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 F_2:4 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; ) and mean accuracy of progeny than their respective single-trait versions. Bayesian analysis provided the credibility intervals for the estimates of . 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.

Breeding programs of the species Coffea canephora rely heavily on the significant genetic variability between and within its two varietal groups (conilon and robusta). The use of hybrid families and individuals has been less common. The objectives of this study were to evaluate parents and families from the populations of conilon, robusta, and its hybrids and to define the best breeding and selection strategies for productivity and disease resistance traits. As such, 71 conilon clones, 56 robusta clones, and 20 hybrid families were evaluated over several years for the following traits: vegetative vigor, incidence of rust and cercosporiosis, fruit ripening time, fruit size, plant height, canopy diameter, and yield per plant. Components of variance and genetic parameters were estimated via residual maximum likelihood (REML) and genotypic values were predicted via best linear unbiased prediction (BLUP). Genetic variability among parents (clones) and hybrid families was detected for most of the evaluated traits. The Mulamba-Rank index suggests potential gains up to 17% for the genotypic aggregate of traits in the hybrid population. An intrapopulation recurrent selection within the hybrid population would be the best breeding strategy because the genetic variability, narrow and broad senses heritabilities and selective accuracies for important traits were maximized in the crossed population. Besides, such strategy is simple, low cost and quicker than the concurrent reciprocal recurrent selection in the two parental populations, and this maximizes the genetic gain for unit of time.