Theoretical and Applied Genetics

, Volume 116, Issue 2, pp 243–260

Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations

  • Huihui Li
  • Jean-Marcel Ribaut
  • Zhonglai Li
  • Jiankang Wang
Original Paper

Abstract

It has long been recognized that epistasis or interactions between non-allelic genes plays an important role in the genetic control and evolution of quantitative traits. However, the detection of epistasis and estimation of epistatic effects are difficult due to the complexity of epistatic patterns, insufficient sample size of mapping populations and lack of efficient statistical methods. Under the assumption of additivity of QTL effects on the phenotype of a trait in interest, the additive effect of a QTL can be completely absorbed by the flanking marker variables, and the epistatic effect between two QTL can be completely absorbed by the four marker-pair multiplication variables between the two pairs of flanking markers. Based on this property, we proposed an inclusive composite interval mapping (ICIM) by simultaneously considering marker variables and marker-pair multiplications in a linear model. Stepwise regression was applied to identify the most significant markers and marker-pair multiplications. Then a two-dimensional scanning (or interval mapping) was conducted to identify QTL with significant digenic epistasis using adjusted phenotypic values based on the best multiple regression model. The adjusted values retain the information of QTL on the two current mapping intervals but exclude the influence of QTL on other intervals and chromosomes. Epistatic QTL can be identified by ICIM, no matter whether the two interacting QTL have any additive effects. Simulated populations and one barley doubled haploids (DH) population were used to demonstrate the efficiency of ICIM in mapping both additive QTL and digenic interactions.

