Application of linear mixed models to overcome challenges of unbalanced data in common bean breeding

Abstract

Common bean breeding faces challenges such as genetic and statistical unbalance across trials. This study aimed to evaluate the impact of using grain yield data (kg ha⁻¹) on selection efficiency by connecting sequential trials of common bean progenies under different experimental designs. Initially, 400 F_4:6 progenies were evaluated in 20 trials using a randomized complete block design (RCBD) during the 2019 dry season in southeast Brazil. Subsequently, 95 selected progenies were tested in three seasons (rainy/2019, winter/2020, and rainy/2020) using an incomplete block design (triple 10 × 10 lattice). Five models were fitted, each considering different (co)variance structures for residuals and progenies within generations. The model assuming a first-order analytic factor structure for progeny within generations and heterogeneous diagonal variance for residuals provided the best fit. This model produced a 68% higher average genetic gain compared to other models, along with a significant increase in average heritability. Changes in progeny classification based on predicted genotypic values were observed across seasons. The use of mixed models to fit (co)variance matrices proved superior to traditional compound symmetry models, especially in scenarios with genetic and statistical unbalance. This approach enhances the selection process by providing more accurate estimates of genetic parameters, ultimately contributing to the development of superior bean lines.