Mapping Quantitative Trait Loci in Crosses between Outbred Lines Using Least Squares

The use of genetic maps based upon molecular markers has allowed the dissection of some of the factors underlying quantitative variation in crosses between inbred lines. For many species crossing inbred lines is not a practical proposition, although crosses between genetically very different outbred lines are possible. Here we develop a least squares method for the analysis of crosses between outbred lines which simultaneously uses information from multiple linked markers. The method is suitable for crosses where the lines may be segregating at marker loci but can be assumed to be fixed for alternative alleles at the major quantitative trait loci (QTLs) affecting the traits under analysis (e.g., crosses between divergent selection lines or breeds with different selection histories). The simultaneous use of multiple markers from a linkage group increases the sensitivity of the test statistic, and thus the power for the detection of QTLs, compared to the use of single markers or markers flanking an interval. The gain is greater for more closely spaced markers and for markers of lower information content. Use of multiple markers can also remove the bias in the estimated position and effect of a QTL which may result when different markers in a linkage group vary in their heterozygosity in the F(1) (and thus in their information content) and are considered only singly or a pair at a time. The method is relatively simple to apply so that more complex models can be fitted than is currently possible by maximum likelihood. Thus fixed effects and effects of background genotype can be fitted simultaneously with the exploration of a single linkage group which will increase the power to detect QTLs by reducing the residual variance. More complex models with several QTLs in the same linkage group and two-locus interactions between QTLs can similarly be examined. Thus least squares provides a powerful tool to extend the range of crosses from which QTLs can be dissected whilst at the same time allowing flexible and realistic models to be explored.     

Mapping Environment-Specific Quantitative Trait Loci

Environment-specific quantitative trait loci (QTL) refer to QTL that express differently in different environments, a phenomenon called QTL-by-environment (Q × E) interaction. Q × E interaction is a difficult problem extended from traditional QTL mapping. The mixture model maximum-likelihood method is commonly adopted for interval mapping of QTL, but the method is not optimal in handling QTL interacting with environments. We partitioned QTL effects into main and interaction effects. The main effects are represented by the means of QTL effects in all environments and the interaction effects are represented by the variances of the QTL effects across environments. We used the Markov chain Monte Carlo (MCMC) implemented Bayesian method to estimate both the main and the interaction effects. The residual error covariance matrix was modeled using the factor analytic covariance structure. A simulation study showed that the factor analytic structure is robust and can handle other structures as special cases. The method was also applied to Q × E interaction mapping for the yield trait of barley. Eight markers showed significant main effects and 18 markers showed significant Q × E interaction. The 18 interacting markers were distributed across all seven chromosomes of the entire genome. Only 1 marker had both the main and the Q × E interaction effects. Each of the other markers had either a main effect or a Q × E interaction effect but not both.GENOTYPE-BY-ENVIRONMENT (G × E) interaction is a very important phenomenon in quantitative genetics. With the advanced molecular technology and statistical methods for quantitative trait loci (QTL) mapping (Lander and Botstein 1989; Jansen 1993; Zeng 1994), G × E interaction analysis has shifted to QTL-by-environment (Q × E) interaction. In the early stage of QTL mapping, almost all statistical methods were developed in a single environment (Paterson et al. 1991; Stuber et al. 1992). Data from different environments were analyzed separately and the conclusions were drawn from the separate analyses of QTL across environments. These methods do not consider the correlation of data under different environments and thus may not extract maximum information from the data. Composite interval mapping for multiple traits can be used for Q × E interaction if different traits are treated as the same trait measured in different environments (Jiang and Zeng 1995). This multivariate composite interval mapping approach makes good use of all data simultaneously and increases statistical power of QTL detection and accuracy of the estimated QTL positions. However, the number of parameters of this method increases dramatically as the number of environments increases. Therefore, the method may not be applied when the number of environments is large. Several other models have been proposed to solve the problem of a large number of environments (Jansen et al. 1995; Beavis and Keim 1996; Romagosa et al. 1996). These methods were based on some special situations and assumptions. One typical assumption was independent errors or constant variances across environments. These assumptions are often violated in real QTL mapping experiments.Earlier investigators realized the problem and adopted the mixed-model methodology to solve the problem (Piepho 2000; Boer et al. 2007). Under the mixed-model framework, people can choose which model effects are random and which are fixed. The mixed-model methodology is very flexible, leading to an easy way to model genetic and environmental correlation between environments using a suitable error structure. Piepho (2000) proposed a mixed model to detect QTL main effect across environments. Similar to the composite interval mapping analysis, his model incorporated one putative QTL and a few cofactors. The Q × E effects in the model were assumed to be random, which greatly reduced the number of estimated parameters. However, the fact that only one QTL is included in the model means that Piepho''s (2000) model remains a single-QTL model rather than a multivariate model. Boer et al. (2007) proposed a step-by-step mixed-model approach to detecting QTL main effects, Q × E interaction effects, and QTL responses to specific environmental covariates. In the final step, Boer et al. (2007) rewrote the model to include all QTL in a multiple-QTL model and reestimated their effects.In this study, we extended the Bayesian shrinkage method (Xu 2003) to map Q × E interaction effects of QTL. In the original study (Xu 2003), we treated each marker as a putative QTL and used the shrinkage method to simultaneously estimate marker effects of the entire genome. In the multiple-environment case, we can still use this approach to simultaneously evaluate marker effects under multiple environments but we can further partition the marker effects into main and Q × E interaction effects. For any particular marker, the mean of the marker effects represents the main effect and the variance of the marker effects represents the Q × E interaction effect for that marker. Under the Bayesian framework, we assigned a normal prior with zero mean and an unknown variance to each marker main effect and a multivariate normal prior with zero vector mean and homogeneous diagonal variance–covariance matrix to the Q × E interaction effects of each maker. In multiple environments, the structure of the error terms might be very complicated since we need to consider the correlation of the same genotype under different environments. In our analysis, we used different variance–covariance structures to model the error terms. The simplest case was the homogeneous diagonal matrix, and the most complex choice was an unstructured matrix. We also used a heterogeneous diagonal matrix whose parameters are somewhere between the two models. Finally, we considered several factor analytic models. The reason to use the factor analytic structure is that it can separate genetic effects into common effects and environment-specific effects. In addition, the factor analytic structure is parsimonious and thus can substantially reduce the computational burden of the mixed-model analyses.     

