Combined yield comparison and stability evaluation of rape genotypes using the mixed model

• Traditional methodology is not optimal for rape yield and stability evaluation.
• Combination with mixed model approach is important for stability evaluation.
• Combination with stability evaluation is useful for genotype yield comparison.

Yield comparison and stability evaluation of genotypes based on multi-environment trials (MET) play an important role in crop breeding and varietal recommendation for crop production. Usually, analysis of variance (ANOVA) is used for yield comparison, whereas other models (e.g. Shukla's and multiplicative models) are used for stability evaluation. This analysis methodology has the weakness that on the one hand the variance heterogeneity of genotypes (i.e. stability) cannot be accounted for in yield comparison, and on the other hand assumptions about variance–covariance of genotype effects stability evaluation are not identical to that in yield comparison though the trial and hence the data are the same. Furthermore, the eventual error variation due to different levels of trial precision across different environments cannot be accounted for in both yield comparison and stability evaluation. In this paper, the mixed model with various variance–covariance structures allowing for accounting for variance heterogeneity of both genotype and residual error effects was used to fit the seed yield data from a (Brassica napus L.) MET with thirteen rape genotypes (QS101–QS113) and randomized complete block design at each test environment for the upper reaches of the Yangtze River of China. The variance components of the best fitting mixed model served as measures of stability, and yield comparisons of genotypes were made also on the basis of the best fitting model. The result showed that the variance–covariance characteristics of both genotypes and residual errors affected stability evaluation of rape genotypes. Appropriately incorporating this information in estimating and statistical testing of genotype effects based on mixed model methodology was important for yield comparison of rape genotypes; Compared to the check (QS108), QS113 highly significantly (α = 0.01) increased yield by 10% with high stability; QS109 highly significantly and QS104 significantly (α = 0.05) increased yield, respectively, by 10.4% and 6.2%, respectively, with low stability; QS102, QS101, QS110 and QS105 were superior only in term of stability; the other six genotypes were inferior in term of both significant yield difference and stability.