全基因组关联分析中混合模型的原理、优化与应用

doi:10.3864/j.issn.0578-1752.2023.09.001

摘要/Abstract

摘要：

全基因组关联分析（genome-wide association study，GWAS）是定位基因组中与性状显著关联的变异位点的有效方法。随着表型记录的完善、高通量基因型分型技术的发展，以及统计方法的改进，全基因组关联分析在人类疾病、动物植物遗传等领域得到了广泛的应用。假阳性是影响全基因组关联分析结果可靠性的重要因素之一。为了控制假阳性，除了校正P值，GWAS模型从最简单的方差分析（或用于质量性状的卡方检验）到加入固定效应协变量的普通线性模型（general linear model，GLM），再到加入随机效应的混合线性模型（mixed linear model，MLM）持续改进，控制了多种混杂因素导致的假阳性。将个体的遗传效应拟合为由基因组亲缘关系矩阵（genomic relationships matrix，GRM）定义的随机效应是目前常用的方法。由于MLM的参数估计大量消耗计算资源，研究人员不断尝试模型求解优化和GRM的构建优化（GRM的构建优化同时也提高了计算效率），最终将基于MLM计算的时间复杂度由O（MN³）逐步改进到O（MN），实现了计算速度与统计功效的飞跃。针对质量性状病例对照比失衡带来的假阳性问题，研究人员进一步对广义混合线性模型（generalized linear mixed model，GLMM）进行了校正。本文较全面地介绍了GWAS的基本原理和发展，着重阐述了GWAS中MLM模型的改进和优化细节，同时，列举了GWAS在农业中的应用，包括在植物、动物和微生物方面的研究成果，以及基于单倍型的GWAS应用。最后，从进一步提高GWAS统计功效和GWAS试验设计2个角度对GWAS未来的发展进行了展望。

关键词: 全基因组关联分析, 复杂性状, 随机效应, 基因组亲缘关系矩阵, 混合线性模型

Abstract:

Genome-wide association study (GWAS) is an effective method to locate genomic loci that are significantly associated with traits. With the accumulated phenotypic data, the continuous development of high-throughput genotyping technology, and the improved statistical methods, it promotes the wide application of GWAS in area of human disease and animal and plant genetics. False positives are one of the important concerns that impair the reliability of genome-wide association results. To control the false positives, in addition to correcting the P-values, GWAS models have been continuously improved from the naive methods like ANOVA (for quantitative trait) or Chi-square test (for quality trait), to general linear model (GLM), which incorporates fixed-effect covariates, to the mixed linear model (MLM), which incorporates random effects. Fitting individual genetic effects into random effects defined by the genomic relationships matrix (GRM) is commonly adapted currently. Since the parameter estimation of MLM consumes a lot of computational resources, researchers have tried to optimize solving models and constructing GRM (which also improves computing efficiency), and the time complexity gradually decreased from O(MN³) to O(MN) for MLM-based methods, achieving a great leap in computational speed and statistical efficacy. For inflations caused by unbalanced case-control data, researchers further correct the generalized mixed linear model (GLMM). This paper comprehensively introduces the basic principles and development of GWAS, with specific emphasis on the model improvement and optimization details. We also list the applications of MLM in GWAS in agriculture, including progress on animals, plants and microbes, as well as the application of haplotype in GWAS. Finally, we give prospects on the future developments of GWAS from the viewpoints of further model optimization and experimental design.

Key words: genome-wide association study, complex traits, random effects, genomic relationships matrix, mixed linear model

谭力治, 赵毅强. 全基因组关联分析中混合模型的原理、优化与应用[J]. 中国农业科学, 2023, 56(9): 1617-1632.

TAN LiZhi, ZHAO YiQiang. Principle, Optimization and Application of Mixed Models in Genome- Wide Association Study[J]. Scientia Agricultura Sinica, 2023, 56(9): 1617-1632.

0
/ / 推荐

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: https://www.chinaagrisci.com/CN/10.3864/j.issn.0578-1752.2023.09.001

https://www.chinaagrisci.com/CN/Y2023/V56/I9/1617

图/表 4

图1

表1

GWAS中MLM的优化模型"

