Principles and applications of information ratio adjustment of GGE biplot— A case study of cotton mega-environment investigation in the Yangtze River Valley

The GGE (genotype main effect plus genotype by environment interaction effect) biplot is the most powerful statistical and visual display tool available for cultivar evaluation, environmental evaluation and mega-envrironment investigation. The versatility of GGE biplot in displaying cultivar stability and high yielding, identifying ideal cultivars and test environments, evaluating the representativeness and discrimination ability of test sites, and differentiating mega- environments have attracted extensive application in analyzing regional trials of many crops. Nevertheless, few reports have focused on the potential loss of fit of GGE biplot models and model adjustment using information ratio (IR). IR is the product of percent variation explained by each principal component and the minor value of degree of freedom of genotypes along with the number of test locatons in GGE biplot analysis of datasets in regional crop trials. As principal component with IR ≥ 1 has useful information, it is a sufficient and necessary condition of GGE model with appropriate goodness of fit to cover all data analysis. In fact, the goodness of fit of GGE biplot models is restricted to the sum of percent variation explained by the first two principal components (PC1 and PC2), rather than the suitable principal components determined by IR. Thus although GGE biplot model is an efficient graphical display of data structure, it is not so efficient to guarantee optimal fitting of effects. Using the GGE biplot method and collected datasets in national regional cotton (Gossypium hirsutum L.) trials in the Yangtze River Valley in 2000?2012, this study showed the effects of IR adjustments of GGE models in maga-environment investigation. The scores of principal components for IR ≥ 1 in 35 groups of regional cotton trials were used to calculate Euclidean distance matrix among the test environments. Also a hierachical cluster analysis was implemented to outline the scheme of differentiation of the mega-environment. A corresponding analysis was also carried out using fixed first two principal components of GGE biplot analysis for the purpose of mutual comparision between GGE biplot model and IR-adjusted GGE model for mega-environment investigation efficiency. The results showed that while only 28.6% was appropriately fitted by GGE biplot model, 68.6% was under-fitted and 2.9% over-fitted in 35 groups of regional cotton trials. The IR-adjusted GGE model enhanced the goodness of fit by 8.7% and reduced loss of fit by 12.2% for under- and over-fitted GGE biplot model trials. Compared with IR-adjusted model, the superiority index of GGE biplot model was 15.9%. This indicated that GGE biplot model performed satisfactorily in depicting the overall pattern of genotype by environment interaction of regional cotton trials. However, the IR-adjusted GGE model was more reliable and had a more precise goodness of fit. The first hierachical mega-environment differentiation by the IR-adjusted GGE model was the same as that of GGE biplot model in terms of identifying cotton planting regions in Nan-Xiang Basin and Sichuan Basin as particular ecological regions. However, they were significantly different in terms of subregion divisions in the middle and lower reaches of the Yangtze River Valley. The mega-environment division scheme based on the IR-adjusted GGE model was of more practical in terms of geographical and ecological factor representation. Thus the study demonstrated an excellent example of the principles and application effects of GGE biplot adjusted with IR. This served as a significant supplement and improvement to GGE biplot application. It also provided the scientific basis and guidline for the application of GGE biplot in mega-environment investigation.