动植物的重要经济性状，如生长（生长速率或饵料系数等）、肌肉品质（脂肪含量或氨基酸比例等）、温度耐受以及环境胁迫等多为数量性状，其通常由多个作用大小不一的基因控制。对于这些数量性状的遗传改良，传统的育种技术是通过群体选育或杂交育种等方式对目标性状进行选种选育。然而，随着分子标记的应用和发展，利用各式分子标记构建遗传连锁图谱可以将控制数量性状的遗传位点定位到染色体的不同区域上，实现数量性状位点（Quantitative Trait Loci, QTL）定位或QTL作图。通过QTL定位能够解析目标性状的遗传机制并发掘与目标性状相关联的遗传标记，继而开展分子标记辅助育种（Marker Aided Selection, MAS）。与传统育种方法相比，MAS借助QTL定位筛选出与目标性状显著关联的分子标记以及筛选的标记与目标性状决定基因紧密连锁的特点来达到选种选育的目的。由传统育种方法获取的后代遗传稳定性差且选育效果容易受到环境影响，而MAS因其快速、精准且不受环境因素干扰的特点，克服了许多传统育种方法中的困难、大大缩短了育种年限并且显著地提高了育种效率。我国是世界上最大的水产养殖国，养殖品种十分广泛，对于每一养殖品种而言其最具经济价值的性状也不尽相同。对各种目标性状相关联的QTL进行遗传评估，发掘影响家系乃至品种间相同的QTL能够更高效地服务遗传育种工作。

       随着基因组学的快速发展以及测序成本的下降，近些年来已有各种水产动物的全基因组序列相继被测定，完善的全基因组信息为水产动物的性状改良提供了具有重要参考价值的基因组资源。而在全基因组水平广泛存在的由单个核苷酸变异所引起的DNS序列多态性即单核苷酸多态性（Single Nucleotide Polymorphism, SNP）则为全基因组范围内的关联分析（Genome-Wide Association Study, GWAS）提供了一种强有力的分子标记工具。GWAS研究在一定程度上取代了QTL定位，它能检测到与目标性状显著关联的数量性状核苷酸QTN（Quantitative Trait Nucleotide）位点，进而为动植物MAS育种提供重要的候选基因。

       数量性状GWAS可归结为线性回归模型或广义线性回归模型的回归分析问题。由于逐个标记GWAS分析涉及到多重检验及存在群体分层等因素的影响导致结果出现较高的假阳性检测率，通过线性混合模型（Linear Mixed Model, LMM）进行GWAS分析能够消除这些混淆效应的影响。LMM求解过程主要包括：1)构建遗传亲缘关系矩阵；2)估计方差组分；3)利用广义线性回归分析计算关联标记的遗传效应并对其进行统计推断。然而，LMM的复杂与日益庞大的高通量数据使得LMM的计算效率愈加受到挑战，诸多简化算法模型被提出以提高LMM的求解速度，包括GRAMMAR、EMMAX和FaST-LMM等算法，这些GWAS算法模型在计算速度和统计功效方面都得以不断改进。上述这些算法主要针对的是单性状逐个标记GWAS分析，而随着表型数据维度的增加，多性状和动态性状GWAS分析的算法模型开发日益成为GWAS方法研究的热点领域。本研究将一般LMM剖分为关于基因组育种值的LMM和关于逐个SNP加性遗传效应的广义线性回归模型两层，利用广义最小二乘方法计算每个SNP的加性遗传效应，实现LMM的分层求解。基于高维的多性状和动态性状表型，本研究提出了多性状分层混合模型关联分析方法（Hi-mvLMM）、一因几效分层混合模型关联分析方法（Hi-mgbvLMM）、动态性状分层混合模型关联分析方法（Hi-dyLMM和Fast-dyLMM）。这一系列算法模型的开发丰富了GWAS分析的算法内容，为有相应需求的研究者提供了更多的算法选择。主要研究结果如下：

(1) 详细地阐述了Hi-mvLMM方法中的分层解析思想，并对Hi-mvLMM方法进行了模拟验证和实例分析。多种模拟组合设计的结果表明，Hi-mvLMM方法在控制假阳性率的同时能够获得较高的一因多效QTN统计检验功效。与现存的GEMMA软件中的多性状线性混合模型（mvLMM）相比，Hi-mvLMM在模拟和实际分析中具有相似或更高的一因多效QTN检测效率，且效率会随着多性状基因组育种值（Genomic Breeding Value, GBV）估计的准确性提高而提高。

