Using quantitative trait loci results to discriminate among crosses on the basis of their progeny mean and variance

Abstract

To develop inbred lines, parents are crossed to generate segregating populations from which superior inbred progeny are selected. The value of a particular cross thus depends on the expected performance of its best progeny, which we call the superior progeny value. Superior progeny value is a linear combination of the mean of the cross's progeny and their standard deviation. In this study we specify theory to predict a cross's progeny standard deviation from QTL results and explore analytically and by simulation the variance of that standard deviation under different genetic models. We then study the impact of different QTL analysis methods on the prediction accuracy of a cross's superior progeny value. We show that including all markers, rather than only markers with significant effects, improves the prediction. Methods that account for the uncertainty of the QTL analysis by integrating over the posterior distributions of effect estimates also produce better predictions than methods that retain only point estimates from the QTL analysis. The utility of including estimates of a cross's among-progeny standard deviation in the prediction increases with increasing heritability and marker density but decreasing genome size and QTL number. This utility is also higher if crosses are envisioned only among the best parents rather than among all parents. Nevertheless, we show that among crosses the variance of progeny means is generally much greater than the variance of progeny standard deviations, restricting the utility of estimates of progeny standard deviations to a relatively small parameter space.

Figure 1.—

Ratio t for independent QTL. Equal exact: the ratio t for QTL with equal variances derived analytically. Unequal simulation: the ratio t for QTL with geometrically distributed variances derived from simulation. Delta method: the ratio t for QTL with either equal or geometrically distributed variances derived from the delta method.

Figure 2.—

Ratio t for different genome sets. (a) Simulation results with equal QTL variances. (b) Simulation results with QTL variances following a geometric series. 5Chr100cM, 5 chromosomes of 100 cM each; 10Chr100cM, 10 chromosomes of 100 cM each; 20Chr100cM, 20 chromosomes of 100 cM each; 20Chr200cM, 20 chromosomes of 200 cM each; Unlinked, independent QTL.

Figure 3.—

Correlations from random crosses between simulated values and different estimators. (a–h) The results under models A–H, respectively. Six selection intensity values, i = 1.40, 1.55, 1.76, 2.06, 2.42, and 2.67, correspond to selected fractions of 20, 15, 10, 5, 2, and 1%, respectively. Note that c and d have different y-axis scales.

Figure 4.—

Correlations, corresponding to model A, from the top 40 parent crosses between the simulation truth and different predictors.