Honesty, power and bootstrapping in composite interval quantitative trait locus mapping

Philip M. Service

Department of Biological Sciences, Northern Arizona University, Flagstaff, USA.

DOI: 10.4236/ojgen.2013.32016                

Abstract

In a typical composite interval mapping experiment, the probability of obtaining false QTL is likely to be at least an order of magnitude greater than the nominal experiment-wise Type I error rate, as set by permutation test. F₂ mapping crosses were simulated with three different genetic maps. Each map contained ten QTL on either three, six or twelve linkage groups. QTL effects were additive only, and heritability was 50%. Each linkage group had 11 evenly-spaced (10 cM) markers. Selective genotyping was used. Simulated data were analyzed by composite interval mapping with the Zmapqtl program of QTL Cartographer. False positives were minimized by using the largest feasible number of markers to control genetic background effects. Bootstrapping was then used to recover mapping power lost to the large number of conditioning markers. Bootstrapping is shown to be a useful tool for QTL discovery, although it can also produce false positives. Quantitative bootstrap support—the proportion of bootstrap replicates in which a significant likelihood maximum occurred in a given marker interval—was positively correlated with the probability that the likelihood maxima revealed a true QTL. X-linked QTL were detected with much lower power than autosomal QTL. It is suggested that QTL mapping experiments should be supported by accompanying simulations that replicate the marker map, crossing design, sample size, and method of analysis used for the actual experiment.

Keywords

Composite Interval Mapping; QTL Cartographer; Selective Genotyping; Power; Bootstrap; Permutation Test; False Discovery Rate

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	[1] Zeng, Z.-B. (1994) Precision mapping of quantitative trait loci. Genetics, 136, 1457-1468.
[2]	Beavis, W.D. (1995) The power and deceit of QTL experiments: Lessons from comparative QTL studies. Proceedings of the Forty-ninth Annual Corn and Sorghum Industry Research Conference ASTA, Washington, 252-268.
[3]	Curtsinger, J.W. (2002) Sex-specificity, lifespan QTLs, and statistical power. Journal of Gerontology. Series A, Biological Sciences and Medical Sciences, 57, B409-B414. doi:10.1093/gerona/57.12.B409
[4]	Darvasi, A. and Soller, M. (1992) Selective genotyping for determination of linkage between a marker locus and a quantitative trait locus. Theoretical and Applied Genetics, 85, 353-359. doi:10.1007/BF00222881
[5]	Churchill, G.A. and Doerge, R.W. (1994) Empirical threshold values for quantitative trait mapping. Genetics, 138, 963-971.
[6]	Zou, F., Xu, Z. and Vision, T. (2006) Assessing the significance of quantitative trait loci in replicable mapping populations. Genetics, 174, 1063-1068. doi:10.1534/genetics.106.059469
[7]	Doerge, R.W. and Churchill, G.A. (1996) Permutation tests for multiple loci affecting a quantitative character. Genetics, 142, 285-294.
[8]	Li, H., Ye, G. and Wang, J. (2007) A modified algorithm for the improvement of composite interval mapping. Genetics, 175, 361-374. doi:10.1534/genetics.106.066811
[9]	Lander, E. and Kruglyak, L. (1995) Genetic dissection of complex traits: Guidelines for interpreting and reporting linkage results. Nature Genetics, 11, 241-247. doi:10.1038/ng1195-241
[10]	Weller, J.I., Song, J.Z., Heyen, D.W., Lewin, H.A. and Ron, M. (1998) A new approach to the problem of multiple comparisons in the genetic dissection of complex traits. Genetics, 150, 1699-1706.
[11]	Benjamini, Y. and Yekutieli, D. (2005) Quantitative trait loci analysis using the false discovery rate. Genetics, 171, 783-790. doi:10.1534/genetics.104.036699
[12]	Lee, H., Dekkers, J.C.M., Soller, M., Malek, M., Fernando, R.L. and Rothschild, M.F. (2002) Application of the false discovery rate to quantitative trait loci interval mapping with multiple traits. Genetics, 161, 905-914.
[13]	Bennewitz, J., Reinsch, N., Guiard, V., Fritz, S., Thomsen, H., Looft, C., Kühn, C., Schwerin, M., Weimann, C., Erhardt, G., Reinhardt, F., Reents, R., Boichard, D. and Kalm, E. (2004) Multiple quantitative trait loci mapping with cofactors and application of alternative variants of the false discovery rate in an enlarged granddaughter design. Genetics, 168, 1019-1027. doi:10.1534/genetics.104.030296
[14]	Basten, C.J., Weir, B.S. and Zeng, Z.-B. (1994) Zmap— A QTL cartographer. In: Smith, C., Gavora, J.S., Benkel, B., Chesnais, J., Fairfull, W., Gibson, J.P., Kennedy, B. W. and Burnside, E.B., Eds., 5th World Congress on Genetics Applied to Livestock Production: Computing Strategies and Software, Organizing Committee, 5th World Congress on Genetics Applied to Livestock Production, Guelph, 65-66.
[15]	Basten, C.J., Weir, B.S. and Zeng, Z.-B. (2003) QTL cartographer, version 1.17. Department of Statistics, North Carolina State University, Raleigh.
[16]	Leips, J. and Mackay, T.C.F. (2000) Quantitative trait loci for life span in Drosophila melanogaster: Interactions with genetic background and larval density. Genetics, 155, 1773-1788.
[17]	Forbes, S.N., Valenzuela, R.K., Keim, P. and Service, P.M. (2004) Quantitative trait loci affecting life span in replicated populations of Drosophila melanogaster. I. Composite interval mapping. Genetics, 168, 301-311. doi:10.1534/genetics.103.023218
[18]	Visscher, P.M., Thompson, R. and Haley, C.S. (1996) Confidence intervals in QTL mapping by bootstrapping. Genetics, 143, 1013-1020.
[19]	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.
[20]	Bennewitz, J., Reinsch, N. and Kalm, E. (2002) Improved confidence intervals in quantitative trait loci mapping by permutation bootstrapping. Genetics, 160, 1673-1686.
[21]	Lynch, M. and Walsh, B. (1998) Genetics and analysis of quantitative traits. Sinauer Associates, Inc., Sunderland.
[22]	Lander, E.S., Green, P., Abrahamson, J., Barlow, A., Daley, M.J., Lincoln, S.E. and Newburg, L. (1987) Mapmaker: an interactive computer package for constructing primary genetic linkage maps of experimental and natural populations. Genomics, 1, 174-181. doi:10.1016/0888-7543(87)90010-3
[23]	Lincoln, S., Daley, M. and Lander, E. (1992) Constructing genetic maps with Mapmaker/Exp 3.0. 3rd Edition, Whitehead Institute, Cambridge.
[24]	Noor, M.A.F., Cunningham, A.L. and Larkin, J.C. (2001) Consequences of recombination rate variation on quantitative trait locus mapping studies: Simulations based on the Drosophila melanogaster genome. Genetics, 159, 581-588.