计算模型 Computational model	功能与方法要点 Methodological highlights	计算速度 Computational speed	发表时间 Publication time	参考文献 Reference	来源网站 Resource
EMMA	似然估计的优化对象为遗传方差和残差方差之比 Optimize the ratio of genetic variance to residual variance in ML or REML	慢 Low	2008	[18]	https://tassel.bitbucket.io
CMLM	对个体间的亲缘关系进行聚类，通过用组的相似性替代个体的相似性，提高计算速度同时提高检测功效 Cluster the kinship among individuals, replace individual similarity with group similarity to improve both computing speed and statistical power	中 Intermediate	2010	[20]	https://tassel.bitbucket.io
EMMAX	单次估计随机效应方差，转化混合线性模型为普通线性模型 Single estimation of variance of random effects, transform mixed linear model into an ordinary linear model	中 Intermediate	2010	[19]	https://csg.sph.umich.edu/kang/emmax
FaST-LMM	通过对随机效应矩阵的特征分解去掉相关性，将混合线性模型转化为包括目标标记效应的普通线性模型 Transform mixed linear model into an ordinary linear model with by performing spectral decomposition of the random effects matrix to remove correlations	中/快（n<m） Intermediate/fast (n<m)	2011	[5]	https://github.com/fastlmm/FaST-LMM
GEMMA	通过优化矩阵运算和迭代算法，加速标记效应的精确估计 Accelerate the exact estimation of marker effects by optimizing algorithms of matrix operations and iterative algorithm	中 Intermediate	2012	[24]	https://www.xzlab.org/software.html
GRAMMAR -Gamma	对表型残差和GRAMMAR-Gamma因子进行估计并优化。对表型残差和基因型之间的关联进行得分检验并校正统计量 Estimate and optimize phenotypic residuals and GRAMMAR-Gamma factors. Implement score-based association test and corrections for the statistic	快 Fast	2012	[23]	https://github.com/GenABEL-Project
MLMM	将多个相关标记作为固定效应拟合到MLM中，以逐步回归的方式压缩由随机效应解释的方差，实现随机效应的消除 Include significant markers in the MLM as fixed covariates, splitting the variance explained by random effects by forward-backward stepwise approach to eliminate random effects	中 Intermediate	2012	[28]	https://github.com/timflutre/mlmm.gwas
SUPER	使用区间内最显著的标记并剔除与待测标记连锁的标记后，对剩余标记构建性状特异的亲缘矩阵 Use the most significant markers to represent each bin and exclude markers that are in LD to the testing markers, construct a complementary trait specific kinship with remaining markers.	中 Intermediate	2014	[26]	https://www.zzlab.net
BOLT-LMM	计算近似表型残差，使用贝叶斯模型与经典关联方法结合的回顾性得分统计量检验残差与检测标记间的关联 Compute approximate phenotypic residuals and tests the residuals for association with candidate markers via a retrospective score statistic that integrate Bayesian modeling and frequentist association testing	很快 Very fast	2015	[6]	https://alkesgroup.broadinstitute.org/BOLT-LMM
FarmCPU	独立随机效应模型筛选位点，独立的固定效应验证位点，两者交替使用直到没有新的候选标记进入到模型中 Markers are estimated by REM and tested by FEM independently, and both methods are used iteratively until no change on new candidate markers	快 Fast	2016	[14]	https://www.zzlab.net/FarmCPU
BLINK	使用贝叶斯信息标准替代随机效应中的REML估计，使用LD信息挑选候选位点，不再使用混合线性模型 Replace REML with BIC in estimating random effects and select candidate markers by LD, the mixed linear model is no longer used	快 Fast	2018	[29]	https://www.zzlab.net/blink
FastGWA	基于亲缘关系矩阵稀疏化和网格搜索的REML算法的计算优化 Computational optimization of REML algorithm based on sparse GRM and grid search	极快 Extremely fast	2019	[7]	https://yanglab.westlake.edu.cn/software/

