Increasing the efficiency of variance component quantitative trait loci analysis by using reduced-rank identity-by-descent matrices

Abstract

Recent technological development in genetics has made large-scale marker genotyping fast and practicable, facilitating studies for detection of QTL in large general pedigrees. We developed a method that speeds up restricted maximum-likelihood (REML) algorithms for QTL analysis by simplifying the inversion of the variance-covariance matrix of the trait vector. The method was tested in an experimental chicken pedigree including 767 phenotyped individuals and 14 genotyped markers on chicken chromosome 1. The computation time in a chromosome scan covering 475 cM was reduced by 43% when the analysis was based on linkage only and by 72% when linkage disequilibrium information was included. The relative advantage of using our method increases with pedigree size, marker density, and linkage disequilibrium, indicating even greater improvements in the future.

Figure 1.—

The rank of (right axis) and the relative computation time (left axis) along chicken chromosome 1. The relative computation time is the ratio of the total number of flops used in AI-REML for the inversion of V by the reduced method and direct inversion. This is [n³ + N_red(n²k +3nk²)]/[N_fulln³/2], where N_red and N_full are the number of iterations until convergence using Π_red and Π, respectively, n is the number of observations, and k is the rank of Π_red. A marker position is given by an “X” along the x-axis.

Figure 2.—

QTL likelihood-ratio curves for body weight at 200 days of age along chicken chromosome 1 for three different variance component models.