Fine-Scale Mapping of Quantitative Trait Loci Using Historical Recombinations

With increasing popularity of QTL mapping in economically important animals and experimental species, the need for statistical methodology for fine-scale QTL mapping becomes increasingly urgent. The ability to disentangle several linked QTL depends on the number of recombination events. An obvious approach to increase the recombination events is to increase sample size, but this approach is often constrained by resources. Moreover, increasing the sample size beyond a certain point will not further reduce the length of confidence interval for QTL map locations. The alternative approach is to use historical recombinations. We use analytical methods to examine the properties of fine QTL mapping using historical recombinations that are accumulated through repeated intercrossing from an F(2) population. We demonstrate that, using the historical recombinations, both simple and multiple regression models can reduce significantly the lengths of support intervals for estimated QTL map locations and the variances of estimated QTL map locations. We also demonstrate that, while the simple regression model using historical recombinations does not reduce the variances of the estimated additive and dominant effects, the multiple regression model does. We further determine the power and threshold values for both the simple and multiple regression models. In addition, we calculate the Kullback-Leibler distance and Fisher information for the simple regression model, in the hope to further understand the advantages and disadvantages of using historical recombinations relative to F(2) data.     

构建数量性状基因图谱的几种统计方法

以线性数学模型为线索,概述了用于构建数量性状基因图谱的几种主要统计方法,包括方差分析法、标记回归法、区间作图法、复合区间作图法、Jansen的复合区间作图法、双侧标记回归法以及新近发展的多区间作图法和多亲本作图法等.讨论了各种方法的优缺点. Abstract:Statistical methods for mapping QTLs were summarized, including one marker analysis, arker regression analysis,interval mapping (IM),composite interval mapping (CIM),Jansen's composite interval mapping, flanking marker regression analysis,multiple interval mapping (MIM) and multiple families mapping.Their advantages and disadvantages were discussed.     

Mapping Quantitative Trait Loci for Grain Appearance Traits of Rice Using a Recombinant Inbred Line Population

