Efforts to identify loci underlying complex traits generally assume that most genetic variance is additive. Here, we examined the genetics of Arabidopsis thaliana root length and found that the genomic narrow-sense heritability for this trait in the examined population was statistically zero. The low amount of additive genetic variance that could be captured by the genome-wide genotypes likely explains why no associations to root length could be found using standard additive-model-based genome-wide association (GWA) approaches. However, as the broad-sense heritability for root length was significantly larger, and primarily due to epistasis, we also performed an epistatic GWA analysis to map loci contributing to the epistatic genetic variance. Four interacting pairs of loci were revealed, involving seven chromosomal loci that passed a standard multiple-testing corrected significance threshold. The genotype-phenotype maps for these pairs revealed epistasis that cancelled out the additive genetic variance, explaining why these loci were not detected in the additive GWA analysis. Small population sizes, such as in our experiment, increase the risk of identifying false epistatic interactions due to testing for associations with very large numbers of multi-marker genotypes in few phenotyped individuals. Therefore, we estimated the false-positive risk using a new statistical approach that suggested half of the associated pairs to be true positive associations. Our experimental evaluation of candidate genes within the seven associated loci suggests that this estimate is conservative; we identified functional candidate genes that affected root development in four loci that were part of three of the pairs. The statistical epistatic analyses were thus indispensable for confirming known, and identifying new, candidate genes for root length in this population of wild-collected A. thaliana accessions. We also illustrate how epistatic cancellation of the additive genetic variance explains the insignificant narrow-sense and significant broad-sense heritability by using a combination of careful statistical epistatic analyses and functional genetic experiments.
References
[1]
Huang W, Richards S, Carbone MA, Zhu D, Anholt RRH, Ayroles JF, et al. Epistasis dominates the genetic architecture of Drosophila quantitative traits. Proc Natl Acad Sci U S A. 2012;109: 15553–9. doi: 10.1073/pnas.1213423109. pmid:22949659
[2]
Mackay TFC. Epistasis and quantitative traits: using model organisms to study gene-gene interactions. Nat Rev Genet. Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.; 2014;15: 22–33.
[3]
Nelson RM, Pettersson ME, Li X, Carlborg ？. Variance Heterogeneity in Saccharomyces cerevisiae Expression Data: Trans-Regulation and Epistasis. PLoS One. Public Library of Science; 2013;8: e79507. doi: 10.1371/journal.pone.0079507
[4]
Queitsch C, Carlson KD, Girirajan S. Lessons from model organisms: phenotypic robustness and missing heritability in complex disease. PLoS Genet. 2012/11/21 ed. Public Library of Science; 2012;8: e1003041. doi: 10.1371/journal.pgen.1003041. PGENETICS-D-12-00749 [pii] pmid:23166511
[5]
Hill WG, Goddard ME, Visscher PM. Data and theory point to mainly additive genetic variance for complex traits. Mackay TFC, editor. PLoS Genet. Public Library of Science; 2008;4: e1000008. doi: 10.1371/journal.pgen.1000008.
[6]
Visscher PM, Brown MA, McCarthy MI, Yang J. Five years of GWAS discovery. Am J Hum Genet. 2012;90: 7–24. doi: 10.1016/j.ajhg.2011.11.029. pmid:22243964
Goodnight CJ. Quantitative trait loci and gene interaction: the quantitative genetics of metapopulations. Heredity (Edinb). Nature Publishing Group; 2000;84: 587–598. doi: 10.1046/j.1365-2540.2000.00698.x
[9]
Whitlock MC, Phillips PC, Moore FB-G, Tonsor SJ. Multiple fitness peaks and epistasis. Annu Rev Ecol Syst. JSTOR; 1995; 601–629. doi: 10.1146/annurev.es.26.110195.003125
[10]
Eitan Y, Soller M. Selection induced genetic variation. Evolutionary theory and processes: Modern horizons. Springer; 2004. pp. 153–176.
