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嬉试蒋
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1 作物学报 ACTA AGRONOMICA SINICA 2013, 39(1): ISSN ; CODEN TSHPA9 xbzw@chinajournal.net.cn DOI: /SP.J 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 * 孙子淇李慧慧张鲁燕王建康 / / CIMMYT, : QTL, LOD,, QTL (LRT) LOD, QTL QTL, LRT, QTL ;, LOD,, BC 1 RIL F 2, BC 1, F 2,, LOD ; QTL, Bonferroni,,,, LOD : QTL ; ; LOD ; ; ; Properties of the Test Statistic under Null Hypothesis and the Calculation of LOD Threshold in Quantitative Trait Loci (QTL) Mapping SUN Zi-Qi, LI Hui-Hui, ZHANG Lu-Yan, and WANG Jian-Kang * Institute of Crop Sciences / National Key Facility for Crop Gene Resources and Genetic Improvement, Chinese Academy of Agricultural Sciences / CIMMYT China Office, Beijing , China Abstract: 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 F 2 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 BC 1, RIL, and F 2 populations, the threshold was the smallest in BC 1 population and the highest in F 2 population. Higher marker density and longer chromosome resulted in higher LOD threshold. It was identified that the effective ( ) * (Corresponding author):, wangjk@caas.net.cn, jkwang@cgiar.org, Tel: : sunziqi777@163.com, Tel: Received( ): ; Accepted( ): ; Published online( ): URL:

2 2 39 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 eff was 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. Keywords: QTL mapping; Likelihood ratio test; LOD score; Null hypothesis; Significance level; Number of independent tests LOD QTL, LOD QTL, QTL LOD QTL, LOD, (quantitative trait locus, QTL),, LOD LOD, [1-2] [1,3-11] [12] (M eff ) [13-16] 4, Lander Botstein [1] 0.05 LOD 2~3, Lander Botstein [1] 2 2 LOD [1,3-11],, [12],,,,, Cheverud [13] Nyholt [14] Li Ji [15] Gao [16] (M eff ) LOD, QTL LOD, QTL [17-19], QTL LOD Churchill Doerge [12] QTL LOD 2 : 1 ; 2 M eff Piepho [9] Zou [10] Chang [11], QTL LRT, (df) QTL Cheverud [13] Nyholt [14] Li Ji [15] Gao [16] (M eff ) QTL QTL LRT ; LOD ; (M eff ), 3 LOD 1 材料与方法 1.1 LOD LOD LOD, [1,10,12,20] 6 LOD,, (BC 1 ) (RIL) F 2 ; (length of chromosome, CL) cm; (marker density, MD) cm; 1 2 4, 200 cm; (population size, PS) ; (error variance, EV) QTL, ,, LOD LOD, LOD LOD 1.2 QTL,

3 1 : QTL LOD 3 BC 1 RIL F 2 ;,, cm;, cm; 200, 0.4 QTL QTL IciMapping ( ) QTL, BC 1 RIL F 2, 50~200 cm 2, 2,, QTL LOD, 2, MD = cm QTL, 500, 0.4, LOD, 3 ( DH [21] RIL [22] F 2 [23] ), [1-2] [12], Cheverud [13] Li Ji [14] Gao [15] M eff LOD DH cm, 405, 21, 7.6 cm RIL cm, 132, 10, 17 cm F cm, 117, 12, 13 cm 1.4 M eff (IM) ( QTL IciMapping [24] IM- ADD IM-EPI ) QTL QTL M eff : LOD, 2 Bonferroni p = g /M eff, : M eff = g / p (1), g LOD ( ), p ( ) QTL Ici- Mapping LOD, (LRT), p, 2ln10 3 g M eff 2 结果与分析 2.1 LRT 1, LRT 1-a b QTL RIL F 2 1-c d QTL RIL F 2, RIL F LRT Piepho [9] Zou [10] Chang [11], QTL LRT, RIL 1, F 2 2 QTL LRT, RIL 1, F 2 4, BC 1 LRT RIL, 1 LRT, p, g LOD g p, g LOD 2.2 LOD, LOD, LOD ;, LOD 2-d~f,, LOD,, 3 LOD, LOD LOD ( 2-a~c), 3 LOD, BC 1 RIL, RIL F 2 ;,,

