基于贝叶斯统计的谷物胚乳性状QTL作图方法
|
摘要
谷类作物种子的胚乳是人类食物的重要来源,胚乳性状的遗传研究是粮食增产和品质改良的必要前提。随着分子标记技术的成熟以及饱和分子标记连锁图的建成,追踪并定位控制数量性状的多个基因座位已成为可能,进而为育种学家研究如何提高粮食产量、改善粮食品质提供了有力的工具。由于种子胚乳遗传控制体系要比通常的二倍体农艺性状更为复杂,种子胚乳性状研究不应该直接套用常规二倍体农艺性状作图方法。为此,研究人员先后提出一系列基于经典数理统计方法的胚乳性状QTL专用模型和方法,如极大似然法,迭代重新加权最小平方法等,以解析胚乳数量性状的遗传结构。近十年来,随着现代统计学、高速计算机的发展以及马尔可夫链蒙特卡罗(MCMC)算法的提出,贝叶斯统计以其鲜明的特点和独到的分析方法,引起了研究者的重视。在数量遗传学研究中，如何将贝叶斯统计学原理和方法应用于三倍体胚乳性状的QTL作图,在国内外尚未见报道。因此,本研究率先将贝叶斯统计原理和胚乳性状的数量遗传模型相结合,以分离群体中各植株的分子标记基因型以及植株上若干粒种子胚乳性状的单粒观测值为数据模式,根据胚乳性状的遗传特点,提出了一种新的基于贝叶斯统计的胚乳性状QTL作图方法,该方法采用基于马尔可夫链蒙特卡罗算法实现的贝叶斯方法估计QTL的遗传参数。
该方法基本过程如下：(1)构建胚乳性状QTL的遗传模型；(2)利用分离群体的分子标记基因型信息,推断种子胚乳QTL基因型的条件概率；(3)依据贝叶斯公式,利用QTL基因型的条件概率和种子性状表型观察值计算各QTL基因型的条件后验概率,获得该粒种子胚乳基因型,从而确定模型中指示变量的取值；(4)根据贝叶斯公式推导出模型中各参数的条件后验分布,包括：平均值、加性效应、第一显性、第二显性效应以及误差方差；(5)利用各参数的条件后验分布,采用基于Gibbs抽样和Metropolis-Hastings算法实现的马尔可夫链蒙特卡罗(MCMC)方法同时获得多个QTL效应和位置的后验样本；(6)收集并分析后验样本,依据后验样本分布特征,选取平均数或众数作为相应参数的贝叶斯估计值。
本研究以分离群体中各植株的分子标记基因型以及植株上若干粒种子胚乳性状的单粒观测值为数据模式,首先发展出基于单QTL模型的谷物胚乳性状QTL区间作图的贝叶斯方法。方法的有效性用染色体水平和基因组水平两套模拟方案进行验证。
在上述研究的基础上,本研究进一步以相同的数据模式,提出了胚乳数量性状基因座(QTL)多区间作图的贝叶斯方法,方法的有效性通过模拟实验进行了验证。模拟实验设置和分析结果报告如下：
方法1：基于单QTL模型的胚乳性状QTL作图的贝叶斯方法
模拟设置1：染色体水平模拟。设F2分离群体的样本容量为200株,每株考察20粒。QTL遗传力h2设置5%、10%和20%,共3个水平。每处理重复模拟100次,QTL位置和效应估计的准确度以100个重复样本相应QTL位置和效应估计值‘的平均值度量,精确度则以100个重复样本相应QTL估计值的标准差度量。
模拟设置2：基因组水平模拟。研究中采用了一个包含4条染色体的全基因组,4个具有不同遗传效应的QTL,分布在各个染色体上,QTL的遗传力分别为6.07%,16.77%,23.96%和13.21%。
模拟结果表明：(1)各遗传力下QTL的统计功效均为100%。(2)在遗传力分别为5%、10%、20%三种处理下,QTL位置估计值的准确度均很高,三种遗传力下相差很小,而精确度却随遗传力的增加而提高。(3)在群体均值和QTL效应估计值上,尤其是两个显性效应的估计值,随着遗传力的增加,估计值的准确度和精确度也随之提高,这与一般期望相符。(4)在全基因组水平下,本研究提出的方法可以清晰地分辨出4个不同QTL所在的基因组位置,并准确估计各个QTL的有关参数。
方法2：基于贝叶斯统计的谷物胚乳性状QTL多区间作图法
模拟设置：设F2分离群体的样本容量为200株,每株考察30粒。假设一条长100cM的染色体,其上均匀分布11个共显性分子标记,控制胚乳性状的3个QTL分别位于15cM,55cM和95cM处,群体均值设为20,各个QTL的遗传力分别接近5%、10%和15%。重复模拟100次,QTL位置和效应估计的准确度和精确度度量方法同上。
模拟结果：(1)贝叶斯方法可以高效发现QTL并准确估计出QTL的遗传位置。例如,在本研究模拟设置下,即使是遗传力只有5%左右的QTL,其统计功效也达100%。此外,贝叶斯多区间方法对群体均值和加性效应的估计也十分准确。(2)从QTL效应估计的准确度以及精确度来看,只有两个显性效应的准确度略差。这一方面可能与模拟试验采用的群体有关,由于本方案采用一阶设计的F2群体,F3胚乳QTL基因型以其所着生的母株QTL基因型推断,由于世代的不对应,必然会造成一定的信息丢失。另一方面,即使加性和显性效应在量值上相等,显性效应引起的变异在胚乳性状遗传方差中所占分量仍然相对很小。
The endosperm of crop seeds is an important source of human food. The genetic study of endosperm traits plays a fundamental and vital role in improving grain yield and quality. With the development of molecular marker technology and the construction of genetic linkage map, it is possible to search and map QTL controlling quantitative traits. This can be used in marker assisted selection for enhancing food production and improving food quality. Because genetic control system of endosperm is more complex than that of diploid, the mapping method for diploid traits has not been suitable to the mapping of triploid endosperm. So the researchers have proposed a series of models and methods for. QTL mapping of endosperm traits based on classical statistical algorithm to dissect the genetic architecture of quantitative traits of endosperm, such as the maximum likelihood method and iteractively reweighted least squares (IRWLS) method. In the recent ten years, with the development of modern statistics and high speed computer as well as MCMC algorithm, Bayesian statistics has been widely uesd in various research area, especically in QTL mapping of diploid traits. However, it has not been used in mapping QTL underlying triploid endosperm traits..In this paper, based on Bayesian statistics and quantitative genetic model of triploid endosperm traits, we first proposed a Bayesian method for mapping QTL underlying endosperm traits, which used the molecular marker genotypes of each plant in segregation population and the single endosperm observation of a few endosperms of each plant as data set to analyze endosperm QTL. The method was implemented via MCMC algorithm.
The process of the method is summarized as follows:(1) Formulate single-QTL model and multiple-QTL model of endosperm traits. (2) Calculate the conditional probabilities of the QTL genotypes by using the molecular marker information. (3) Calculate the conditional posterior probabilities of the QTL genotypes. (4) Sample the QTL genotypes using the posterior probabilities and get the indicator variables of QTL genotypes. (5) Derive the conditional posterior distributions of population mean, additive effect, first dominance effect, second dominance effect, residual variance and the postions of QTL. (6) Sample the conditional posterior samples by using Gibbs sampling and Metropolis-Hastings algorithm. (7) Collect posterior samples and obtain the Bayesian estimates.
By using the molecular marker genotypes of each plant in segregation population and the single endosperm observation of a few endosperms of each plant as data set, we proposed the interval mapping and the composite interval mapping methods for endosperm QTL. Efficiency of the methods is demonstrated via both chromosome level and genome level simulation studies.
ⅠBayesian Statistics-Based Interval Mapping of QTL Controlling Endosperm Traits in Cereals
For chromosome level simulation, the sample size of an F2 segeregating population was set on 200 plants and 20 endosperms of each plant. The QTL heritability was simulated at three levels:5%,10% and 20%, respectively. Each treatment of the simulation experiments was replicated 100 times. Precision and accuracy of estimates for QTL location and effects were measured by means and standard deviations of estimates respectively.
For genome level simulation, a genome containing four chromosomes was simulated. Four QTL with different heritabilities were set at four different chromosomes. The QTL heritability was set at 6.07%,16.77%,23.96% and 13.21%, respectively.
The results showed that (1) The power of each treatment was 100%; (2) Both the effect and position estimates of these QTL were reasonably close to the true value. (3) Higher QTL heritability tended to produce more accurate and precise estimates, whereas lower heritability produced less accurate estimates with large estimation errors, which was in accordance with our general expectations. (4) The genome level simulation showed that the proposed method not only clearly pick up the multiple QTL, but estimate the QTL parameters.
ⅡBayesian Statistics-Based Multiple Interval Mapping of QTL Controlling Endosperm Traits in Cereals
Simulation study was set on 200 F2 plants each with 30 endosperms. A chromosome of length 100 cM covered by eleven evenly spaced markers was simulated. Three QTL affecting endosperm traits were set at 15cM,55cM and 95cM respectively. The population mean was set as 20. The QTL heritability was set at about 5%,10% and 15%. The simulation experiment was replicated 100 times. Precision and accuracy of estimates for QTL location and effects are measured same as above.
The results showed that (1) The proposed Bayesian method had high statistical power and accurate estimates of QTL position, mean and additive effects. For example, even with the heritability of 5%, the statistical power can still reach 100%. (2) The two dominance effects were found slightly biased. This may have two possible reasons. The first reason is that the QTL genotype of F3 endosperms are just infered from the marker genotypes of F2 maternal genome other than from the marker genotypes of F3 endosperm genome. The second reason is that even if the additive and dominance effects had equal sizes, the variation caused by dominance effect just had a limited weight in the total genetic variance.
该方法基本过程如下：(1)构建胚乳性状QTL的遗传模型；(2)利用分离群体的分子标记基因型信息,推断种子胚乳QTL基因型的条件概率；(3)依据贝叶斯公式,利用QTL基因型的条件概率和种子性状表型观察值计算各QTL基因型的条件后验概率,获得该粒种子胚乳基因型,从而确定模型中指示变量的取值；(4)根据贝叶斯公式推导出模型中各参数的条件后验分布,包括：平均值、加性效应、第一显性、第二显性效应以及误差方差；(5)利用各参数的条件后验分布,采用基于Gibbs抽样和Metropolis-Hastings算法实现的马尔可夫链蒙特卡罗(MCMC)方法同时获得多个QTL效应和位置的后验样本；(6)收集并分析后验样本,依据后验样本分布特征,选取平均数或众数作为相应参数的贝叶斯估计值。
本研究以分离群体中各植株的分子标记基因型以及植株上若干粒种子胚乳性状的单粒观测值为数据模式,首先发展出基于单QTL模型的谷物胚乳性状QTL区间作图的贝叶斯方法。方法的有效性用染色体水平和基因组水平两套模拟方案进行验证。
在上述研究的基础上,本研究进一步以相同的数据模式,提出了胚乳数量性状基因座(QTL)多区间作图的贝叶斯方法,方法的有效性通过模拟实验进行了验证。模拟实验设置和分析结果报告如下：
方法1：基于单QTL模型的胚乳性状QTL作图的贝叶斯方法
模拟设置1：染色体水平模拟。设F2分离群体的样本容量为200株,每株考察20粒。QTL遗传力h2设置5%、10%和20%,共3个水平。每处理重复模拟100次,QTL位置和效应估计的准确度以100个重复样本相应QTL位置和效应估计值‘的平均值度量,精确度则以100个重复样本相应QTL估计值的标准差度量。
模拟设置2：基因组水平模拟。研究中采用了一个包含4条染色体的全基因组,4个具有不同遗传效应的QTL,分布在各个染色体上,QTL的遗传力分别为6.07%,16.77%,23.96%和13.21%。
模拟结果表明：(1)各遗传力下QTL的统计功效均为100%。(2)在遗传力分别为5%、10%、20%三种处理下,QTL位置估计值的准确度均很高,三种遗传力下相差很小,而精确度却随遗传力的增加而提高。(3)在群体均值和QTL效应估计值上,尤其是两个显性效应的估计值,随着遗传力的增加,估计值的准确度和精确度也随之提高,这与一般期望相符。(4)在全基因组水平下,本研究提出的方法可以清晰地分辨出4个不同QTL所在的基因组位置,并准确估计各个QTL的有关参数。
方法2：基于贝叶斯统计的谷物胚乳性状QTL多区间作图法
模拟设置：设F2分离群体的样本容量为200株,每株考察30粒。假设一条长100cM的染色体,其上均匀分布11个共显性分子标记,控制胚乳性状的3个QTL分别位于15cM,55cM和95cM处,群体均值设为20,各个QTL的遗传力分别接近5%、10%和15%。重复模拟100次,QTL位置和效应估计的准确度和精确度度量方法同上。
模拟结果：(1)贝叶斯方法可以高效发现QTL并准确估计出QTL的遗传位置。例如,在本研究模拟设置下,即使是遗传力只有5%左右的QTL,其统计功效也达100%。此外,贝叶斯多区间方法对群体均值和加性效应的估计也十分准确。(2)从QTL效应估计的准确度以及精确度来看,只有两个显性效应的准确度略差。这一方面可能与模拟试验采用的群体有关,由于本方案采用一阶设计的F2群体,F3胚乳QTL基因型以其所着生的母株QTL基因型推断,由于世代的不对应,必然会造成一定的信息丢失。另一方面,即使加性和显性效应在量值上相等,显性效应引起的变异在胚乳性状遗传方差中所占分量仍然相对很小。
The endosperm of crop seeds is an important source of human food. The genetic study of endosperm traits plays a fundamental and vital role in improving grain yield and quality. With the development of molecular marker technology and the construction of genetic linkage map, it is possible to search and map QTL controlling quantitative traits. This can be used in marker assisted selection for enhancing food production and improving food quality. Because genetic control system of endosperm is more complex than that of diploid, the mapping method for diploid traits has not been suitable to the mapping of triploid endosperm. So the researchers have proposed a series of models and methods for. QTL mapping of endosperm traits based on classical statistical algorithm to dissect the genetic architecture of quantitative traits of endosperm, such as the maximum likelihood method and iteractively reweighted least squares (IRWLS) method. In the recent ten years, with the development of modern statistics and high speed computer as well as MCMC algorithm, Bayesian statistics has been widely uesd in various research area, especically in QTL mapping of diploid traits. However, it has not been used in mapping QTL underlying triploid endosperm traits..In this paper, based on Bayesian statistics and quantitative genetic model of triploid endosperm traits, we first proposed a Bayesian method for mapping QTL underlying endosperm traits, which used the molecular marker genotypes of each plant in segregation population and the single endosperm observation of a few endosperms of each plant as data set to analyze endosperm QTL. The method was implemented via MCMC algorithm.
