Mapping quantitative trait loci by an extension of the Haley-Knott regression method using estimating equations

Abstract

The Haley-Knott (HK) regression method continues to be a popular approximation to standard interval mapping (IM) of quantitative trait loci (QTL) in experimental crosses. The HK method is favored for its dramatic reduction in computation time compared to the IM method, something that is particularly important in simultaneous searches for multiple interacting QTL. While the HK method often approximates the IM method well in estimating QTL effects and in power to detect QTL, it may perform poorly if, for example, there is strong epistasis between QTL or if QTL are linked. Also, it is well known that the estimation of the residual variance by the HK method is biased. Here, we present an extension of the HK method that uses estimating equations based on both means and variances. For normally distributed phenotypes this estimating equation (EE) method is more efficient than the HK method. Furthermore, computer simulations show that the EE method performs well for very different genetic models and data set structures, including nonnormal phenotype distributions, nonrandom missing data patterns, varying degrees of epistasis, and varying degrees of linkage between QTL. The EE method retains key qualities of the HK method such as computational speed and robustness against nonnormal phenotype distributions, while approximating the IM method better in terms of accuracy and precision of parameter estimates and power to detect QTL.

Figure 1.—

A simulation example of QTL mapping with a population of 250 backcross individuals and a single QTL at 45 cM. The right side magnifies the box in the left side. The HK method inflates the LOD curve in the case of selective genotyping. The EE method almost completely avoids inflation of the LOD curve.

Figure 2.—

Haley–Knott regression lines at the position with largest LOD score in a simulated data set. Lines are shown in the case of full marker data (left side, dashed line) and in the case of selective genotyping with missing marker data for the intermediate 20% of individuals (right side, solid line).

Figure 3.—

LOD scores for a two-dimensional, two-QTL genome scan of a simulated population of 80 backcross individuals with two interacting QTL on chromosomes 1 and 2. Values below the diagonal correspond to a test of two additively acting QTL vs. none. Values above the diagonal correspond to a test for two-locus epistasis. In the gray-tone scale, the numbers to the right and left correspond to values below and above the diagonal, respectively. (A) Results from the IM method. (B) Results from the EE method.

Figure 3.—

LOD scores for a two-dimensional, two-QTL genome scan of a simulated population of 80 backcross individuals with two interacting QTL on chromosomes 1 and 2. Values below the diagonal correspond to a test of two additively acting QTL vs. none. Values above the diagonal correspond to a test for two-locus epistasis. In the gray-tone scale, the numbers to the right and left correspond to values below and above the diagonal, respectively. (A) Results from the IM method. (B) Results from the EE method.