Skip to main content
NCBI home page
Genetics logoLink to Genetics
. 2003 Oct;165(2):867–883. doi: 10.1093/genetics/165.2.867

Bayesian model choice and search strategies for mapping interacting quantitative trait Loci.

Nengjun Yi 1, Shizhong Xu 1, David B Allison 1
PMCID: PMC1462771  PMID: 14573494

Abstract

Most complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.

Full Text

The Full Text of this article is available as a PDF (239.1 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Ball R. D. Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion. Genetics. 2001 Nov;159(3):1351–1364. doi: 10.1093/genetics/159.3.1351. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Bink M., Uimari P., Sillanpä J., Janss G., Jansen C. Multiple QTL mapping in related plant populations via a pedigree-analysis approach. Theor Appl Genet. 2002 Mar 7;104(5):751–762. doi: 10.1007/s00122-001-0796-x. [DOI] [PubMed] [Google Scholar]
  3. Boer Martin P., Ter Braak Cajo J. F., Jansen Ritsert C. A penalized likelihood method for mapping epistatic quantitative trait Loci with one-dimensional genome searches. Genetics. 2002 Oct;162(2):951–960. doi: 10.1093/genetics/162.2.951. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Carlborg O., Andersson L., Kinghorn B. The use of a genetic algorithm for simultaneous mapping of multiple interacting quantitative trait loci. Genetics. 2000 Aug;155(4):2003–2010. doi: 10.1093/genetics/155.4.2003. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Cheverud J. M., Routman E. J. Epistasis and its contribution to genetic variance components. Genetics. 1995 Mar;139(3):1455–1461. doi: 10.1093/genetics/139.3.1455. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Culverhouse Robert, Suarez Brian K., Lin Jennifer, Reich Theodore. A perspective on epistasis: limits of models displaying no main effect. Am J Hum Genet. 2002 Jan 8;70(2):461–471. doi: 10.1086/338759. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Daw E. W., Heath S. C., Wijsman E. M. Multipoint oligogenic analysis of age-at-onset data with applications to Alzheimer disease pedigrees. Am J Hum Genet. 1999 Mar;64(3):839–851. doi: 10.1086/302276. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Dong Chuanhui, Wang Shuang, Li Wei-Dong, Li Ding, Zhao Hongyu, Price R. Arlen. Interacting genetic loci on chromosomes 20 and 10 influence extreme human obesity. Am J Hum Genet. 2002 Dec 11;72(1):115–124. doi: 10.1086/345648. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Fernández J. R., Tarantino L. M., Hofer S. M., Vogler G. P., McClearn G. E. Epistatic quantitative trait loci for alcohol preference in mice. Behav Genet. 2000 Nov;30(6):431–437. doi: 10.1023/a:1010232900342. [DOI] [PubMed] [Google Scholar]
  10. Fijneman R. J., de Vries S. S., Jansen R. C., Demant P. Complex interactions of new quantitative trait loci, Sluc1, Sluc2, Sluc3, and Sluc4, that influence the susceptibility to lung cancer in the mouse. Nat Genet. 1996 Dec;14(4):465–467. doi: 10.1038/ng1296-465. [DOI] [PubMed] [Google Scholar]
  11. Frankel W. N., Schork N. J. Who's afraid of epistasis? Nat Genet. 1996 Dec;14(4):371–373. doi: 10.1038/ng1296-371. [DOI] [PubMed] [Google Scholar]
  12. Gauderman W. J., Thomas D. C. The role of interacting determinants in the localization of genes. Adv Genet. 2001;42:393–412. doi: 10.1016/s0065-2660(01)42033-5. [DOI] [PubMed] [Google Scholar]
  13. Haley C. S., Knott S. A. A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity (Edinb) 1992 Oct;69(4):315–324. doi: 10.1038/hdy.1992.131. [DOI] [PubMed] [Google Scholar]
  14. Heath S. C. Markov chain Monte Carlo segregation and linkage analysis for oligogenic models. Am J Hum Genet. 1997 Sep;61(3):748–760. doi: 10.1086/515506. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Hoeschele I., Uimari P., Grignola F. E., Zhang Q., Gage K. M. Advances in statistical methods to map quantitative trait loci in outbred populations. Genetics. 1997 Nov;147(3):1445–1457. doi: 10.1093/genetics/147.3.1445. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Hoti Fabian J., Sillanpä Mikko J., Holmström Lasse. A note on estimating the posterior density of a quantitative trait locus from a Markov chain Monte Carlo sample. Genet Epidemiol. 2002 Apr;22(4):369–376. doi: 10.1002/gepi.01125. [DOI] [PubMed] [Google Scholar]
  17. Hurme P., Sillanpä M. J., Arjas E., Repo T., Savolainen O. Genetic basis of climatic adaptation in scots pine by bayesian quantitative trait locus analysis. Genetics. 2000 Nov;156(3):1309–1322. doi: 10.1093/genetics/156.3.1309. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Jannink J. L., Jansen R. Mapping epistatic quantitative trait loci with one-dimensional genome searches. Genetics. 2001 Jan;157(1):445–454. doi: 10.1093/genetics/157.1.445. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Jansen R. C., Stam P. High resolution of quantitative traits into multiple loci via interval mapping. Genetics. 1994 Apr;136(4):1447–1455. doi: 10.1093/genetics/136.4.1447. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Kao C. H., Zeng Z. B., Teasdale R. D. Multiple interval mapping for quantitative trait loci. Genetics. 1999 Jul;152(3):1203–1216. doi: 10.1093/genetics/152.3.1203. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Kao Chen-Hung, Zeng Zhao-Bang. Modeling epistasis of quantitative trait loci using Cockerham's model. Genetics. 2002 Mar;160(3):1243–1261. doi: 10.1093/genetics/160.3.1243. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Krause B. R., Schork N. J., Kieft K. A., Smith M. P., Maciejko J. J. High correlation but lack of agreement between direct high-performance gel chromatography analysis and conventional indirect methods for determining lipoprotein cholesterol. Clin Chem. 1996 Dec;42(12):1996–2001. [PubMed] [Google Scholar]