表1

图2

表2

参考文献 88

[1]	BOTSTEIN D, RISCH N. Discovering genotypes underlying human phenotypes: Past successes for Mendelian disease, future approaches for complex disease. Nature Genetics, 2003, 33(3): 228-237. doi: 10.1038/ng1090
[2]	VISSCHER P M, BROWN M A, MCCARTHY M I, YANG J. Five years of GWAS discovery. The American Journal of Human Genetics, 2012, 90(1): 7-24. doi: 10.1016/j.ajhg.2011.11.029
[3]	VISSCHER P M, WRAY N R, ZHANG Q, SKLAR P, MCCARTHY M I, BROWN M A, YANG J. 10 years of GWAS discovery: Biology, function, and translation. The American Journal of Human Genetics, 2017, 101(1): 5-22. doi: 10.1016/j.ajhg.2017.06.005
[4]	YU J, PRESSOIR G, BRIGGS W H, BI I V, YAMASAKI M, DOEBLEY J F, MCMULLEN M D, GAUT B S, NIELSEN D M, HOLLAND J B, KRESOVICH S, BUCKLER E S. A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nature Genetics, 2006, 38(2): 203-208. doi: 10.1038/ng1702 pmid: 16380716
[5]	LIPPERT C, LISTGARTEN J, LIU Y, KADIE C M, DAVIDSON R I, HECKERMAN D. FaST linear mixed models for genome-wide association studies. Nature Methods, 2011, 8(10): 833-835. doi: 10.1038/nmeth.1681 pmid: 21892150
[6]	LOH P R, TUCKER G, BULIK-SULLIVAN B K, VILHJÁLMSSON B J, FINUCANE H K, SALEM R M, CHASMAN D I, RIDKER P M, NEALE B M, BERGER B, PATTERSON N, PRICE A L. Efficient Bayesian mixed-model analysis increases association power in large cohorts. Nature Genetics, 2015, 47(3): 284-290. doi: 10.1038/ng.3190
[7]	JIANG L, ZHENG Z, QI T, KEMPER K E, WRAY N R, VISSCHER P M, YANG J. A resource-efficient tool for mixed model association analysis of large-scale data. Nature Genetics, 2019, 51(12): 1749-1755. doi: 10.1038/s41588-019-0530-8 pmid: 31768069
[8]	卜李那, 赵毅强. 全基因组关联分析及其扩展方法的研究进展. 农业生物技术学报, 2019, 27(1): 150-158.
	BU L N, ZHAO Y Q. Research progress of genome-wide association study and its extension methods. Journal of Agricultural Biotechnology, 2019, 27(1): 150-158. (in Chinese)
[9]	CARDON L R, PALMER L J. Population stratification and spurious allelic association. The Lancet, 2003, 361(9357): 598-604. doi: 10.1016/S0140-6736(03)12520-2
[10]	DEVLIN B, ROEDER K. Genomic control for association studies. Biometrics, 1999, 55(4): 997-1004. doi: 10.1111/j.0006-341x.1999.00997.x pmid: 11315092
[11]	PRICE A L, PATTERSON N J, PLENGE R M, WEINBLATT M E, SHADICK N A, REICH D. Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics, 2006, 38(8): 904-909. doi: 10.1038/ng1847 pmid: 16862161
[12]	SHAM P C, PURCELL S M. Statistical power and significance testing in large-scale genetic studies. Nature Reviews Genetics, 2014, 15(5): 335-346. doi: 10.1038/nrg3706 pmid: 24739678
[13]	GAO X, BECKER L C, BECKER D M, STARMER J D, PROVINCE M A. Avoiding the high Bonferroni penalty in genome-wide association studies. Genetic Epidemiology, 2010, 34(1): 100-105. doi: 10.1002/gepi.20430 pmid: 19434714
[14]	LIU X L, HUANG M, FAN B, BUCKLER E S, ZHANG Z. Iterative usage of fixed and random effect models for powerful and efficient genome-wide association studies. PLoS Genetics, 2016, 12(2): 1-24.
[15]	ZHAO K Y, ARANZANA M J, KIM S, LISTER C, SHINDO C, TANG C, TOOMAJIAN C, ZHENG H G, DEAN C, MARJORAM P, NORDBORG M. An Arabidopsis example of association mapping in structured samples. PLoS Genetics, 2007, 3(1): 71-82.
[16]	XIAO Y J, LIU H J, WU L J, WARBURTON M, YAN J B. Genome-wide association studies in maize: Praise and stargaze. Molecular Plant, 2017, 10(3): 359-374. doi: S1674-2052(16)30308-2 pmid: 28039028
[17]	温阳俊, 冯建英, 张瑾. 多位点关联分析方法学的研究进展. 南京农业大学学报, 2022, 45(1): 1-10.
	WEN Y J, FENG J Y, ZHANG J. Research progress of multi-locus genome-wide association study. Journal of Nanjing Agricultural University, 2022, 45(1): 1-10. (in Chinese)
[18]	KANG H M, ZAITLEN N A, WADE C M, KIRBY A, HECKERMAN D, DALY M J, ESKIN E. Efficient control of population structure in model organism association mapping. Genetics, 2008, 178(3): 1709-1723. doi: 10.1534/genetics.107.080101 pmid: 18385116
