QTL作图中零假设检验统计量分布特征及LOD临界值估计方法研究

研究QTL作图的零假设检验统计量分布特征, 可以帮助我们选取合适的LOD临界值, 以控制全基因组第一类错误的概率。本文利用模拟方法, 研究了QTL作图中单个扫描位点的似然比检验(LRT)统计量在零假设下的分布特征、影响最大LOD统计量累积分布的因素以及不同群体在不同标记密度下有效独立检验次数与染色体长度的关系。结果表明, 在定位加显性效应QTL的一维扫描和定位上位性互作QTL的二维扫描中, 单个扫描位置上的LRT统计量均服从卡方分布, 其自由度等于检测QTL遗传参数的个数; 染色体个数、群体大小和表型测量误差对零假设下检验统计量的分布没有影响, 即不影响LOD临界值的选取, 而群体类型、标记密度和染色体长度有明显影响, BC₁、RIL和F₂三种类型的群体中, BC₁群体的临界值最小, F₂群体的临界值最大, 标记越密、染色体越长, 对应的LOD临界值越大; QTL一维扫描中有效独立检验次数与染色体长度呈正比, 二维扫描中有效独立检验次数与染色体长度呈二次幂关系。借助Bonferroni矫正, 给出了全基因组显著性水平与单个扫描位点显著性水平间的关系, 因此, 研究者可根据作图群体的群体类型、标记密度和基因组长度, 很方便地确定特定全局显著性概率水平下的LOD临界值。

Properties of the Test Statistic under Null Hypothesis and the Calculation of LOD Threshold in Quantitative Trait Loci (QTL) Mapping

Selecting an appropriate LOD threshold is of great interest in QTL mapping studies. Many approaches can be considered to calculate the critical value throughout a genome, such as simulation-based method, analytical approximation, and empirical method based on permutation test. Many tests are conducted in QTL mapping, which are not mutually independent because the linkage relationship of adjacent markers on chromosomes. In order to declare a significant QTL at a genome-wide significance level, it is necessary to understand the behavior of test statistic under null hypothesis in QTL mapping and to deal with the dependent multiple-test problem arising in the genome-wide test. Our objectives in this study were (1) to investigate the properties of LRT (likelihood ratio test) statistic of one-point scanning under null hypothesis in QTL mapping, (2) to determine the factors affecting the cumulative distribution of maximum LOD score, and (3) to identify the relationship between the effective number of independent tests and the length of chromosome by simulation method. Results indicated that the LRT test statistic in one-dimensional scanning of additive-dominant QTL and two-dimensional scanning of epistatic QTL followed chi-square distributions, and the degree of freedom (df) was equal to the number of genetic parameters to be estimated. For example, degree of freedom in recombinant inbred lines (RIL) population was equal to 1 in one dimensional or two dimensional scanning. Degree of freedom in F₂ populations was equal to 2 in one-dimensional scanning and 4 in two-dimensional scanning. Number of chromosome, population size and phenotyping error variance did not have any effect on the distribution of LRT under null hypothesis, and therefore will not affect the selection of LOD threshold. On the contrary, population type, genome size and marker density had significant impacts. For BC₁, RIL and F₂ populations, the threshold was the smallest in BC₁ population and the highest in F₂ population. Higher marker density and longer chromosome resulted in higher LOD threshold. It wasidentified that the effective number of independent tests (M_eff) was proportional to the length of chromosome in one-dimensional scanning of additive-dominant QTL. In two-dimensional scanning of epistatic QTL, it was identified that M_effwas in a squared relationship to the length of chromosome. With the help of Bonferroni correction, we could acquire the relationship between point-wise and genome-wide significance levels. Therefore, it is convenient to calculate the threshold LOD in QTL mapping, given the genome-wide significance level, the population type, marker density and genome size.