[1]Risch N, Merikangas K. The future of genetic studies of complex human diseases. Science, 1996, 273: 1516–1517
[2]Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira M, Bender D, Maller J, Sklar P, De Bakker P, Daly M, Sham P C. PLINK: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet, 2007, 81: 559–575
[3]Wan X, Yang C, Yang Q, Xue H, Fan X D, Tang N L S, Yu W C. BOOST: a fast approach to detecting gene-gene interactions in genome-wide case-control studies. Am J Hum Genet, 2010, 87: 325–340
[4]Takeuchi F, Serizawa M, Yamamoto K, Fujisawa T, Nakashima E, Ohnaka K, Ikegami H, Sugiyama T, Katsuya T, Miyagishi M, Nakashima N, Nawata H, Nakamura J, Kono S, Takayanagi R, Kato N. Confirmation of multiple risk loci and genetic impacts by a genome-wide association study of type 2 diabetes in the Japanese population. Diabetes, 2009, 3: 1690–1699
[5]Michailidou K, Beesley J, Lindstrom S, Canisius S, Dennis J, Lush M J, Maranian M J, Bolla M K, Wang Q, Shah M, Perkins B J, Czene K, Eriksson M, Darabi H, Brand J S, Bojesen S E, Nordestgaard B G, Flyger H, Nielsen S F, Rahman N, Turnbull C; BOCS, Fletcher O, Peto J, Gibson L, dos-Santos-Silva I, Chang-Claude J, Flesch-Janys D, Rudolph A, Eilber U, Behrens S, Nevanlinna H, Muranen T A, Aittomäki K, Blomqvist C, Khan S, Aaltonen K, Ahsan H, Kibriya M G, Whittemore A S, John E M, Malone K E, Gammon M D, Santella R M, Ursin G, Makalic E, Schmidt D F, Casey G, Hunter D J, Gapstur S M, Gaudet M M, Diver W R, Haiman C A, Schumacher F, Henderson B E, Le Marchand L, Berg C D, Chanock S J, Figueroa J, Hoover R N, Lambrechts D, Neven P, Wildiers H, van Limbergen E, Schmidt M K, Broeks A, Verhoef S, Cornelissen S, Couch F J, Olson J E, Hallberg E, Vachon C, Waisfisz Q, Meijers-Heijboer H, Adank M A, van der Luijt R B, Li J, Liu J, Humphreys K, Kang D, Choi J Y, Park S K, Yoo K Y, Matsuo K, Ito H, Iwata H, Tajima K, Guénel P, Truong T, Mulot C, Sanchez M, Burwinkel B, Marme F, Surowy H, Sohn C, Wu A H, Tseng C C, Van Den Berg D, Stram D O, González-Neira A, Benitez J, Zamora M P, Perez J I, Shu X O, Lu W, Gao Y T, Cai H, Cox A, Cross S S, Reed M W, Andrulis I L, Knight J A, Glendon G, Mulligan A M, Sawyer E J, Tomlinson I, Kerin M J, Miller N; kConFab Investigators; AOCS Group, Lindblom A, Margolin S, Teo S H, Yip C H, Taib N A, Tan G H, Hooning M J, Hollestelle A, Martens J W, Collée J M, Blot W, Signorello L B, Cai Q, Hopper J L, Southey M C, Tsimiklis H, Apicella C, Shen C Y, Hsiung C N, Wu P E, Hou M F, Kristensen V N, Nord S, Alnaes G I; NBCS, Giles G G, Milne R L, McLean C, Canzian F, Trichopoulos D, Peeters P, Lund E, Sund M, Khaw K T, Gunter M J, Palli D, Mortensen L M, Dossus L, Huerta J M, Meindl A, Schmutzler R K, Sutter C, Yang R, Muir K, Lophatananon A, Stewart-Brown S, Siriwanarangsan P, Hartman M, Miao H, Chia K S, Chan C W, Fasching P A, Hein A, Beckmann M W, Haeberle L, Brenner H, Dieffenbach A K, Arndt V, Stegmaier C, Ashworth A, Orr N, Schoemaker M J, Swerdlow A J, Brinton L, Garcia-Closas M, Zheng W, Halverson S L, Shrubsole M, Long J, Goldberg M S, Labrèche F, Dumont M, Winqvist R, Pylkäs K, Jukkola-Vuorinen A, Grip M, Brauch H, Hamann U, Brüning T; GENICA Network, Radice P, Peterlongo P, Manoukian S, Bernard L, Bogdanova N V, Dörk T, Mannermaa A, Kataja V, Kosma V M, Hartikainen J M, Devilee P, Tollenaar R A, Seynaeve C, Van Asperen C J, Jakubowska A, Lubinski J, Jaworska K, Huzarski T, Sangrajrang S, Gaborieau V, Brennan P, McKay J, Slager S, Toland A E, Ambrosone C B, Yannoukakos D, Kabisch M, Torres D, Neuhausen S L, Anton-Culver H, Luccarini C, Baynes C, Ahmed S, Healey C S, Tessier D C, Vincent D, Bacot F, Pita G, Alonso M R, Álvarez N, Herrero D, Simard J, Pharoah P P, Kraft P, Dunning A M, Chenevix-Trench G, Hall P, Easton D F. Genome-wide association analysis of more than 120 000 individuals identifies 15 new susceptibility loci for breast cancer. Nat Genet, 2015, 47: 373–380