[19]	KANG H M, SUL J H, SERVICE S K, ZAITLEN N A, KONG S Y, FREIMER N B, SABATTI C, ESKIN E. Variance component model to account for sample structure in genome-wide association studies. Nature Genetics, 2010, 42(4): 348-354. doi: 10.1038/ng.548 pmid: 20208533
[20]	ZHANG Z W, ERSOZ E, LAI C Q, TODHUNTER R J, TIWARI H K, GORE M A, BRADBURY P J, YU J M, ARNETT D K, ORDOVAS J M, BUCKLER E S. Mixed linear model approach adapted for genome-wide association studies. Nature Genetics, 2010, 42(4): 355-360. doi: 10.1038/ng.546 pmid: 20208535
[21]	LI M, LIU X L, BRADBURY P, YU J M, ZHANG Y M, TODHUNTER R J, BUCKLER E S, ZHANG Z W. Enrichment of statistical power for genome-wide association studies. BMC Biology, 2014, 12(1): 1-10. doi: 10.1186/1741-7007-12-1
[22]	AULCHENKO Y S, DE KONING D J, HALEY C. Genomewide rapid association using mixed model and regression: A fast and simple method for genomewide pedigree-based quantitative trait loci association analysis. Genetics, 2007, 177(1): 577-585. doi: 10.1534/genetics.107.075614 pmid: 17660554
[23]	SVISHCHEVA G R, AXENOVICH T I, BELONOGOVA N M, VAN DUIJN C M, AULCHENKO Y S. Rapid variance components-based method for whole-genome association analysis. Nature Genetics, 2012, 44(10): 1166-1170. doi: 10.1038/ng.2410 pmid: 22983301
[24]	ZHOU X, STEPHENS M. Genome-wide efficient mixed-model analysis for association studies. Nature Genetics, 2012, 44(7): 821-824. doi: 10.1038/ng.2310 pmid: 22706312
[25]	LISTGARTEN J, LIPPERT C, KADIE C M, DAVIDSON R I, ESKIN E, HECKERMAN D. Improved linear mixed models for genome-wide association studies. Nature Methods, 2012, 9(6): 525-526. doi: 10.1038/nmeth.2037 pmid: 22669648
[26]	WANG Q S, TIAN F, PAN Y C, BUCKLER E S, ZHANG Z W. A SUPER powerful method for genome wide association study. PLoS ONE, 2014, 9(9): 1-9.
[27]	BULIK-SULLIVAN B K, LOH P R, FINUCANE H K, RIPKE S, YANG J, PATTERSON N, DALY M J, PRICE A L, NEALE B M. LD Score regression distinguishes confounding from polygenicity in genome-wide association studies. Nature Genetics, 2015, 47(3): 291-295. doi: 10.1038/ng.3211
[28]	SEGURA V, VILHJÁLMSSON B J, PLATT A, KORTE A, SEREN Ü, LONG Q, NORDBORG M. An efficient multi-locus mixed-model approach for genome-wide association studies in structured populations. Nature Genetics, 2012, 44(7): 825-830. doi: 10.1038/ng.2314 pmid: 22706313
[29]	HUANG M, LIU X L, ZHOU Y, SUMMERS R M, ZHANG Z W. BLINK: A package for the next level of genome-wide association studies with both individuals and markers in the millions. GigaScience, 2019, 8(2): 1-12.
[30]	FU W W, WANG R, XU N Y, WANG J X, LI R, NANAEI H A, NIE Q H, ZHAO X, HAN J L, YANG N, JIANG Y. Galbase: A comprehensive repository for integrating chicken multi-omics data. BMC Genomics, 2022, 23(1): 1-11. doi: 10.1186/s12864-021-08243-4
[31]	YANG J, LEE S H, GODDARD M E, VISSCHER P M. GCTA: A tool for genome-wide complex trait analysis. American Journal of Human Genetics. 2011, 88(1): 76-82. doi: 10.1016/j.ajhg.2010.11.011 pmid: 21167468
[32]	CHEN H, WANG C L, CONOMOS M P, STILP A M, LI Z L, SOFER T, SZPIRO A A, CHEN W, BREHM J M, CELEDON J C, REDLINE S, PAPANICOLAOU G J, THORNTON T A, LAURIE C C, RICE K, LIN X H. Control for population structure and relatedness for binary traits in genetic association studies via logistic mixed models. The American Journal of Human Genetics, 2016, 98(4): 653-666. doi: 10.1016/j.ajhg.2016.02.012
[33]	ZHOU W, NIELSEN J B, FRITSCHE L G, DEY R, GABRIELSEN M E, WOLFORD B N, LEFAIVE J, VANDEHAAR P, GAGLIANO S A, GIFFORD A, BASTARACHE L A, WEI W Q, DENNY J C, LIN M X, HVEEM K, KANG H M, ABECASIS G R, WILLER C J, LEE S. Efficiently controlling for case-control imbalance and sample relatedness in large-scale genetic association studies. Nature Genetics, 2018, 50(9): 1335-1341. doi: 10.1038/s41588-018-0184-y pmid: 30104761
