Adaptive Penalized Maximum Likelihood Method In QTL Mapping

Most diseases in human and important traits in plants and animals are quantitative traits, controlled by several major genes, many minor genes and their interactions. To improve these important traits in animals and plants and control these diseases in human, the prerequisite for the improvement and control is to detect the above genes and their interactions.With the rapid development of biological techniques, the applications of large scale SNP markers and the detection of epistasis result in the situation that the number of variables in the genetic model is much larger than sample size. The case makes the traditional QTL mapping methods infeasible. Therefore, Zhang and Xu (2005) incorporated the idea of Bayesian sgrinkage estimation approach into maximum likelihood framework in order to develop penalized maximum likelihood method. The method with simple algorithm and quick speed may be widely adopted. However, lower power in the detection of linked QTL with effects in opposite directions and minor QTL, along with biased estimates for QTL effects and posittions, is observed in real data analysis. To overcome the issues, biasedness correction coefficient for QTL effect is incorporated into the estimation of QTL effect. To carry out the correction automatically, the above coefficient is further changed into a founction about QTL effect. This method is called adaptive penalized maximum likelihood method. A Monte Carlo simulation experiment, along with a Barley kernel weight dataset of145doubled lines and maize flowering time dataset of277inbred lines, was used to validate the proposed methods in this study. The main results were as follows.1. Biasedness correction coefficients are incorporated into penalized function, and uniform distribution for prior variance of QTL effect is replaced by inverse chi-square prior distribution. Thus, various estimations for QTL effect and its prior variance are obtained in this study. Results from Monte Carlo simulation experiment show that the power is increased from25%to88%in the detection of linked QTL with effects in opposite directions and from60%to80%in the detection of minor QTL; the biasedness and standard deviation of position and effects of QTL are decreased; lower false positive rate and quick speed remain. The proposed approach is validated by mapping QTL for kernel weight in145barley doubled lines and its cross validation experiment.2. To perform the above method automatically, the above coefficient should be replaced by a function of QTL effect. This method calls adaptive penalized maximum likelihood method. Results from Monte Carlo simulation experiments show that the power for detection of the above QTL is further increased to more than95%; standard deviation and mean squared error of QTL effect is further decreased; and false positive rate is1.2%. Results from cross-validation experiment of145doubled lines in barley show that the new method is better than the LASSO method; and ones from real data analysis of maize dataset show that the new method has better model goodness-of-fit than mixed linear model and compression mixed linear model approaches.In high-throughout data analysis, epistatic detection, novel gene mining and genome-wide marker assisted selection, new method provides a new approach.