(2) 为进一步提高一因多效QTN的检验效率，在Hi-mvLMM方法的基础上，本研究提出了Hi-mvLMM联合分析，即以相对于Bonferroni阈值更低的显著水准筛选出更多的候选QTNs（候选个数少于样本个数），再对关于候选QTNs加性遗传效应的多性状广义多元线性回归模型进行求解。由于联合分析考虑了候选QTNs之间的相关，理论上将获得比联合分析前更高的统计检验功效。相应的模拟和实例分析结果表明，Hi-mvLMM联合分析的一因多效QTN检测效率显著高于Hi-mvLMM和mvLMM方法。

(3) 在Hi-mvLMM方法中除一因多效QTN检测外，本研究还在多性状模拟验证和小鼠、大菱鲆及虹鳟的多性状数据实例分析中进行了一因几效QTN的检测，即一因几效分层混合模型关联分析（Hi-mgbvLMM）。Hi-mgbvLMM方法利用多性状GBV逐个性状进行单性状分层混合模型关联分析，模拟和实例分析结果表明，Hi-mgbvLMM方法能够一定程度上提高单性状GWAS分析的QTN检测效率。

(4) 动态性状可被视为多性状的一种特殊形式，这种性状的表型受动态轨迹的影响，经表型分层后可转换为个体动态性状回归系数。以个体动态性状回归系数构建多性状LMM，利用Hi-mvLMM和mvLMM方法求解该多性状LMM，即本研究提出的动态性状分层混合模型关联分析方法（Hi-dyLMM和Fast-dyLMM）。这两种动态性状关联分析方法的模拟验证和实例分析表明，分层解析策略完全适用于动态性状GWAS分析，且能够定位到影响动态轨迹、效应随时间动态变化的动态性状QTN。

    Most important economic traits in plant and animal studies are quantitative traits, such as growth function (growth rate or feed conversion ratio, etc.), muscle quality (fat content or proportion of each amino acid, etc.), temperature tolerance and environment stress. All of these traits are controlled by lots of genes with different roles and are affected by environmental factors. For genetic improvement of those quantitative traits, the traditional breeding technique always use population selection or cross breeding to selective breeding. However, with the application and development of molecular markers, using various molecular markers to construct genetic linkage maps can mapping the genetic loci controlling quantitative traits on different regions of chromosomes. QTL mapping can resolve the genetic mechanism of target traits and explore the genetic markers associated with target traits, and then carry out marker-assisted breeding (MAS). Compared with traditional breeding methods, MAS uses QTL mapping to select molecular markers that are significantly related to target traits, as well as the feature that the selected markers are closely linked to the target traits to achieve the purpose of selective breeding. Descendant obtained by traditional breeding methods also have poor genetic stability and breeding results are susceptible to environmental influences. Because of characteristics of quickness, precision and free from environmental impact, MAS overcomes many difficulties of traditional breeding methods. The breeding period is greatly shortened and breeding efficiency is significantly improved with MAS. China has the largest aquaculture production in the world and extensive breeds, most important economic traits are different from each other among these breeds. Genetic evaluation of QTLs associated to various traits and detection of the same QTL in different families and breeds can promote genetic improvement and breeding work efficiently.

    With the rapid development of genomics and the cost of sequencing technology goes down, the whole genome sequence of lots of aquatic animals was sequenced successively. Complete genomic information provides important resources of reference genome to genetic improvement of aquatic animals. DNS sequence polymorphism (Single Nucleotide Polymorphism, SNP) caused by variation of a single nucleotide exist extensively on the whole genome, it is a powerful tool of molecular marker for Genome-Wide Association Study (GWAS). QTL mapping have been replaced by GWAS to some extent, because GWAS can detect significant Quantitative Trait Nucleotide (QTN) associated to interested traits and further provide important candidate genes for MAS of plant and animal.

