Abstract
This paper gives an overview of the statistical theory suitable for mapping quantitative trait loci in experimental populations derived from inbred parents, with a particular emphasis on methodology for cereal crops. The basic theory is described, and some new areas of statistical research appropriate for mapping in cereal crops are discussed.
Similar content being viewed by others
References
Basten, C.J., Weir, B.S. and Zeng, Z.B. 1994. Zmap: a QTL cartographer. In: C. Smith, J.S. Gavora, B. Benkel, J. Chesnais, W. Fairfull, J.P. Gibson, B.W. Kennedy and E.B. Burnside (Eds.) Proceedings of the 5th World Congress on Genetics Applied to Livestock Production: Computing Strategies and Software, Vol. 22, pp. 65-66.
Basten, C.J., Weir, B.S. and Zeng, Z.B. 1999. QTL Cartographer, Version 1.13: A Reference Manual and Tutorial for QTL Mapping. Department of Statistics, North Carolina State University, Raleigh, NC.
Beavis, W.D. 1994. The power and deceit of QTL experiments: lessons from comparative QTL studies. In: D.B. Wilkinson (Ed.) 49th Annual Corn and Sorghum Industry Research Conference, American Seed Trade Association, Washington, DC, pp. 250-266.
Chase, K., Adler, F.R. and Lark, K.G. 1997. EPISTAT: a computer program for identifying and testing interactions between pairs of quantitative trait loci. Theor. Appl. Genet. 94: 724-730.
Churchill, G.A. and Doerge, R.W. 1994. Empirical threshold values for quantitative trait mapping. Genetics 138: 963-971.
Crossa, J., Vargas, M., van Eeuwijk, F.A., Jiang, C., Edmeades, G.O. and Hoisington, D. 1999. Interpreting genotype × environment interaction in tropical maize using linked molecular markers and environmental covariables. Theor. Appl. Genet. 99: 611-625.
Darvasi, A., Weintreb, A., Minke, V., Weller, J. and Soller, M. 1993. Detecting marker-QTL linkage and estimating QTL gene effect and map location using a saturated genetic map. Genetics 134: 943-951.
Davies, R.B. 1987. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74: 33-43.
Doerge, R.W. and Churchill, G.A. 1996. Permutation tests for multiple loci affecting a quantitative character. Genetics 142: 285-294.
Doerge, R.W. and Rebai, A. 1996. Significance thresholds for QTL interval mapping tests. Heredity 76: 459-464.
Doerge, R.W., Zeng, Z.-B. and Weir, B.S. 1997. Statistical issues in the search for genes affecting quantitative traits in experimental populations. Stat. Sci. 12: 195-219.
East, E.M. 1910. A Mendelian interpretation of variation that is apparently continuous. Am. Nat. 44: 65-82.
East, E.M. and Hayes, H.K. 1911. Inheritance in maize. Connecticut Agricultural Experimental Station Bulletin 167; 142 pp.
Edwards, M.D., Stuber, C.W. and Wendel, J.F. 1987. Molecular-marker-facilitated investigation of quantitative-trait loci in maize. I. Numbers, genomic distribution and types of gene action. Genetics 116: 113-125.
Emerson, R.A. and East, E.M. 1913. The inheritance of quantitative characters in maize. Bulletin of the Agricultural Experimental Station, Nebraska 2; 118 pp.
Fisher, R.A. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Transact. R. Soc. Edinb. 52: 399-433.
Genstat 5 Committee 1997. Genstat 5 Release 4.1 Manual Supplement. Numerical Algorithms Group, Oxford.
George, E.I. 2000. The variable selection problem. J. Am. Stat. Ass. 95: 1304-1308.
Goffinet, B. and Gerber, S. 2000. Quantitative trait loci: a meta-analysis. Genetics 155: 463-473.
Hackett, C.A. 1994. Selection of markers linked to quantitative trait loci by regression techniques. In: J.W. van Ooijen and J. Jansen (Eds.) Biometrics in Plant Breeding: Applications of Molecular Markers, pp. 99-106. Proceedings of the Ninth Meeting of the Eucarpia Section Biometrics in Plant Breeding, CPRO-DLO, Wageningen, Netherlands.
Hackett, C.A., Meyer, R.C. and Thomas, W.T.B. 2001. Multi-trait QTL mapping in barley using multivariate regression. Genet. Res. 77: 95-106.
Haley, C.S. and Knott, S.A. 1992. A sinple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69: 315-324.
Hayes, P.M., Liu, B.H., Knapp, S.J., Chen, F., Jones, B., Blake, T., Franckowiak, J., Rasmusson, D., Sorrells, M., Ullrich, S.E., Wesenberg, D. and Kleinhofs, A. 1993. Quantitative trait locus effects and environmental interaction in a sample of North American barley germ plasm. Theor. Appl. Genet. 87: 392-401.
Jannink, J.L. and Jansen, R. 2001. Mapping epistatic quantitative trait loci with one-dimensional genome searches. Genetics 157: 445-454.
Jansen, R.C. 1992. A general mixture model for mapping quantitative trait loci by using molecular markers. Theor. Appl. Genet. 85: 252-260.
