Iteratively reweighted LASSO for mapping multiple quantitative trait loci.

The iteratively reweighted least square (IRLS) method is mostly identical to maximum likelihood (ML) method in terms of parameter estimation and power of quantitative trait locus (QTL) detection. But the IRLS is greatly superior to ML in terms of computing speed and the robustness of parameter estimation. In conjunction with the priors of parameters, ML can analyze multiple QTL model based on Bayesian theory, whereas under a single QTL model, IRLS has very limited statistical power to detect multiple QTLs. In this study, we proposed the iteratively reweighted least absolute shrinkage and selection operator (IRLASSO) for extending IRLS to simultaneously map multiple QTLs. The LASSO with coordinate descent step is employed to efficiently estimate non-zero genetic effect of each locus scanned over entire genome. Simulations demonstrate that IRLASSO has a higher precision of parameter estimation and power to detect QTL than IRLS, and is able to estimate residual variance more accurately than the unweighted LASSO based on LS. Especially, IRLASSO is very fast, usually taking less than five iterations to converge. The barley dataset from the North American Barley Genome Mapping Project is reanalyzed by our proposed method.