The process of the method is summarized as follows:(1) Formulate single-QTL model and multiple-QTL model of endosperm traits. (2) Calculate the conditional probabilities of the QTL genotypes by using the molecular marker information. (3) Calculate the conditional posterior probabilities of the QTL genotypes. (4) Sample the QTL genotypes using the posterior probabilities and get the indicator variables of QTL genotypes. (5) Derive the conditional posterior distributions of population mean, additive effect, first dominance effect, second dominance effect, residual variance and the postions of QTL. (6) Sample the conditional posterior samples by using Gibbs sampling and Metropolis-Hastings algorithm. (7) Collect posterior samples and obtain the Bayesian estimates.
By using the molecular marker genotypes of each plant in segregation population and the single endosperm observation of a few endosperms of each plant as data set, we proposed the interval mapping and the composite interval mapping methods for endosperm QTL. Efficiency of the methods is demonstrated via both chromosome level and genome level simulation studies.
ⅠBayesian Statistics-Based Interval Mapping of QTL Controlling Endosperm Traits in Cereals
For chromosome level simulation, the sample size of an F2 segeregating population was set on 200 plants and 20 endosperms of each plant. The QTL heritability was simulated at three levels:5%,10% and 20%, respectively. Each treatment of the simulation experiments was replicated 100 times. Precision and accuracy of estimates for QTL location and effects were measured by means and standard deviations of estimates respectively.
For genome level simulation, a genome containing four chromosomes was simulated. Four QTL with different heritabilities were set at four different chromosomes. The QTL heritability was set at 6.07%,16.77%,23.96% and 13.21%, respectively.
The results showed that (1) The power of each treatment was 100%; (2) Both the effect and position estimates of these QTL were reasonably close to the true value. (3) Higher QTL heritability tended to produce more accurate and precise estimates, whereas lower heritability produced less accurate estimates with large estimation errors, which was in accordance with our general expectations. (4) The genome level simulation showed that the proposed method not only clearly pick up the multiple QTL, but estimate the QTL parameters.
ⅡBayesian Statistics-Based Multiple Interval Mapping of QTL Controlling Endosperm Traits in Cereals
Simulation study was set on 200 F2 plants each with 30 endosperms. A chromosome of length 100 cM covered by eleven evenly spaced markers was simulated. Three QTL affecting endosperm traits were set at 15cM,55cM and 95cM respectively. The population mean was set as 20. The QTL heritability was set at about 5%,10% and 15%. The simulation experiment was replicated 100 times. Precision and accuracy of estimates for QTL location and effects are measured same as above.
The results showed that (1) The proposed Bayesian method had high statistical power and accurate estimates of QTL position, mean and additive effects. For example, even with the heritability of 5%, the statistical power can still reach 100%. (2) The two dominance effects were found slightly biased. This may have two possible reasons. The first reason is that the QTL genotype of F3 endosperms are just infered from the marker genotypes of F2 maternal genome other than from the marker genotypes of F3 endosperm genome. The second reason is that even if the additive and dominance effects had equal sizes, the variation caused by dominance effect just had a limited weight in the total genetic variance.
引文
[1]莫惠栋.种子性状及其遗传效应的鉴别.江苏农学院学报.1990,11(2)：11-15
[2]Mo H. Genetic expression for endosperm traits. In:Weir B S, Eisen E J, Goodman M M, Namkoong G, eds. In Proceedings of the Second International Conference on Quantitative Genetics[C]. Massachusetts:Sinauer Associates, Inc.1988:478-487
[3]莫惠栋.谷类作物胚乳品质性状的遗传研究.中国农业科学.1995,28(2)：1-7
[4]Sood B C, Siddiq E A. A rapid technique for scent determination in rice. Indian Journal of Genetics & Plant Breeding.1978,38:268-271
[5]Tripathi R S, Rao M. Inheritance and linkage relationship of scent in rice. Euphytica.1979, 28(2):319-323
[6]Reddy P R, K S. Inheritance of aroma in rice. Indian Journal of Genetics & Plant Breeding. 1980,40:327-329
[7]黄英金,刘宜柏,饶治祥.香稻品种香味性状的遗传研究.江西农业学报.1995,7(2)：88-93
[8]徐辰武,莫惠栋.胚乳性状的质量-数量遗传分析.江苏农学院学报.1995,16(1)：9-13
[9]Felker F C, Peterson D M, Nelson O E. Anatomy of immature grains of eight maternal effect shrunken endosperm barley mutants. American Journal of Botany.1985,72(2):248-256
[10]Hueros G, Gomez E, Cheikh N, et al. Identification of a promoter sequence from the BETL1 gene cluster able to confer transfer-cell-specific expression in transgenic maize. Plant Physiol. 1999,121(4):1143-1152
[11]Maitz M, Santandrea G, Zhang Z, et al. rgfl, a mutation reducing grain filling in maize through effects on basal endosperm and pedicel development. Plant J.2000,23(1):29-42
[12]Cheng W H, Taliercio E W, Chourey P S. The miniaturel seed locus of maize encodes a cell wall invertase required for normal development of endosperm and maternal cells in the pedicel. Plant Cell.1996,8(6):971-983
[13]Colombo L, Franken J, Van der Krol A R, et al. Downregulation of Ovule-Specific MADS Box Genes from Petunia Results in Maternally Controlled Defects in Seed Development. Plant Cell. 1997,9(5):703-715
[14]Li L, Zhao Y, McCaig B C, et al. The tomato homolog of CORONATINE-INSENSITIVE1 is required for the maternal control of seed maturation, jasmonate-signaled defense responses, and glandular trichome development. Plant Cell.2004,16(1):126-143
[15]Garcia D, Fitz Gerald J N, Berger F. Maternal Control of Integument Cell Elongation and Zygotic Control of Endosperm Growth Are Coordinated to Determine Seed Size in Arabidopsis. Plant Cell.2005,17(1):52-60
[16]Gasser C S, Broadhvest J, Hauser B A. Genetic analysis of ovule development. Annual Review of Plant Physiology and Plant Molecular Biology.1998,49(1):1-24
[17]Baker S C, Robinson-Beers K, Villanueva J M, et al. Interactions Among Genes Regulating Ovule Development in Arabidopsis thaliana. Genetics.1997,145(4):1109-1124
[18]Portereiko M F, Lloyd A, Steffen J G, et al. AGL80 is Required for Central Cell and Endosperm Development in Arabidopsis. Plant Cell.2006,18(8):1862-1872
[19]孟凡荣,倪中福,吴利民等.不同优势小麦正反杂交种子与亲本自交种子发育前期基因表达差异.作物学报.2005,31(1)：119-123
[20]Allen J O. Effect of teosinte cytoplasmic genomes on maize phenotype. Genetics.2005,169(2): 863-880
[21]Rand D M, Haney R A, Fry A J. Cytonuclear coevolution:the genomics of cooperation. Trends in Ecology and Evolution.2004,19(12):645-653
[22]Kermicle J L. Dependence of the R-Mottled Aleurone Phenotype in Maize on Mode of Sexual Transmission. Genetics.1970,66(1):69-85
[23]Kiyosue T, Ohad N, Yadegari R, et al. Control of fertilization-independent endosperm development by the MEDEA polycomb gene in Arabidopsis. Proceedings of the National Academy of Sciences.1999,96(7):4186-4191
[24]Gehring M, Choi Y, Fischer R L. Imprinting and seed development. Plant Cell.2004,16 Suppl: S203-213
[25]莫惠栋.谷类作物胚乳性状遗传控制的鉴别.遗传学报.1995,22(2)：126-132
[26]Zhu J, Weir B S. Analysis of cytoplasmic and maternal effects. Ⅱ. Genetic models for triploid endosperms. Theoretical and Applied Genetics.1994,89:160-166
[27]孟祥勋,王曙明,刘宝泉等.大豆蛋白质含量的种子性状广义遗传模型分析.大豆科学.2001,20(2)：79-83
[28]石春海,何慈信,朱军.稻米碾磨品质性状遗传主效应及其与环境互作的遗传分析.遗传学报.1998,25(1)：46-53
[29]石春海,朱军.稻米营养品质种子效应和母体效应的遗传分析.遗传学报.1995,22(5)：372-379
[30]章清杞,陈健勇,张书标等.巨胚稻胚重与糙米粒形的关系.福建农林大学学报(自然科学版).2006,35(1)：1-5
[31]张光恒,曾大力,郭龙彪等.稻米胚重相关性状QTL分析.作物学报.2005,31(12)：224-228
[32]张忠臣,战秀玲,陈庆山等.大豆油分和蛋白性状的基因定位.大豆科学.2004,32(2)：81-85
[33]郑永战,盖钧镒,卢为国等.大豆脂肪及脂肪酸组分含量的QTL定位.作物学报.2006,32(12)：1823-1830
[34]陈庆山,张忠臣,刘春燕等.大豆主要农艺性状的QTL分析.中国农业科学.2007,40(1)：41-47
[35]Wang Z Y, Wu Z L, et al. Nucleotide sequence of rice waxy gene. Nucleic Acids Research. 1990,18(19):5898
[36]吴长明,孙传清,付秀林等.稻米胶稠度、碱消值与籼粳分化度的QTL及其相互关系的研究.吉林农业科学.2003,28(1)：3-8
[37]黄祖六,谭学林,[ragoonrung S, Vanavichit A.稻米直链淀粉含量基因座位的分子标记定位.作物学报.2000,26(6)：777-782
[38]Gao Z, Zeng D, Cui X, et al. Map-based cloning of the ALK gene, which controls the gelatinization temperature of rice. Science in China Series (Life Sciences).2003,46(6): 661-668
[39]Chen S, Wu J, Yang Y, et al. The fgr gene responsible for rice fragrance was restricted within 69 kb. Plant Science.2006,171(4):505-514
[40]Thomson M J, Tai T H, McClung A M, et al. Mapping quantitative trait loci for yield, yield components and morphological traits in an advanced backcross population between Oryza rufipogon and the Oryza sativa cultivar Jefferson. Theoretical and Applied Genetics.2003, 107(3):479-493
[41]Li J, Thomson M, McCouch S R. Fine mapping of a grain-weight quantitative trait locus in the pericentromeric region of rice chromosome 3. Genetics.2004,168(4):2187-2195
[42]Fan C, Xing Y, Mao H, et al. GS3, a major QTL for grain length and weight and minor QTL for grain width and thickness in rice, encodes a putative transmembrane protein. Theoretical and Applied Genetics.2006,112(6):1164-1171
[43]Song X J, Huang W, Shi M, et al. A QTL for rice grain width and weight encodes a previously unknown RING-type E3 ubiquitin ligase. Nature Genetics.2007,39(5):623-630
[44]Jofuku K D, Omidyar P K, Gee Z, et al. Control of seed mass and seed yield by the floral homeotic gene APETALA2. Proceedings of the National Academy of Sciences.2005,102(8): 3117-3122
[45]Ohto M A, Fischer R L, Goldberg R B, et al. Control of seed mass by APETALA2. Proceedings of the National Academy of Sciences.2005,102(8):3123-3128
[46]Ashikari M, Sakakibara H, Lin S, et al. Cytokinin oxidase regulates rice grain production. Science.2005,309(5735):741-745
[47]Kucera B, Cohn M A, Leubner-Metzger G. Plant hormone interactions during seed dormancy release and germination. Seed Science Research.2005,15(4):281-307
[48]Alonso-Blanco C, Bentsink L, Hanhart C J, et al. Analysis of natural allelic variation at seed dormancy loci of Arabidopsis thaliana. Genetics.2003,164(2):711-729
[49]Clerkx E J, El-Lithy M E, Vierling E, et al. Analysis of natural allelic variation of Arabidopsis seed germination and seed longevity traits between,the accessions Landsberg erecta and Shakdara, using a new recombinant inbred line population. Plant Physiol.2004,135(1): 432-443
[50]Miura K, Lin Y, Yano M, et al. Mapping quantitative trait loci controlling seed longevity in rice (Oryza sativa L.). Theoretical and Applied Genetics.2002,104(6-7):981-986
[51]Wan J M, Jiang L, Tang J Y, et al. Genetic dissection of the seed dormancy trait in cultivated rice (Oryza sativa L.). Plant Science.2006,170:786-792