[11]
Le Rouzic A, Siegel PB, Carlborg ？. Phenotypic evolution from genetic polymorphisms in a radial network architecture. BMC Biol. BioMed Central Ltd; 2007;5: 50. doi: 10.1186/1741-7007-5-50
[12]
Le Rouzic A, Carlborg ？. Evolutionary potential of hidden genetic variation. Trends Ecol Evol. Elsevier; 2008;23: 33–37. doi: 10.1016/j.tree.2007.09.014
[13]
Monnahan PJ, Kelly JK. Epistasis Is a Major Determinant of the Additive Genetic Variance in Mimulus guttatus. Carlborg ？, editor. PLOS Genet. 2015;11: e1005201. doi: 10.1371/journal.pgen.1005201. pmid:25946702
[14]
Carlborg O, Haley CS. Epistasis: too often neglected in complex trait studies? Nat Rev Genet. Nature Publishing Group; 2004;5: 618–25. doi: 10.1038/nrg1407.
[15]
Mackay TF. The genetic architecture of quantitative traits. Annu Rev Genet. Annual Reviews 4139 El Camino Way, P.O. Box 10139, Palo Alto, CA 94303–0139, USA; 2001;35: 303–39. doi: 10.1146/annurev.genet.35.102401.090633. pmid:11700286
Pyun J-A, Kim S, Cha DH, Kwack K. Epistasis between polymorphisms in TSHB and ADAMTS16 is associated with premature ovarian failure. Menopause (New York, NY). 2013; doi: 10.1097/gme.0000000000000172
[18]
Sapkota Y, Mackey JR, Lai R, Franco-Villalobos C, Lupichuk S, Robson PJ, et al. Assessing SNP-SNP interactions among DNA repair, modification and metabolism related pathway genes in breast cancer susceptibility. PLoS One. Public Library of Science; 2013;8: e64896. doi: 10.1371/journal.pone.0064896
[19]
Vanhaeren H, Gonzalez N, Coppens F, De Milde L, Van Daele T, Vermeersch M, et al. Combining growth-promoting genes leads to positive epistasis in Arabidopsis thaliana. Elife. eLife Sciences Publications Limited; 2014;3: e02252. doi: 10.7554/eLife.02252.
[20]
Carlborg ？, Jacobsson L, ？hgren P, Siegel P, Andersson L. Epistasis and the release of genetic variation during long-term selection. Nat Genet. Nature Publishing Group; 2006;38: 418–420. doi: 10.1038/ng1761
[21]
Carlborg ？, Andersson L, Kinghorn B. The use of a genetic algorithm for simultaneous mapping of multiple interacting quantitative trait loci. Genetics. Genetics Soc America; 2000;155: 2003–2010.
[22]
Cao J, Schneeberger K, Ossowski S, Günther T, Bender S, Fitz J, et al. Whole-genome sequencing of multiple Arabidopsis thaliana populations. Nat Genet. Nature Publishing Group; 2011;43: 956–963. doi: 10.1038/ng.911
[23]
Mackay TFC, Richards S, Stone EA, Barbadilla A, Ayroles JF, Zhu D, et al. The Drosophila melanogaster genetic reference panel. Nature. Nature Publishing Group; 2012;482: 173–178. doi: 10.1038/nature10811
[24]
Gibson G. Rare and common variants: twenty arguments. Nat Rev Genet. Nature Publishing Group; 2012;13: 135–145. doi: 10.1038/nrg3118.
