On the use of linear regression and maximum likelihood for QTL mapping in half-sib designs

Methods of identification of quantitative trait loci (QTL) using a half-sib design are generally based on least-squares or maximum likelihood approaches. These methods differ in the genetical model considered and in the information used. Despite these differences, the power of the two methods in a daughter design is very similar. Using an analogy with a one-way analysis of variance, we propose an equation connecting the two test-statistics (F ratio for regression and likelihood ratio test in the case of the maximum likelihood). The robustness of this relationship is tested by simulation for different single QTL models. In general, the correspondence between the two statistics is good under both the null hypothesis and the alternative hypothesis of a single QTL segregating. Practical implications are discussed with particular emphasis on the theoretical distribution of the likelihood ratio test.