Efficient Algorithms for Quantitative Trait Loci Mapping Problems

Rapid advances in molecular genetics push the need for efficient data analysis. Advanced algorithms are necessary for extracting all possible information from large experimental data sets. We present a general linear algebra framework for quantitative trait loci (QTL) mapping, using both linear regression and maximum likelihood estimation. The formulation simplifies future comparisons between and theoretical analyses of the methods. We show how the common structure of QTL analysis models can be used to improve the kernel algorithms, drastically reducing the computational effort while retaining the original analysis results. We have evaluated our new algorithms on data sets originating from two large F(2) populations of domestic animals. Using an updating approach, we show that 1-3 orders of magnitude reduction in computational demand can be achieved for matrix factorizations. For interval-mapping/composite-interval-mapping settings using a maximum likelihood model, we also show how to use the original EM algorithm instead of the ECM approximation, significantly improving the convergence and further reducing the computational time. The algorithmic improvements makes it feasible to perform analyses which have previously been deemed impractical or even impossible. For example, using the new algorithms, it is reasonable to perform permutation testing using exhaustive search on populations of 200 individuals using an epistatic two-QTL model.