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How to deal with genotype uncertainty in variance component quantitative trait loci analyses

  • XIA SHEN (a1) (a2), LARS RÖNNEGÅRD (a2) (a3) and ÖRJAN CARLBORG (a1) (a3)

Dealing with genotype uncertainty is an ongoing issue in genetic analyses of complex traits. Here we consider genotype uncertainty in quantitative trait loci (QTL) analyses for large crosses in variance component models, where the genetic information is included in identity-by-descent (IBD) matrices. An IBD matrix is one realization from a distribution of potential IBD matrices given available marker information. In QTL analyses, its expectation is normally used resulting in potentially reduced accuracy and loss of power. Previously, IBD distributions have been included in models for small human full-sib families. We develop an Expectation–Maximization (EM) algorithm for estimating a full model based on Monte Carlo imputation for applications in large animal pedigrees. Our simulations show that the bias of variance component estimates using traditional expected IBD matrix can be adjusted by accounting for the distribution and that the calculations are computationally feasible for large pedigrees.

Corresponding author
*Corresponding author: The Linnaeus Centre for Bioinformatics, Uppsala University, Uppsala, Sweden. E-mail:
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Andersson, L., Haley, C., Ellegren, H., Knott, S., Johansson, M., Andersson, A.-E. L., Edfors-Lilja, K. I., Fredholm, M., Hansson, I., Håkansson, J. & Lundström, K. (1994). Genetic mapping of quantitative trait loci for growth and fatness in pigs. Science 263, 17711774.
Arendonk, V., Tier, B. J. A. M. & Kinghorn, B. (1994). Use of multiple genetic markers in prediction of breeding values. Genetics 137, 319329.
Besnier, F. & Carlborg, Ö. (2007). A general and efficient method for estimating continuous IBD functions for use in genome scans for QTL. BMC Bioinformatics 8, 440.
Blangero, J., Williams, J. & Almasy, L. (2001). Variance component methods for detecting complex trait loci. Advances in Genetics 42, 151181.
Botstein, D., White, R., Skolnick, M. & Davis, R. (1980). Construction of a genetic linkage map in man using restriction fragment length polymorphisms. American Journal of Human Genetics 32, 314331.
Carlborg, Ö. & Haley, C. S. (2004). Epistasis: too often neglected in complex trait studies? Nature Reviews, Genetics 5, 618625.
Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B 39, 138.
Eaves, L., Neale, M. & Maes, H. (1996). Multivariate multipoint linkage analysis of quantitative trait loci. Behavior Genetics 26, 519525.
Elston, R. & Stewart, J. (1971). A general model for the genetic analysis of pedigree data. Human Heredity 21, 523542.
Felsenstein, J. (2004). Inferring Phylogenies. Sunderland, MA: Sinauer Associates.
Fernando, R. & Grossman, M. (1989). Marker-assisted selection using best linear unbiased prediction. Genetics, Selection, Evolution 21, 467477.
Fulker, D. & Cardon, L. (1994). A sib-pair approach to interval mapping of quantitative trait loci. American Journal of Human Genetics 54, 10921103.
Garey, M. R. & Johnson, D. S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco, CA: W. H. Freeman.
George, A. W., Visscher, P. & Haley, C. (2000). Mapping quantitative trait loci in complex pedigrees: A two-step variance component approach. Genetics 156, 20812092.
Gessler, D. D. G. & Xu, S. (1996). Using the expectation or the distribution of the identity by descent for mapping quantitative trait loci under the random model. American Journal of Human Genetics 59, 13821390.
Goddard, M. (1992). A mixed model for analyses of data on multiple genetic markers. Theory and Applied Genetics 83, 878886.
Goldgar, D. (1990). Multipoint analysis of human quantitative genetic variation. American Journal of Human Genetics 47, 957967.
Haley, C. & Knott, S. (1992). A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69, 315324.
Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association 72, 320338.
