Genetic Gain Increases by Applying the Usefulness Criterion with Improved Variance Prediction in Selection of Crosses

Abstract

A crucial step in plant breeding is the selection and combination of parents to form new crosses. Genome-based prediction guides the selection of high-performing parental lines in many crop breeding programs which ensures a high mean performance of progeny. To warrant maximum selection progress, a new cross should also provide a large progeny variance. The usefulness concept as measure of the gain that can be obtained from a specific cross accounts for variation in progeny variance. Here, it is shown that genetic gain can be considerably increased when crosses are selected based on their genomic usefulness criterion compared to selection based on mean genomic estimated breeding values. An efficient and improved method to predict the genetic variance of a cross based on Markov chain Monte Carlo samples of marker effects from a whole-genome regression model is suggested. In simulations representing selection procedures in crop breeding programs, the performance of this novel approach is compared with existing methods, like selection based on mean genomic estimated breeding values and optimal haploid values. In all cases, higher genetic gain was obtained compared with previously suggested methods. When 1% of progenies per cross were selected, the genetic gain based on the estimated usefulness criterion increased by 0.14 genetic standard deviation compared to a selection based on mean genomic estimated breeding values. Analytical derivations of the progeny genotypic variance-covariance matrix based on parental genotypes and genetic map information make simulations of progeny dispensable, and allow fast implementation in large-scale breeding programs.

Keywords: Bayesian statistics; genomic selection; plant breeding; progeny variance; usefulness criterion.

Figure 1

Scheme of simulation part 2.

Figure 2

Bias and predictive correlations of the genetic variance estimates for only-QTL scenario. Estimates for 200 randomly generated crosses were obtained with methods VPM and PMV for different $h^2$and training population sizes N. Simulation scenario with 300 QTL genotypes coded in the marker matrix.

Figure 3

Bias and predictive correlations of the genetic variance estimates for only-marker scenario. Estimates for 200 randomly generated crosses were obtained with methods VPM and PMV for different $h^2$and training population sizes N. Simulation scenario with 3000 non-QTL marker genotypes coded in the marker matrix.

Figure 4

Additional gain of selecting crosses based on estimated UC and OHV. Gain is given as the difference in mean genotypic values of the selected lines from selection based on UC or OHV compared to selecting based on mean GEBV alone, standardized by the true genotypic standard deviation ${\sigma }_g$ in the training population. Different variance estimates were used to estimate the UC (VPM and PMV). Gain is given for different fractions of selected lines per cross. Results are shown for preselected crosses based on minimum Rogers’ distance between parents of 0.2 and a heritability of 0.2 (A) and 0.6 (B), as well as for crosses not preselected by parental distance, and a heritability of 0.2 (C) and 0.6 (D).

Figure 5

Additional gain of selecting crosses based on true UC, true OHV, or biased UC. For the biased UC, either an underestimated variance (${\widehat{\sigma }}_g^2=0.5{\sigma }_g^2$) or a variance estimate with predictive correlation of $cor\left({\sigma }_g^2,{\widehat{\sigma }}_g^2\right)=0.5$ was considered. Gain is given in comparison to the genetic gain of selection based on mean parental true genotypic values, standardized by the genetic standard deviation of the training population.