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Statistical methods to map quantitative trait loci (QTL) often neglect the X chromosome and may focus exclusively on autosomal loci. But the X chromosome often requires special treatment sex and cross-direction covariates may need to be included to avoid spurious evidence of linkage, and the X chromosome may require a separate significance threshold. In multiple-QTL analyses, including the consideration of epistatic interactions, the X chromosome also requires special care and consideration. We extend a penalized likelihood method for m