Application of mixed models for evaluating stability and adaptability of maize using unbalanced data

Abstract

The aim of this study was to use a multienvironment trial approach from a mixed model point of view for factor analysis (FA) of the stability and adaptability of hybrids. Twenty-eight hybrids were analyzed in 35 environments across four seasons/years (summer season 2010, winter season 2011, summer season 2011 and winter season 2012). Several of these hybrids were analyzed during the first seasons and were not evaluated in later seasons or vice versa. Therefore, the dataset used in this study simulated the dynamics of a genetic breeding program with removal and inclusion of genotypes over the years. A biplot of the factor scores and loadings showed that the environments were more similar within seasons than between seasons, thereby suggesting that a given site may behave differently year after year. The season was more effective in discovery megaenvironments. The FA models may be directly interpreted as GGE biplot analysis since the first factor score had a perfect fit (r 2 ¼ 0:99) with the empirical best linear unbiased predictors of the genotypes. Given the assumption of normality for the factor scores, confidence ellipses could be created to directly compare the genotypes in the biplot. Stability and adaptability could be analyzed in unbalanced experiments with the removal and inclusion of genotypes over time. This approach allowed certain trends in a breeding program to be measured by directly comparing hybrids developed for the first or winter season. The biplot interpretation was direct and intuitive, and it has the same properties as the GGE biplot obtained by singular value decomposition.

Maize hybrid stability in environments under water restriction using mixed models and factor analysis

“…This is even more interesting when considering the situation of plant breeding programs in general, in which unbalanced data are common, as in the case of this study, which considers a series of data from VCU trials, set up over a series of years, in which better performing hybrids are retained for at least 2 years and the others substituted by new hybrids. Figueiredo et al (2014) also found that the AF methodology can safely be used in studies of adaptability and stability in trials with a high degree of unbalanced data. Moreover, we can highlight the study of Smith et al (2015) who emphasized the superiority of this methodology for evaluation of trials in multi-environments over several years.…”

“…In the same context, Smith et al (2001) proposed a general class of analytic factor (AF) models that encompassed the approach of Piepho (1998) and included spatial errors for each trial based on Figueiredo et al (2014). In this way, the authors sought to develop models that could provide considerations by data from various evaluation environments.…”

Stacking Tolerance to Drought and Resistance to a Parasitic Weed in Tropical Hybrid Maize for Enhancing Resilience to Stress Combinations

“…While environments were considered as fixed effects in these analyses, replicates within environments, hybrids and hybrid by environment interaction were regarded as random effects (Piepho, 1998;Smith et al, 2001). This approach has proven to be effective in generating biplots which graphically represent genotype stability and adaptability in MET (Burgueño et al, 2008;Crossa et al, 2010;Crossa et al, 2013;Figueiredo et al, 2015). The two factor analysis (FA(2)) that has become a standard model for MET analysis (Kelly et al, 2007) was used in the analyses of all data sets.…”

Research Article Adaptability and stability of corn hybrids in the off season across various agricultural regions in Brazil

“…Corn cultivation occurs practically throughout the country and production occurs at different periods of the year (agricultural crops) depending on the region (IBGE, 2015). The first crop or summer crop is grown mainly between September and March, while the second harvest in the off or "second" season is grown mostly between the months of January and May (Figueiredo et al, 2014).…”

“…The edaphoclimatic conditions of cultivation in the off season and summer vary considerably, but the vast majority of cultivars planted in the first harvest are also recommended for off season since corn breeding programs for off season are newer and less developed than those for summer corn breeding programs, and many cultivars from the breeding programs of the summer harvest show good performance and adaptation in the off season (Figueiredo et al, 2014). According to Fritsche-Neto et al (2010) the success of a cultivar in the market is associated with high productive performance and the agronomic characteristics.…”