References

  1. Baierl A, Bogdan M, Frommlet F, Futschik A (2006) On locating multiple interacting quantitative trait loci in intercross designs. Genetics 173:1693–1703PubMedCrossRefGoogle Scholar
  2. Boer MP, Ter Braak CJF, Jansen RC (2002) A penalized likelihood method for mapping epistatic quantitative trait loci with one-dimensional genome searches. Genetics 162:951–960PubMedGoogle Scholar
  3. Bogdan M, Ghosh JK, Doerge RW (2004) Modifying the Schwarz Bayesian information criterion to locate multiple interacting quantitative trait loci. Genetics 167:989–999PubMedCrossRefGoogle Scholar
  4. Broman KW, Speed TP (2002) A model selection approach for the identification of quantitative trait loci in experimental crosses. J R Statist Soc B 64:641–656CrossRefGoogle Scholar
  5. Carlborg Ö, Haley C (2004) Epistasis: too often neglected in complex trait studies? Nat Rev Genet 5:618–625PubMedCrossRefGoogle Scholar
  6. Carlborg Ö, Kerje S, Schütz K, Jacobsson L, Jensen P, Andersson L (2003) A global search reveals epistatic interaction between QTL for early growth in the chicken. Genome Res 13:413–421PubMedCrossRefGoogle Scholar
  7. Carlborg Ö, Jacobsson L, Ahgren P, Siegel P, Andersson L (2006) Epistasis and the release of genetic variation during long-term selection. Nat Genet 38:418–420PubMedCrossRefGoogle Scholar
  8. Dempster A, Laird N, Rubin D (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B 39:1–38Google Scholar
  9. Doerge RW (2002) Mapping and analysis of quantitative trait loci in experiment populations. Nat Rev Genet 3:43–52PubMedCrossRefGoogle Scholar
  10. Falconer DS, Mackay TFC (1996) Introduction to quantitative genetics, 4 edn. Longman, EssenxGoogle Scholar
  11. Feenstra B, Skovgaard IM, Broman KW (2006) Mapping quantitative trait loci by an extension of the Haley–Knott regression method using estimating equations. Genetics 173:2269–2282PubMedCrossRefGoogle Scholar
  12. Frankel WN, Schork NJ (1996) Who’s afraid of epistasis. Nat Genet 14:371–373PubMedCrossRefGoogle Scholar
  13. Haley CS, Knott SA (1992) A simple regression method for mapping quantitative loci in line crosses using flanking markers. Heredity 69:315–324PubMedGoogle Scholar
  14. Jannink J, Jansen R (2001) Mapping epistatic quantitative trait loci with one-dimensional genome searches. Genetics 157:445–454PubMedGoogle Scholar
  15. Kao C-H, Zeng Z-B, Teasdale RD (1999) Multiple interval mapping for quantitative trait loci. Genetics 152:1203–1206PubMedGoogle Scholar
  16. Kroymann J, Mitchell-Olds T (2005) Epistasis and balanced polymorphism influencing complex trait variation. Nature 435:95–98PubMedCrossRefGoogle Scholar
  17. Lander ES, Botstein D (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185–199PubMedGoogle Scholar
  18. Li H, Ye G, Wang J (2007) A modified algorithm for the improvement of composite interval mapping. Genetics 175:361–374PubMedCrossRefGoogle Scholar
  19. Lynch M, Walsh B (1998) Genetic and analysis of quantitative Traits. Sinauer Associates, SunderlandGoogle Scholar
  20. Mackay TFC (2001) Quantitative trait loci in Drosophila. Nat Rev Genet 2:11–20PubMedCrossRefGoogle Scholar
  21. Malmberg RL, Held S, Waits A, Mauricio R (2005) Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse. Genetics 171:2013–2027PubMedCrossRefGoogle Scholar
  22. Meng X, Rubin DB (1993) Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80:267–268CrossRefGoogle Scholar
  23. Miller AJ (1990) Subset selection in regression (Monographs on statistics and applied probability 40). Chapman and Hall, LondonGoogle Scholar
  24. Nadeau JH, Singer JB, Martin A, Lander ES (2000) Analysis complex genetics traits with chromosome substitution strains. Nat Genet 24:221–225PubMedCrossRefGoogle Scholar
  25. Piepho H-P, Gauch HG (2001) Marker pair selection for mapping quantitative trait loci. Genetics 157:433–444PubMedGoogle Scholar
  26. Satagopan JM, Yandell BS, Newton MA, Osborn TC (1996) A Bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. Genetics 144:805–816PubMedGoogle Scholar
  27. Sen S, Churchill GA (2001) A statistical framework for quantitative trait mapping. Genetics 159:371–387PubMedGoogle Scholar
  28. Sillanpää MJ, Arjas E (1999) Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics 151:1605–1619PubMedGoogle Scholar
  29. Sillanpää MJ, Corander J (2002) Model choice in gene mapping: what and why. Trends Genet 18:302–307CrossRefGoogle Scholar
  30. Tinker NA, Mather DE, Rossnagel BG, Kasha KJ, Kleinhofs A, Hayes PM, Falk DE, Ferguson T, Shugar LP, Legge WG, Irvine RB, Choo TM, Briggs KG, Ullrich SE, Franckowiak JD, Blake TK, Graf RJ, Dofing SM, Saghai Maroof MA, Scoles GJ, Hoffman D, Dahleen LS, Kilian A, Chen F, Biyashev RM, Kudrna DA, and Steffenson BJ (1996) Regions of the genome that affect agronomic performance in two-row barley. Crop Sci 36:1053–1062CrossRefGoogle Scholar
  31. Uimari P, Hoeschele I (1997) Mapping-linked quantitative trait loci using Bayesian analysis and Markov chain Monte Carlo algorithms. Genetics 146:735–743PubMedGoogle Scholar
  32. Uimari P, Thaller G, Hoeschele I (1996) The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics 143:1831–1842PubMedGoogle Scholar
  33. Wade MJ (2002) A gene’s eye view of epistasis, selection and speciation. J Evol Biol 15:337–346CrossRefGoogle Scholar
  34. Wang S, Basten CJ, Zeng Z-B (2005) Windows QTL Cartographer 2.5. Department of Statistics, North Carolina State University, Raleigh, NCGoogle Scholar
  35. Whittaker JC, Thompson R, Visscher PM (1996) On the mapping of QTL by regression of phenotype on marker-type. Heredity 77:23–32CrossRefGoogle Scholar
  36. Xu S, Jia Z (2007) Genomewide analysis of epistatic effects for quantitative traits in barley. Genetics 175:1955–1963PubMedCrossRefGoogle Scholar
  37. Yi N (2004) A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics 167:967–975PubMedCrossRefGoogle Scholar
  38. Yi N, Xu S, Allison DB (2003) Bayesian model choice and search strategies for mapping interacting quantitative trait loci. Genetics 165:867–883PubMedGoogle Scholar
  39. Yi N, Yandell BS, Churchill GA, Allison DB, Eisen EJ, Pomp D (2005) Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics 170:1333–1344PubMedCrossRefGoogle Scholar
  40. Zeng Z-B (1994) Precision mapping of quantitative trait loci. Genetics 136:1457–1468PubMedGoogle Scholar
  41. Zeng Z-B (2005) Modeling quantitative trait loci and interpretation of models. Genetics 169:1711–1725PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Huihui Li
    • 1
    • 3
  • Jean-Marcel Ribaut
    • 2
  • Zhonglai Li
    • 1
  • Jiankang Wang
    • 3
  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  2. 2.Generation Challenge ProgrammeMexico, D.F.Mexico
  3. 3.The National Key Facility for Crop Gene Resources and Genetic Improvement, Institute of Crop Science and CIMMYT China OfficeChinese Academy of Agricultural SciencesBeijingChina

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