Assessing a multiple QTL search using the variance component model.

Development of variance component algorithms in genetics has previously mainly focused on animal breeding models or problems in human genetics with a simple data structure. We study alternative methods for constrained likelihood maximization in quantitative trait loci (QTL) analysis for large complex pedigrees. We apply a forward selection scheme to include several QTL and interaction effects, as well as polygenic effects, with up to five variance components in the model. We show that the implemented active set and primal-dual schemes result in accurate solutions and that they are robust. In terms of computational speed, a comparison of two approaches for approximating the Hessian of the log-likelihood shows that the method using an average information matrix is the method of choice for the five-dimensional problem. The active set method, with the average information method for Hessian computation, exhibits the fastest convergence with an average of 20 iterations per tested position, where the change in variance components <0.0001 was used as convergence criterion.