Modeling (co)variance structures for genetic and non-genetic effects in the selection of common bean progenies

In common bean breeding programs, experiments are conducted in different environments to select plants with high potential for inbred lines extraction and/or recombination. The occurrence of genetic and/or statistical unbalance is common in these experiments. Moreover, there may be (co)variance between genetic and non-genetic effects when treatments are assessed in different environments. Our aim was to (1) test different (co)variance structures between seasons for genetic and non-genetic effects; (2) choose the model with the highest predictive capacity of the genotypic value; and (3) select the superior progenies to mitigate the effects of genotype-by-environment interactions. To this end, two experiments were conducted in the 2015 drought and winter seasons. The grain yield and grain aspect were assessed. Model 4, with an unstructured (co)variance for genetic effects, homogeneous block variance, and heterogeneous residual diagonal variance, was the model that best fit the data. The heritability estimates and their accuracy differed between the different adjusted models, with the most accurate estimates observed in model 4. The genetic correlation between the drought and winter seasons was of low magnitude (− 0.04) for grain yield, which corroborates the strong genotype by environment interaction. The average gain predicted with the recombination of the selected progenies in model 4 was 2.97% for grain yield. The modeling of different (co)variance structures for genetic and non-genetic effects could be applicable for analyses involving statistical unbalance and the assessment of progenies in different environments, with the aim of selecting those with high potential for recombination.