[6]Scuteri A, Sanna S, Chen W M, Uda M, Albai G, Strait J, Najjar S, Nagaraja R, Orrú M, Usala G, Dei M, Lai S, Maschio A, Busonero F, Mulas A, Ehret G B, Fink A A, Weder A B, Cooper R S, Galan P, Chakravarti A, Schlessinger D, Cao A, Lakatta E, Abecasis G R. Genome-wide association scan shows genetic variants in the FTO gene are associated with obesity-related traits. PLoS Genet, 2007, 3(7): e115
[7]Thornsberry J M, Goodman M M, Doebley J, Kresovich S, Nielsen D, Buckler E S. Dwarf8 polymorphisms associate with variation in flowering time. Nat Genet, 2001, 28: 286–289
[8]Hansen M, Kraft T, Ganestam S, Säll T, Nilsson N O. Linkage disequilibrium mapping of the bolting gene in sea beet using AFLP markers. Genet Res, 2001, 77: 61–66
[9]Zhang Y M, Mao Y C, Xie C Q, Smith H, Luo L, Xu S. Mapping quantitative trait loci using naturally occurring genetic variance among commercial inbred lines of maize (Zea mays L.). Genetics, 2005, 169: 2267–2275
[10]Yu J, Pressoir G, Briggs W H, Vroh Bi I, 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. Nat Genet, 2006, 38: 203–208
[11]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: 1709–1723
[12]Zhang Z, 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. Nat Genet, 2010, 42: 355–360
[13]Atwell S, Huang Y S, Vilhjálmsson B J, Willems G, Horton M, Li Y, Meng D, 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, Michael T, Nemri A, Roux F, Salt D E, Tang C, 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. J Am Soc Mass Spectrom, 2010, 465: 627–631
[14]Wang S B, Feng J Y, Ren W L, Huang B, Zhou L, Wen Y J, Zhang J, Jim M D, Xu S Z, Zhang Y M. Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology. Sci Rep, 2016, 6: 19444
[15]Liu X L, Huang M, Fan B, Buckler E S, Zhang Z W. Iterative usage of fixed and random effect models for powerful and efficient genome-wide association studies. PLoS Genet, 2016, 12(2): e1005767
[16]Zhang F T, Zhu Z H, Tong X R, Zhu Z X, Qi T, Zhu J. Mixed linear model approaches of association mapping for complex traits based on omics variants. Sci Rep, 2015, 5: 10298
[17]Devlin B, Roeder K. Genomic control for association studies. Biometrics, 1999, 55: 997–1004
[18]Song M, Hao W, Storey J D. Testing for genetic associations in arbitrarily structured populations. Nat Genet, 2015, 47: 550–556
[19]Pritchard J K, Stephens M, Donnelly P. Inference of population structure using multilocus genotype data. Genetics, 2000, 155: 945–959
[20]Wilson L M, Whitt S R, Ibáez A M, Rocheford T R, Goodman M M, Buckler E S. Dissection of maize kernel composition and starch production by candidate gene associations. Plant Cell, 2004, 16: 2719–2733
[21]Sabatti C, Service S K, Hartikainen A L, Pouta A, Ripatti S, Brodsky J, Jones C G, Zaitlen N A, Varilo T, Kaakinen M, Sovio U, Ruokonen A, Laitinen J, Jakkula E, Coin L, Hoggart C, Collins A, Turunen H, Gabriel S, Elliot P, McCarthy M I, Daly M J, Järvelin M R, Freimer N B, Peltonen L. Genome-wide association analysis of metabolic traits in a birth cohort from a founder population. Nat Genet, 2009, 41: 35–46
[22]Price A L, Pattersom N J, Plenge R M, Weinblatt M E, Shadick N A, Reich D. Principal components analysis corrects for stratification in genome-wide association studies. Nat Genet, 2006, 38: 904–909