4 4 39 图 1 一维和二维 QTL 作图扫描过程中单个扫描位点 LRT 统计量与卡方分布的拟合 Fig. 1 Goodness of fit of single point LRTs in one-dimensional and two-dimensional scanning in QTL mapping,, a b QTL RIL F 2, 1 2; c d QTL RIL F 2, 1 4 The curve line stands for the chi-square distribution and the vertical line stands for the observed distribution, a and b correspond to RIL and F 2 population respectively, in one-dimensional scanning of additive-dominant QTL, and the degrees of freedom are 1 and 2, respectively; c and d correspond to RIL and F 2 population respectively, in two-dimensional scanning of epistatic QTL, and the degrees of freedom are 1, 4 respectively. Fig. 2 图 2 不同因素对最大 LOD 统计量累积分布的影响 Factors affecting the cumulative distribution of the maximum LOD statistic a, b, c, d, e, f a for population type, b for length of chromosome, c for marker density, d for chromosome number, e for population size, and f for error variance.

5 1 : QTL LOD QTL (M eff ) (MD) (CL) 2, LOD, BC 1 RIL F cm, cm (M eff ) 3, QTL, (M eff ) 3-a c e g =0.05 BC 1 RIL F 2 M eff 3-b d f g =0.01 BC 1 RIL F 2 M eff (CL), (M eff ) M eff,, M eff y M eff, x g, ;,, 3-a, BC 1 1 cm, 0.153; 20 cm, 0.054, g =0.01 g =0.05, BC 1 RIL, F 2 RIL, g =0.05, 5 cm 10 cm ( 3-c e) LOD, (CL) (genome length, GL), 3 M eff, Bonferroni p = g /M eff g = p, LOD, Microsoft Excel Excel Chiinv LOD, Chiinv, BC 1 RIL 1, F 2 2 LRT, 2ln 10 LOD, LOD=Chiinv( p, df)/2ln10 (2), LOD, 3 (M eff ) (M eff ), Bonferroni g = p, (2) LOD 1 2 QTL 表 1 定位加显性效应 QTL 的一维扫描中, MD = 1 cm 时 3 种群体在不同基因组长度下的 LOD 临界值 Table 1 LOD threshold of three populations with different genome lengths in one dimensional scanning of additive-dominant QTL when MD = 1 cm BC 1 RIL F 2 Genome length (cm) α g =0.05 α g =0.01 α g =0.05 α g =0.01 α g =0.05 α g =

6 6 39 表 2 定位加显性效应 QTL 的一维扫描中, MD = 20 cm 时 3 种群体在不同基因组长度下的 LOD 临界值 Table 2 LOD threshold of three populations with different genome lengths in one dimensional scanning of additive-dominant QTL when MD = 20 cm BC 1 RIL F 2 Genome length (cm) α g =0.05 α g =0.01 α g =0.05 α g =0.01 α g =0.05 α g = , MD = 1 cm 20 cm, g = , BC 1 RIL F 2 LOD,,, LOD, RIL LOD BC 1, F 2 ( 1 2) RIL F 2 ( 3-c e, 3-d f),, RIL df = 1, F 2 df = 2, F 2 LOD RIL 1 2, 1~20 cm, 250~4000 cm, BC 1 RIL F 2 g =0.05 LOD 1.83~ ~ ~4.30; g =0.01 LOD 2.64~ ~ ~ QTL (M eff ) (MD) (CL) QTL cm 2, 2, 2 QTL LOD QTL,, 500 4, QTL, (M eff ) QTL,,, M eff, g =0.01 M eff g = a b, BC cm, g =0.05, ; g =0.01, , BC 1 RIL, F 2 RIL ( 4-c, e) QTL LOD 2,, 2, QTL,, 2 LOD,, n, 2, n, 2 n C,