[34]	JIANG L D, ZHENG Z L, FANG H L, YANG J. A generalized linear mixed model association tool for biobank-scale data. Nature Genetics, 2021, 53(11): 1616-1621. doi: 10.1038/s41588-021-00954-4 pmid: 34737426
[35]	BI W J, ZHOU W, DEY R, MUKHERJEE B, SAMPSON J N, LEE S. Efficient mixed model approach for large-scale genome-wide association studies of ordinal categorical phenotypes. The American Journal of Human Genetics, 2021, 108(5): 825-839. doi: 10.1016/j.ajhg.2021.03.019
[36]	HANSEN M, KRAFT T, GANESTAM S, SÄLL T, NILSSON N O. Linkage disequilibrium mapping of the bolting gene in sea beet using AFLP markers. Genetical Research, 2001, 77(1): 61-66. doi: 10.1017/S0016672300004857
[37]	ATWELL S, HUANG Y S, VILHJÁLMSSON B J, WILLEMS G, HORTON M, LI Y, MENG D Z, PLATT A, TARONE A M, HU T T, JIANG R, MULIYATI N W, ZHANG X, AMER M A, BAXTER I, BRACHI B, CHORY J, DEAN C, DEBIEU M, DE MEAUX J, ECKER J R, FAURE N, KNISKERN J M, JONES J D G, MICHAEL T, NEMRI A, ROUX F, SALT D E, TANG C L, TODESCO M, TRAW M B, WEIGEL D, MARJORAM P, BOREVITZ J O, BERGELSON J, NORDBORG M. Genome-wide association study of 107 phenotypes in Arabidopsis thaliana inbred lines. Nature, 2010, 465(7298): 627-631. doi: 10.1038/nature08800
[38]	ZHAO K Y, TUNG C W, EIZENGA G C, WRIGHT M H, ALI M L, H PRICE A, NORTON G J, ISLAM M R, REYNOLDS A, MEZEY J, MCCLUNG A M, BUSTAMANTE C D, MCCOUCH S R. Genome-wide association mapping reveals a rich genetic architecture of complex traits in Oryza sativa. Nature Communications, 2011, 2(1): 1-10.
[39]	HUANG X H, WEI X H, SANG T, ZHAO Q, FENG Q, ZHAO Y, LI C Y, ZHU C R, LU T T, ZHANG Z W, LI M, FAN D L, GUO Y L, WANG A H, WANG L, DENG L W, LI W J, LU Y Q, WENG Q J, LIU K Y, HUANG T, ZHOU T Y, JING Y F, LI W, LIN Z, BUCKLER E S, QIAN Q, ZHANG Q F, LI J Y, HAN B. Genome-wide association studies of 14 agronomic traits in rice landraces. Nature Genetics, 2010, 42(11): 961-967. doi: 10.1038/ng.695 pmid: 20972439
[40]	HUANG X H, ZHAO Y, WEI X H, LI C Y, WANG A H, ZHAO Q, LI W J, GUO Y L, DENG L W, ZHU C R, FAN D L, LU Y Q, WENG Q J, LIU K Y, ZHOU T F, JING Y F, SI L Z, DONG G J, HUANG T, LU T T, FENG Q, QIAN Q, LI J Y, HAN B. Genome-wide association study of flowering time and grain yield traits in a worldwide collection of rice germplasm. Nature Genetics, 2012, 44(1): 32-39. doi: 10.1038/ng.1018
[41]	YONEMARU J I, MIZOBUCHI R, KATO H, YAMAMOTO T, YAMAMOTO E, MATSUBARA K, HIRABAYASHI H, TAKEUCHI Y, TSUNEMATSU H, ISHII T, OHTA H, MAEDA H, EBANA K, YANO M. Genomic regions involved in yield potential detected by genome-wide association analysis in Japanese high-yielding rice cultivars. BMC Genomics, 2014, 15(1): 1-12. doi: 10.1186/1471-2164-15-1
[42]	WANG M, YAN J B, ZHAO J R, SONG W, ZHANG X B, XIAO Y N, ZHENG Y L. Genome-wide association study (GWAS) of resistance to head smut in maize. Plant Science, 2012, 196(1): 125-131. doi: 10.1016/j.plantsci.2012.08.004
[43]	LI H, PENG Z Y, YANG X H, WANG W D, FU J J, WANG J H, HAN Y J, CHAI Y C, GUO T T, YANG N, LIU J, WARBURTON M L, CHENG Y B, HAO X M, ZHANG P, ZHAO J Y, LIU Y J, WANG G Y, LI J S, YAN J B. Genome-wide association study dissects the genetic architecture of oil biosynthesis in maize kernels. Nature Genetics, 2013, 45(1): 43-50. doi: 10.1038/ng.2484 pmid: 23242369
[44]	LI Y X, LI C H, BRADBURY P J, LIU X L, LU F, ROMAY C M, GLAUBITZ J C, WU X, PENG B, SHI Y S, SONG Y C, ZHANG D F, BUCKLER E S, ZHANG Z W, LI Y, WANG T Y. Identification of genetic variants associated with maize flowering time using an extremely large multi-genetic background population. The Plant Journal, 2016, 86(5): 391-402. doi: 10.1111/tpj.2016.86.issue-5
[45]	SEKHON R S, SASKI C, KUMAR R, FLINN B S, LUO F, BEISSINGER T M, ACKERMAN A J, BREITZMAN M W, BRIDGES W C, DE LEON N, KAEPPLER S M. Integrated genome-scale analysis identifies novel genes and networks underlying senescence in maize. The Plant Cell, 2019, 31(9): 1968-1989. doi: 10.1105/tpc.18.00930 pmid: 31239390