A linkage map consisting of 221 markers was constructed based on a recombinant inbred line (RIL) population from the cross between Zhenshan 97 and Minghui 63. Quantitative trait loci (QTL) mapping was carried out for grain appearance traits such as grain length, grain width and grain shape in rice in 1998 and 1999. Based on interval mapping method at the threshold LOD≥2.4, six, two and two QTLs were detected for grain length, grain width and grain shape, respectively, in 1998; In 1999, three, two and two QTLs were identified for the three traits, respectively. Of them, seven QTLs were simultaneously identified in both of the years. The QTL with large effects located in the interval RG393-C1087 on chromosome 3 not only controlled the grain length, but also influenced the grain shape. It explained 57.5%, 61.4% and 26.7%, 29.9% of phenotypic variation of the grain length and the grain shape in two years, respectively. The QTL with large effects located in the interval RG360-C734B on chromosome 5 affected the grain width and the grain shape. It explained 44.2%, 53.2% and 32.1%, 36.0% of phenotypic variation of the grain width and the shape in two years, respectively. Eight, five and five QTLs were identified for the grain length, width and shape, respectively, based on mixed linear-model composite interval mapping method at P =0.005. Their general contributions were 58.81%, 44.75%, and 57.47%. One QTL for the grain length was found to be significant interaction with environment.     

利用水稻重组自交系群体定位谷粒外观性状的数量性状基因

用区间作图和混合线性模型的复合区间作图两种方法,对水稻（Oryza sativa L）珍汕97和明恢63组合的重组自交系群体的谷粒外观性状－粒长,粒宽和粒形进行了数量性状基因（QTL）定位,用区间作图法在LOD≥2．4水平上（近拟于a=0.005),1998年对粒长,粒宽和粒形分别检测到6,2放2个QTLs,1999年对以上3个性状分别检测到3,2和2个QTLs,其中7个QTLs在两年均检测到,位于第3染色体RG393－C1087区间的QTL效应大,同时影响粒长和粒形,两年贡献分别为57．5％,61．4％和26．7％,29．9％,位于第5染色体RG360－C734B区间的QTL效应大,同时影响粒宽和粒形,两年贡献率分别为44．2％,53．2％和32．1％和36．0％,用混合线性模型的复合区间作图法在P＝0．005水平上,对粒长,粒宽和粒形分别检测到8,5和5个QTLs,共解释各自性状变异的58．81％,44．75％和57．47％,只检测到1个QTL与环境之间存在的显互作。     

微卫星标记与奶牛数量性状QTL定位

本文对奶牛产奶性能（产奶量、乳脂率、乳脂量、蛋白率、蛋白量）、乳房炎及体细胞数、繁殖性能、生产寿命等数量性状QTL定位研究进展进行了综述。 Abstract:Mapping of quantitative trait loci for some important traits (milk yield,fat percentage,fat yield,protein percentage,protein yield,clinical mastitis and somatic cell count,reproductive performance,productive life,etc.) in dairy cattle was introduced in this review.     

Precision Mapping of Quantitative Trait Loci

Adequate separation of effects of possible multiple linked quantitative trait loci (QTLs) on mapping QTLs is the key to increasing the precision of QTL mapping. A new method of QTL mapping is proposed and analyzed in this paper by combining interval mapping with multiple regression. The basis of the proposed method is an interval test in which the test statistic on a marker interval is made to be unaffected by QTLs located outside a defined interval. This is achieved by fitting other genetic markers in the statistical model as a control when performing interval mapping. Compared with the current QTL mapping method (i.e., the interval mapping method which uses a pair or two pairs of markers for mapping QTLs), this method has several advantages. (1) By confining the test to one region at a time, it reduces a multiple dimensional search problem (for multiple QTLs) to a one dimensional search problem. (2) By conditioning linked markers in the test, the sensitivity of the test statistic to the position of individual QTLs is increased, and the precision of QTL mapping can be improved. (3) By selectively and simultaneously using other markers in the analysis, the efficiency of QTL mapping can be also improved. The behavior of the test statistic under the null hypothesis and appropriate critical value of the test statistic for an overall test in a genome are discussed and analyzed. A simulation study of QTL mapping is also presented which illustrates the utility, properties, advantages and disadvantages of the method.     

Multiple Trait Analysis of Genetic Mapping for Quantitative Trait Loci

We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.     

Maximum Likelihood Mapping of Quantitative Trait Loci Using Full-Sib Families

A maximum likelihood method is presented for the detection of quantitative trait loci (QTL) using flanking markers in full-sib families. This method incorporates a random component for common family effects due to additional QTL or the environment. Simulated data have been used to investigate this method. With a fixed total number of full sibs power of detection decreased substantially with decreasing family size. Increasing the number of alleles at the marker loci (i.e., polymorphism information content) and decreasing the interval size about the QTL increased power. Flanking markers were more powerful than single markers. In testing for a linked QTL the test must be made against a model which allows for between family variation (i.e., including an unlinked QTL or a between family variance component) or the test statistic may be grossly inflated. Mean parameter estimates were close to the simulated values in all situations when fitting the full model (including a linked QTL and common family effect). If the common family component was omitted the QTL effect was overestimated in data in which additional genetic variance was simulated and when compared with an unlinked QTL model there was reduced power. The test statistic curves, reflecting the likelihood of the QTL at each position along the chromosome, have discontinuities at the markers caused by adjacent pairs of markers providing different amounts of information. This must be accounted for when using flanking markers to search for a QTL in an outbred population.     