[52]Gu X Y, Kianian S F, Foley M E. Multiple loci and epistases control genetic variation for seed dormancy in weedy rice (Oryza sativa). Genetics.2004,166(3):1503-1516
[53]Gu X Y, Kianian S F, Foley M E. Isolation of three dormancy QTLs as Mendelian factors in rice. Heredity.2006,96(1):93-99
[54]江玲,曹雅君,王春明等.利用RIL和CSSL群体检测水稻种子休眠性QTL.遗传学报.2003,30(5)：453-458
[55]唐九友,江玲,王春明等.水稻种子休眠性QTL定位及其对干热处理的响应.中国农业科学.2004,37(12)：1791-1796
[56]曹雅君,江玲,王春明等.利用重组自交系群体检测水稻种子休眠性数量性状位点.南京农业大学学报.2003,26(3)：110-112
[57]王松凤,贾育红,江玲等.控制水稻种子休眠和抽穗期的数量基因位点.南京农业大学学报.2006,29(1)：1-6
[58]兰海,李新海,王凤格等.玉米种子休眠性的QTL定位.作物学报.2007,33(9)：1474-1478
[59]Bentsink L, Jowett J, Hanhart C J, et al. Cloning of DOG1, a quantitative trait locus controlling seed dormancy in Arabidopsis. Proceedings of the National Academy of Sciences.2006, 103(45):17042-17047
[60]Liu Y, Koornneef M, Soppe W J. The absence of histone H2B monoubiquitination in the Arabidopsis hub1 (rdo4) mutant reveals a role for chromatin remodeling in seed dormancy. Plant Cell.2007,19(2):433-444
[61]Peeters A J, Blankestijn-De Vries H, Hanhart C J, et al. Characterization of mutants with reduced seed dormancy at two novel rdo loci and a further characterization of rdol and rdo2 in Arabidopsis. Plant Physiology.2002,115(4):604-612
[62]Keurentjes J J, Bentsink L, Alonso-Blanco C, et al. Development of a near-isogenic line population of Arabidopsis thaliana and comparison of mapping power with a recombinant inbred line population. Genetics.2007,175(2):891-905
[63]Glazier A M, Nadeau J H, Aitman T J. Finding genes that underlie complex traits. science.2002, 298(5602):2345-2349
[64]Salvi S, Tuberosa R. To clone or not to clone plant QTLs:present and future challenges. Trends in Plant Science.2005,10(6):297-304
[65]Bai S, Chen L, Yund M A, et al. Mechanisms of plant embryo development. Current Topics in Developmental Biology.2000,50:61-88
[66]Olsen O A, Linnestad C, Nichols S E. Developmental biology of the cereal endosperm. Trends in Plant Science.1999,4(7):253-257
[67]蒋丽,齐兴云,龚化勤等.被子植物胚胎发育的分子调控.植物学通报.2007,24(3)：389-398
[68]汤在祥,徐辰武.复杂性状遗传分析策略和方法研究进展.中国农业科学.2008：48(2)：1-6
[69]徐辰武,何小红,蒯建敏等.谷物胚乳性状数量基因图的构建方法.中国农业科学.2001,34(2)：117-122
[70]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity.2003,90(3):228-235
[71]Cui Y, Casella G, Wu R. Mapping quantitative trait Loci interactions from the maternal and offspring genomes. Genetics.2004,167(2):1017-1026
[72]Cui Y, Wu J, Shi C, et al, Wu R. Modelling epistatic effects of embryo and endosperm QTL on seed quality traits. Genetic Research.2006,87(1):61-71
[73]徐辰武,王伟,胡治球等.基于株平均值的胚乳性状QTL作图的极大似然方法.作物学报.2005,31(10)：1271-1276
[74]Wang X, Hu Z, Wang W, et al. A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples. Genetica.2007:
[75]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits. Chinese Science Bulletin.2005,50(14):1470-1476
[76]Hu Z, Wang X, Xu C. A method for identification of the expression mode and mapping of QTL underlying embryo-specific characters. Journal of Heredity.2006,97(5):473-482
[77]Tibshirani R. Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society B.1996,58:267-288
[78]Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001,96:1348-1360
[79]Peleman J D, van der Voort J R. Breeding by design. Trends in Plant Science.2003,8(7): 330-334
[1]Lopes M A, Larkins B A. Endosperm origin, development, and function. Plant Cell.1993,5(10): 1383-1399
[2]Becraft P W. Cell fate specification in the cereal endosperm. Seminars in Cell and Developmental Biology.2001,12(5):387-394
[3]Olsen O-A, ed Endosperm:developmental and molecular biology. Springer-Verlag, Heidelberg, 2007
[4]Sabelli P A, Larkins B A. The development of endosperm in grasses. Plant Physiology.2009, 149(1):14-26
[5]Friedman W E, Madrid E N, Williams J H. Origin of the fittest and survival of the fittest: relating female gametophyte development to endosperm genetics. International Journal of Plant Sciences.2008,169:79-92
[6]Capitanio R, Getinentta E, Motto M. Grain weight and its components in maize inbred lines. Maydica 1983,ⅩⅩⅧ:365-379
[7]Reddy V M, Daynard T B. Endosperm characteristics associated with rate of grain filling and kernel size in corn. Maydica.1985, ⅩⅩⅧ:339-355
[8]Larkins B A, Dilkes B P, Dante R A, Coelho C M, Woo Y M, Liu Y. Investigating the hows and whys of DNA endoreduplication. Journal of Experimental Botany.2001,52(355):183-192
[9]Friedman W E. Developmental and evolutionary hypotheses for the origin of double fertilization and endosperm. C R Acad Sci Ⅲ.2001,324(6):559-567
[10]Sargant E. Recent work on the results of fertilization in angiosperms. Annals of Botany.1900, 14:689-712
[11]Friedman W E. Double fertilization in ephedra, a nonflowering seed plant:its bearing on the origin of angiosperms. Science.1990,247(4945):951-954
[12]Carmichael J S, Friedman W E. Double fertilization in gnetum gnemon:the relationship between the cell cycle and sexual reproduction. Plant Cell.1995,7(12):1975-1988
[13]Friedman W E, Williams J H. Developmental evolution of the sexual process in ancient flowering plant lineages. Plant Cell.2004,16 Suppl:S119-132
[14]Mo H. Genetic expression for endosperm traits. In:Weir B S, Eisen E J, Goodman M M, et al., eds. In Proceedings of the Second International Conference on Quantitative Genetics. Massachusetts:Sinauer Associates, Inc.1988:478-487
[15]Bogyo T, PLance R C, Chevalier R, Nilan R A. Genetic models for quantitatively inherited endosperm characters. Heredity.1988,60:61-67
[16]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity.2003,90:228-235
[17]Wu R, Ma C X, Gallo-Meagher M, Littell R C, Casella G. Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model. Genetics.2002, 162(2):875-892
[18]Wen Y, Wu W. Interval mapping of quantitative trait loci underlying triploid endosperm traits using F3 seeds. Journal of Genetics and Genomics.2007,34(5):429-436
[19]徐辰武,何小红,蒯建敏,顾世梁.谷物胚乳性状数量基因图的构建方法.中国农业科学.2001,34(2)：117-122
[20]Xu S. Further investigation on the regression method of mapping quantitative trait loci. Heredity.1998,80(3):364-373
[21]Xu S. Iteratively reweighted least squares mapping of quantitative trait loci. Behavior Genetics. 1998,28(5):341-355
[22]Haley C S, Knott S A. A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity.1992,69(4):315-324
[23]Lander E S, Botstein D. Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics.1989,121(1):185-199
[24]Wu R, Lou X Y, Ma C X, Wang X, Larkins B A, Casella G. An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm. Proceedings of the National Academy of Sciences.2002,99(17):11281-11286
[25]Cui Y, Casella G, Wu R. Mapping quantitative trait loci interactions from the maternal and offspring genomes. Genetics.2004,167(2):1017-1026
[26]Cui Y, Wu J, Shi C, Littell R C, Wu R. Modelling epistatic effects of embryo and endosperm QTL on seed quality traits. Genetical Research.2006,87(1):61-71
[27]徐辰武,王伟,胡治球,孙长森.基于株平均值的胚乳性状QTL作图的极大似然方法.作物学报.2005,31(10)：1271-1276
[28]Wang X, Song W, Tang Z, Wang Y, Xu C. Improved genetic mapping of endosperm traits using NCIII and TTC designs. J. Hered.2009 (In press):
[29]李玉玲,董永彬,崔党群,牛素贞,王延召,余永亮.利用三倍体胚乳遗传模型定位爆裂玉米膨爆特性QTL.中国农业科学.2006,39(3)：488-455
[30]温永仙,吴为人.基于随机交配设计的胚乳性状QTL定位方法.科学通报.2006,51(14)：1666-1670
[31]Becraft P W, Stinard P S, McCarty D R. CRINKLY4:A TNFR-like receptor kinase involved in maize epidermal differentiation. Science.1996,273(5280):1406-1409
[32]Gifford M L, Dean S, Ingram G C. The Arabidopsis ACR4 gene plays a role in cell layer organisation during ovule integument and sepal margin development. Development.2003, 130(18):4249-4258
[33]Ma C X, Casella G, Wu R. Functional mapping of quantitative trait loci underlying the character process:a theoretical framework. Genetics.2002,161(4):1751-1762
[34]Wu R, Ma C X, Lin M, Casella G. A general framework for analyzing the genetic architecture of developmental characteristics. Genetics.2004,166(3):1541-1551
[35]Wu R, Lin M. Functional mapping-how to map and study the genetic architecture of complex dynamic traits. Nature Reviews Genetics.2006,7:229-237
[36]Schweizer L, Yerk-Davis G L, Phillips R L, Srienc F, Jones R J. Dynamics of maize endosperm development and DNA endoreduplication. Proceedings of the National Academy of Sciences. 1995,92(15):7070-7074
[37]Birchler J A. Dosage analysis of maize endosperm development. Annual Review of Genetics. 1993,27:181-204
[38]Dilkes B P, Dante R A, Coelho C, Larkins B A. Genetic analyses of endoreduplication in Zea mays endosperm:evidence of sporophytic and zygotic maternal control. Genetics.2002,160(3): 1163-1177
[39]Colombo L, Franken J, Van der Krol A R, Wittich P E, Dons H J, Angenent G C. Downregulation of ovule-specific MADS box genes from petunia results in maternally controlled defects in seed development. Plant Cell.1997,9(5):703-715
[40]Shi C H, Xue J M, Yu Y G, Yang X E, zhu J. Analysis of genetic effects for nutrient quality traits in indica rice. Theoretical and Applied Genetics.1997,92:1099-1102
[41]Zheng X, Wu J G, Lou X Y, Xu H M, Shi C H. The QTL analysis on maternal and endosperm genome and their environmental interactions for characters of cooking quality in rice (Oryza sativa L.). Theoretical and Applied Genetics.2008,116:335-342
[42]Cockerham C, and Weir, B.. Quadratic analyses of reciprocal crosses. Biometrics.1977: 187-203
[43]Foolad M, Jones R. Models to estimate maternally controlled genetic variation in quantitative seed characters. Theoretical and Applied Genetics.1992,83:360-366
[44]Zhu J, Weir B S. Mixed model approaches for genetic analysis of quantitative traits. Advanced topics in biomathematics:Proceedings of the International Conference on Mathematical Biology. Singapore:World Scientific Publ. Co.1998:321-330
[45]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits. Chinese Science Bulletin.2005,50(14):1470-1476
[46]Hu Z, Wang X, Xu C. A method for identification of the expression mode and mapping of QTL underlying embryo-specific characters. Journal of heredity.2006,97(5):473-482
[47]Cui Y, Wu R. Statistical model for characterizing epistatic control of triploid endosperm triggered by maternal and offspring QTLs. Genetical Research.2005,86(01):65-75
[48]Cui Y, Wu R. Mapping genome-genome epistasis:a high-dimensional model. Bioinformatics. 2005,21(10):2447-2455
[49]Johnston S A, den Nijs T P M, Peloquin S J, Hanneman Jr R E. Johnston, S., et al. The significance of genetic balance to endosperm development in interspecific crosses. Theoretical and Applied Genetics.1980(57):5-9
[50]Haig D, Westoby M. Parent-Specific Gene Expression and the Triploid Endosperm. American Naturalist.1989,134:147-155
[51]Vinkenoog R, Bushell C, Spielman M, Adams S, Dickinson H G, Scott R J. Genomic imprinting and endosperm development in flowering plants. Molecular Biotechnology.2003,25(2): 149-184