[23]Lee A B, Luca D, Klei L, Devlin B, Roeder K. Discovering genetic ancestry using spectral graph theory. Genet Epidemiol, 2010, 34: 51–59
[24]Bulik-Sullivan B K, Loh P R, Finucane H K, Ripke S, Yang J; Schizophrenia Working Group of the Psychiatric Genomics Consortium, Patterson N, Daly M J, Price A L, Neale B M. LD score regression distinguishes confounding from polygenicity in genome-wide association studies. Nat Genet, 2015, 47: 291–295
[25]Bu S H , Zhao X W, Yi C, Wen J, Tu J X, Zhang Y M. Interacted QTL mapping in partial NCII design provides evidences for breeding by design. PLoS One, 2015, 10(3): e0121034
[26] 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 Biol, 2014, 12: 73–82
[27]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. Nat Genet, 2010, 42: 348–354
[28]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. Nat Genet, 2012, 44: 1166–1170
[29]Zhou X, Stephens M. Genome-wide efficient mixed-model analysis for association studies. Nat Genet, 2012, 44: 821–826
[30]Lippert C, Listqarten J, Liu Y, Kadie C M, Davidson R I, Heckerman D. Fast linear mixed models for genome-wide association studies. Nat Methods, 2011, 8: 833–835
[31]Listgarten J, Lippert C, Kadie C M, Davidson R I, Eskin E, Heckerman D. Improved linear mixed models for genome-wide association studies. Nat Methods, 2012, 9: 525–526
[32]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. Nat Genet, 2015, 47: 284–290
[33]Wang Q, Tian F, Pan Y, Buckler E S, Zhang Z. A SUPER powerful method for genome wide association study. PLoS One, 2014, 9: e107684
[34]Zhao K, Tung C W, Eizenga G C, Wright M H, Ali M L, Price A H, 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. Nat Commun, 2011, 2: 467–476
[35]Wen Z X, Tan R J, Yuan J Z, Bales C, Du W Y, Zhang S C, Chilvers M I, Schmidt C, Song Q J, Cregan P B, Wang D C. Genome-wide association mapping of quantitative resistance to sudden death syndrome in soybean. BMC Genomics, 2014, 15: 809–819
[36]Yang N, Lu Y L, Yang X H, Huang J, Zhou Y, Ali F, Wen W W, Liu J, Li J S, Yan J B. Genome wide association studies using a new nonparametric model reveal the genetic architecture of 17 agronomic traits in an enlarged maize association panel. PLoS Genet, 2014, 10(9): e1004573
[37]McCullagh P, Nelder J A. Generalized Linear Models, 2nd edn. London: Chapman and Hall, 1989
[38]Yi N, Liu N J, Zhi D G, Li J. Hierarchical generalized linear models for multiple groups of rare and common variants: jointly estimating group and individual-variant effects. PLoS Genet, 2011, 7(12): e1002382
[39]Feng J Y, Zhang J, Zhang W J, Wang S B, Han S F, Zhang Y M. An efficient hierarchical generalized linear mixed model for mapping QTL of ordinal traits in crop cultivars. PLoS One, 2013, 8(4): e59541
[40]Wang L, Jia P, Wolfinger R D, Chen X, Grayson B L, Aune T M, Zhao Z. An efficient hierarchical generalized linear mixed model for pathway analysis of genome-wide association studies. Bioinformatics, 2011, 27(5): 686–692
[41]Iwata H, Uga Y, Yoshioka Y, Ebana K, Hayashi T. Bayesian association mapping of multiple quantitative trait loci and its application to the analysis of genetic variation among (Oryza sativa L.) germplasms. Theor Appl Genet, 2007, 114: 1437–1449
[42]Iwata H, Ebana K, Fukuoka S, Jannink J L, Hayashi T. Bayesian multilocus association mapping on ordinal and censored traits and its application to the analysis of genetic variation among (Oryza sativa L.) germplasms. Theor Appl Genet, 2009, 118: 865–880
[43]Zhang Y M, Xu S. A penalized maximum likelihood method for estimating epistatic effects of QTL. Heredity, 2005, 95: 96–104
