Prediction of Genetic Variance in Biparental Maize Populations: Genomewide Marker Effects versus Mean Genetic Variance in Prior Populations

Abstract

Good methods are lacking for predicting the genetic variance (VG) in biparental populations. Our objective was to determine whether genomewide marker effects and related populations could be used to predict the VG when two parents (A and B) are crossed to form a segregating population. For each of 85 A/B populations, 2 to 23 maize (Zea mays L.) populations with A and B as one of the parents were used as the training population. In the genomewide selection model, the testcross VG in A/B was predicted as the variance among the predicted genotypic values of progeny from a simulated A/B population. In the mean variance model, VG in A/B was predicted as the mean of VG in a series of A/* populations and */B populations, where * denotes a random parent. The correlations between observed and predicted VG were significant (P = 0.05) for both the genomewide selection model (0.18 for yield, 0.49 for moisture, and 0.52 for test weight) and the mean variance model (0.26 for yield, 0.46 for moisture, and 0.50 for test weight). The percentages of bias in estimates of VG were −28 to −60% for the genomewide selection model, but were only −1 to 5% for the mean variance model. Our results indicated that the VG in an A/B population could be predicted as the mean variance among populations with A and B as one of the parents. The mean variance model should be practical in breeding programs because it simply uses phenotypic data from prior, related populations.

Predicting genetic variance in bi-parental breeding populations is more accurate when explicitly modeling the segregation of informative genomewide markers

“…This is reflected in the notation for a method's prediction accuracy. For example, PD-based prediction accuracy is denoted rðVP PD ; V b G Þ. Fisher's Z-transformation was used to calculate p values denoting the significance (a = 0.05) of the alternative hypothesis where r is greater than zero (i.e., a onesided test), and a nonparametric bootstrap procedure (Efron 1979) was implemented to construct confidence intervals for r. Confidence intervals were constructed from 2000 bootstrap samples where the 50th highest numerical value represents the lower bound of the 95 % confidence interval and the 1950th highest value represents the upper bound and will appear within parentheses following r (Lian et al 2015).…”

“…PopVar per se refers to the exact methodology presented in Mohammadi et al (2015) and implemented in the R extension (R Core Team 2013) 'PopVar' , which has not yet been validated. However, the application of genomewide markers to predict r 2 G and methodology similar to PopVar has been previously described (Zhong and Jannink 2007;Bernardo 2014) and was the subject of a recent validation study (Lian et al 2015). Lian et al (2015) evaluated the r 2 G prediction methodology of Bernardo (2014) that is akin to PopVar and which they term the 'genomewide selection model' using a maize breeding dataset.…”

“…However, the application of genomewide markers to predict r 2 G and methodology similar to PopVar has been previously described (Zhong and Jannink 2007;Bernardo 2014) and was the subject of a recent validation study (Lian et al 2015). Lian et al (2015) evaluated the r 2 G prediction methodology of Bernardo (2014) that is akin to PopVar and which they term the 'genomewide selection model' using a maize breeding dataset. Although the accuracy of their genomewide selection model was numerically comparable to other models tested, it was not the authors' preferred method due to the comparatively larger biases of its r 2 G prediction (Lian et al 2015).…”

“…Lian et al (2015) evaluated the r 2 G prediction methodology of Bernardo (2014) that is akin to PopVar and which they term the 'genomewide selection model' using a maize breeding dataset. Although the accuracy of their genomewide selection model was numerically comparable to other models tested, it was not the authors' preferred method due to the comparatively larger biases of its r 2 G prediction (Lian et al 2015). Such biases, which are noted to have likely resulted from the shrinkage of marker effects toward zero upon estimation with ridge regression BLUP (Lian et al 2015), would become problematic when carried into other parameters derived from the r 2 G predictions.…”

“…Although the accuracy of their genomewide selection model was numerically comparable to other models tested, it was not the authors' preferred method due to the comparatively larger biases of its r 2 G prediction (Lian et al 2015). Such biases, which are noted to have likely resulted from the shrinkage of marker effects toward zero upon estimation with ridge regression BLUP (Lian et al 2015), would become problematic when carried into other parameters derived from the r 2 G predictions. It is important to note that each of the 85 bi-parental populations considered by Lian et al The six r 2 G prediction methods include phenotypic distance (PD), genetic distance (GD), relationship-based distance (RD), breeding value distance (BVD), QTL-GD, and PopVar a Relationship distances can be calculated from either pedigree or genotypic data (2015) utilized a different training population (which are at times referred to as training sets in the genomic selection literature) with different heritabilities for a given trait to estimate marker effects.…”