A Nonparametric Approach for Mapping Quantitative Trait Loci

Genetic mapping of quantitative trait loci (QTLs) is performed typically by using a parametric approach, based on the assumption that the phenotype follows a normal distribution. Many traits of interest, however, are not normally distributed. In this paper, we present a nonparametric approach to QTL mapping applicable to any phenotypic distribution. The method is based on a statistic Z(w), which generalizes the nonparametric Wilcoxon rank-sum test to the situation of whole-genome search by interval mapping. We determine the appropriate significance level for the statistic Z(w), by showing that its asymptotic null distribution follows an Ornstein-Uhlenbeck process. These results provide a robust, distribution-free method for mapping QTLs.     

Binary Trait Mapping in Experimental Crosses With Selective Genotyping

Selective genotyping is an efficient strategy for mapping quantitative trait loci. For binary traits, where there are only two distinct phenotypic values (e.g., affected/unaffected or present/absent), one may consider selective genotyping of affected individuals, while genotyping none or only some of the unaffecteds. If selective genotyping of this sort is employed, the usual method for binary trait mapping, which considers phenotypes conditional on genotypes, cannot be used. We present an alternative approach, instead considering genotypes conditional on phenotypes, and compare this to the more standard method of analysis, both analytically and by example. For studies of rare binary phenotypes, we recommend performing an initial genome scan with all affected individuals and an equal number of unaffecteds, followed by genotyping the full cross in genomic regions of interest to confirm results from the initial screen.WE consider the problem of mapping genetic loci contributing to a binary trait in an experimental cross with selective genotyping. There are two clear approaches for linkage analysis with a binary trait. Typically, we compare the proportion of affected individuals across genotype groups (Xu and Atchley 1996). Alternatively, we can compare genotype frequencies between affected and unaffected individuals, similar to Henshall and Goddard (1999). Beyond these two basic approaches, binary trait mapping has seen fundamental advances in regression models (McIntyre et al. 2001; Deng et al. 2006), extensions to multiple-QTL mapping (Coffman et al. 2005; Chen and Liu 2009), and the development of Bayesian algorithms (Yi and Xu 2000; Huang et al. 2007). However, the original data structure and approach have remained intact. Existing methods for binary trait mapping largely require the availability of genotype and phenotype data for a representative sample of both affected and unaffected individuals, and we have not yet seen a well-developed framework for binary trait mapping in the presence of selective genotyping.It is not uncommon to see genotype data on affected individuals only, in which case the above methods cannot be used. Instead, we can compare observed genotype frequencies to the expected segregation ratios given the cross type, in a test for segregation distortion (see Faris et al. 1998; Lambrides et al. 2004). For example, the expected segregation proportions for an intercross are 1:2:1. The observed genotypes can then be described by a multinomial model, and statistically significant deviation from the expected segregation ratios among the genotyped affected individuals would suggest genotype–phenotype association. Gene mapping approaches that model genotypes rather than phenotypes have been developed extensively in the analysis of affected human relative pairs (see, for example, Risch 1990; Holmans 1993; Hauser and Boehnke 1998). In the analysis of experimental crosses, however, this type of approach has been developed primarily for the identification of monogenic mutants (Moran et al. 2006).Once all affected individuals are genotyped, an investigator may go on to genotype unaffected individuals. With this genotyping strategy in mind, we present several potential methods of analysis that might be applied in this context. First, we consider a standard analysis of the genotyped individuals, with disease proportions compared across genotype groups (Xu and Atchley 1996). Having omitted ungenotyped individuals, this method of analysis appears invalid because the estimated disease proportions are biased upward, reflecting an overrepresentation of affecteds in the set of genotyped individuals under consideration. As an alternative, we develop a reverse approach with genotype frequencies compared across phenotype groups. Because selective genotyping does provide a representative sample of genotypes for each phenotype group, this reverse approach does not face the bias in parameter estimation seen with the standard approach. We further extend the reverse approach to incorporate a segregation assumption, as is necessary for an affecteds only analysis. Finally, we present a full-likelihood analysis accounting for selective genotyping, similar to that suggested by Lander and Botstein (1989) for quantitative traits. We develop the full-likelihood approach both with and without incorporating an assumption on the genotype segregation proportions.Having put forth each of these methods, we derive analytic relationships among them. These relationships provide important insight regarding application of the presented methods under selective genotyping. Most notably, we find that making a segregation assumption can lead to spurious evidence of a QTL, but is necessary to treat the case of affecteds only genotyping. We demonstrate properties of the methods in an analysis of recovery from infection by Listeria monocytogenes in intercross mice and further compare power of the methods through computer simulations. Finally, we synthesize our analytical and simulation results to offer more general suggestions for the analysis of binary trait data with selective genotyping.     

