Best linear unbiased prediction and optimum allocation of test resources in maize breeding with doubled haploids.

With best linear unbiased prediction (BLUP), information from genetically related candidates is combined to obtain more precise estimates of genotypic values of test candidates and thereby increase progress from selection. We developed and applied theory and Monte Carlo simulations implementing BLUP in 2 two-stage maize breeding schemes and various selection strategies. Our objectives were to (1) derive analytical solutions of the mixed model equations under two breeding schemes, (2) determine the optimum allocation of test resources with BLUP under different assumptions regarding the variance component ratios for grain yield in maize, (3) compare the progress from selection using BLUP and conventional phenotypic selection based on mean performance solely of the candidates, and (4) analyze the potential of BLUP for further improving the progress from selection. The breeding schemes involved selection for testcross performance either of DH lines at both stages (DHTC) or of S(1) families at the first stage and DH lines at the second stage (S(1)TC-DHTC). Our analytical solutions allowed much faster calculations of the optimum allocations and superseded matrix inversions to solve the mixed model equations. Compared to conventional phenotypic selection, the progress from selection was slightly higher with BLUP for both optimization criteria, namely the selection gain and the probability to select the best genotypes. The optimum allocation of test resources in S(1)TC-DHTC involved ≥ 10 test locations at both stages, a low number of crosses (≤ 6) each with 100-300 S(1) families at the first stage, and 500-1,000 DH lines at the second stage. In breeding scheme DHTC, the optimum number of test candidates at the first stage was 5-10 times larger, whereas the number of test locations at the first stage and the number of test candidates at the second stage were strongly reduced compared to S(1)TC-DHTC.