| In genome-wide association analysis,linear mixed models are always used to analyze quantitative traits in order to avoid false positive errors.To solve the linear mixed model,it is necessary to construct the kinship matrix first,then estimate the residual variance components,and finally use the weighted least squares to solve the current marked effect value and test.The variance component estimation process involves complex nonlinear solutions,so re-estimating the remaining variance components for high-throughput SNPs one by one will make the complete solution of the linear mixed model consume a lot of time and computer memory.Researchers have proposed many simplified algorithms to reduce the computational cost of LMM.These methods are mainly divided into two categories: one is the GRAMMAR method which fixes polygenic effects as genomic breeding values;and the other is the EMMAX method which replaces random effects with polygenic heritability.Although there are only two phenotypes of binary traits in quantitative traits,they have many similarities to the traits of continuous normal distribution that many binary traits are also affected by polygenic effects.Generalized Linear Mixed Model(GLMM)is therefore required for genome-wide association analysis of binary traits,as linear regression would result in false positives.Compared with the general linear mixed model,the complete GLMM solving process is similar to LMM,but it is more difficult to solve.The linear mixed model simplified solution idea was transplanted to the generalized linear mixed model,in order to simplify the GLMM solution process.In this way,a series of simplified algorithms were produced accordingly,such as milor GWAS and SAIGE,which are similar to GRAMMAR method,and GMMAT and LTMLM,which are similar to EMMAX method.However,the complexity of the generalized linear mixed model leads to the unstable performance of these transplanted simplified algorithms at this stage.The simplified algorithm of the generalized linear mixed model needs to be continuously developed.Although the GRAMMAR method has extremely low computational complexity during scanning,there are serious false-negative errors in the whole-genome association analysis,which affects the detection of QTN.Therefore,in this study,a simplified algorithm for the generalized linear mixing model of binary traits was proposed and named as Binary Emmax method,which followed the idea of Emmax method and was based on the generalized linear mixing model.In the Binary Emmax method,the spectral decomposition of the relationship matrix is firstly carried out,after that uses the marginal maximum likelihood method to estimate the variance components and fixes them,and then solves the generalized linear mixed model by iterative weighted least squares method.Compared with GMMAT which is also based on the EMMAX method,the binary EMMAX method is more stable and has higher accuracy in the estimation of variance components,at the same time,it also has better statistical properties and QTN detection power.We conducted simulation experiments using human and maize genome datas sets with different genetic relationship complexity,and simulated binary trait combinations with different heritability and different numbers of QTN.The performance of Binary Emmax method is judged from three aspects: heritability estimation,statistical properties,and QTN detection power.Computer simulation experiments show:(1).Heritability estimation: The heritability estimated by Binary Emmax method is very close to the true value,and there is no case where the estimated heritability is not in the range of 0-1,while the estimated heritability of GMMAT in many combinations is quite different from the true value,the estimated heritability is not in the range of 0-1more often.Binary Emmax method has high accuracy and good robustness at heritability estimation.(2).Statistical properties and QTN detection power: The statistical properties and QTN detection power of Binary Emmax method are slightly better than GMMAT method.In order to verify the performance of the new method,a genome-wide association analysis was performed on the half-smooth tongue sole(Cynoglossus semilaevis)sex reversal traits and CFW mouse osteoporosis traits.For the half-smooth tongue sole dataset,the Binary Emmax method detected 1 QTN on chromosome 21 and detected 5 QTN on chromosome 22,GMMAT Method only detects two QTN on chromosome 22;for the CFW mouse data set,the Binary Emmax method and GMMAT showed the same detection efficiency,and both detected a QTN on chromosome 11.Therefore,it can be confirmed that the Binary Emmax method can detect more QTNs than the GMMAT method.In addition,we also proposed a simple regression scale transformation method for efficiently locating binary traits.Firstly,the eigenvectors solved by spectral decomposition of the kinship matrix will be considered as the principal components to correct the population stratification in the binary traits dataset.After that,a whole new covariate formed through the sum of the multiplications of each covariate and its regression coefficient of the principal component computed by solving the linear regression model.Then the new covariates were used as the covariable of linear regression to carry out correlation test one by one.Finally the candidate Quantitative Trait Nucleotide(QTN)was analyzed by generalized linear model regression,the effects and variance were transformed into the generalized linear model scale.The method was applied to genome-wide association analysis of sex reversal traits in half-smooth tongue sole to locate the associated QTN. |
