The Full EM Algorithm for the MLEs of QTL Effects and Positions and Their Estimated Variances in Multiple-Interval Mapping

The advent of complete genetic linkage maps of DNA markers has made systematic studies of mapping quantitative trait loci (QTL) in experimental organisms feasible. The method of multiple-interval mapping provides an appropriate way for mapping QTL using genetic markers. However, efficient algorithms for the computation involved remain to be developed. In this article, a full EM algorithm for the simultaneous computation of the MLEs of QTL effects and positions is developed. EM-based formulas are derived for computing the observed Fisher information matrix. The full EM algorithm is compared with an ECM algorithm developed by Kao and Zeng (1997, Biometrics53, 653–665). The validity of the inverted observed Fisher information matrix as an estimate of the variance matrix of the MLEs is demonstrated by a simulation study.