Genetic Gain in Common Bean with Black Grain by Indirect Estimation Methods

Abstract

The objective of this study was to estimate the genetic gain for yield of black‐grained common bean (Phaseolus vulgaris L.) developed by the Embrapa breeding program of Brazil. Genetic gain estimates were generated from 403 field tests conducted in all regions of Brazil in three growing seasons over 16 yr, from 1993 to 2008. Genetic gains were estimated by two indirect methods and were compared with those found through a direct estimation method. The first methodology used the mixed model approach to calculate the best unbiased linear estimate of cycle means, as fixed effects, and the best unbiased predictor of the genotype effect within cycles, as random effects. The second methodology of generalized least squares considered a model of fixed effects, except for the error. For the direct method, 24 lines consisting of the three highest yielding of each of the eight breeding cycles were evaluated in 21 environments. The estimated percentage of annual genetic gain in grain yield by the direct method over the 16‐yr period (1.23%, P < 0.01) was significant and close to the result of the fixed model analysis (1.20%, P < 0.05) and by the mixed model (1.02%, P = 0.068). These results show that the indirect methods using a fixed model and the mixed model were consistent in determining genetic gain and can be used as an alternative to the direct method.