RESUMO
At present, single-trait best linear unbiased prediction (BLUP) is the standard method for genetic selection in soybean. However, when genetic selection is performed based on two or more genetically correlated traits and these are analyzed individually, selection bias may arise. Under these conditions, considering the correlation structure between the evaluated traits may provide more-accurate genetic estimates for the evaluated parameters, even under environmental influences. The present study was thus developed to examine the efficiency and applicability of multi-trait multi-environment (MTME) models by the residual maximum likelihood (REML/BLUP) and Bayesian approaches in the genetic selection of segregating soybean progeny. The study involved data pertaining to 203 soybean F2:4 progeny assessed in two environments for the following traits: number of days to maturity (DM), 100-seed weight (SW), and average seed yield per plot (SY). Variance components and genetic and non-genetic parameters were estimated via the REML/BLUP and Bayesian methods. The variance components estimated and the breeding values and genetic gains predicted with selection through the Bayesian procedure were similar to those obtained by REML/BLUP. The frequentist and Bayesian MTME models provided higher estimates of broad-sense heritability per plot (or heritability of total effects of progeny; [Formula: see text]) and mean accuracy of progeny than their respective single-trait versions. Bayesian analysis provided the credibility intervals for the estimates of [Formula: see text]. Therefore, MTME led to greater predicted gains from selection. On this basis, this procedure can be efficiently applied in the genetic selection of segregating soybean progeny.