[46]	CHAO Z F, CHEN Y Y, JI C, WANG Y L, HUANG X, ZHANG C Y, YANG J, SONG T, WU J C, GUO L X, LIU C B, HAN M L, WU Y R, YAN J B, CHAO D Y. A genome-wide association study identifies a transporter for zinc uploading to maize kernels. EMBO Reports, 2023, 24(1): 1-19.
[47]	REN J, DUAN Y Y, QIAO R M, YAO F, ZHANG Z Y, YANG B, GUO Y M, XIAO S J, WEI R X, OUYANG Z X, DING N S, AI H S, HUANG L S. A missense mutation in PPARD causes a major QTL effect on ear size in pigs. PLoS Genetics, 2011, 7(5): 1-10.
[48]	MA J W, YANG J, ZHOU L S, REN J, LIU X X, ZHANG H, YANG B, ZHANG Z Y, MA H B, XIE X H, XING Y Y, GUO Y M, HUANG L S. A splice mutation in the PHKG1 gene causes high glycogen content and low meat quality in pig skeletal muscle. PLoS Genetics, 2014, 10(10): 1-13.
[49]	WANG X M, LIU X L, DENG D D, YU M, LI X P. Genetic determinants of pig birth weight variability. BMC Genetics, 2016, 17(1): 41-48. doi: 10.1186/s12863-016-0351-z
[50]	GUO X Y, SU G S, CHRISTENSEN O F, JANSS L, LUND M S. Genome-wide association analyses using a Bayesian approach for litter size and piglet mortality in Danish Landrace and Yorkshire pigs. BMC Genomics, 2016, 17(1): 1-12.
[51]	GOZALO-MARCILLA M, BUNTJER J, JOHNSSON M, BATISTA L, DIEZ F, WERNER C R, CHEN C Y, GORJANC G, MELLANBY R J, HICKEY J M, ROS-FREIXEDES R. Genetic architecture and major genes for backfat thickness in pig lines of diverse genetic backgrounds. Genetics, Selection, Evolution, 2021, 53(1): 1-14. doi: 10.1186/s12711-020-00598-8
[52]	GU X R, FENG C G, MA L, SONG C, WANG Y Q, DA Y, LI H F, CHEN K W, YE S H, GE C R, HU X X, LI N. Genome-wide association study of body weight in chicken F₂ resource population. PLoS ONE, 2011, 6(7): 1-5.
[53]	IMSLAND F, FENG C G, BOIJE H, BED'HOM B, FILLON V, DORSHORST B, RUBIN C J, LIU R R, GAO Y, GU X R, WANG Y Q, GOURICHON D, ZODY M C, ZECCHIN W, VIEAUD A, TIXIER-BOICHARD M, HU X X, HALLBÖÖK F, LI N, ANDERSSON L. The Rose-comb mutation in chickens constitutes a structural rearrangement causing both altered comb morphology and defective sperm motility. PLoS Genetics, 2012, 8(6): 1-12.
[54]	GUO Y, GU X R, SHENG Z Y, WANG Y Q, LUO C L, LIU R R, QU H, SHU D M, WEN J, CROOIJMANS R P M A, CARLBORG Ö, ZHAO Y Q, HU X X, LI N. A complex structural variation on chromosome 27 leads to the ectopic expression of hoxb8 and the muffs and beard phenotype in chickens. PLoS Genetics, 2016, 12(6): 1-24.
[55]	WANG Y Z, CAO X M, LUO C L, SHENG Z Y, ZHANG C Y, BIAN C, FENG C G, LI J X, GAO F, ZHAO Y Q, JIANG Z Q, QU H, SHU D M, CARLBORG Ö, HU X X, LI N. Multiple ancestral haplotypes harboring regulatory mutations cumulatively contribute to a QTL affecting chicken growth traits. Communications Biology, 2020, 3(1): 1-13. doi: 10.1038/s42003-019-0734-6
[56]	FAN Q C, WU P F, DAI G J, ZHANG G X, ZHANG T, XUE Q, SHI H Q, WANG J Y. Identification of 19 loci for reproductive traits in a local Chinese chicken by genome-wide study. Genetics and Molecular Research, 2017, 16(1): 1-8.
[57]	LI Q L, DUAN Z Y, SUN C J, ZHENG J X, XU G Y, YANG N. Genetic variations for the eggshell crystal structure revealed by genome-wide association study in chickens. BMC Genomics, 2021, 22(1): 1-12. doi: 10.1186/s12864-020-07350-y
[58]	GUO Y P, HUANG H T, ZHANG Z Z, MA Y C, LI J Z, TANG H H, MA H X, LI Z J, LI W T, LIU X J, KANG X T, HAN R L. Genome-wide association study identifies SNPs for growth performance and serum indicators in Valgus-Varus deformity broilers (Gallus gallus) using ddGBS sequencing. BMC Genomics, 2022, 23(1): 1-11. doi: 10.1186/s12864-021-08243-4
[59]	张统雨, 朱才业, 杜立新, 赵福平. 羊重要性状全基因组关联分析研究进展. 遗传, 2017, 39(06): 491-500.
	ZHANG T Y, ZHU C Y, DU L X, ZHAO F P. Advances in genome-wide association studies for important traits in sheep and goats. Hereditas(Beijing), 2017, 39(6): 491-500. (in Chinese)