[52]Khachatourians G G, et al. Transgenic plants and crops. CRC Press,2002
[53]Spencer H G. Effects of genomic imprinting on quantitative traits. Genetica.,2008:DOI: 10.1007/S10709-10008-19300-10708
[54]Cui Y, Lu Q, Cheverud J M, Littell R C, Wu R. Model for mapping imprinted quantitative trait loci in an inbred F2 design. Genomics.2006,87(4):543-551
[55]Cui Y, Cheverud J M, Wu R. A statistical model for dissecting genomic imprinting through genetic mapping. Genetica.2007,130(3):227-239
[56]Cui Y. A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci. Journal of Theoretical Biology.2007,244(1):115-126
[57]Li Y, Coelho C M, Liu T, Wu S, Wu J, Zeng Y, Li Y, Hunter B, Dante R A, Larkins B A, Wu R. A statistical model for estimating maternal-zygotic interactions and parent-of-origin effects of QTLs for seed development. PLoS ONE.2008,3(9):e3131
[58]He X H, Zhang Y M. Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design. Heredity,2008,101:39-47
[1]Bayes,T. R.,An essay towards solving a problem in the doctrine of chances,Phil.Trans.Roy., London, pp.53,370-1763.
[2]Uimari P, Thaller G'and Hoeschele I. The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics,1996,143(4):1831-1842
[3]Uimari P and Hoeschele I. Mapping-linked quantitative trait loci using Bayesian analysis and Markov chain Monte Carlo algorithms. Genetics,1997,146(2):735-743
[4]Xu S. Estimating polygenic effects using markers of the entire genome. Genetics,2003,163(2): 789-801
[5]Satagopan J M, Yandell B S, Newton M A and Osborn T C. A bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. Genetics,1996,144(2):805-816
[6]敖雁,徐辰武.贝叶斯回归分析方法及其在QTL作图中的应用.扬州大学学报(农业与生 命科学版),2005,26(2)：44-49
[7]王亚民,孙长深,汤在祥,胡治球,徐辰武.谷物胚乳性状QTL区间作图的贝叶斯方法.扬州大学学报(农业与生命科学版),2008,29(3)：12-17
[8]茆诗松,贝叶斯统计,中国统计出版社,1999。
[9]张尧庭,陈汉峰,贝叶斯统计推断,科学出版社,1991。
[10]朱慧明,韩玉启,贝叶斯多元统计推断理论,科学出版社,2006。
[11]A.帕普里斯,S.U佩莱,概率、随机变量与随机过程,保铮,冯大政,水鹏朗译,西安交通大学出版社,2004。
[12]Morris H.DeGroot and Mark J.Schervish,概率统计,叶中行,王蓉华,徐晓岭译,人民邮电出版社,2007。
[13]李裕奇,刘赪,王沁,随机过程,国防工业出版社,2008。
[14]Geman S and Geman D. Stochastic relaxation, gibbs distribution, and the Bayesian restoration of images. IEEE Trans. Pattn. Anal. Mach. Intell,1984,6:721-741
[15]Gelfand A E.Smith AFM.1990.Sampling based on approaches to calculating marginal densities.Journal of American Statistical Association,85(2):339-355
[16]苏良军,高等数理统计,北京大学出版社,2007。
[17]Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H and Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys,1953,21:1087-1092
[18]Hastings W K.1970.Monte Carlo sampling methods using Markov Chains and their applications.Biometrika,57(1):72～89
[19]Casella G and George E I. Explaining the Gibbs sampler. American Statistician,1992, 46:167-174
[20]Hastings W K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika,1970,57:97-109
[21]Chib S and Greenberg E. Understanding the Metropolis-Hastings algorithm. American Statistician,1995,49:327-335
[22]Hoeschele I. Mapping quantitative trait loci in outbred pedigrees. Handbook of Statistical Genetics. Balding D, Bishop M, Cannings C(eds), Wiley,2001,599-644
[23]Carlin B P and Louis T A. Bayes and Empirical Bayes methods for data analysis.2nd edition. Chapman & Hall. London, UK,2000
[24]Green P J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika,1995,82:711-732
[25]Sillanpaa M J and Arjas E. Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data. Genetics,1998,148(3):1373-1388
[26]Stephens D A and FischR D. Bayesian analysis of quantitative trait locus data using reservible jump Markov chain Monte Carlo. Biometrics,1998,54:1334-1347
[27]莫惠栋.数量性状遗传基础研究的回顾与思考-后基因组时代数量遗传领域的挑战.扬州大学学报(农业与生命科学版),2003,24(2)：24-31
[28]Zhang M, Montooth K L, Wells M T, Clark A G and Zhang D. Mapping multiple Quantitative Trait Loci by Bayesian classification. Genetics,2005,169(4):2305-2318
[29]Price A H and Courtois B. Mapping QTLs associated with drought resistance in rice:progress, problems and prospects. Plant Growth Reg,1999,29:123-133
[30]Price A H, Cairns J E, Horton P, Jones H G and Griffiths H. Linking drought-resistance mechanisms to drought avoidance in upland rice using a QTL approach:progress and new opportunities to integrate stomatal and mesophyll responses. J Exp Bot,2002,53(371): 989-1004
[31]Sugiyama F, Churchill G A, Higgins D C, Johns C, Makaritsis K P, Gavras H and Paigen B. Concordance of murine quantitative trait loci for salt-induced hypertension with rat and human loci. Genomics,2001,71(1):70-77
[32]Helentjaris T and Burr B. Development and Application of molecular markers to problems in plant genetics. Cold Spring Harbor Press,1989,1-165
[33]Thomas D C and Cortessis V. A Gibbs sampling approach to linkage analysis. Hum Hered, 1992,42(1):63-76
[34]Hoeschele I and Vanranden P. Bayesian analysis of linkage between genetic markers and quantitative trait loci.I.Prior knowledge. Theor Appl Genet,1993a,85:953-960
[35]Hoeschele I and Vanranden P. Bayesian analysis of linkage between genetic markers and quantitative trait loci.Ⅱ.Combining Prior knowledge with experimental evidence. Theor Appl Genet,1993b,85:946-952
[36]Tai J J. Application of Bayesian decision procedure to the inference of genetic linkage. J. Am. Statist. Assoc,1989,84:669-673
[37]Smith A F M and Roberts G O. Bayesian computation via the Gibbs sampler and related Markov Chain Monte Carlo methods. J. Roy. Statist. Soc., Ser. B,1993,55:3-23
[38]Stephens D A and Smith A F. Bayesian inference in multipoint gene mapping. Ann Hum Genet, 1993,57(Pt 1):65-82
[39]Thaller G and Hoeschele I. A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. Ⅰ. Methodology. Theor Appl Genet,1996a,93: 1161-1166
[40]Thaller G and Hoeschele I. A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci:Ⅱ. A Simulation study. Theor Appl Genet,1996b,93: 1,167-1174
[41]Knott S A and Haley C S. Aspects of maximum likelihood methods for the mapping of quantitative trait loci in line crosses. Genet. Res. Camb,1992,60:139-151
[42]Uimari P, Thaller G and Hoeschele I. The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics,1996,143(4):1831-1842
[43]Piepho H P and Gauch H G, Jr. Marker pair selection for mapping quantitative trait loci. Genetics,2001,157(1):433-444
[44]Broman K W and Speed T P. A model selection approach for the identification of quantitative trait loci in experimental crosses. J. R. Stat. Soc. B,2002,64:641-656
[45]Sillanpaa M J and Corander J. Model choice in gene mapping:what and why. Trends Genet, 2002,18(6):301-307
[46]Ball R D. Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion. Genetics,2001,159(3): 1351-1364
[47]Sen S and Churchill G. A statistical framework for quantitative trait mapping. Genetics,2001, 159:371-387
[48]Yi N, George V and Allison D B. Stochastic search variable selection for identifying multiple quantitative trait loci. Genetics,2003,164(3):1129-1138
[49]Stephens D A and Fisch R D. Bayesian analysis of quantitative trait locus data using reversible jump Markov chain Monte Carlo. Technical report. (available at http://www.ma.ic.ac.uk/ statistics/techrep.html),1996
[50]Sillanpaa M J and Arjas E. Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics,1999,151(4):1605-1619
[51]Vogl C and Xu S. QTL analysis in arbitrary pedigrees with incomplete marker information. Heredity,2002,89(5):339-345
[52]Yi N and Xu S. Linkage analysis of quantitative trait loci in multiple line crosses. Genetica, 2002,114(3):217-230
[53]Meuwissen T H, Hayes B J and Goddard M E. Prediction of total genetic value using genome-wide dense marker maps. Genetics,2001,157(4):1819-1829
[54]Heath S C. Markov chain Monte Carlo segregation and linkage analysis for oligogenic models. Am J Hum Genet,1997,61(3):748-760
[55]Xu S and Yi N. Mixed model analysis of quantitative trait loci. Proc Natl Acad Sci,2000, 97(26):14542-14547
[56]Yi N and Xu S. Bayesian mapping of quantitative trait loci for complex binary traits. Genetics, 2000,155(1391-1403
[57]Yi N and Xu S. Bayesian mapping of quantitative trait loci under complicated mating designs. Genetics,2001,157(4):1759-1771
[58]Kass R and Raftery A. Bayes factors. J. Am. Stat. Assoc,1995,90:773-795
[59]George E I and McCulloch R E. Variable selection via Gibbs sampling. J. Am. Stat. Assoc, 1993,88:881-889
[60]Min Z, Kristi L and Montooth. Mapping multiple quantitative trait loci by Bayesian classification. Genetics,2005,169:2305-2318
[61]Yi N. A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics,2004,167(2):967-975
[62]Sauerbrei W. The use of resampling methods to simplify regression models in medical statistics. Appl Stat,1999,48:313-329
[63]Bink M, Uimari P, Sillanpaa J, Janss G and Jansen C. Multiple QTL mapping in related plant populations via a pedigree-analysis approach. Theor Appl Genet,2002,104(5):751-762
[64]Hurme P, Sillanpaa M J, Arjas E, Repo T and Savolainen O. Genetic basis of climatic adaptation in scots pine by bayesian quantitative trait locus analysis. Genetics,2000,156(3): 1309-1322
[65]Hua J, Xing Y, Wu W, Xu C, Sun X, Yu S and Zhang Q. Single-locus heterotic effects and dominance by dominance interactions can adequately explain the genetic basis of heterosis in an elite rice hybrid. Proc Natl Acad Sci,2003,100(5):2574-2579
[66]Carlborg O and Haley C S. Epistasis:too often neglected in complex trait studies? Nat Rev Genet,2004,5(8):618-625
[67]Segre D, Deluna A, Church G M and Kishony R. Modular epistasis in yeast metabolism. Nat Genet,2005,37(1):77-83
[68]Yi N and Xu S. Mapping quantitative trait loci with epistatic effects. Genet Res,2002,79(2): 185-198
[69]Yi N, Diament A, Chiu S, Fisler J and Warden C. Characterization of epistasis influencing complex spontaneous obesity in the BSB model. Genetics,2004a,167:399-409
[70]Yi N, Diament A, Chiu S, Fisler J and Warden C. Epistatic interaction between chromosomes 7 and 3 influences hepatic lipase activity in BSB mice. Journal of Lipid Research,2004b, 45:2063-2070
[71]Yi N, Brian S, Gary A, Churchill, David B and Allison. Bayesian model selection for genome-wide epistatic QTL analysis. Genetics,2005,104
[72]Wang H, Zhang Y M, Li X, Masinde G L, Mohan S, Baylink D J and Xu S. Bayesian shrinkage estimation of quantitative trait loci parameters. Genetics,2005,170(1):465-480
[73]Zhang Y M and Xu S. Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny. Genetics,2004,166(4):1981-1993
[74]Wu R and Lin M. Functional mapping-how to map and study the genetic architecture of dynamic complex traits. Nat Rev Genet,2006,7(3):229-237
[75]Zhang Y M and Xu S. Advanced statistical methods for detecting multiple quantitative trait loci. Recent Research Developments in Genetics & Breeding,2005,2:1-23
[76]Zhang Y M and Xu S. A penalized maximum likelihood method for estimating epistatic effects of QTL. Heredity,2005,95(1):96-104
[1]莫惠栋.谷类作物胚乳品质性状的遗传研究.中国农业科学.1995,28(2)：1-7.
