On locating multiple interacting quantitative trait loci in intercross designs

Abstract

A modified version (mBIC) of the Bayesian Information Criterion (BIC) has been previously proposed for backcross designs to locate multiple interacting quantitative trait loci. In this article, we extend the method to intercross designs. We also propose two modifications of the mBIC. First we investigate a two-stage procedure in the spirit of empirical Bayes methods involving an adaptive (i.e., data-based) choice of the penalty. The purpose of the second modification is to increase the power of detecting epistasis effects at loci where main effects have already been detected. We investigate the proposed methods by computer simulations under a wide range of realistic genetic models, with nonequidistant marker spacings and missing data. In the case of large intermarker distances we use imputations according to Haley and Knott regression to reduce the distance between searched positions to not more than 10 cM. Haley and Knott regression is also used to handle missing data. The simulation study as well as real data analyses demonstrates good properties of the proposed method of QTL detection.

Figure 1.—

Comparison of the Bonferroni type I error bounds under the null model (no effects) for the intercross design when the same penalty as in backcross is used and when the penalty is adjusted accordingly.

Figure 2.—

The solid curves show the percentage of correctly identified additive, dominance, and epistatic effects depending on the heritability. The shaded curves display the expected number of incorrectly selected (linked and unlinked) markers (n = 200).

Figure 3.—

Percentage of correctly identified additive effects vs. number of additive effects. The QTL are unlinked, i.e., located on different chromosomes, and have effect sizes of 0.5. The solid line is based on simulations where no prior information is used to derive the penalty terms of the modified BIC. The dashed line represents simulations with the correct number of underlying effects (1, 2, 4, 7, and 10) assumed known. The dotted line corresponds to the two-step search procedure based on formula (4).

Figure 4.—

Percentage of correctly identified additive, dominance, and epistatic effects vs. individual effect heritabilities . Detection rates are taken from simulations of scenarios 1–9 (see Table 3) for n = 200.

Figure 5.—

Percentage of correctly identified additive, dominance, and epistatic effects vs. individual effect heritabilities . Detection rates are taken from simulations of scenarios 1–9 (see Table 3) for n = 500.

Figure 6.—

Genetic map for the D. virilis experiment by Huttunen et al. (2004). Solid horizontal lines indicate observed marker positions, and dotted lines show imputed positions. QTL localized by our proposed method are symbolized by diamonds. Intervals with significant additive and/or dominance effects found by Huttunen et al. (2004) applying composite interval mapping are indicated by solid vertical lines.