[25]
Hemani G, Shakhbazov K, Westra H-J, Esko T, Henders AK, McRae AF, et al. Detection and replication of epistasis influencing transcription in humans. Nature. Nature Publishing Group; 2014; doi: 10.1038/nature13005
[26]
Horton MW, Hancock AM, Huang YS, Toomajian C, Atwell S, Auton A, et al. Genome-wide patterns of genetic variation in worldwide Arabidopsis thaliana accessions from the RegMap panel. Nat Genet. Nature Publishing Group; 2012;44: 212–216. doi: 10.1038/ng.1042
[27]
Atwell S, Huang YS, Vilhjalmsson BJ, Willems G, Horton M, Li Y, et al. Genome-wide association study of 107 phenotypes in Arabidopsis thaliana inbred lines. Nature. 2010/03/26 ed. 2010;465: 627–631. pmid:20336072 doi: 10.1038/nature08800
[28]
Filiault DL, Maloof JN. A genome-wide association study identifies variants underlying the Arabidopsis thaliana shade avoidance response. PLoS Genet. Public Library of Science; 2012;8: e1002589. doi: 10.1371/journal.pgen.1002589.
[29]
Meijón M, Satbhai SB, Tsuchimatsu T, Busch W. Genome-wide association study using cellular traits identifies a new regulator of root development in Arabidopsis. Nat Genet. Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.; 2014;46: 77–81. doi: 10.1038/ng.2824.
[30]
Slovak R, G？schl C, Su X, Shimotani K, Shiina T, Busch W. A Scalable Open-Source Pipeline for Large-Scale Root Phenotyping of Arabidopsis. Plant Cell. 2014;26: 2390–2403. doi: 10.1105/tpc.114.124032. pmid:24920330
[31]
Rosas U, Cibrian-Jaramillo A, Ristova D, Banta JA, Gifford ML, Fan AH, et al. Integration of responses within and across Arabidopsis natural accessions uncovers loci controlling root systems architecture. Proc Natl Acad Sci U S A. 2013;110: 15133–8. doi: 10.1073/pnas.1305883110. pmid:23980140
[32]
Wood AR, Tuke MA, Nalls MA, Hernandez DG, Bandinelli S, Singleton AB, et al. Another explanation for apparent epistasis. Nature. Nature Publishing Group; 2014;514: E3–E5. doi: 10.1038/nature13691
[33]
Fujikura U, Horiguchi G, Ponce MR, Micol JL, Tsukaya H. Coordination of cell proliferation and cell expansion mediated by ribosome‐related processes in the leaves of Arabidopsis thaliana. Plant J. Wiley Online Library; 2009;59: 499–508. doi: 10.1111/j.1365-313x.2009.03886.x
[34]
Sangster TA, Salathia N, Undurraga , Milo R, Schellenberg K, Lindquist SL, et al. HSP90 affects the expression of genetic variation and developmental stability in quantitative traits. Proc Natl Acad Sci U S A. 2008/02/22 ed. 2008;105: 2963–2968. doi: 10.1073/pnas.0712200105. pmid:18287065
[35]
Lempe J, Lachowiec J, Sullivan AM, Queitsch C. Molecular mechanisms of robustness in plants. Curr Opin Plant Biol. 2013/01/03 ed. 2012; S1369-5266(12)00172-0 [pii] doi: 10.1016/j.pbi.2012.12.002.
[36]
Geiler-Samerotte K, Bauer C, Li S, Ziv N, Gresham D, Siegal M. The details in the distributions: why and how to study phenotypic variability. Curr Opin Biotechnol. 2013;24: 752–9. doi: 10.1016/j.copbio.2013.03.010. pmid:23566377
[37]
R？nneg？rd L, Shen X, Alam M. hglm: A Package for Fitting Hierarchical Generalized Linear Models. R J. 2010;2.