Knott, S., Marklund, L., Haley, C., Andersson, K., Davies, D., Ellegren, H., Fredholm, M., Hansson, I., Hoyheim, B., Lundström, K., Moller, M. & Andersson, L. (1998). Multiple marker mapping of quantitative trait loci in a cross between outbred wild boar and large white pigs. Genetics 149, 10691080.
Kruglyak, L. & Lander, E. (1995). Complete multipoint sib-pair analysis of qualitative and quantitative traits. American Journal of Human Genetics 57, 439454.
Kutalik, Z., Johnson, T., Bochud, M., Mooser, V., Vollenweider, P., Waeber, G., Waterworth, D., Beckmann, J. S. & Bergmann, S. (2011). Methods for testing association between uncertain genotypes and quantitative traits. Biostatistics 12, 117.
Lander, E. & Botstein, D. (1989). Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121, 185199.
Lundström, K., Karlsson, A., Håkansson, J., Hansson, I., Johansson, M., Andersson, L. & Andersson, K. (1995). Production, carcass and meat quality traits of f2-crosses between european wild pigs and domestic pigs including halothane gene carriers. Animal Science 61, 325331.
Lynch, M. & Walsh, B. (1997). Genetics and Analysis of Quantitative Traits. Sunderland, MA: Sinauer Associates.
Mao, Y. & Xu, S. (2005). A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information. Heredity 94(3), 305315. doi: 10.1038/sj.hdy.6800564.
Marchini, J. & Howie, B. (2010). Genotype imputation for genome-wide association studies. Nature Reviews, Genetics 11, 499511. doi: 10.1038/nrg2796.
Morton, N. & Maclean, C. (1974). Analysis of family resemblance. III. complex segregation of quantitative traits. American Journal of Human Genetics 26, 489503.
Olson, J. (1995). Robust multipoint linkage analysis: an extension of the Haseman-Elston method. Genetics Epidemiology 12, 177193.
Pérez-Enciso, M., Varona, L. & Rothschild, M. (2000). Computation of identity by descent probabilities conditional on DNA markers via a Monte Carlo Markov Chain method. Genetics, Selection, Evolution 32, 467482.
Pong-Wong, R., George, A., Woolliams, J. & Haley, C. (2001). A simple and rapid method for calculating identity-by-descent matrices using multiple markers. Genetics, Selection, Evolution 33, 453471.
R Development Core Team. (2010). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0.
Rönnegård, L. & Carlborg, Ö. (2007). Separation of base allele and sampling term effects gives new insights in variance component QTL analysis. BMC Genetics 8, 1. doi: 10.1186/1471-2156-8-1.
Rönnegård, L., Mischenko, K., Holmgren, S. & Carlborg, Ö. (2007). Increasing the efficiency of variance component quantitative trait loci analysis by using reduced-rank identity-by-descent matrices. Genetics 176, 19351938. doi: 10.1534/genetics.107.071977.
Rönnegård, L., Pong-Wong, R. & Carlborg, Ö. (2008). Defining the assumptions underlying modeling of epistatic QTL using variance component methods. The Journal of Heredity 99, 421425. doi: 10.1093/jhered/esn017.
Schork, N. J. (1993). Extended multipoint identity-by-descent analysis of human quantitative traits: Efficiency, power, and modeling considerations. American Journal of Human Genetics 53, 13061319.
Sorensen, D. & Gianola, D. (2002). Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics. Berlin: Springer.
Stern, M., Duggirala, R., Mitchell, B., Reinhart, L., Sivakumar, S., Shipman, P., Uresandi, O., Benavides, E., Blangero, J. & O'Connell, P. (1996). Evidence for linkage of regions on chromosome 6 and 11 to plasma glucose concentrations in Mexican Americans. Genome Research 6, 724734.
Thompson, E. A. & Heath, S. C. (1999). Estimation of conditional multilocus gene identity among relatives. Lecture Notes-Monograph Series 33, 95–113.
Wang, T., Fernando, R., van der Beek, S., Grossman, M. & van Arendonk, J. (1995). Covariance between relatives for a marked quantitative trait locus. Genetics, Selection, Evolution 27, 251274.
Xu, S. (1996). Computation of the full likelihood function for estimating variance at a quantitative trait locus. Genetics 144, 19511960.
Xu, S. & Atchley, W. R. (1995). A random model approach to interval mapping of quantitative trait loci. Genetics 141, 11891197.
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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
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