提供影响遗传变异及调整发育进程的有关因素的信息的模型。建立在群体遗传学基础上的直接效应模型适用于单一基因控制的简单性状。渐成模型将遗传变异分解成直接分量和渐成分量(母体效应和互作效应),能更好地反映有机体遗传和发育的生物学机制。生长轨迹模型有效地综合了复杂性状各分量的发育动态,可获得连续的、综合的、详细的、动态的发育信息。条件遗传分析方法不仅可以估算特定时间段的净效应,且可将净效应分解为不同遗传分量,了解各效应分量的相对贡献。 Abstract：Developmental genetic models and analysis methods for quantitative traits are presented.Developmental genetic models should reflect the genetic and developmental essence,and provide the information of the factors influencing the genetic variation and the developmental process.Direct effect models,which based on the population genetics,may be suitable to analyze simple traits with single gene.Epigenetic models can decompose the whole genetic variation into direct and epigenetic components (maternal effects and epigenetic interaction effects),so that biological mechanism can be better understood.Growth trace models effectively synthesize the developmental dynamics of components of complex traits.With them,continuous,compositive,detailed,and dynamic information of development is available.Conditional analysis method can not only estimate the net effects in a specific time interval,but also depose them into genetic components and help to appreciate the contributions of different effects.     

Progress in the Study of Molecular Genetic Improvements of Poplar in China

The poplar is one of the most economically important and intensively studied tree species owing to its wide application in the timber industry and as a model material for the study of woody plants. The natural resource of poplars in China is replete. Over the past 10 years, the application of molecular biological techniques to genetic improvements in poplar species has been widely studied in China. Recent advances in molecular genetic improvements of poplar, including cDNA library construction, gene cloning and identification, genetic engineering, gene expression, genetic linkage map construction, mapping of quantitative trait loci （QTL） and molecular-assisted selection, are reviewed in the present paper. In addition, the application of modern biotechnology to molecular improvements in the genetic traits of the poplar and some unsolved problems are discussed.     

参数连锁分析方法

通过拟合的数据资料,对目前最常用的参数型连锁分析方法进行了比较,为有针对性地选择连锁分析方法提供了依据。 Abstract：We present here two parametric statistics for linkage analysis ( linkage and genehunter).Using the simulated pedigrees, we introduced the usage of the two methods.     

混合线性模型下猪群间遗传联系的度量

采用关联指数(IC)和决定系数(CD)两种方法,度量混合线性模型遗传评估下 猪群体间的遗传关联性。结果表明,加拿大安大略省的大约克夏猪、长白猪、杜洛克猪和汉普夏猪4个主要品种群体间具有良好的遗传联系。CD法既组合了数据结构和信息量,又考虑了预测误差方差和遗传变异性,是一个选择判断遗传评估精度的好方法。 Abstract:Two criteria for the measures of genetic connectedness in mixed linear model of genetic evaluation are used:the degree of connectedness(IC)and the generalized coefficient of determination(CD).The results indicated that the data of four dominant swine breeds:Yorkshire,Landrace,Duroc and Hampshire in Ontario,Canada are well connected.The CD,which combines data structure and amount of information and also accounts for both prediction error variance and genetic variability,is a good method to select for judging the precision of a genetic evaluation.     

MapDraw，在Excel中绘制遗传连锁图的宏

MAPMAKER是现今广泛使用的遗传连锁数据分析软件,然而其广泛使用的DOS版本却不具有连锁图绘制功能,给连锁作图工作带来了相当大的麻烦。为了解决这一问题,我们以大家广泛使用的数据处理软件Microsoft Excel为平台,编写了一个Excel宏——MapDraw来在轻松的操作中实现遗传连锁图的绘制。 Abstract:MAPMAKER is one of the most widely used computer software package for constructing genetic linkage maps.However,the PC version,MAPMAKER 3.0 for PC,could not draw the genetic linkage maps that its Macintosh version,MAPMAKER 3.0 for Macintosh,was able to do.Especially in recent years,Macintosh computer is much less popular than PC.Most of the geneticists use PC to analyze their genetic linkage data.So a new computer software to draw the same genetic linkage maps on PC as the MAPMAKER for Macintosh to do on Macintosh has been crying for.Microsoft Excel,one component of Microsoft Office package,is one of the most popular software in laboratory data processing.Microsoft Visual Basic for Applications (VBA) is one of the most powerful functions of Microsoft Excel.Using this program language,we can take creative control of Excel,including genetic linkage map construction,automatic data processing and more.In this paper,a Microsoft Excel macro called MapDraw is constructed to draw genetic linkage maps on PC computer based on given genetic linkage data.Use this software,you can freely construct beautiful genetic linkage map in Excel and freely edit and copy it to Word or other application.This software is just an Excel format file.You can freely copy it from ftp://211.69.140.177 or ftp://brassica.hzau.edu.cn and the source code can be found in Excel′s Visual Basic Editor.     

Quantitative genetic models for the balance between migration and stabilizing selection

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.     