[44]Hoggart C J, Whittaker J C, De Iorio M, Balding D J. Simultaneous analysis of all SNPs in genome-wide and resequencing association studies. PLoS Genet, 2008, 4: e1000130
[45]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. Nat Genet, 2012, 44: 825–830
[46]Yang J, Lee S H, Goddard M E, Visscher P M. GCTA: a tool for genome-wide complex trait analysis. Am J Hum Genet, 2011, 88: 76–82
[47]Goddard M E, Wray N R, Verbyla K, Visscher P M. Estimating effects and making predictions from genome- wide marker data. Stat Sci, 2009, 24: 517–529
[48]Zhou X, Carbonetto P, Stephens M. Polygenic modeling with Bayesian sparse linear mixed models. PLoS Genet, 2013, 9(2): e1003264
[49]Moser G, Lee S H, Hayes B J, Goddard M E, Wray N R, Visscher P M. Simultaneous discovery, estimation and prediction analysis of complex traits using a Bayesian mixture model. PLoS Genet, 2015, 11(4): e1004969
[50]Zhang Y, Liu J S. Bayesian inference of epistatic interactions in case-control studies. Nat Genet, 2007, 39: 1167–1173
[51]Tang W W, Wu X B, Jiang R. Epistatic module detection for case-control studies: a Bayesian model with a Gibbs sampling strategy. PLoS Genet, 2009, 5(5): e1000464
[52]Cho S, Kim H, Oh S, Kim K, Park T. Elastic-net regularization approaches for genome-wide association studies of rheumatoid arthritis. BMC Proc, 2009, 3(suppl 7): S25
[53]Han B, Park M, Chen X W. A Markov blanket-based method for detecting causal SNPs in GWAS. BMC Bioinformatics, 2010, 11(suppl 3): S5
[54]Han B, Chen X W, Talebizadeh Z. FEPI-MB: identifying SNPs-disease association using a Markov blanket-based approach. BMC Bioinformatics, 2011, 12(Suppl 12): S3
[55]Li J, Dan J, Li C L, Wu R L. A model-free approach for detecting interactions in genetic association studies. Brief Bioinform, 2014, 15: 1057–1068
[56]Wang D, Eskridge K M, Crossa J. Identifying QTLs and epistasis in structured plant populations using adaptive mixed LASSO. J Agric Biol Environ Stat, 2011, 16: 170–184
[57]Lü H Y, Liu X F, Wei S P, Zhang Y M. Epistatic association mapping in homozygous crop cultivars. PLoS One, 2011, 6(3): e17773
[58]Wen J, Zhao X W, Wu G R, Xiang D, Liu Q, Bu S H, Yi C, Song Q J, Dunwell J M, Tu J X, Zhang T Z, Zhang Y M. Genetic dissection of heterosis using epistatic association mapping in a partial NCII mating design. Sci Rep, 2015, 5: 18376
[59]Aschard H, Vilhjálmsson B J, Greliche N, Morange P E, Trégouët D A, Kraft P. Maximizing the power of principal-component analysis of correlated phenotypes in genome-wide association studies. Am J Hum Genet, 2014, 94: 662–676
[60]Ferreira M A, Purcell S M. A multivariate test of association. Bioinformatics, 2009, 25: 132–133
[61]Bottolo L, Chadeau-Hyam M, Hastie D I, Zeller T, Liquet B, Newcombe P, Yengo L, Wild P S, Schillert A, Ziegler A, Nielsen S F, Butterworth A S, Ho W K, Castagné R, Munzel T, Tregouet D, Falchi M, Cambien F, Nordestgaard B G, Fumeron F, Tybjærg-Hansen A, Froguel P, Danesh J, Petretto E, Blankenberg S, Tiret L, Richardson S. GUESS-ing polygenic associations with multiple phenotypes using a GPU-Based evolutionary stochastic search algorithm. PLoS Genet, 2013, 9: e1003657
[62]Bolormaa S, Pryce J E, Reverter A, Zhang Y, Barendse W, Kemper K, Tier B, Savin K, Hayes B J, Goddard M E. A multi-trait, meta-analysis for detecting pleiotropic polymorphisms for stature, fatness and reproduction in beef cattle. PLoS Genet, 2014, 10: e1004198
[63]Xu Y, Hu W M, Yang Z F, Xu C W. A multivariate partial least squares approach to joint analysis for multiple correlated traits. Crop J, 2016, 4(1): 21–29