[2]徐辰武,何小红,蒯建敏,等.谷物胚乳性状数量基因图的构建方法.中国农业科学,2001，34(2)：117-122.
[3]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity.2003,90(3):228-235.
[4]Wu R, Lou X Y, Ma C X, et al. An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm. Proceedings of the National Academy of Sciences.2002,99(17):11281-11286.
[5]Cui Y, Casella G, Wu R. Mapping quantitative trait loci interactions from the maternal and offspring genomes. Genetics,2004,167(2):1017-1026.
[6]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits Chinese Science Bulletin,2005,50(14):1470-1476.
[7]徐辰武,王伟,胡治球,孙长森.基于株平均值的胚乳性状QTL作图的极大似然方法作物学报.2005,31(10)：1271-1276.
[8]Wang X, Hu Z, Wang W, et al. A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples. Genetica,2008,132(1):59-70.
[9]Yi N, Yandell B S, Churchill G A, et al. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics.2005,170(3):1333-1344.
[10]敖雁,徐辰武.贝叶斯回归分析方法及其QTL作图中的应用.扬州大学学报：农业与生命科学版,2005,26(2)：44-49.
[11]莫惠栋.胚乳性状的遗传模型和世代平均数.遗传学报.1989,16(2)：111-117.
[12]Chib S, Greenberg E. Understanding the metropolis-hastings algorithm. The Amer Statistician. 1995,49(4):327-335.
[13]王伟,胡治球,孙长森,徐辰武.基于单粒观察值的胚乳性状QTL图的构建方法.作物学报.2005,31(8)：989-994
[14]Cui Y, Wu J, Shi C, Littell R C, Wu R. Modelling epistatic effects of embryo and endosperm QTL on seed quality traits. Genet Res.2006,87(1):61-71.
[15]李玉玲,王延召,董永彬.利用三倍体胚乳遗传模型定位爆裂玉米子粒蛋白含量QTL玉米科学,2006,14(6)：13-16.
[16]Jansen J, de Jong A G, van Ooijen J W. Constructing dense genetic linkage maps. Theor Appl Gnent.2001,102(7):1113-1122.
[17]Smith A, Roberts G. Bayesian computation via the gibbs sampler and related markov chain monte carlo methods. J Royal Stat Soc(Series B),1993,55(1):3-24.
[18]Garcia D, Fitz Gerald J N, Berger F. Maternal control of integument cell elongation and zygotic control of endosperm growth are coordinated to determine seed size in arabidopsis. Plant Cell.2005,17(1):52-60.
[19]Li L, Zhao Y, McCaig B C, Wingerd B A, Wang J, Whalon M E, Pichersky E, Howe G A. The tomato homolog of CORONATINE-INSENSITIVE1 is required for the maternal control of seed maturation, jasmonate-signaled defense responses, and glandular trichome development. Plant Cell,2004,16(1):126-143
[1]莫惠栋.谷类作物胚乳品质性状的遗传研究.中国农业科学,1995,28(2)：1-7
[2]Mo H. Genetic expression for endosperm traits. In:Weir B S, Eisen E J, Goodman M M, et al., eds. In Proceedings of the Second International Conference on Quantitative Genetics. Massachusetts:Sinauer Associates, Inc.1988:478-487
[3]徐辰武,何小红,蒯建敏,顾世梁.谷物胚乳性状数量基因图的构建方法.中国农业科学,2001,34(2)：117-122
[4]Wu R, Lou X Y, Ma C X, Wang X, Larkins B A, Casella G. An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm. Proceedings of the National Academy of Sciences,2002,99:11281-11286
[5]Wu R, Ma C X, Gallo-Meagher M, Littell R C, Casella G. Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model. Genetics.2002, 162(2):875-892
[6]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity,2003,90:228-235
[7]Kao C H. Multiple-interval mapping for quantitative trait loci controlling endosperm traits. Genetics.2004,167(4):1987-2002
[8]Cui Y, Casella G, Wu R. Mapping quantitative trait loci interactions from the maternal and offspring genomes. Genetics.2004,167(2):1017-1026
[9]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits. Chinese Science Bulletion.2005,50(14):1470-1476
[10]Wen Y X, Wu W R. Methods for mapping QTLs underlying endosperm traits based on random hybridization design. Chinese Science Bulletion.2006,51(16):1976-1981
[11]王学枫,汤在祥,王亚民,宋雯,徐辰武.基于NCⅢ和TTC设计的胚乳性状QTL区间作图方法.作物学报,2008,34(10)：1734-1743
[12]He X H, Zhang Y M. Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design. Heredity,2008,101: 39-47
[13]Wang H, Zhang Y M, Li X, Masinde G L, Mohan S, Baylink D J, Xu S. Bayesian shrinkage estimation of quantitative trait loci parameters. Genetics,2005,170:465-480
[14]Yi N. A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics.2004,167(2):967-975
[15]Xu S. Estimating polygenic effects using markers of the entire genome. Genetics,2003,163: 789-801
[16]Yi N, Yandell B S, Churchill G A, Allison D B, Eisen E J, Pomp D. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics.2005,170(3):1333-1344
[17]王亚民,孙长森,汤在祥,胡治球,徐辰武.谷物胚乳性状QTL区间作图的贝叶斯方法,扬州大学学报(农业与生命科学版)，2008：29(4)：12-17
[18]Jiang C, Zeng Z B. Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines. Genetica,1997,101:47-58
[19]Xu S, Yi N. Mixed model analysis of quantitative trait loci. Proceedings of the National Academy of Sciences.2000,97(26):14542-14547
[20]王伟,胡治球,孙长森,徐辰武.基于单粒观察值的胚乳性状QTL图的构建方法.作物学报,2005,31(8)：989-994
[21]徐辰武,王伟,胡治球,孙长森.基于株平均值的胚乳性状QTL作图的极大似然方法.作物学报,2005,31(10)：1271-1276
[22]Wen Y, Wu W. Interval mapping of quantitative trait loci underlying triploid endosperm traits using F3 seeds. Journal of Genetics & Genomics,2007,34:429-436
[23]Wen Y, Wu W. Experimental designs and statistical methods for mapping quantitative trait loci underlying triploid endosperm traits without maternal genetic variation. Journal of Hered, 2008,99:546-551
[2]Mo H. Genetic expression for endosperm traits. In:Weir B S, Eisen E J, Goodman M M, Namkoong G, eds. In Proceedings of the Second International Conference on Quantitative Genetics[C]. Massachusetts:Sinauer Associates, Inc.1988:478-487
[3]莫惠栋.谷类作物胚乳品质性状的遗传研究.中国农业科学.1995,28(2)：1-7
[4]Sood B C, Siddiq E A. A rapid technique for scent determination in rice. Indian Journal of Genetics & Plant Breeding.1978,38:268-271
[5]Tripathi R S, Rao M. Inheritance and linkage relationship of scent in rice. Euphytica.1979, 28(2):319-323
[6]Reddy P R, K S. Inheritance of aroma in rice. Indian Journal of Genetics & Plant Breeding. 1980,40:327-329
[7]黄英金,刘宜柏,饶治祥.香稻品种香味性状的遗传研究.江西农业学报.1995,7(2)：88-93
[8]徐辰武,莫惠栋.胚乳性状的质量-数量遗传分析.江苏农学院学报.1995,16(1)：9-13
[9]Felker F C, Peterson D M, Nelson O E. Anatomy of immature grains of eight maternal effect shrunken endosperm barley mutants. American Journal of Botany.1985,72(2):248-256
[10]Hueros G, Gomez E, Cheikh N, et al. Identification of a promoter sequence from the BETL1 gene cluster able to confer transfer-cell-specific expression in transgenic maize. Plant Physiol. 1999,121(4):1143-1152
[11]Maitz M, Santandrea G, Zhang Z, et al. rgfl, a mutation reducing grain filling in maize through effects on basal endosperm and pedicel development. Plant J.2000,23(1):29-42
[12]Cheng W H, Taliercio E W, Chourey P S. The miniaturel seed locus of maize encodes a cell wall invertase required for normal development of endosperm and maternal cells in the pedicel. Plant Cell.1996,8(6):971-983
[13]Colombo L, Franken J, Van der Krol A R, et al. Downregulation of Ovule-Specific MADS Box Genes from Petunia Results in Maternally Controlled Defects in Seed Development. Plant Cell. 1997,9(5):703-715
[14]Li L, Zhao Y, McCaig B C, et al. The tomato homolog of CORONATINE-INSENSITIVE1 is required for the maternal control of seed maturation, jasmonate-signaled defense responses, and glandular trichome development. Plant Cell.2004,16(1):126-143
[15]Garcia D, Fitz Gerald J N, Berger F. Maternal Control of Integument Cell Elongation and Zygotic Control of Endosperm Growth Are Coordinated to Determine Seed Size in Arabidopsis. Plant Cell.2005,17(1):52-60
[16]Gasser C S, Broadhvest J, Hauser B A. Genetic analysis of ovule development. Annual Review of Plant Physiology and Plant Molecular Biology.1998,49(1):1-24
[17]Baker S C, Robinson-Beers K, Villanueva J M, et al. Interactions Among Genes Regulating Ovule Development in Arabidopsis thaliana. Genetics.1997,145(4):1109-1124
[18]Portereiko M F, Lloyd A, Steffen J G, et al. AGL80 is Required for Central Cell and Endosperm Development in Arabidopsis. Plant Cell.2006,18(8):1862-1872
[19]孟凡荣,倪中福,吴利民等.不同优势小麦正反杂交种子与亲本自交种子发育前期基因表达差异.作物学报.2005,31(1)：119-123
[20]Allen J O. Effect of teosinte cytoplasmic genomes on maize phenotype. Genetics.2005,169(2): 863-880
[21]Rand D M, Haney R A, Fry A J. Cytonuclear coevolution:the genomics of cooperation. Trends in Ecology and Evolution.2004,19(12):645-653
[22]Kermicle J L. Dependence of the R-Mottled Aleurone Phenotype in Maize on Mode of Sexual Transmission. Genetics.1970,66(1):69-85
[23]Kiyosue T, Ohad N, Yadegari R, et al. Control of fertilization-independent endosperm development by the MEDEA polycomb gene in Arabidopsis. Proceedings of the National Academy of Sciences.1999,96(7):4186-4191
[24]Gehring M, Choi Y, Fischer R L. Imprinting and seed development. Plant Cell.2004,16 Suppl: S203-213
[25]莫惠栋.谷类作物胚乳性状遗传控制的鉴别.遗传学报.1995,22(2)：126-132
[26]Zhu J, Weir B S. Analysis of cytoplasmic and maternal effects. Ⅱ. Genetic models for triploid endosperms. Theoretical and Applied Genetics.1994,89:160-166
[27]孟祥勋,王曙明,刘宝泉等.大豆蛋白质含量的种子性状广义遗传模型分析.大豆科学.2001,20(2)：79-83
[28]石春海,何慈信,朱军.稻米碾磨品质性状遗传主效应及其与环境互作的遗传分析.遗传学报.1998,25(1)：46-53
[29]石春海,朱军.稻米营养品质种子效应和母体效应的遗传分析.遗传学报.1995,22(5)：372-379
[30]章清杞,陈健勇,张书标等.巨胚稻胚重与糙米粒形的关系.福建农林大学学报(自然科学版).2006,35(1)：1-5
[31]张光恒,曾大力,郭龙彪等.稻米胚重相关性状QTL分析.作物学报.2005,31(12)：224-228
[32]张忠臣,战秀玲,陈庆山等.大豆油分和蛋白性状的基因定位.大豆科学.2004,32(2)：81-85
[33]郑永战,盖钧镒,卢为国等.大豆脂肪及脂肪酸组分含量的QTL定位.作物学报.2006,32(12)：1823-1830
[34]陈庆山,张忠臣,刘春燕等.大豆主要农艺性状的QTL分析.中国农业科学.2007,40(1)：41-47
[35]Wang Z Y, Wu Z L, et al. Nucleotide sequence of rice waxy gene. Nucleic Acids Research. 1990,18(19):5898
[36]吴长明,孙传清,付秀林等.稻米胶稠度、碱消值与籼粳分化度的QTL及其相互关系的研究.吉林农业科学.2003,28(1)：3-8
[37]黄祖六,谭学林,[ragoonrung S, Vanavichit A.稻米直链淀粉含量基因座位的分子标记定位.作物学报.2000,26(6)：777-782
[38]Gao Z, Zeng D, Cui X, et al. Map-based cloning of the ALK gene, which controls the gelatinization temperature of rice. Science in China Series (Life Sciences).2003,46(6): 661-668
[39]Chen S, Wu J, Yang Y, et al. The fgr gene responsible for rice fragrance was restricted within 69 kb. Plant Science.2006,171(4):505-514