Jansen, R.C. 1993. Interval mapping of multiple quantitative trait loci. Genetics 135: 205-211.
Jansen, R.C. 1994. Controlling the type I and type II errors in mapping quantitative trait loci. Genetics 138: 871-881.
Jansen, R.C. and Stam, P. 1994. High resolution of quantitative traits into multiple loci via interval mapping. Genetics 136: 1447-1455.
Jiang, C. and Zeng, Z.-B. 1995. Multiple trait analysis of genetic mapping for quantitative trait loci. Genetics 140: 1111-1127.
Johannsen, W. 1909. Elemente der exakten Erblichkeitslehre. Gustav Fischer, Jena, Germany.
Jourjon, M.F., Frayssines, S. and Vinceller, K. 2000. MCQTL software: demonstration. In: A. Gallais, C. Dillman and I. Goldringer (Eds.) Quantitative Genetics and Breeding Methods: The Way Ahead, pp. 301-305. Proceedings of the Eleventh Meeting of the Eucarpia Section Biometrics in Plant Breeding, INRA, Paris.
Kao, C.-H. 2000. On the differences between maximum likelihood and regression interval mapping in the analysis of quantitative trait loci. Genetics 156: 855-865.
Kearsey, M.J. and Farquhar, A.G.L. 1998. QTL analysis in plants: where are we now? Heredity 80: 137-142.
Korol, A.B., Ronin, Y.I. and Kirzhner, V.M. 1995. Interval mapping of quantitative trait loci employing correlated trait complexes. Genetics 140: 1137-1147.
Lander, E.S. and Botstein, D. 1989. Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121: 185-199.
Lander, E.S. and Botstein, D. 1994. Corrigendum. Genetics 136: 705.
Lebreton, C.M. and Visscher, P.M. 1998. Empirical nonparametric bootstrap strategies in quantitative trait loci mapping: conditioning on the genetic model. Genetics 148: 525-535.
Lin, H.X., Yamamoto, T., Sasaki, T. and Yano, M. 2000. Characterization and detection of epistatic interactions of 3 QTLs, Hd1, Hd2, and Hd3, controlling heading date in rice using nearly isogenic lines. Theor. Appl. Genet. 101: 1021-1028.
Liu, B.H. 1998. Statistical Genomics: Linkage, Mapping and QTL Analysis. CRC Press, Boca Raton, FL.
Liu, Y.F. and Zeng, Z.-B. 2000. A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines. Genet. Res. 75: 345-355.
Lynch, M. and Walsh, B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer Associates.
Mangin, B., Goffinet, B. and Rebai, A. 1994. Constructing confidence intervals for QTL location. Genetics 138: 1301-1308.
Mangin, B., Thoquet, P. and Grimsley, N. 1998. Pleiotropic QTL analysis. Biometrics 54: 88-99.
Martinez, O. and Curnow, R.N. 1992 Estimating the locations and the sizes of the effects of quantitative trait loci using flanking markers. Theor. Appl. Genet. 85: 480-488.
McCullagh, P. and Nelder, J.A. 1989. Generalized Linear Models, 2nd ed. Chapman & Hall, London.
Melchinger, A.E., Utz, H.F. and Schön, C.C. 1998. Quantitative trait locus (QTL) mapping using different testers and independent population samples in maize reveals low power of QTL detection and large bias in estimates of QTL effects. Genetics 149: 383-403.
Nettleton, D. and Doerge, R.W. 2000. Accounting for variability in the use of permutation testing to detect quantitative trait loci. Biometrics 56: 52-58.
Nilsson-Ehle, H. 1909 Kreuzunguntersuchungen an Hafer und Weizen. Lunds Univ. Åarskr. 5 (2) 1-122.
Piepho, H.P. 2001. A quick method for computing approximate thresholds for quantitative trait loci detection. Genetics 157: 425-432.
Piepho, H.P. and Gauch, H.G. Jr. 2001. Marker pair selection for mapping quantitative trait loci. Genetics 157: 433-444.
Pressoir, G., Albar, L., Ahmadi, N., Rimbault, I., Lorieux, M., Fargette, D. and Ghesquiere, A. 1998. Genetic basis and mapping of the resistance to rice yellow mottle virus. II. Evidence of a complementary epistasis between two QTLs. Theor. Appl. Genet. 97: 1155-1161.
Rebai, A. and Goffinet, B. 1993. Power of tests for QTL detection using replicated progenies derived from a diallel cross. Theor. Appl. Genet. 86: 1014-1022.
Rebai, A. and Goffinet, B. 2000. More about quantitative trait locus mapping with diallel designs. Genet. Res. 75: 243-247.
Rebai, A., Goffinet, B. and Mangin, B. 1994. Approximate thresholds of interval mapping tests for QTL detection. Genetics 138: 235-240.
Rebai, A., Blanchard, P., Perret, D and Vincourt, P. 1997. Mapping quantitative trait loci controlling silking date in a diallel cross among four lines of maize. Theor. Appl. Genet. 95: 451-459.