[38]
Aulchenko YS, Ripke S, Isaacs A, Van Duijn CM. GenABEL: an R library for genome-wide association analysis. Bioinformatics. Oxford Univ Press; 2007;23: 1294–1296. doi: 10.1093/bioinformatics/btm108
[39]
Shen X, Alam M, Fikse F, R？nneg？rd L. A novel generalized ridge regression method for quantitative genetics. Genetics. Genetics Soc America; 2013;193: 1255–1268. doi: 10.1534/genetics.112.146720
[40]
Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MAR, Bender D, et al. PLINK: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet. Elsevier; 2007;81: 559–575. doi: 10.1086/519795
[41]
Kim S, Plagnol V, Hu TT, Toomajian C, Clark RM, Ossowski S, et al. Recombination and linkage disequilibrium in Arabidopsis thaliana. Nat Genet. Nature Publishing Group; 2007;39: 1151–1155. doi: 10.1038/ng2115
[42]
Shen X. Flaw or discovery? Calculating exact p-values for genome-wide association studies in inbred populations. bioRxiv. 2015;
[43]
Ossowski S, Schneeberger K, Clark RM, Lanz C, Warthmann N, Weigel D. Sequencing of natural strains of Arabidopsis thaliana with short reads. Genome Res. Cold Spring Harbor Lab; 2008;18: 2024–2033. doi: 10.1101/gr.080200.108
[44]
Winter D, Vinegar B, Nahal H, Ammar R, Wilson G V, Provart NJ. An “Electronic Fluorescent Pictograph” browser for exploring and analyzing large-scale biological data sets. PLoS One. Public Library of Science; 2007;2: e718. doi: 10.1371/journal.pone.0000718
[45]
Sullivan AM, Arsovski AA, Lempe J, Bubb KL, Weirauch MT, Sabo PJ, et al. Mapping and Dynamics of Regulatory DNA and Transcription Factor Networks in A. thaliana. Cell Rep. 2014;8: 2015–2030. doi: 10.1016/j.celrep.2014.08.019. pmid:25220462
[46]
Aeong Oh S, Park J-H, In Lee G, Hee Paek K, Ki Park S, Gil Nam H. Identification of three genetic loci controlling leaf senescence in Arabidopsis thaliana. Plant J. Blackwell Science Ltd; 1997;12: 527–535. doi: 10.1046/j.1365-313X.1997.00489.x.
[47]
Jack T. Molecular and genetic mechanisms of floral control. Plant Cell. 2004;16 Suppl: S1–17. doi: 10.1105/tpc.017038. pmid:15020744
[48]
Sohn EJ, Rojas-Pierce M, Pan S, Carter C, Serrano-Mislata A, Madue？o F, et al. The shoot meristem identity gene TFL1 is involved in flower development and trafficking to the protein storage vacuole. Proc Natl Acad Sci U S A. 2007;104: 18801–6. doi: 10.1073/pnas.0708236104. pmid:18003908
[49]
Larsson AS, Landberg K, Meeks-Wagner DR. The TERMINAL FLOWER2 (TFL2) Gene Controls the Reproductive Transition and Meristem Identity in Arabidopsis thaliana. Genetics. 1998;149: 597–605.
[50]
Bolle C, Huep G, Kleinb？lting N, Haberer G, Mayer K, Leister D, et al. GABI-DUPLO: a collection of double mutants to overcome genetic redundancy in Arabidopsis thaliana. Plant J. 2013;75: 157–71. doi: 10.1111/tpj.12197. pmid:23573814
[51]
Jung JKH, McCouch S. Getting to the roots of it: Genetic and hormonal control of root architecture. Front Plant Sci. Frontiers; 2013;4: 186. doi: 10.3389/fpls.2013.00186.
[52]
Ajjawi I, Lu Y, Savage LJ, Bell SM, Last RL. Large-scale reverse genetics in Arabidopsis: case studies from the Chloroplast 2010 Project. Plant Physiol. 2010;152: 529–40. doi: 10.1104/pp.109.148494. pmid:19906890
[53]
Chan EKF, Rowe HC, Corwin JA, Joseph B, Kliebenstein DJ. Combining genome-wide association mapping and transcriptional networks to identify novel genes controlling glucosinolates in Arabidopsis thaliana. PLoS Biol. Public Library of Science; 2011;9: e1001125. doi: 10.1371/journal.pbio.1001125.
[54]
Schneider CA, Rasband WS, Eliceiri KW. NIH Image to ImageJ: 25 years of image analysis. Nat Methods. 2012;9: 671–675. pmid:22930834 doi: 10.1038/nmeth.2089