7 1 : QTL LOD 7 图 3 定位加显性效应 QTL 的一维扫描中不同标记密度下有效独立检验次数 (M eff ) 与染色体长度 (CL) 呈线性关系 Fig. 3 Relationship between the effective number of independent test (M eff ) and the length of chromosome (CL) in one dimensional scanning of additive-dominant QTL a, c, e g =0.05 BC 1 RIL F 2 M eff CL ; b, d, f g =0.01 BC 1 RIL F 2 M eff CL a, c, e correspond to BC 1, RIL, and F 2 population respectively when g =0.05 and b, d, f correspond to BC 1, RIL, and F 2 population respectively when g = n C M eff, Bonferroni, 2 n p = g /( C M eff ) (3) 3 4 QTL, MD = 5 cm 20 cm, g = BC 1 RIL F 2 LOD 10, GL/10 4 M eff, C Bonferroni g = p, (3) LOD, BC 1 RIL df=1, F 2 df=4 3 4, QTL LOD QTL 5~20 cm, 250~4000 cm, BC 1 RIL F 2 g =0.05 LOD 3.13~ ~ ~8.19; g =0.01 LOD 3.88~ ~ ~9.90

8 8 39 图 4 定位上位性互作 QTL 的二维扫描中不同标记密度下有效独立检验次数 (M eff ) 与染色体长度 (CL) 呈二次幂关系 Fig. 4 Relationship between the effective number of independent test (M eff ) and the length of chromosome (CL) in two dimensional scanning of epistatic QTL a c e g =0.05 BC 1 RIL F 2 M eff CL, b d f g =0.01 BC 1 RIL F 2 M eff CL a, c, e correspond to BC 1, RIL, and F 2 population respectively when g =0.05 and b, d, f correspond to BC 1, RIL, and F 2 population respectively when g = LOD, 3 DH RIL F 2 Cheverud [13] Li Ji [15] Gao [16] (M eff ), [2] [12] Cheverud [13] Li Ji [15] Gao [16] QTL LOD,, QTL 0.05 LOD 5, Cheverud [13] Li Ji [15] Gao [16] 3, Li Ji [15], Gao [16], Cheverud [13], Cheverud [13] DH LOD,, 3 F 2, LOD 3

9 1 : QTL LOD 9 Table 3 表 3 定位上位性互作 QTL 的二维扫描中, MD = 5 cm 时 3 种群体在不同基因组长度下的 LOD 临界值 LOD threshold of three populations with different genome lengths in two dimensional scanning of epistatic QTL when MD = 5 cm BC 1 RIL F 2 Genome length (cm) α g =0.05 α g =0.01 α g =0.05 α g =0.01 α g =0.05 α g = Table 4 表 4 定位上位性互作 QTL 的二维扫描中, MD = 20 cm 时 3 种群体在不同基因组长度下的 LOD 临界值 LOD threshold of three populations with different genome lengths in two dimensional scanning of epistatic QTL when MD = 20 cm BC 1 RIL F 2 Genome length (cm) α g =0.05 α g =0.01 α g =0.05 α g =0.01 α g =0.05 α g = 表 5 不同方法估算的 LOD 临界值 Table 5 LOD threshold calculated by different methods Cheverud [13] Li & Ji [15] Gao [16] a M eff Population Simulation Permutation test DH Wheat DH population RIL Maize RIL population F 2 Rice F 2 population a a Method proposed by this study.

10 , 3 DH RIL 0.1 F 2, 3,, 3 讨论 QTL QTL (M eff ),, Bonferroni, LOD, 3 4, g =0.01 g =0.05,, , g =0.05,, BC 1 RIL QTL 0.05 ( g =0.05) LOD 2~3 [1] F 2, 2.6~4.3 QTL LOD QTL, BC 1 RIL QTL 3.1~6.0, F 2 5.1~8.2 3 BC 1 RIL F 2,, BC 1 2, ; RIL 2, ; F 2 3,, DH QTL DH BC 1, 2, 5 DH LOD BC 1 IM [1] (ICIM) [17-18,24], IM ICIM QTL,, QTL,,, LOD, LOD QTL, 5 cm,, QTL LOD cm LOD [25] QTL, QTL, QTL QTL LOD, QTL, QTL, QTL,, QTL LOD, QTL QTL, 4 结论 QTL QTL, LRT, QTL ; LOD ; BC 1 RIL F 2, BC 1, F 2 ;,, LOD QTL, (M eff ) ; QTL, (M eff ) Bonferroni,,, LOD, 0.05, BC 1 RIL F 2 QTL LOD 1.83~ ~ ~4.30; QTL LOD 3.13~ ~ ~8.19