[40]Thomson M J, Tai T H, McClung A M, et al. Mapping quantitative trait loci for yield, yield components and morphological traits in an advanced backcross population between Oryza rufipogon and the Oryza sativa cultivar Jefferson. Theoretical and Applied Genetics.2003, 107(3):479-493
[41]Li J, Thomson M, McCouch S R. Fine mapping of a grain-weight quantitative trait locus in the pericentromeric region of rice chromosome 3. Genetics.2004,168(4):2187-2195
[42]Fan C, Xing Y, Mao H, et al. GS3, a major QTL for grain length and weight and minor QTL for grain width and thickness in rice, encodes a putative transmembrane protein. Theoretical and Applied Genetics.2006,112(6):1164-1171
[43]Song X J, Huang W, Shi M, et al. A QTL for rice grain width and weight encodes a previously unknown RING-type E3 ubiquitin ligase. Nature Genetics.2007,39(5):623-630
[44]Jofuku K D, Omidyar P K, Gee Z, et al. Control of seed mass and seed yield by the floral homeotic gene APETALA2. Proceedings of the National Academy of Sciences.2005,102(8): 3117-3122
[45]Ohto M A, Fischer R L, Goldberg R B, et al. Control of seed mass by APETALA2. Proceedings of the National Academy of Sciences.2005,102(8):3123-3128
[46]Ashikari M, Sakakibara H, Lin S, et al. Cytokinin oxidase regulates rice grain production. Science.2005,309(5735):741-745
[47]Kucera B, Cohn M A, Leubner-Metzger G. Plant hormone interactions during seed dormancy release and germination. Seed Science Research.2005,15(4):281-307
[48]Alonso-Blanco C, Bentsink L, Hanhart C J, et al. Analysis of natural allelic variation at seed dormancy loci of Arabidopsis thaliana. Genetics.2003,164(2):711-729
[49]Clerkx E J, El-Lithy M E, Vierling E, et al. Analysis of natural allelic variation of Arabidopsis seed germination and seed longevity traits between,the accessions Landsberg erecta and Shakdara, using a new recombinant inbred line population. Plant Physiol.2004,135(1): 432-443
[50]Miura K, Lin Y, Yano M, et al. Mapping quantitative trait loci controlling seed longevity in rice (Oryza sativa L.). Theoretical and Applied Genetics.2002,104(6-7):981-986
[51]Wan J M, Jiang L, Tang J Y, et al. Genetic dissection of the seed dormancy trait in cultivated rice (Oryza sativa L.). Plant Science.2006,170:786-792
[52]Gu X Y, Kianian S F, Foley M E. Multiple loci and epistases control genetic variation for seed dormancy in weedy rice (Oryza sativa). Genetics.2004,166(3):1503-1516
[53]Gu X Y, Kianian S F, Foley M E. Isolation of three dormancy QTLs as Mendelian factors in rice. Heredity.2006,96(1):93-99
[54]江玲,曹雅君,王春明等.利用RIL和CSSL群体检测水稻种子休眠性QTL.遗传学报.2003,30(5)：453-458
[55]唐九友,江玲,王春明等.水稻种子休眠性QTL定位及其对干热处理的响应.中国农业科学.2004,37(12)：1791-1796
[56]曹雅君,江玲,王春明等.利用重组自交系群体检测水稻种子休眠性数量性状位点.南京农业大学学报.2003,26(3)：110-112
[57]王松凤,贾育红,江玲等.控制水稻种子休眠和抽穗期的数量基因位点.南京农业大学学报.2006,29(1)：1-6
[58]兰海,李新海,王凤格等.玉米种子休眠性的QTL定位.作物学报.2007,33(9)：1474-1478
[59]Bentsink L, Jowett J, Hanhart C J, et al. Cloning of DOG1, a quantitative trait locus controlling seed dormancy in Arabidopsis. Proceedings of the National Academy of Sciences.2006, 103(45):17042-17047
[60]Liu Y, Koornneef M, Soppe W J. The absence of histone H2B monoubiquitination in the Arabidopsis hub1 (rdo4) mutant reveals a role for chromatin remodeling in seed dormancy. Plant Cell.2007,19(2):433-444
[61]Peeters A J, Blankestijn-De Vries H, Hanhart C J, et al. Characterization of mutants with reduced seed dormancy at two novel rdo loci and a further characterization of rdol and rdo2 in Arabidopsis. Plant Physiology.2002,115(4):604-612
[62]Keurentjes J J, Bentsink L, Alonso-Blanco C, et al. Development of a near-isogenic line population of Arabidopsis thaliana and comparison of mapping power with a recombinant inbred line population. Genetics.2007,175(2):891-905
[63]Glazier A M, Nadeau J H, Aitman T J. Finding genes that underlie complex traits. science.2002, 298(5602):2345-2349
[64]Salvi S, Tuberosa R. To clone or not to clone plant QTLs:present and future challenges. Trends in Plant Science.2005,10(6):297-304
[65]Bai S, Chen L, Yund M A, et al. Mechanisms of plant embryo development. Current Topics in Developmental Biology.2000,50:61-88
[66]Olsen O A, Linnestad C, Nichols S E. Developmental biology of the cereal endosperm. Trends in Plant Science.1999,4(7):253-257
[67]蒋丽,齐兴云,龚化勤等.被子植物胚胎发育的分子调控.植物学通报.2007,24(3)：389-398
[68]汤在祥,徐辰武.复杂性状遗传分析策略和方法研究进展.中国农业科学.2008：48(2)：1-6
[69]徐辰武,何小红,蒯建敏等.谷物胚乳性状数量基因图的构建方法.中国农业科学.2001,34(2)：117-122
[70]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity.2003,90(3):228-235
[71]Cui Y, Casella G, Wu R. Mapping quantitative trait Loci interactions from the maternal and offspring genomes. Genetics.2004,167(2):1017-1026
[72]Cui Y, Wu J, Shi C, et al, Wu R. Modelling epistatic effects of embryo and endosperm QTL on seed quality traits. Genetic Research.2006,87(1):61-71
[73]徐辰武,王伟,胡治球等.基于株平均值的胚乳性状QTL作图的极大似然方法.作物学报.2005,31(10)：1271-1276
[74]Wang X, Hu Z, Wang W, et al. A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples. Genetica.2007:
[75]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits. Chinese Science Bulletin.2005,50(14):1470-1476
[76]Hu Z, Wang X, Xu C. A method for identification of the expression mode and mapping of QTL underlying embryo-specific characters. Journal of Heredity.2006,97(5):473-482
[77]Tibshirani R. Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society B.1996,58:267-288
[78]Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001,96:1348-1360
[79]Peleman J D, van der Voort J R. Breeding by design. Trends in Plant Science.2003,8(7): 330-334
[1]Lopes M A, Larkins B A. Endosperm origin, development, and function. Plant Cell.1993,5(10): 1383-1399
[2]Becraft P W. Cell fate specification in the cereal endosperm. Seminars in Cell and Developmental Biology.2001,12(5):387-394
[3]Olsen O-A, ed Endosperm:developmental and molecular biology. Springer-Verlag, Heidelberg, 2007
[4]Sabelli P A, Larkins B A. The development of endosperm in grasses. Plant Physiology.2009, 149(1):14-26
[5]Friedman W E, Madrid E N, Williams J H. Origin of the fittest and survival of the fittest: relating female gametophyte development to endosperm genetics. International Journal of Plant Sciences.2008,169:79-92
[6]Capitanio R, Getinentta E, Motto M. Grain weight and its components in maize inbred lines. Maydica 1983,ⅩⅩⅧ:365-379
[7]Reddy V M, Daynard T B. Endosperm characteristics associated with rate of grain filling and kernel size in corn. Maydica.1985, ⅩⅩⅧ:339-355
[8]Larkins B A, Dilkes B P, Dante R A, Coelho C M, Woo Y M, Liu Y. Investigating the hows and whys of DNA endoreduplication. Journal of Experimental Botany.2001,52(355):183-192
[9]Friedman W E. Developmental and evolutionary hypotheses for the origin of double fertilization and endosperm. C R Acad Sci Ⅲ.2001,324(6):559-567
[10]Sargant E. Recent work on the results of fertilization in angiosperms. Annals of Botany.1900, 14:689-712
[11]Friedman W E. Double fertilization in ephedra, a nonflowering seed plant:its bearing on the origin of angiosperms. Science.1990,247(4945):951-954
[12]Carmichael J S, Friedman W E. Double fertilization in gnetum gnemon:the relationship between the cell cycle and sexual reproduction. Plant Cell.1995,7(12):1975-1988
[13]Friedman W E, Williams J H. Developmental evolution of the sexual process in ancient flowering plant lineages. Plant Cell.2004,16 Suppl:S119-132
[14]Mo H. Genetic expression for endosperm traits. In:Weir B S, Eisen E J, Goodman M M, et al., eds. In Proceedings of the Second International Conference on Quantitative Genetics. Massachusetts:Sinauer Associates, Inc.1988:478-487
[15]Bogyo T, PLance R C, Chevalier R, Nilan R A. Genetic models for quantitatively inherited endosperm characters. Heredity.1988,60:61-67
[16]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity.2003,90:228-235
[17]Wu R, Ma C X, Gallo-Meagher M, Littell R C, Casella G. Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model. Genetics.2002, 162(2):875-892
[18]Wen Y, Wu W. Interval mapping of quantitative trait loci underlying triploid endosperm traits using F3 seeds. Journal of Genetics and Genomics.2007,34(5):429-436
[19]徐辰武,何小红,蒯建敏,顾世梁.谷物胚乳性状数量基因图的构建方法.中国农业科学.2001,34(2)：117-122
[20]Xu S. Further investigation on the regression method of mapping quantitative trait loci. Heredity.1998,80(3):364-373
[21]Xu S. Iteratively reweighted least squares mapping of quantitative trait loci. Behavior Genetics. 1998,28(5):341-355
[22]Haley C S, Knott S A. A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity.1992,69(4):315-324
[23]Lander E S, Botstein D. Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics.1989,121(1):185-199
[24]Wu R, Lou X Y, Ma C X, Wang X, Larkins B A, Casella G. An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm. Proceedings of the National Academy of Sciences.2002,99(17):11281-11286
[25]Cui Y, Casella G, Wu R. Mapping quantitative trait loci interactions from the maternal and offspring genomes. Genetics.2004,167(2):1017-1026
[26]Cui Y, Wu J, Shi C, Littell R C, Wu R. Modelling epistatic effects of embryo and endosperm QTL on seed quality traits. Genetical Research.2006,87(1):61-71
[27]徐辰武,王伟,胡治球,孙长森.基于株平均值的胚乳性状QTL作图的极大似然方法.作物学报.2005,31(10)：1271-1276
[28]Wang X, Song W, Tang Z, Wang Y, Xu C. Improved genetic mapping of endosperm traits using NCIII and TTC designs. J. Hered.2009 (In press):
[29]李玉玲,董永彬,崔党群,牛素贞,王延召,余永亮.利用三倍体胚乳遗传模型定位爆裂玉米膨爆特性QTL.中国农业科学.2006,39(3)：488-455
[30]温永仙,吴为人.基于随机交配设计的胚乳性状QTL定位方法.科学通报.2006,51(14)：1666-1670
[31]Becraft P W, Stinard P S, McCarty D R. CRINKLY4:A TNFR-like receptor kinase involved in maize epidermal differentiation. Science.1996,273(5280):1406-1409