    GWAS of quantitative trait can be summarized as a regression analysis problem of linear regression model or generalized linear regression model. Due to single-locus GWAS analysis involves multiple tests and factors such as the presence of population stratification, resulting in a higher false positive rate of the results, the linear mixed model (LMM) for GWAS analysis can be used to eliminate the impact of these confounding effects. Solving process of LMM consisted mainly of construction of genetic relationship matrix, estimation of variances, calculating associated statistics with generalized linear regression and inference of QTN. However, heavy computational burden to LMM is emerged because of its complexity and increasing high throughput datasets. A lot of simplified algorithm models have been improved to speed up solution of LMM including GRAMMAR, EMMAX and FaST-LMM, etc. The above popular algorithm models are mainly for single-trait GWAS, however, the algorithmic effort in multiple-trait and dynamic-trait GWAS have become a focused research area of GWAS methods. In this study, we partition the genomic LMM into two hierarchies, the first hierarchy is a LMM refers to genomic breeding values and the second one is a generalized linear regression model refers to additive genetic effect of each SNP. The genetic effect of the tested SNP can be statistically inferred by generalized least square in hierarchical solution. Based on higher dimensional phenotype of multiple and dynamic traits, we have developed multiple-trait hierarchical mixed model method for association study (Hi-mvLMM), hierarchical mixed model method for association study in one of multiple related traits (Hi-mgbvLMM), dynamic-trait hierarchical mixed model method for association study (Hi-dyLMM and Fast-dyLMM). The development of this series of algorithm models enriches the algorithm content of GWAS analysis and provides more algorithm choices for researchers with corresponding requirements. The main results are as follows:

1) The idea of hierarchical solution in Hi-mvLMM method is elaborated in this study, meanwhile, we have implemented simulation verification and analysis of case datasets for the developed method. Results of various designs of our simulations show that higher power of a statistical test of pleiotropic QTN and well control of false positive rates can be obtained in multiple-trait GWAS by using Hi-mvLMM method. Compared to multivariate linear mixed model (mvLMM) in current GEMMA software, Hi-mvLMM method has higher or similar statistical power of pleiotropic QTN and the power will increases with accuracy of multiple-trait genomic breeding value (GBV).

2) To further improve detection efficiency of pleiotropic QTN, we will perform joint analysis of Hi-mvLMM method based on results from association analysis with Hi-mvLMM method. The joint analysis use significant level which is lower than Bonferroni correction to select more candidate QTNs (the number of candidate QTN should be less than the samples), then it will solve a multiple-trait generalized multiple linear regression model. Because correlation among candidate QTNs have been considered in joint analysis, it will obtain higher power of a statistical test of pleiotropic QTN than Hi-mvLMM method in theory. The corresponding simulation verification and analysis of case datasets show that detection efficiency of pleiotropic QTN in multi-trait GWAS with joint analysis is significantly higher than with Hi-mvLMM or mvLMM.

3) In addition to detection of pleiotropic QTN in Hi-mvLMM method, QTNs for each trait which analyzed in multiple correlated traits have also been detected in multi-trait simulation verification and case analysis of multiple-trait dataset of mice, turbot and rainbow trout, that is, hierarchical mixed model association analysis for one of multiple correlated traits (Hi-mgbvLMM). The Hi-mgbvLMM method uses multi-trait GBV as phenotype to carry out single-rait hierarchical mixed model. The results of multi-trait simulation and case analysis show that Hi-mgbvLMM method can improve the QTN detection efficiency of single-trait GWAS to some extent.

4) Dynamic traits can be regarded as a special form of multiple traits, and the phenotype of this trait is affected by dynamic trajectory. After hierarchical solution of dynamic phenotype, it can be transformed into multiple correlated phenotypes of parameters to dynamic trajectory (individual dynamic trait regression coefficient). By constructing multiple-trait LMM based on individual dynamic trait regression coefficient and using Hi-mvLMM and mvLMM methods to solve the LMM, we developed the dynamic-trait hierarchical mixed model association analysis method (Hi-dyLMM and Fast-dyLMM). The simulation verification of the two dynamic-trait association analysis methods and the case analysis of the dynamic-trait datasets of chicken egg weight and turbot body mass show that the strategy of hierarchical analysis is completely applicable to dynamic-trait GWAS. QTNs which affect the dynamic trajectory can be detected easily by Hi-dyLMM or Fast-dyLMM, and the genetic effects of those QTNs can change over time.

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