11 1 : QTL LOD 11 References [1] Lander E S, Botstein D. Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 1989, 121: [2] van Ooijen J W. LOD significance thresholds for QTL analysis in experimental populations of diploid species. Heredity, 1999, 83: [3] Dupuis J, Siegmund D. Statistical methods for mapping quantitative trait loci from a dense set of markers. Genetics, 1999, 151: [4] Feingold E, Brown P O, Siegmund D. Gaussian models for genetic linkage analysis using complete high-resolution maps of identity by descent. Am J Hum Genet, 1993, 53: [5] Rebaï A, Goffinet B, Mangin B. Approximate thresh olds of interval mapping tests for QTL detection. Genetics, 1994, 138: [6] Dupuis J. Statistical Problems Associated with Mapping Complex and Quantitative Traits from Genomic Mismatch Scanning Data. PhD Dissertation of Stanford University, 1994 [7] Kruglyak L, Lander E S. A nonparametric approach for mapping quantitative trait loci. Genetics, 1995, 139: [8] Lander E, Kruglyak L. Genetic dissection of complex traits: guidelines for interpreting and reporting linkage results. Nat Genet, 1995, 11: [9] Piepho H P. A quick method for computing approximate thresholds for quantitative trait loci detection. Genetics, 2001, 157: [10] Zou F, Fine J P, Hu J H, Lin D Y. An efficient resampling method for assessing genome-wide statistical significance in mapping quantitative trait loci. Genetics, 2004, 168: [11] Chang M N, Wu R, Wu S S, Casella G. Score statistics for mapping quantitative trait loci. Stat Appl Genet Mol Biol, 2009, 8: 16 [12] Churchill G A, Doerge R W. Empirical threshold values for quantitative trait mapping. Genetics, 1994, 138: [13] Cheverud J M. A simple correction for multiple comparisons in interval mapping genome scans. Heredity, 2001, 87: [14] Nyholt D R. A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with each other. Am J Hum Genet, 2004, 74: [15] Li J, Ji L. Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix. Heredity, 2005, 95: [16] Gao X, Starmer J, Martin E R. A multiple testing correction method for genetic association studies using correlated single nucleotide polymorphisms. Genet Epidemiol, 2008, 32: [17] Li H, Ribaut J M, Li Z, Wang J. Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations. Theor Appl Genet, 2008, 116: [18] Zhang L, Li H, Li Z, Wang J. Interactions between markers can be caused by the dominance effect of QTL. Genetics, 2008, 180: [19] Zhang L, Li H, Wang J. Statistical power of inclusive composite interval mapping in detecting digenic epistasis showing common F 2 segregation ratios. J Integr Plant Biol, 2012, 54: [20] Doerge R W, Rebaï A. Significance thresholds for QTL interval mapping tests. Heredity, 1996, 76: [21] Wang J, Chapman S C, Bonnett D G, Rebetzke G J. Simultaneous selection of major and minor genes: use of QTL to increase selection efficiency of coleoptiles length of wheat (Triticum aestivum L.). Theor Appl Genet, 2009, 119: [22] Ribaut J M, Hoisington D A, Deutsch J A, Jiang C, González-de-León D. Identification of quantitative trait loci under drought conditions in tropical maize: 1. Flowering parameters and the anthesis-silking interval. Theor Appl Genet, 1996, 92: [23] Zhang L, Wang S, Li H, Deng Q, Zheng A, Li S, Li P, Li Z, Wang J. Effects of missing marker and segregation distortion on QTL mapping in F 2 populations. Theor Appl Genet, 2010, 121: [24] Li H, Ye G, Wang J. A modified algorithm for the improvement of composite interval mapping. Genetics, 2007, 175: [25] Li H-H( ), Zhang L-Y( ), Wang J-K( ). Analytical answers to frequently asked questions in quantitative trait locus mapping. Acta Agron Sin ( ), 2010, 36(6): (in Chinese with English abstract)

Microsoft Word - 李慧慧.doc

Microsoft Word - 李慧慧.doc 作物学报 ACTA AGRONOMICA SINICA 010, 36(6): 918 931 http://www.chinacrops.org/zwxb/ ISSN 0496-3490; CODEN TSHPA9 E-mail: xbzw@chinajournal.net.cn DOI: 10.374/SP.J.1006.010.00918 数量性状基因定位研究中若干常见问题的分析与解答 * 李慧慧张鲁燕王建康