[32]Gifford M L, Dean S, Ingram G C. The Arabidopsis ACR4 gene plays a role in cell layer organisation during ovule integument and sepal margin development. Development.2003, 130(18):4249-4258
[33]Ma C X, Casella G, Wu R. Functional mapping of quantitative trait loci underlying the character process:a theoretical framework. Genetics.2002,161(4):1751-1762
[34]Wu R, Ma C X, Lin M, Casella G. A general framework for analyzing the genetic architecture of developmental characteristics. Genetics.2004,166(3):1541-1551
[35]Wu R, Lin M. Functional mapping-how to map and study the genetic architecture of complex dynamic traits. Nature Reviews Genetics.2006,7:229-237
[36]Schweizer L, Yerk-Davis G L, Phillips R L, Srienc F, Jones R J. Dynamics of maize endosperm development and DNA endoreduplication. Proceedings of the National Academy of Sciences. 1995,92(15):7070-7074
[37]Birchler J A. Dosage analysis of maize endosperm development. Annual Review of Genetics. 1993,27:181-204
[38]Dilkes B P, Dante R A, Coelho C, Larkins B A. Genetic analyses of endoreduplication in Zea mays endosperm:evidence of sporophytic and zygotic maternal control. Genetics.2002,160(3): 1163-1177
[39]Colombo L, Franken J, Van der Krol A R, Wittich P E, Dons H J, Angenent G C. Downregulation of ovule-specific MADS box genes from petunia results in maternally controlled defects in seed development. Plant Cell.1997,9(5):703-715
[40]Shi C H, Xue J M, Yu Y G, Yang X E, zhu J. Analysis of genetic effects for nutrient quality traits in indica rice. Theoretical and Applied Genetics.1997,92:1099-1102
[41]Zheng X, Wu J G, Lou X Y, Xu H M, Shi C H. The QTL analysis on maternal and endosperm genome and their environmental interactions for characters of cooking quality in rice (Oryza sativa L.). Theoretical and Applied Genetics.2008,116:335-342
[42]Cockerham C, and Weir, B.. Quadratic analyses of reciprocal crosses. Biometrics.1977: 187-203
[43]Foolad M, Jones R. Models to estimate maternally controlled genetic variation in quantitative seed characters. Theoretical and Applied Genetics.1992,83:360-366
[44]Zhu J, Weir B S. Mixed model approaches for genetic analysis of quantitative traits. Advanced topics in biomathematics:Proceedings of the International Conference on Mathematical Biology. Singapore:World Scientific Publ. Co.1998:321-330
[45]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits. Chinese Science Bulletin.2005,50(14):1470-1476
[46]Hu Z, Wang X, Xu C. A method for identification of the expression mode and mapping of QTL underlying embryo-specific characters. Journal of heredity.2006,97(5):473-482
[47]Cui Y, Wu R. Statistical model for characterizing epistatic control of triploid endosperm triggered by maternal and offspring QTLs. Genetical Research.2005,86(01):65-75
[48]Cui Y, Wu R. Mapping genome-genome epistasis:a high-dimensional model. Bioinformatics. 2005,21(10):2447-2455
[49]Johnston S A, den Nijs T P M, Peloquin S J, Hanneman Jr R E. Johnston, S., et al. The significance of genetic balance to endosperm development in interspecific crosses. Theoretical and Applied Genetics.1980(57):5-9
[50]Haig D, Westoby M. Parent-Specific Gene Expression and the Triploid Endosperm. American Naturalist.1989,134:147-155
[51]Vinkenoog R, Bushell C, Spielman M, Adams S, Dickinson H G, Scott R J. Genomic imprinting and endosperm development in flowering plants. Molecular Biotechnology.2003,25(2): 149-184
[52]Khachatourians G G, et al. Transgenic plants and crops. CRC Press,2002
[53]Spencer H G. Effects of genomic imprinting on quantitative traits. Genetica.,2008:DOI: 10.1007/S10709-10008-19300-10708
[54]Cui Y, Lu Q, Cheverud J M, Littell R C, Wu R. Model for mapping imprinted quantitative trait loci in an inbred F2 design. Genomics.2006,87(4):543-551
[55]Cui Y, Cheverud J M, Wu R. A statistical model for dissecting genomic imprinting through genetic mapping. Genetica.2007,130(3):227-239
[56]Cui Y. A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci. Journal of Theoretical Biology.2007,244(1):115-126
[57]Li Y, Coelho C M, Liu T, Wu S, Wu J, Zeng Y, Li Y, Hunter B, Dante R A, Larkins B A, Wu R. A statistical model for estimating maternal-zygotic interactions and parent-of-origin effects of QTLs for seed development. PLoS ONE.2008,3(9):e3131
[58]He X H, Zhang Y M. Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design. Heredity,2008,101:39-47
[1]Bayes,T. R.,An essay towards solving a problem in the doctrine of chances,Phil.Trans.Roy., London, pp.53,370-1763.
[2]Uimari P, Thaller G'and Hoeschele I. The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics,1996,143(4):1831-1842
[3]Uimari P and Hoeschele I. Mapping-linked quantitative trait loci using Bayesian analysis and Markov chain Monte Carlo algorithms. Genetics,1997,146(2):735-743
[4]Xu S. Estimating polygenic effects using markers of the entire genome. Genetics,2003,163(2): 789-801
[5]Satagopan J M, Yandell B S, Newton M A and Osborn T C. A bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. Genetics,1996,144(2):805-816
[6]敖雁,徐辰武.贝叶斯回归分析方法及其在QTL作图中的应用.扬州大学学报(农业与生 命科学版),2005,26(2)：44-49
[7]王亚民,孙长深,汤在祥,胡治球,徐辰武.谷物胚乳性状QTL区间作图的贝叶斯方法.扬州大学学报(农业与生命科学版),2008,29(3)：12-17
[8]茆诗松,贝叶斯统计,中国统计出版社,1999。
[9]张尧庭,陈汉峰,贝叶斯统计推断,科学出版社,1991。
[10]朱慧明,韩玉启,贝叶斯多元统计推断理论,科学出版社,2006。
[11]A.帕普里斯,S.U佩莱,概率、随机变量与随机过程,保铮,冯大政,水鹏朗译,西安交通大学出版社,2004。
[12]Morris H.DeGroot and Mark J.Schervish,概率统计,叶中行,王蓉华,徐晓岭译,人民邮电出版社,2007。
[13]李裕奇,刘赪,王沁,随机过程,国防工业出版社,2008。
[14]Geman S and Geman D. Stochastic relaxation, gibbs distribution, and the Bayesian restoration of images. IEEE Trans. Pattn. Anal. Mach. Intell,1984,6:721-741
[15]Gelfand A E.Smith AFM.1990.Sampling based on approaches to calculating marginal densities.Journal of American Statistical Association,85(2):339-355
[16]苏良军,高等数理统计,北京大学出版社,2007。
[17]Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H and Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys,1953,21:1087-1092
[18]Hastings W K.1970.Monte Carlo sampling methods using Markov Chains and their applications.Biometrika,57(1):72～89
[19]Casella G and George E I. Explaining the Gibbs sampler. American Statistician,1992, 46:167-174
[20]Hastings W K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika,1970,57:97-109
[21]Chib S and Greenberg E. Understanding the Metropolis-Hastings algorithm. American Statistician,1995,49:327-335
[22]Hoeschele I. Mapping quantitative trait loci in outbred pedigrees. Handbook of Statistical Genetics. Balding D, Bishop M, Cannings C(eds), Wiley,2001,599-644
[23]Carlin B P and Louis T A. Bayes and Empirical Bayes methods for data analysis.2nd edition. Chapman & Hall. London, UK,2000
[24]Green P J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika,1995,82:711-732
[25]Sillanpaa M J and Arjas E. Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data. Genetics,1998,148(3):1373-1388
[26]Stephens D A and FischR D. Bayesian analysis of quantitative trait locus data using reservible jump Markov chain Monte Carlo. Biometrics,1998,54:1334-1347
[27]莫惠栋.数量性状遗传基础研究的回顾与思考-后基因组时代数量遗传领域的挑战.扬州大学学报(农业与生命科学版),2003,24(2)：24-31
[28]Zhang M, Montooth K L, Wells M T, Clark A G and Zhang D. Mapping multiple Quantitative Trait Loci by Bayesian classification. Genetics,2005,169(4):2305-2318
[29]Price A H and Courtois B. Mapping QTLs associated with drought resistance in rice:progress, problems and prospects. Plant Growth Reg,1999,29:123-133
[30]Price A H, Cairns J E, Horton P, Jones H G and Griffiths H. Linking drought-resistance mechanisms to drought avoidance in upland rice using a QTL approach:progress and new opportunities to integrate stomatal and mesophyll responses. J Exp Bot,2002,53(371): 989-1004
[31]Sugiyama F, Churchill G A, Higgins D C, Johns C, Makaritsis K P, Gavras H and Paigen B. Concordance of murine quantitative trait loci for salt-induced hypertension with rat and human loci. Genomics,2001,71(1):70-77
[32]Helentjaris T and Burr B. Development and Application of molecular markers to problems in plant genetics. Cold Spring Harbor Press,1989,1-165
[33]Thomas D C and Cortessis V. A Gibbs sampling approach to linkage analysis. Hum Hered, 1992,42(1):63-76
[34]Hoeschele I and Vanranden P. Bayesian analysis of linkage between genetic markers and quantitative trait loci.I.Prior knowledge. Theor Appl Genet,1993a,85:953-960
[35]Hoeschele I and Vanranden P. Bayesian analysis of linkage between genetic markers and quantitative trait loci.Ⅱ.Combining Prior knowledge with experimental evidence. Theor Appl Genet,1993b,85:946-952
[36]Tai J J. Application of Bayesian decision procedure to the inference of genetic linkage. J. Am. Statist. Assoc,1989,84:669-673
[37]Smith A F M and Roberts G O. Bayesian computation via the Gibbs sampler and related Markov Chain Monte Carlo methods. J. Roy. Statist. Soc., Ser. B,1993,55:3-23
[38]Stephens D A and Smith A F. Bayesian inference in multipoint gene mapping. Ann Hum Genet, 1993,57(Pt 1):65-82
[39]Thaller G and Hoeschele I. A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. Ⅰ. Methodology. Theor Appl Genet,1996a,93: 1161-1166
[40]Thaller G and Hoeschele I. A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci:Ⅱ. A Simulation study. Theor Appl Genet,1996b,93: 1,167-1174
[41]Knott S A and Haley C S. Aspects of maximum likelihood methods for the mapping of quantitative trait loci in line crosses. Genet. Res. Camb,1992,60:139-151
[42]Uimari P, Thaller G and Hoeschele I. The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics,1996,143(4):1831-1842
[43]Piepho H P and Gauch H G, Jr. Marker pair selection for mapping quantitative trait loci. Genetics,2001,157(1):433-444
