FACTOR ANALYSIS AND GGE BIPLOT FOR ENVIRONMENTAL AND .

Funcional Plant Breeding Journal / v.1, n.2, a.3After identifying a significant GE interaction, thedata were subjected to the factor analysis (Murakami andCruz, 2004) and GGE biplot (Yan et al., 2000). The factoranalysis was performed according to the model expressedin Equation 2:(Eq. 2)In which xj is the mean of the grain yield in thej environment, with j 1, 2, , v (variables), l kj is thefactor loading for the jth variable associated to the kthfactor,in which k 1, 2, , m (common factors); Fk is the kthcommon factor and, εj is the specific factor associated tothe jth variable. The definition of ME or factor numberwas given by the number of principal components thatexplained at least 80% of the total variation of genotypes inthe environments or, similarly, by a communality averagevalue that exceeded the minimum of 0.80 (Cruz et al.,2014). The final factor loadings, obtained after applyinga varimax rotation method, were clustered according totheir magnitudes. Within a given factor, the environmentswith factor loadings greater than or equal to 0.70 indicateda similarity pattern and the formation of an ME, whileloadings between 0.50 and 0.70 indicated the uncertaintyof adding the environment to the ME, and loadings lessthan 0.50 indicated the exclusion of the environmentassociated with the formed ME (Cruz et al., 2014). Anadaptability assessment was graphically performed,according to Murakami and Cruz (2004). Considering thatthe factor loadings were positive and that there is interestin enhancing the variable value, it was possible to identifygenotypes with wide adaptability to the pairs of MEs,which were located in the first quadrant of the scatter plot.Genotypes specifically adapted to the region determinedby the factor (or specific ME), which were located inthe second and fourth quadrants, and poorly adaptedgenotypes, which were located in the third quadrant.The GGE biplot analysis was carried out accordingto the model expressed in Equation 3:(Eq. 3)thIn which Yij is the average yield of genotype i inenvironment j; µ is the overall average; βj is the maineffect in environment j; λ1 and λ2 are the singular values(SV) for the first and second principal components (PC),respectively; ξi1 and ξi2 are eigenvectors of genotype i forPC1 and PC2, respectively; ηj1 and ηj2 are eigenvectorsof environment j for PC1 and PC2, respectively; and εijis the residual of the model associated with the genotypei in environment j.The data were centered on the environment(column-metric preserving) to visualize the environmentalrelationships. Thus, similarity (covariance) between thetwo environments was given by both the length and thecosine of the angle between them (Mare et al., 2017; Yanand Tinker, 2006). Environment discriminant ability wasdetermined by the length of the environmental vector,which was proportional to the standard deviation, and theenvironment representativeness was given by a relationbetween the distance of each environment in relation toan average environment (Yan et al., 2000).Mega-environment identification was performed byvisualizing the which-won-where graph. The outermostgenotypes were connected by vertices that formed apolygon that contained all other genotypes inside it. Aset of perpendicular lines was drawn from the originbiplot subdividing it into sectors to facilitate visualization(Mare et al., 2017). For genotypic evaluation, the datawere centered on the genotype (row-metric preserving).Genotype stability and average performance throughoutthe environments belonging to the same ME wereevaluated by examining the abscissa and ordinate axes ofthe mean environment (Yan and Tinker, 2006).The adequacy of GGE biplot analysis was measuredby the criterion proposed by Gauch and Zobel (1996),which is based on the percentage of total variation of G GE that is absorbed by biplots. By this criterion, theexpected noise of sum of squares (SS) is estimated bythe degrees of freedom multiplied by the error of meanof squares (MS) of each variation source, the expectedpattern SS is given by the total SS for the source minusits expected error, and the expected pattern SS vs. totalSS ratio is calculated for each source. Expected patternvalues greater than 80% are considered suitable for biplotanalysis (Yan and Tinker, 2006). All the analyses wereperformed by the software Genes (Cruz, 2016).Results and discussionThe analysis of variance showed significantdifferences for genotype, environment, and GE interactioneffects (p 0.01) (Table 3). Among the sources of variationthat affected grain yield, environment accounted forapproximately 82% of the total phenotypic variation (G E GE interaction), while genotypes and interactionscontributed 6.32% and 11.47%, respectively. Similarresults were reported by Tonk et al. (2011), Abate et al.(2015) and Pan-pan et al. (2016), which confirms theimportance of environmental studies for cultivar selection(Mortazavian et al., 2014).It was verified in the factor analysis that fiveeigenvalues explained approximately 84% of the totalvariation (that corresponds to the communality average ofthe common factors) regarding the genotype performancefor grain yield in the environments (Table 5). Initially, fivedifferent MEs were defined. Communalities presentedacceptable values, with the exception of the experimentcarried out in Planaltina 2013, in which the variance dueto the common factors reached 0.5797 (Table 5) and,therefore, did not allow for inferences about environmentalstrata or genotypic adaptability (Cruz et al., 2014).However, in the previous year in this same municipality,the communality value was high, suggesting that externalp. 31