  23. Lander E. S., Botstein D. Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics. 1989 Jan;121(1):185–199. doi: 10.1093/genetics/121.1.185. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Lark K. G., Chase K., Adler F., Mansur L. M., Orf J. H. Interactions between quantitative trait loci in soybean in which trait variation at one locus is conditional upon a specific allele at another. Proc Natl Acad Sci U S A. 1995 May 9;92(10):4656–4660. doi: 10.1073/pnas.92.10.4656. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Lee J. K., Thomas D. C. Performance of Markov chain-Monte Carlo approaches for mapping genes in oligogenic models with an unknown number of loci. Am J Hum Genet. 2000 Oct 13;67(5):1232–1250. doi: 10.1016/s0002-9297(07)62953-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Satagopan J. M., Yandell B. S., Newton M. A., Osborn T. C. A bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. Genetics. 1996 Oct;144(2):805–816. doi: 10.1093/genetics/144.2.805. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Sen S., Churchill G. A. A statistical framework for quantitative trait mapping. Genetics. 2001 Sep;159(1):371–387. doi: 10.1093/genetics/159.1.371. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Sillanpä M. J., Arjas E. Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data. Genetics. 1998 Mar;148(3):1373–1388. doi: 10.1093/genetics/148.3.1373. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Sillanpä M. J., Arjas E. Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics. 1999 Apr;151(4):1605–1619. doi: 10.1093/genetics/151.4.1605. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Sillanpä Mikko J., Corander Jukka. Model choice in gene mapping: what and why. Trends Genet. 2002 Jun;18(6):301–307. doi: 10.1016/S0168-9525(02)02688-4. [DOI] [PubMed] [Google Scholar]
  31. Sugiyama F., Churchill G. A., Higgins D. C., Johns C., Makaritsis K. P., Gavras H., Paigen B. Concordance of murine quantitative trait loci for salt-induced hypertension with rat and human loci. Genomics. 2001 Jan 1;71(1):70–77. doi: 10.1006/geno.2000.6401. [DOI] [PubMed] [Google Scholar]
  32. Thomas D. C., Richardson S., Gauderman J., Pitkäniemi J. A Bayesian approach to multipoint mapping in nuclear families. Genet Epidemiol. 1997;14(6):903–908. doi: 10.1002/(SICI)1098-2272(1997)14:6<903::AID-GEPI57>3.0.CO;2-Q. [DOI] [PubMed] [Google Scholar]
  33. Uimari P., Hoeschele I. Mapping-linked quantitative trait loci using Bayesian analysis and Markov chain Monte Carlo algorithms. Genetics. 1997 Jun;146(2):735–743. doi: 10.1093/genetics/146.2.735. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Uimari P., Sillanpä M. J. Bayesian oligogenic analysis of quantitative and qualitative traits in general pedigrees. Genet Epidemiol. 2001 Nov;21(3):224–242. doi: 10.1002/gepi.1031. [DOI] [PubMed] [Google Scholar]
  35. Uimari P., Thaller G., Hoeschele I. The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics. 1996 Aug;143(4):1831–1842. doi: 10.1093/genetics/143.4.1831. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Wade M. J. Epistasis, complex traits, and mapping genes. Genetica. 2001;112-113:59–69. [PubMed] [Google Scholar]
  37. Xu S., Yi N. Mixed model analysis of quantitative trait loci. Proc Natl Acad Sci U S A. 2000 Dec 19;97(26):14542–14547. doi: 10.1073/pnas.250235197. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Yi N., Xu S. Bayesian mapping of quantitative trait loci for complex binary traits. Genetics. 2000 Jul;155(3):1391–1403. doi: 10.1093/genetics/155.3.1391. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Yi N., Xu S. Bayesian mapping of quantitative trait loci under complicated mating designs. Genetics. 2001 Apr;157(4):1759–1771. doi: 10.1093/genetics/157.4.1759. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Yu S. B., Li J. X., Xu C. G., Tan Y. F., Gao Y. J., Li X. H., Zhang Q., Saghai Maroof M. A. Importance of epistasis as the genetic basis of heterosis in an elite rice hybrid. Proc Natl Acad Sci U S A. 1997 Aug 19;94(17):9226–9231. doi: 10.1073/pnas.94.17.9226. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Yuan B., Neuman R., Duan S. H., Weber J. L., Kwok P. Y., Saccone N. L., Wu J. S., Liu K. Y., Schonfeld G. Linkage of a gene for familial hypobetalipoproteinemia to chromosome 3p21.1-22. Am J Hum Genet. 2000 Apr 10;66(5):1699–1704. doi: 10.1086/302904. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Zeng Z. B., Kao C. H., Basten C. J. Estimating the genetic architecture of quantitative traits. Genet Res. 1999 Dec;74(3):279–289. doi: 10.1017/s0016672399004255. [DOI] [PubMed] [Google Scholar]
  43. Zeng Z. B. Precision mapping of quantitative trait loci. Genetics. 1994 Apr;136(4):1457–1468. doi: 10.1093/genetics/136.4.1457. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Genetics are provided here courtesy of Oxford University Press

RESOURCES