Hierarchical Generalized Linear Mixed Model Method In The Association Studies Of Ordinal Traits

Many novel genes available for crop genetics and breeding by design are preserved among crop germplasm resources with large genetic variation and multiple historic recombinants. Among these genes, some are responsible for important resistance traits that are binary or ordinal. These traits do not obey Mendelian’s law and their genetic basises are complex. Meanwhile, interaction between genes, named epistasis, is an important compo-nent in the genetic basis of quantitative traits and breeding by design. Therefore, there is a critical need for in-depth study of methodology for detecting main-effect and epistatic quantitative trait loci (QTL) for ordinal traits in crop cultivars.Most methods of identifying QTL for ordinal traits are based on bi-parental segregation population. However, these methods do not work in crop cultivars. Although Bayesian linkage analysis and variance-components approach have been presented at the situation of the known cultivar pedigree information, relatively little has been known at the situation of the unknown cultivar pedigree information. To solve this issue, especially for the detection of epistasis, in this study conditional probability of ordinal trait phenotypes had been approximated by normal distribution of pseudo data in order to construct pseudo-likelihood. In the likelihood, all the main and epistatic effects, and QTL-by-environment interaction effects were treated as random effect, and estimated by empirical Bayes method, whilst population mean, environmental effect and population structure effect were viewed as fixed effect, and estimated by maximum likelihood approach. A series of Monte Carlo simulation experiments and a real data analysis of root-length-based alkaline-salt tolerance in soybean seedings were used to validate the proposed method in this study. The results were as follows.A hierarchical generalized linear mixed model method was proposed. In the genetic model of this method, population mean, environmental effect and population structure effects were viewed as fixed effect, multi-QTL effects and QTL-by-environment interaction effects were viewed as random effect. Thus, main-effect QTL and environmental interaction could be detected. Results from a series of Monte Carlo simulation experiments showed that:1) The statistical power of QTL detection is the maximum for the new method than those for single-QTL method and test of independence;2) The new method works well with satisfactory statistical power and precision, and low false positive rate; and3) The optimal power occurred at the situation of the bell-shaped distribution of trait phenotype, and the power for QTL detection increases as the number of phenotypic categories, sample size and QTL heritabiliry increase. It verified validity of the method. And, the methed is also confirmed by dissecting the genetic basis of alkaline-salt tolerance of root-length using257soybean cultivars.The above approach was extented from multi-QTL genetic model to epistatic genetic model, and similar results were observed. In the epistatic genetic model, the model is saturated quickly as the number of QTL increases. To solve this problem, Chi-square test at the0.25significance level was adopted to delete non-significant effects in the model. Using this method, the above real dataset is re-analyzed. The simulation experiments and analysis of real data proved the epistatic association analysis method.