Iteratively reweighted least squares mapping of quantitative trait loci

Mapping quantitative trait loci (QTL) is a typical problem of regression with uncertain independent variables because the genotype of a putative QTL is not observed. Rather, the genotype is inferred from marker information. The method of maximum likelihood (ML) methods is considered to be the optimal solution for this problem because the distribution of the unobserved QTL genotype is fully taken into account. The simple linear regression method (REG) is a first-order approximation to ML and usually performs very well. In this study, an iteratively reweighted least squares method (IRWLS) is proposed. The new method is a second-order approximation to ML because both the expectation and the variance of the unobserved QTL genotype are taken into consideration. The IRWLS is developed in the context of a single large outbred family. The properties of IRWLS are demonstrated and compared with REG and ML via replicated Monte Carlo simulations. The conclusions are: (1) when marker information content is high, the three methods perform equally well, but ML and IRWLS outperform REG when marker information content is low and the variance explained by the QTL is high; (2) when the residual distribution is not normal, ML can fail or have low power to detect small QTLs, but REG and IRWLS are robust to non-normality; and (3) when the residual distribution is normal, the performance of IRWLS is almost identical to ML, but the computational speed of IRWLS is many times faster than that of ML.