Mapping Multiple Quantitative Trait Loci for Ordinal Traits

Many complex traits in humans and other organisms show ordinal phenotypic variation but do not follow a simple Mendelian pattern of inheritance. These ordinal traits are presumably determined by many factors, including genetic and environmental components. Several statistical approaches to mapping quantitative trait loci (QTL) for such traits have been developed based on a single-QTL model. However, statistical methods for mapping multiple QTL are not well studied as continuous traits. In this paper, we propose a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to map multiple QTL for ordinal traits in experimental crosses. We model the ordinal traits under the multiple threshold model, which assumes a latent continuous variable underlying the ordinal phenotypes. The ordinal phenotype and the latent continuous variable are linked through some fixed but unknown thresholds. We adopt a standardized threshold model, which has several attractive features. An efficient sampling scheme is developed to jointly generate the threshold values and the values of latent variable. With the simulated latent variable, the posterior distributions of other unknowns, for example, the number, locations, genetic effects, and genotypes of QTL, can be computed using existing algorithms for normally distributed traits. To this end, we provide a unified approach to mapping multiple QTL for continuous, binary, and ordinal traits. Utility and flexibility of the method are demonstrated using simulated data.