[60]	DEMARS J, FABRE S, SARRY J, ROSSETTI R, GILBERT H, PERSANI L, TOSSER-KLOPP G, MULSANT P, NOWAK Z, DROBIK W, MARTYNIUK E, BODIN L. Genome-wide association studies identify two novel BMP15 mutations responsible for an atypical hyperprolificacy phenotype in sheep. PLoS Genetics, 2013, 9(4): 1-13.
[61]	HE X H, ZHOU Z K, PU Y B, CHEN X F, MA Y H, JIANG L. Mapping the four-horned locus and testing the polled locus in three Chinese sheep breeds. Animal Genetics, 2016, 47(5): 623-627. doi: 10.1111/age.12464 pmid: 27427781
[62]	GJEDREM T. Genetic improvement for the development of efficient global aquaculture: A personal opinion review. Aquaculture, 2012, 344- 349(1): 12-22.
[63]	HOLBORN M K, ANG K P, ELLIOTT J A K, POWELL F, BOULDING E G. Genome wide association analysis for bacterial kidney disease resistance in a commercial North American Atlantic salmon (Salmo salar) population using a 50K SNP panel. Aquaculture, 2018, 495(1): 465-471. doi: 10.1016/j.aquaculture.2018.06.014
[64]	PENG W Z, XU J, ZHANG Y, FENG J X, DONG C J, JIANG L K, FENG J Y, CHEN B H, GONG Y W, CHEN L, XU P. An ultra-high density linkage map and QTL mapping for sex and growth-related traits of common carp (Cyprinus carpio). Scientific Reports, 2016, 6(1): 1-16. doi: 10.1038/s41598-016-0001-8
[65]	LIN H L, ZHOU Z X, ZHAO J, ZHOU T, BAI H Q, KE Q Z, PU F, ZHENG W Q, XU P. Genome-wide association study identifies genomic loci of sex determination and gonadosomatic index traits in large yellow croaker (Larimichthys crocea). Marine Biotechnology, 2021, 23(1): 127-139. doi: 10.1007/s10126-020-10007-2 pmid: 33196953
[66]	DAVILA OLIVAS N H, KRUIJER W, GORT G, WIJNEN C L, VAN LOON J J A, DICKE M. Genome-wide association analysis reveals distinct genetic architectures for single and combined stress responses in Arabidopsis thaliana. New Phytologist, 2017, 213(2): 838-851. doi: 10.1111/nph.2017.213.issue-2
[67]	ZHANG F, HU Z Q, WU Z C, LU J L, SHI Y Y, XU J L, WANG X Y, WANG J P, ZHANG F, WANG M M, SHI X R, CUI Y R, VERA CRUZ C, ZHUO D L, HU D D, LI M, WANG W S, ZHAO X Q, ZHENG T Q, FU B Y, ALI J, ZHOU Y L, LI Z K. Reciprocal adaptation of rice and Xanthomonas oryzae pv. oryzae: Cross-species 2D GWAS reveals the underlying genetics. The Plant Cell, 2021, 33(8): 2538-2561. doi: 10.1093/plcell/koab146
[68]	MARTINS L B, BALINT-KURTI P, REBERG-HORTON S C. Genome-wide association study for morphological traits and resistance to Peryonella pinodes in the USDA pea single plant plus collection. G3 Genes\|Genomes\|Genetics, 2022, 12(9): 1-8.
[69]	KARASOV T L, CHAE E, HERMAN J J, BERGELSON J. Mechanisms to mitigate the trade-off between growth and defense. The Plant Cell, 2017, 29(4): 666-680. doi: 10.1105/tpc.16.00931 pmid: 28320784
[70]	DE RONNE M, SANTHANAM P, CINGET B, LABBÉ C, LEBRETON A, YE H, VUONG T D, HU H F, VALLIYODAN B, EDWARDS D, NGUYEN H T, BELZILE F, BÉLANGER R. Mapping of partial resistance to Phytophthora sojae in soybean PIs using whole-genome sequencing reveals a major QTL. The Plant Genome, 2022, 15(1): 1-16.
[71]	LIU Q, CHENG L, NIAN H, JIN J, LIAN T X. Linking plant functional genes to rhizosphere microbes: A review. Plant Biotechnology Journal, 2023, 21(5): 902-917. doi: 10.1111/pbi.v21.5
[72]	BAI B, LIU W D, QIU X Y, ZHANG J, ZHANG J Y, BAI Y. The root microbiome: Community assembly and its contributions to plant fitness. Journal of Integrative Plant Biology, 2022, 64(2): 230-243. doi: 10.1111/jipb.13226
[73]	BERGELSON J, MITTELSTRASS J, HORTON M W. Characterizing both bacteria and fungi improves understanding of the Arabidopsis root microbiome. Scientific Reports, 2019, 9(1): 1-11. doi: 10.1038/s41598-018-37186-2
[74]	DENG S W, CADDELL D F, XU G, DAHLEN L, WASHINGTON L, YANG J L, COLEMAN-DERR D. Genome wide association study reveals plant loci controlling heritability of the rhizosphere microbiome. The ISME Journal, 2021, 15(11): 3181-3194. doi: 10.1038/s41396-021-00993-z