离散性状QTL区间定位的最大似然方法

采用最大似然区间定位法对阈模型与一般线性模型的QTL定位效率进行了比较,并对影响离散性状QTL检测效率的主要因素（QTL效应、性状的遗传力和表型发生率）进行了模拟研究,实验设计为多个家系的女儿设计．资源群体大小为500头。研究结果表明：在QTL参数估计及检验功效方面,阈模型方法具有较大的优势,对离散性状QTL定位的效率明显高于LM（Linear Model）方法,定位的准确性也较高。另外,性状遗传力、QTL效应的大小和性状表型发生率对QTL定位的准确度也有直接的影响,随着性状遗传力和表型发生率的提高,随着QTL效应的增大,QTL定位的效率也进一步提高。     

Interval Mapping of Multiple Quantitative Trait Loci

The interval mapping method is widely used for the mapping of quantitative trait loci (QTLs) in segregating generations derived from crosses between inbred lines. The efficiency of detecting and the accuracy of mapping multiple QTLs by using genetic markers are much increased by employing multiple QTL models instead of the single QTL models (and no QTL models) used in interval mapping. However, the computational work involved with multiple QTL models is considerable when the number of QTLs is large. In this paper it is proposed to combine multiple linear regression methods with conventional interval mapping. This is achieved by fitting one QTL at a time in a given interval and simultaneously using (part of) the markers as cofactors to eliminate the effects of additional QTLs. It is shown that the proposed method combines the easy computation of the single QTL interval mapping method with much of the efficiency and accuracy of multiple QTL models.     

林木数量性状基因定位中的若干问题

随着ＤＮＡ分子标记技术的迅速发展,ＱＴＬ定位已成为当前生物学研究领域的前沿。迄今已对许多种动、植物定位了许多重要性状的ＱＴＬ。这些研究促进了遗传学的发展,并将作为育种的新策略应用。与作物相比,林木ＱＴＬ定位有其特性。本文详细讨论了林木的生物学特性对ＱＴＬ定位的影响、ＱＴＬ定位的系谱设计和统计分析方法。     

Unraveling the Complex Trait of Crop Yield With Quantitative Trait Loci Mapping in Brassica napus

