Abstract
A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameters were estimated by marginal posterior means computed with a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), the event of linkage or nonlinkage, and the parameters (allele frequencies, QTL substitution effect, recombination rate, polygenic and residual variances). The analysis was evaluated empirically via application to simulated granddaughter designs consisting of 2000 sons, 20 related sires and their ancestors. Results obtained in this study and preliminary work on multiple linked markers and multiple QTLs support the usefulness of the Bayesian method for the statistical mapping of QTLs.
Similar content being viewed by others
References
Da Y, Ron M, Yanai A, Band M, Everts RE, Heyen DW, Weller JI, Wiggans GR, Lewin HA (1994) The dairy bull DNA repository: a resource for mapping quantitative trait loci. Proc 5th World Congr Genet Appl Livest Prod Sci 21:229–232
Geyer CJ (1992) Practical Markov chain Monte Carlo (with discussion). Stat Sci 7:467–511
Hoeschele I (1994) Bayesian QTL mapping via the Gibbs sampler. Proc 5th World Congr Genet Appl Livst Prod 21, Guelph, Canada, pp 241–244
Hoeschele I, VanRaden PM (1993a) Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge. Theor Appl Genet 85:953–960
Hoeschele I, VanRaden PM (1993b) Bayesian analysis of linkage between genetic markers and quantitative trait loci. II. Combining prior knowledge with experimental evidence. Theor Appl Genet 85:946–952
Janss LLG, Thompson R, van Arendonk JAM (1995) Application of Gibbs sampling in a mixed major gene polygenic inheritance model in animal populations. Theor Appl Genet 91:1137–1147
Meng X-L, Wong WH (1993) Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Technical Report No. 365, Department of Statistics, The University of Chicago
Newton MA, Raftery AE (1994) Approximate Bayesian inference with the weighted likelihood bootstrap. J Roy Stat Soc B 56:3–48
Satagopan JM, Yandell BS, Newton MA, Osborn TC (1996) Markov chain Monte Carlo approach to detect polygene loci for complex traits. Genetics (in press)
Scott WD (1992) Multivariate density estimation. Wiley and Sons, New York
Sorensen DA, Anderson S, Gianola D, Korsgaard I (1995) Bayesian inference in threshold models using Gibbs sampling. Genet Selec Evol 27:229–249
Thaller G, Hoeschele I (1996) A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology. Theor Appl Genet (in press)
Thomas DC, Cortessis V (1992) A Gibbs sampling approach to linkage analysis. Hum Hered 42:63–76
Uimari P, Thaller G, Hoeschele I (1996) A Monte Carlo method for Bayesian analysis of linkage between multiple linked markers and a quantitative trait locus. Genetics 143:1831–1842
VanRaden PM, Wiggans GR (1991) Derivation, calculation and use of national animal model information. J Dairy Sci 74:2737–2746
Author information
Authors and Affiliations
Additional information
Communicated by E. J. Eisen
Rights and permissions
About this article
Cite this article
Thaller, G., Hoeschele, I. A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. II. A simulation study. Theoret. Appl. Genetics 93, 1167–1174 (1996). https://doi.org/10.1007/BF00230142
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00230142