[64]Korte A, Vilhjálmsson B J, Segura V, Platt A, Long Q, Nordborg M. A mixed-model approach for genome-wide association studies of correlated traits in structured populations. Nat Genet, 2012, 44: 1066–1071
[65]Zhou X, Stephens M. Efficient algorithm for multivariate linear mixed models in genome-wide association studies. Nat Methods, 2014, 11: 407–409
[66]Casale F P, Rakitsch B, Lippert C, Stegle O. Efficient set tests for the genetic analysis of correlated traits. Nat Methods, 2015, 12: 755–758
[67]Furlotte N A, Eskin E. Efficient multiple-trait association and estimation of genetic correlation using the matrix-variate linear mixed model. Genetics, 2015, 200: 59–68
[68]Wan X, Yang C, Yang Q, Xue H, Tang N L S, Yu W C. Predictive rule inference for epistatic interaction detection in genome-wide association studies. Bioinformatics, 2010, 26: 30–37
[69]Bradbury P J, Zhang Z, Kroon D E, Casstevens T M, Ramdoss Y, Buckler E S. TASSEL: software for association mapping of complex traits in diverse samples. Bioinformatics, 2007, 23: 2633–2635
[70]Tang Y, Liu X, Wang J, Li M, Wang Q, Tian F, Su Z, Pan Y, Liu D, Lipka A E, Buckler E S, Zhang Z. GAPIT Version 2: Enhanced integrated tool for genomic association and prediction. Plant Genome, 2016, 9(2): doi: 10.3835/plantgenome2015.11.0120
[71]张福涛. 遗传分析方法的GPU并行计算与优化研究. 浙江大学博士学位论文, 浙江杭州, 2014. pp 89–97
Zhang F T. Parallelization and Optimization of GPU Computation for Genetic Analysis Methods. PhD Dissertation of Zhejiang University, Hangzhou, China, 2014. pp 89–97 (in Chinese with English abstract)
[72]Sul J H, Bilow M, Yang W-Y, Kostem E, Furlotte N, He D, Eskin E. Accounting for population structure in gene-by-environment interactions in genome-wide association studies using mixed models. PLoS Genet, 2016, 12(3): e1005849
[73]Collard B C Y, Mackill D J. Marker-assisted selection: an approach for precision plant breeding in the twenty-first century. Philos Trans R Soc Lond B Biol Sci, 2008, 363(1491): 557–572
[74]Andersen J R, Lǜbberstedt T. Functional markers in plants. Trends Plant Sci, 2003, 8: 554–560
[75]杨小红, 严建兵, 郑艳萍, 余建明, 李建生. 植物数量性状关联分析研究进展. 作物学报, 2007, 33: 523–530
Yang X H, Yan J B, Zheng Y P, Yu J M, Li J S. Reviews of association analysis for quantitative traits in plants. Acta Agron Sin, 2007, 33: 523–530 (in Chinese)
[76]谭贤杰, 吴子恺, 程伟东, 王天宇, 黎裕. 关联分析及其在植物遗传学研究中的应用. 植物学报, 2011, 46: 108–118
Tan X J, Wu Z K, Cheng W D, Wang T Y, Li Y. Association analysis and its application in plant genetic research. Chin Bull Bot, 2011, 46: 108–118 (in Chinese)
[77]布素红. 多亲本群体QTL定位和优异杂交组合预测. 南京农业大学博士学位论文, 江苏南京, 2015. pp 57–68
Bu S H. Mapping of Quantitative Trait Loci and Prediction of Elite Hybrid Combination in Multi-parental Populations. PhD Dissertation of Nanjing Agricultural University, Nanjing, China, 2015. pp 57–68 (in Chinese with English abstract)
[78]Chan E K F, Rowe H C, Kliebenstein D J. Understanding the evolution of defense metabolites in Arabidopsis thaliana using genome-wide association mapping. Genetics, 2010, 185: 991–1007
[79]Riedelsheimer C, Lisec J, Czedik-Eysenbreg A, Sulpice R, Flis A, Grieder C, Altmann T, Stitt M, Willmitzer L, Melchinger A E. Genome-wide association mapping of leaf metabolic profiles for dissecting complex traits in maize. Proc Natl Acad Sci USA, 2012, 109: 8872–8877
[80]Wen W W, Li D, Li X, Gao Y Q, Li W Q, Li H H, Liu J, Liu H J, Chen W, Luo J, Yan J B. Metabolome-based genome-wide association study of maize kernel leads to novel biochemical insights. Nat Commun, 2014, 5: 3438–3447