Yield is the most important and complex trait for the genetic improvement of crops. Although much research into the genetic basis of yield and yield-associated traits has been reported, in each such experiment the genetic architecture and determinants of yield have remained ambiguous. One of the most intractable problems is the interaction between genes and the environment. We identified 85 quantitative trait loci (QTL) for seed yield along with 785 QTL for eight yield-associated traits, from 10 natural environments and two related populations of rapeseed. A trait-by-trait meta-analysis revealed 401 consensus QTL, of which 82.5% were clustered and integrated into 111 pleiotropic unique QTL by meta-analysis, 47 of which were relevant for seed yield. The complexity of the genetic architecture of yield was demonstrated, illustrating the pleiotropy, synthesis, variability, and plasticity of yield QTL. The idea of estimating indicator QTL for yield QTL and identifying potential candidate genes for yield provides an advance in methodology for complex traits.YIELD is the most important and complex trait in crops. It reflects the interaction of the environment with all growth and development processes that occur throughout the life cycle (Quarrie et al. 2006). Crop yield is directly and multiply determined by yield-component traits (such as seed weight and seed number). Yield-related traits (such as biomass, harvest index, plant architecture, adaptation, resistance to biotic and abiotic constraints) may also indirectly affect yield by affecting the yield-component traits or by other, unknown mechanisms. Increasing evidence suggests that “fine-mapped” quantitative trait loci (QTL) or genes identified as affecting crop yield involve diverse pathways, such as seed number (Ashikari et al. 2005; Tian et al. 2006b; Burstin et al. 2007; Xie et al. 2008; Xing et al. 2008; Xue et al. 2008), seed weight (Ishimaru 2003; Song et al. 2005; Shomura et al. 2008; Wang et al. 2008; Xie et al. 2006, 2008; Xing et al. 2008; Xue et al. 2008), flowering time (Cockram et al. 2007; Song et al. 2007; Xie et al. 2008; Xue et al. 2008), plant height (Salamini 2003; Ashikari et al. 2005; Xie et al. 2008; Xue et al. 2008), branching (Clark et al. 2006; Burstin et al. 2007; Xing et al. 2008), biomass yield (Quarrie et al. 2006; Burstin et al. 2007), resistance and tolerance to biotic and abiotic stresses (Khush 2001; Brown 2002; Yuan et al. 2002; Waller et al. 2005; Zhang 2007; Warrington et al. 2008), and root architecture (Hochholdinger et al. 2008).Many experiments have explored the genetic basis of yield and yield-associated traits (yield components and yield-related traits) in crops. Summaries of identified QTL have been published for wheat (MacCaferri et al. 2008), barley (Von Korff et al. 2008), rice, and maize (http://www.gramene.org/). The results show several common patterns. First, QTL for yield and yield-associated traits tend to be clustered in the genome, which suggests that the QTL of the yield-associated traits have pleiotropic effects on yield. Second, this kind of pleiotropy has not been well analyzed genetically. The QTL for yield (complicated factor), therefore, have not been associated with any yield-associated traits (relatively simple factors, such as plant height). Therefore, they are unlikely to predict accurately potential candidate genes for yield. Third, only a few loci (rarely >10) have been found for each of these traits. Thus, the genetic architecture of yield has remained ambiguous. Fourth, trials were carried out in a few environments and how the mode of expression of QTL for these complex traits might respond in different environments is unclear.In this study, the genetic architecture of crop yield was analyzed through the QTL mapping of seed yield and eight yield-associated traits in two related populations of rapeseed (Brassica napus) that were grown in 10 natural environments. The complexity of the genetic architecture of seed yield was demonstrated by QTL meta-analysis. The idea of estimating indicator QTL (QTL of yield-associated traits, which are defined as the potential genetic determinants of the colocalized QTL for yield) for yield QTL in conjunction with the identification of candidate genes is described.     

Shrinkage Estimation Method for Mapping Multiple Quantitative Trait Loci

In this article, shrinkage estimation method for multiple-marker analysis and for mapping multiple quantitative trait loci (QTL) was reviewed. For multiple-marker analysis, Xu (Genetics, 2003, 163:789-801) developed a Bayesian shrinkage estimation (BSE) method. The key to the success of this method is to allow each marker effect have its own variance parameter, which in turn has its own prior distribution so that the variance can be estimated from the data. Under this hierarchical model, a large number of markers can be handled although most of them may have negligible effects. Under epistatic genetic model, however, the running time is very long. To overcome this problem, a novel method of incorporating the idea described above into maximum likelihood, known as penalized likelihood method, was proposed. A simulated study showed that this method can handle a model with multiple effects, which are ten times larger than the sample size. For multiple QTL analysis, two modified versions for the BSE method were introduced: one is the fixed-interval method and another is the variable-interval method. The former deals with markers with intermediate density, and the latter can handle markers with extremely high density as well as model with epistatic effects. For the detection of epistatic effects, penalized likelihood method and the variable-interval approach of the BSE method are available.     

多QTL定位的压缩估计方法

本文综述了多标记分析和多QTL定位的压缩估计方法。对于前者,Xu（Genetics,2003,163：789—801）首先提出了Bayesian压缩估计方法。其关键在于让每个效应有一个特定的方差参数,而该方差又服从一定的先验分布,以致能从资料中估计之。由此,能够同时估计大量分子标记基因座的遗传效应,即使大多数标记的效应是可忽略的。然而,对于上位性遗传模型,其运算时间还是过长。为此,笔者将上述思想嵌入极大似然法,提出了惩罚最大似然方法。模拟研究显示：该方法能处理变量个数大于样本容量10倍左右的线性遗传模型。对于后者,本文详细介绍了基于固定区间和可变区间的Bayesian压缩估计方法。固定区间方法可处理中等密度的分子标记资料;可变区间方法则可分析高密度分子标记资料,甚至是上位性遗传模型。对于上位性检测,已介绍的惩罚最大似然方法和可变区间Bayesian压缩估计方法可供利用。应当指出,压缩估计方法在今后的eQTL和QTN定位以及基因互作网络分析等研究中也是有应用价值的。