Abstract
Simulations demonstrated that estimates of realized genetic gain from linear mixed models using regional trials are biased to some degree. Thus, we recommend multiple selected models to obtain a range of reasonable estimates. Genetic improvements of discrete characteristics are obvious and easy to demonstrate, while quantitative traits require reliable and accurate methods to disentangle the confounding genetic and non-genetic components. Stochastic simulations of soybean [Glycine max (L.) Merr.] breeding programs were performed to evaluate linear mixed models to estimate the realized genetic gain (RGG) from annual multi-environment trials (MET). True breeding values were simulated under an infinitesimal model to represent the genetic contributions to soybean seed yield under various MET conditions. Estimators were evaluated using objective criteria of bias and linearity. Covariance modeling and direct versus indirect estimation-based models resulted in a substantial range of estimated values, all of which were biased to some degree. Although no models produced unbiased estimates, the three best-performing models resulted in an average bias of [Formula: see text] kg/ha[Formula: see text]/yr[Formula: see text] ([Formula: see text] bu/ac[Formula: see text]/yr[Formula: see text]). Rather than relying on a single model to estimate RGG, we recommend the application of several models with minimal and directional bias. Further, based on the parameters used in the simulations, we do not think it is appropriate to use any single model to compare breeding programs or quantify the efficiency of proposed new breeding strategies. Lastly, for public soybean programs breeding for maturity groups II and III in North America, the estimated RGG values ranged from 18.16 to 39.68 kg/ha[Formula: see text]/yr[Formula: see text] (0.27-0.59 bu/ac[Formula: see text]/yr[Formula: see text]) from 1989 to 2019. These results provide strong evidence that public breeders have significantly improved soybean germplasm for seed yield in the primary production areas of North America.