Adding further power to the Haseman and Elston method for detecting linkage in larger sibships: weighting sums and differences

Haseman and Elston (H-E) proposed a robust test to detect linkage between a quantitative trait and a genetic marker. In their method the squared sib-pair trait difference is regressed on the estimated proportion of alleles at a locus shared identical by descent by sib pairs. This method has recently been improved by changing the dependent variable from the squared difference to the mean-corrected product of the sib-pair trait values, a significantly positive regression indicating linkage. Because situations arise in which the original test is more powerful, a further improvement of the H-E method occurs when the dependent variable is changed to a weighted average of the squared sib-pair trait difference and the squared sib-pair mean-corrected trait sum. Here we propose an optimal method of performing this weighting for larger sibships, allowing for the correlation between pairs within a sibship. The optimal weights are inversely proportional to the residual variances obtained from the two different regressions based on the squared sib-pair trait differences and the squared sib-pair mean-corrected trait sums, respectively, allowing for correlations among sib pairs. The proposed method is compared with the existing extension of the H-E approach for larger sibships. Control of the type I error probabilities for sibships of any size can be improved by using a generalized estimating equation approach and the robust sandwich estimate of the variance, or a Monte-Carlo permutation test.     

X-linked extension of the revised Haseman-Elston algorithm for linkage analysis in sib pairs

Haseman and Elston (H-E) proposed a regression-based robust test of linkage between a marker and an autosomal quantitative trait locus, using the squared sib pair trait difference as a dependent variable and the proportion of alleles shared identical by descent by the sib pair as an independent variable. Several authors have proposed improvement of the original H-E's seminal work by using an optimal linear combination of squared sum and squared difference as the dependent variable. In this paper, we extend Haseman and Elston's sib pair method to an X-linked locus. We give a general formulation of the complete regression model and details of the regression coefficients in terms of variance components. Simulation results are presented to describe the power of this technique for a theoretical best case scenario.     

Comparative Studies on the Estimation of Genetic Variances by Several Variance Components Estimation Method

Using a quantitative genetic model, this paper compares four different methods for estimating genetic variance components. Given various genetic parameters, data were generated and estimates computed. The number of negative estimates, the sample mean, the sample variance, and the sample mean squared error were computed for each method. It is shown that, if the genetic values are not very small, the traditional MATHER -JINKS method is at least as good as any other method. The ML method might be preferable only if the genetic values are very small and the number of loci large.     

Nonparametric trend statistic incorporating dispersion differences in sib pair linkage for quantitative traits

The Haseman-Elston (HE) regression method and its extensions are widely used in genetic studies for detecting linkage to quantitative trait loci (QTL) using sib pairs. The principle underlying the simple HE regression method is that the similarity in phenotypes between two siblings increases as they share an increasing number of alleles identical by descent (IBD) from their parents at a particular marker locus. In such a procedure, similarity was identified with the locations, that is, means of groups of sib pairs sharing 0, 1, and 2 alleles IBD. A more powerful, rank-based nonparametric test to detect increasing similarity in sib pairs is presented by combining univariate trend statistics not only of locations, but also of dispersions of the squared phenotypic differences of two siblings for three groups. This trend test does not rely on distributional assumptions, and is applicable to the skewed or leptokurtic phenotypic distributions, in addition to normal or near normal phenotypic distributions. The performances of nonparametric trend statistics, including nonparametric regression slope, are compared with the HE regression methods as genetic linkage strategies.     

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.     

A genome scan for quantitative trait loci in a wild population of red deer (Cervus elaphus)

Recent empirical evidence indicates that although fitness and fitness components tend to have low heritability in natural populations, they may nonetheless have relatively large components of additive genetic variance. The molecular basis of additive genetic variation has been investigated in model organisms but never in the wild. In this article we describe an attempt to map quantitative trait loci (QTL) for birth weight (a trait positively associated with overall fitness) in an unmanipulated, wild population of red deer (Cervus elaphus). Two approaches were used: interval mapping by linear regression within half-sib families and a variance components analysis of a six-generation pedigree of >350 animals. Evidence for segregating QTL was found on three linkage groups, one of which was significant at the genome-wide suggestive linkage threshold. To our knowledge this is the first time that a QTL for any trait has been mapped in a wild mammal population. It is hoped that this study will stimulate further investigations of the genetic architecture of fitness traits in the wild.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Simultaneous fine mapping of closely linked epistatic quantitative trait loci using combined linkage disequilibrium and linkage with a general pedigree

Causal mutations and their intra- and inter-locus interactions play a critical role in complex trait variation. It is often not easy to detect epistatic quantitative trait loci (QTL) due to complicated population structure requirements for detecting epistatic effects in linkage analysis studies and due to main effects often being hidden by interaction effects. Mapping their positions is even harder when they are closely linked. The data structure requirement may be overcome when information on linkage disequilibrium is used. We present an approach using a mixed linear model nested in an empirical Bayesian approach, which simultaneously takes into account additive, dominance and epistatic effects due to multiple QTL. The covariance structure used in the mixed linear model is based on combined linkage disequilibrium and linkage information. In a simulation study where there are complex epistatic interactions between QTL, it is possible to simultaneously map interacting QTL into a small region using the proposed approach. The estimated variance components are accurate and less biased with the proposed approach compared with traditional models.