[44]Broman K W and Speed T P. A model selection approach for the identification of quantitative trait loci in experimental crosses. J. R. Stat. Soc. B,2002,64:641-656
[45]Sillanpaa M J and Corander J. Model choice in gene mapping:what and why. Trends Genet, 2002,18(6):301-307
[46]Ball R D. Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion. Genetics,2001,159(3): 1351-1364
[47]Sen S and Churchill G. A statistical framework for quantitative trait mapping. Genetics,2001, 159:371-387
[48]Yi N, George V and Allison D B. Stochastic search variable selection for identifying multiple quantitative trait loci. Genetics,2003,164(3):1129-1138
[49]Stephens D A and Fisch R D. Bayesian analysis of quantitative trait locus data using reversible jump Markov chain Monte Carlo. Technical report. (available at http://www.ma.ic.ac.uk/ statistics/techrep.html),1996
[50]Sillanpaa M J and Arjas E. Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics,1999,151(4):1605-1619
[51]Vogl C and Xu S. QTL analysis in arbitrary pedigrees with incomplete marker information. Heredity,2002,89(5):339-345
[52]Yi N and Xu S. Linkage analysis of quantitative trait loci in multiple line crosses. Genetica, 2002,114(3):217-230
[53]Meuwissen T H, Hayes B J and Goddard M E. Prediction of total genetic value using genome-wide dense marker maps. Genetics,2001,157(4):1819-1829
[54]Heath S C. Markov chain Monte Carlo segregation and linkage analysis for oligogenic models. Am J Hum Genet,1997,61(3):748-760
[55]Xu S and Yi N. Mixed model analysis of quantitative trait loci. Proc Natl Acad Sci,2000, 97(26):14542-14547
[56]Yi N and Xu S. Bayesian mapping of quantitative trait loci for complex binary traits. Genetics, 2000,155(1391-1403
[57]Yi N and Xu S. Bayesian mapping of quantitative trait loci under complicated mating designs. Genetics,2001,157(4):1759-1771
[58]Kass R and Raftery A. Bayes factors. J. Am. Stat. Assoc,1995,90:773-795
[59]George E I and McCulloch R E. Variable selection via Gibbs sampling. J. Am. Stat. Assoc, 1993,88:881-889
[60]Min Z, Kristi L and Montooth. Mapping multiple quantitative trait loci by Bayesian classification. Genetics,2005,169:2305-2318
[61]Yi N. A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics,2004,167(2):967-975
[62]Sauerbrei W. The use of resampling methods to simplify regression models in medical statistics. Appl Stat,1999,48:313-329
[63]Bink M, Uimari P, Sillanpaa J, Janss G and Jansen C. Multiple QTL mapping in related plant populations via a pedigree-analysis approach. Theor Appl Genet,2002,104(5):751-762
[64]Hurme P, Sillanpaa M J, Arjas E, Repo T and Savolainen O. Genetic basis of climatic adaptation in scots pine by bayesian quantitative trait locus analysis. Genetics,2000,156(3): 1309-1322
[65]Hua J, Xing Y, Wu W, Xu C, Sun X, Yu S and Zhang Q. Single-locus heterotic effects and dominance by dominance interactions can adequately explain the genetic basis of heterosis in an elite rice hybrid. Proc Natl Acad Sci,2003,100(5):2574-2579
[66]Carlborg O and Haley C S. Epistasis:too often neglected in complex trait studies? Nat Rev Genet,2004,5(8):618-625
[67]Segre D, Deluna A, Church G M and Kishony R. Modular epistasis in yeast metabolism. Nat Genet,2005,37(1):77-83
[68]Yi N and Xu S. Mapping quantitative trait loci with epistatic effects. Genet Res,2002,79(2): 185-198
[69]Yi N, Diament A, Chiu S, Fisler J and Warden C. Characterization of epistasis influencing complex spontaneous obesity in the BSB model. Genetics,2004a,167:399-409
[70]Yi N, Diament A, Chiu S, Fisler J and Warden C. Epistatic interaction between chromosomes 7 and 3 influences hepatic lipase activity in BSB mice. Journal of Lipid Research,2004b, 45:2063-2070
[71]Yi N, Brian S, Gary A, Churchill, David B and Allison. Bayesian model selection for genome-wide epistatic QTL analysis. Genetics,2005,104
[72]Wang H, Zhang Y M, Li X, Masinde G L, Mohan S, Baylink D J and Xu S. Bayesian shrinkage estimation of quantitative trait loci parameters. Genetics,2005,170(1):465-480
[73]Zhang Y M and Xu S. Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny. Genetics,2004,166(4):1981-1993
[74]Wu R and Lin M. Functional mapping-how to map and study the genetic architecture of dynamic complex traits. Nat Rev Genet,2006,7(3):229-237
[75]Zhang Y M and Xu S. Advanced statistical methods for detecting multiple quantitative trait loci. Recent Research Developments in Genetics & Breeding,2005,2:1-23
[76]Zhang Y M and Xu S. A penalized maximum likelihood method for estimating epistatic effects of QTL. Heredity,2005,95(1):96-104
[1]莫惠栋.谷类作物胚乳品质性状的遗传研究.中国农业科学.1995,28(2)：1-7.
[2]徐辰武,何小红,蒯建敏,等.谷物胚乳性状数量基因图的构建方法.中国农业科学,2001，34(2)：117-122.
[3]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity.2003,90(3):228-235.
[4]Wu R, Lou X Y, Ma C X, et al. An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm. Proceedings of the National Academy of Sciences.2002,99(17):11281-11286.
[5]Cui Y, Casella G, Wu R. Mapping quantitative trait loci interactions from the maternal and offspring genomes. Genetics,2004,167(2):1017-1026.
[6]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits Chinese Science Bulletin,2005,50(14):1470-1476.
[7]徐辰武,王伟,胡治球,孙长森.基于株平均值的胚乳性状QTL作图的极大似然方法作物学报.2005,31(10)：1271-1276.
[8]Wang X, Hu Z, Wang W, et al. A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples. Genetica,2008,132(1):59-70.
[9]Yi N, Yandell B S, Churchill G A, et al. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics.2005,170(3):1333-1344.
[10]敖雁,徐辰武.贝叶斯回归分析方法及其QTL作图中的应用.扬州大学学报：农业与生命科学版,2005,26(2)：44-49.
[11]莫惠栋.胚乳性状的遗传模型和世代平均数.遗传学报.1989,16(2)：111-117.
[12]Chib S, Greenberg E. Understanding the metropolis-hastings algorithm. The Amer Statistician. 1995,49(4):327-335.
[13]王伟,胡治球,孙长森,徐辰武.基于单粒观察值的胚乳性状QTL图的构建方法.作物学报.2005,31(8)：989-994
[14]Cui Y, Wu J, Shi C, Littell R C, Wu R. Modelling epistatic effects of embryo and endosperm QTL on seed quality traits. Genet Res.2006,87(1):61-71.
[15]李玉玲,王延召,董永彬.利用三倍体胚乳遗传模型定位爆裂玉米子粒蛋白含量QTL玉米科学,2006,14(6)：13-16.
[16]Jansen J, de Jong A G, van Ooijen J W. Constructing dense genetic linkage maps. Theor Appl Gnent.2001,102(7):1113-1122.
[17]Smith A, Roberts G. Bayesian computation via the gibbs sampler and related markov chain monte carlo methods. J Royal Stat Soc(Series B),1993,55(1):3-24.
[18]Garcia D, Fitz Gerald J N, Berger F. Maternal control of integument cell elongation and zygotic control of endosperm growth are coordinated to determine seed size in arabidopsis. Plant Cell.2005,17(1):52-60.
[19]Li L, Zhao Y, McCaig B C, Wingerd B A, Wang J, Whalon M E, Pichersky E, Howe G A. The tomato homolog of CORONATINE-INSENSITIVE1 is required for the maternal control of seed maturation, jasmonate-signaled defense responses, and glandular trichome development. Plant Cell,2004,16(1):126-143
[1]莫惠栋.谷类作物胚乳品质性状的遗传研究.中国农业科学,1995,28(2)：1-7
[2]Mo H. Genetic expression for endosperm traits. In:Weir B S, Eisen E J, Goodman M M, et al., eds. In Proceedings of the Second International Conference on Quantitative Genetics. Massachusetts:Sinauer Associates, Inc.1988:478-487
[3]徐辰武,何小红,蒯建敏,顾世梁.谷物胚乳性状数量基因图的构建方法.中国农业科学,2001,34(2)：117-122
[4]Wu R, Lou X Y, Ma C X, Wang X, Larkins B A, Casella G. An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm. Proceedings of the National Academy of Sciences,2002,99:11281-11286
[5]Wu R, Ma C X, Gallo-Meagher M, Littell R C, Casella G. Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model. Genetics.2002, 162(2):875-892
[6]Xu C, He X, Xu S. Mapping quantitative trait loci underlying triploid endosperm traits. Heredity,2003,90:228-235
[7]Kao C H. Multiple-interval mapping for quantitative trait loci controlling endosperm traits. Genetics.2004,167(4):1987-2002
[8]Cui Y, Casella G, Wu R. Mapping quantitative trait loci interactions from the maternal and offspring genomes. Genetics.2004,167(2):1017-1026
[9]Hu Z, Xu C. A new statistical method for mapping QTLs underlying endosperm traits. Chinese Science Bulletion.2005,50(14):1470-1476
[10]Wen Y X, Wu W R. Methods for mapping QTLs underlying endosperm traits based on random hybridization design. Chinese Science Bulletion.2006,51(16):1976-1981
[11]王学枫,汤在祥,王亚民,宋雯,徐辰武.基于NCⅢ和TTC设计的胚乳性状QTL区间作图方法.作物学报,2008,34(10)：1734-1743
[12]He X H, Zhang Y M. Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design. Heredity,2008,101: 39-47
[13]Wang H, Zhang Y M, Li X, Masinde G L, Mohan S, Baylink D J, Xu S. Bayesian shrinkage estimation of quantitative trait loci parameters. Genetics,2005,170:465-480
[14]Yi N. A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics.2004,167(2):967-975
[15]Xu S. Estimating polygenic effects using markers of the entire genome. Genetics,2003,163: 789-801
[16]Yi N, Yandell B S, Churchill G A, Allison D B, Eisen E J, Pomp D. Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics.2005,170(3):1333-1344
[17]王亚民,孙长森,汤在祥,胡治球,徐辰武.谷物胚乳性状QTL区间作图的贝叶斯方法,扬州大学学报(农业与生命科学版)，2008：29(4)：12-17
[18]Jiang C, Zeng Z B. Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines. Genetica,1997,101:47-58
[19]Xu S, Yi N. Mixed model analysis of quantitative trait loci. Proceedings of the National Academy of Sciences.2000,97(26):14542-14547
[20]王伟,胡治球,孙长森,徐辰武.基于单粒观察值的胚乳性状QTL图的构建方法.作物学报,2005,31(8)：989-994
[21]徐辰武,王伟,胡治球,孙长森.基于株平均值的胚乳性状QTL作图的极大似然方法.作物学报,2005,31(10)：1271-1276
[22]Wen Y, Wu W. Interval mapping of quantitative trait loci underlying triploid endosperm traits using F3 seeds. Journal of Genetics & Genomics,2007,34:429-436
[23]Wen Y, Wu W. Experimental designs and statistical methods for mapping quantitative trait loci underlying triploid endosperm traits without maternal genetic variation. Journal of Hered, 2008,99:546-551