[75]	DE FREITAS A S, DE DAVID D B, TAKAGAKI B M, ROESCH L F W. Microbial patterns in rumen are associated with gain of weight in beef cattle. Antonie Van Leeuwenhoek, 2020, 113(9): 1299-1312. doi: 10.1007/s10482-020-01440-3 pmid: 32577920
[76]	MALTECCA C, BERGAMASCHI M, TIEZZI F. The interaction between microbiome and pig efficiency: A review. Journal of Animal Breeding and Genetics, 2020, 137(1): 4-13. doi: 10.1111/jbg.12443 pmid: 31576623
[77]	XUE M Y, SUN H Z, WU X H, LIU J X, GUAN L L. Multi-omics reveals that the rumen microbiome and its metabolome together with the host metabolome contribute to individualized dairy cow performance. Microbiome, 2020, 8(1): 1-19. doi: 10.1186/s40168-019-0777-4
[78]	ELOKIL A A, MAGDY M, MELAK S, ISHFAQ H, BHUIYAN A, CUI L, JAMIL M, ZHAO S, LI S. Faecal microbiome sequences in relation to the egg-laying performance of hens using amplicon-based metagenomic association analysis. Animal, 2020, 14(4): 706-715. doi: 10.1017/S1751731119002428 pmid: 31619307
[79]	CRESPO-PIAZUELO D, MIGURA-GARCIA L, ESTELLÉ J, CRIADO-MESAS L, REVILLA M, CASTELLÓ A, MUÑOZ M, GARCÍA-CASCO J M, FERNÁNDEZ A I, BALLESTER M, FOLCH J M. Association between the pig genome and its gut microbiota composition. Scientific Reports, 2019, 9(1): 1-11. doi: 10.1038/s41598-018-37186-2
[80]	BERGAMASCHI M, MALTECCA C, SCHILLEBEECKX C, MCNULTY N P, SCHWAB C, SHULL C, FIX J, TIEZZI F. Heritability and genome-wide association of swine gut microbiome features with growth and fatness parameters. Scientific Reports, 2020, 10(1): 1-12. doi: 10.1038/s41598-019-56847-4
[81]	WANG Y T, SUNG P Y, LIN P L, YU Y W, CHUNG R H. A multi-SNP association test for complex diseases incorporating an optimal P-value threshold algorithm in nuclear families. BMC Genomics, 2015, 16(1): 1-10. doi: 10.1186/1471-2164-16-1
[82]	WANG F, MEYER N J, WALLEY K R, RUSSELL J A, FENG R. Causal genetic inference using haplotypes as instrumental variables. Genetic Epidemiology, 2016, 40(1): 35-44. doi: 10.1002/gepi.21940 pmid: 26625855
[83]	N'DIAYE A, HAILE J K, CORY A T, CLARKE F R, CLARKE J M, KNOX R E, POZNIAK C J. Single marker and haplotype-based association analysis of semolina and pasta colour in elite durum wheat breeding lines using a high-density consensus map. PLoS ONE, 2017, 12(1): 1-24.
[84]	YANO K, YAMAMOTO E, AYA K, TAKEUCHI H, LO P C, HU L, YAMASAKI M, YOSHIDA S, KITANO H, HIRANO K, MATSUOKA M. Genome-wide association study using whole-genome sequencing rapidly identifies new genes influencing agronomic traits in rice. Nature Genetics, 2016, 48(8): 927-934. doi: 10.1038/ng.3596 pmid: 27322545
[85]	OGAWA D, YAMAMOTO E, OHTANI T, KANNO N, TSUNEMATSU H, NONOUE Y, YANO M, YAMAMOTO T, YONEMARU J I. Haplotype-based allele mining in the Japan-MAGIC rice population. Scientific Reports, 2018, 8(1): 1-11.
[86]	ZHANG Z, GUILLAUME F, SARTELET A, CHARLIER C, GEORGES M, FARNIR F, DRUET T. Ancestral haplotype-based association mapping with generalized linear mixed models accounting for stratification. Bioinformatics, 2012, 28(19): 2467-2473. pmid: 22711794
[87]	ZHANG H, SHEN L Y, XU Z C, KRAMER L M, YU J Q, ZHANG X Y, NA W, YANG L L, CAO Z P, LUAN P, REECY J M, LI H. Haplotype-based genome-wide association studies for carcass and growth traits in chicken. Poultry Science, 2020, 99(5): 2349-2361. doi: S0032-5791(20)30086-9 pmid: 32359570
[88]	HOWARD D M, HALL L S, HAFFERTY J D, ZENG Y N, ADAMS M J, CLARKE T K, PORTEOUS D J, NAGY R, HAYWARD C, SMITH B H, MURRAY A D, RYAN N M, EVANS K L, HALEY C S, DEARY I J, THOMSON P A, MCINTOSH A M. Genome-wide haplotype-based association analysis of major depressive disorder in Generation Scotland and UK Biobank. Translational Psychiatry, 2017, 7(11): 1-9. doi: 10.1038/s41398-017-0009-2