Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduce d variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as mul tiple (QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian sta tistics arts particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitat ive genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to genera te the value of a hypothetical underlying variable (called the liability) a nd a threshold, which in turn allow the use of existing Bayesian statistics . The reversible jump Markov chain Monte Carlo algorithm is used to simulat e the posterior samples of all unknowns, including the number of QTL, the l ocations and effects of identified QTL, genotypes of each individual at bot h the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distributi on of the number of QTL and the locations and effects of the identified QTL . Utilities of the method are demonstrated using a simulated outbred full-s ib family. A computer program written in FORTRAN language is freely availab le on request.