Romagosa, I., Ullrich, S.E., Han, F. and Hayes, P.M. 1996. Use of the additive main effects and multiplicative interaction model in QTL mapping for adaptation in barley. Theor. Appl. Genet. 93: 30-37.
Ronin, Y.I., Kirzhner, V.M. and Korol, A.B. 1995. Linkage between loci of quantitative traits and marker loci: multi-trait analysis with a single marker. Theor. Appl. Genet. 90: 776-786.
Sax, K. 1923. The association of size differences with seed-coat pattern and pigmentation in Phaseolus vulgaris. Genetics 8: 552-560.
Schwarz, G. 1978. Estimating the dimension of a model. Ann. Stat. 6: 461-464.
Thomas, W.T.B., Powell, W., Waugh, R., Chalmers, K.J., Barua, U.M., Jack, P., Lea, V., Forster, B.P., Swanston, J.S., Ellis, R.P., Hanson, P.R. and Lance, R.C.M. 1995. Detection of quantitative trait loci for agronomic, yield, grain and disease characters in spring barley (Hordeum vulgare L.) Theor. Appl. Genet. 91: 1037-1047.
Thomas, W.T.B., Powell, W., Swanston, J.S., Ellis, R.P., Chalmers, K.J., Barua, U.M., Jack, P., Lea, V., Forster, B.P., Waugh, R. and Smith, D.B. 1996. Quantitative trait loci for germination and malting quality characters in a spring barley cross. Crop Sci. 36: 265-273.
Trow, A.H. 1913. Forms of reduplication: primary and secondary. J. Genet. 2: 313-324.
Utz, H.F. and Melchinger, A.E. 1994. Comparison of different approaches to interval mapping of quantitative trait loci. In: J.W. van Ooijen and J. Jansen (Eds.) Biometrics in Plant Breeding: Applications of Molecular Markers. Proceedings of the Ninth Meeting of the Eucarpia Section Biometrics in Plant Breeding, CPRO-DLO, Wageningen, Netherlands, pp.195-204.
Utz, H.F. and Melchinger, A.E. 1996. PLABQTL: a program for composite interval mapping of QTL. J. Quant. Trait Loci 2(1).
Utz, H.F., Melchinger, A.E. and Schön, C.C. 2000. Bias and sampling error of the estimated proportion of genotypic variance explained by quantitative trait loci determined from experimental data in maize using cross validation and validation with independent samples. Genetics 154: 1839-1849.
van Ooijen, J.W. 1992. Accuracy of mapping quantitative trait loci in autogamous species. Theor. Appl. Genet. 84: 803-811.
van Ooijen, J.W. and Maliepaard, C. 1996. MapQTL version 3.0: software for the calculation of QTL positions on genetic maps. CPRO-DLO, Wageningen, Netherlands.
van Ooijen, J.W. 1999. LOD significance thresholds for QTL analysis in experimental populations of diploid species. Heredity 5: 613-624.
Visscher, P.M., Thompson, R. and Haley, C.S. 1996. Confidence intervals in QTL mapping by bootstrapping. Genetics 143: 1013-1020.
Wang, D.L., Zhu, J., Li, Z.K. and Paterson, A.H. 1999. Mapping QTLs with epistatic effects and QTL x environment interactions by mixed linear model approaches. Theor. Appl. Genet. 99: 1255-1264.
Weller, J.I. 1986. Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers. Biometrics 42: 627-640.
Weller, J.I. 1987. Mapping and analysis of quantitative trait loci in Lycopersicon (tomato) with the aid of genetic markers using approximate maximum likelihood methods. Heredity 59: 413-421.
Weller, J.I., Wiggans, G.R., van Raden, P.M. and Ron, M. 1996. Application of a canonical transformation to detection of quantitative trait loci with the aid of genetic markers in a multi-trait experiment. Theor. Appl. Genet. 92: 998-1002.
Whittaker, J.C., Thompson, R. and Visscher, P.M. 1996. On the mapping of QTL by regression of phenotype on marker type. Heredity 77: 23-32.
Wright, S. 1968. Evolution and the Genetics of Populations. I. Genetic and Biometric Foundations. University of Chicago Press, Chicago.
Wu, P., Liao, C.Y., Hu, B., Yi, K.K., Jin, W.Z., Ni, J.J. and He, C. 2000. QTLs and epistasis for aluminum tolerance in rice (Oryza sativa L.) at different seedling stages. Theor. Appl. Genet. 100: 1295-1303.
Xu, S. 1995. A comment on the simple regression method for interval mapping. Genetics 141: 1657-1659.
Zeng, Z.-B. 1993. Theoretical basis for separation of multiple linked gene effects in mapping quantitative trait loci. Proc. Natl. Acad. Sci. USA 90: 10972-10976.
Zeng, Z.-B. 1994. Precision mapping of quantitative trait loci. Genetics 136: 1457-1468.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hackett, C.A. Statistical methods for QTL mapping in cereals. Plant Mol Biol 48, 585–599 (2002). https://doi.org/10.1023/A:1014896712447
Issue Date:
DOI: https://doi.org/10.1023/A:1014896712447