| 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 markerassisted 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on the whole genome,it is a powerful tool of molecular marker for Genome-Wide Association Study(GWAS).QTL mapping have been replaced by GWAS to some extent,because GWAS can detect significant Quantitative Trait Nucleotide(QTN)associated to interested traits and further provide important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 HimvLMM 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 multitrait 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 rnulti-trait simulation and case analysis show that Hi-mgbvLMM method can improve the QTN detection efficiency of single-trait GWAS to some extent4)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 dynamictrait 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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