factors influenced the assay of 2013.Factor loading values indicated that the MEdetermined by Factor 1 was constituted by the experimentscarried out in 2012 and 2013 in Vilhena and by theexperiment carried out in Muzambinho in 2013. Althoughthe municipalities described are located in differentregions, both experienced adequate rainfall during theevaluated periods and are located at altitudes varyingfrom 615 to 944 meters (Table 2). The second ME wasformed by the environments of Nova Porteirinha 2012and Campo Verde 2013, while the third ME was formedby Chapadão do Sul 2013. The fifth ME was formedsolely by the experiment carried out in Jaíba 2013.The environments Planaltina 2013, Manduri 2013 andUberlândia 2012 presented factor loadings less than0.70 for all factors and, therefore, were not included in aspecific ME. The fourth ME, constituted by the trialscarried out in 2012 in the municipalities of Palmas andPlanaltina, added locations with a negative performancecorrelation. For recommendation purposes, this ME wasignored because GE interaction impacted the performanceof some genotypes.Mega-environment formation was independent ofaltitude, since contrasting environments formed an ME.In addition to indicating the sunflower plasticity (Bezerraet al., 2014). In relation to the water regime, additionalirrigation applied in some places made it difficult toevaluate the importance of this trait for the environmentstratification. Therefore, the mega-environments pointedout in the analysis should be better investigated in orderto confirm its subdivision.Genotypic adaptability in the ME one, two, threeand five indicated a lack of adaptability of the BRS 324and BRS 315 genotypes (Figure 1) in most of the MEs,since these were located mainly in the third quadrant. Thehybrid BRS 387 was classified as widely adapted since itwas located mainly in the first quadrant.In the dispersionsinvolving ME5 (which presented a negative factorloading), there was a change in the quadrant interpretationsand, therefore, genotypes of wide adaptability werelocated in the third quadrant; those that were poorlyadapted were located in the second quadrat and thosespecifically adapted were located in quadrants one andthree. Of the three times that HLE 20 hybrid appeared inthe second quadrant, two of these times were in dispersionsthat involved ME5, a fact that allowed us to classify it aspoorly adapted to this ME. The variety Embrapa 122 (T)showed specifically adaptability based on informationfrom half of the dispersion charts. This variety appearedat least twice in ME3 and was therefore consideredspecifically adapted to this ME. When not classified asspecifically adapted to this ME, it corresponded to thegenotype class of wide adaptability in ME1 and ME2 andto the poorly adapted class in ME5 (Figure 1).Some studies involving GE interactions based32 - FPBJ - Scientific Journalon a graphical analysis tend to use only two axes forthe purpose of Cartesian dispersion. However, whena technique is capable of identifying and mapping anunfixed number of axes or factors, the one that is moreaccurate tends to be the genotypic recommendation, sincethe researcher will be able to observe the classificationpattern repeatability and make decisions based on a morerobust criterion. In situations in which only two axes areadopted as sufficient to absorb large portions of genotypeand environment variation, decisions are made based on asimplified genotype behavior pattern, which may reducethe recommendation reliability (Cruz et al., 2014).The first two PC accounted for 84% of the variationof G GE in the biplots, which means that GGE biplotshould account for approximately 84% of the total G GE, value considered adequate to perform the analysis,according to Gauch and Zobel (1996). It was possible toobserve that, except for the environment pairs Planaltinain 2012 and Vilhena A in 2013, and Planaltina in 2012 and2013, all the others were positively correlated (Figure 2 a).The experimental conditions that occurred in Planaltina inthe evaluation years may have caused this result since itwas the same location, and a high correlation was expectedbetween them. As there were no environments in whichthe correlation was highly negative, it was possible toinfer that the complex interaction among environmentswas of a low magnitude.Three MEs were identified by the GGE biplotanalysis (Figure 2 b). A curious fact is that the two trialscarried out in the municipality of Planaltina constitutedtwo different mega-environments. In the trial of Planaltinain 2012, the genotype that presented the best performancewas the hybrid HLE 20. However, in Planaltina in 2013,the genotype with the best performance in it was thehybrid HLE 23. The other environments constituted thethird ME, highlighting the hybrid BRS G39. As shownin Figure 2 a, the only environmental pair that presentedsome complex interaction (negative correlation betweenenvironments) was Planaltina in 2012 and 2013. Althoughthe interaction was of low magnitude, this was sufficientto demonst

A factor analysis and GGE biplot were used for evaluating the individual effects of genotypes, environments, interactions and mega-environment discrimination based on the data from 16 sunflower genotypes evaluated in 14 environments. The factor analysis was able to identify mega-environment inconsistency and, consequently, excluded a mega .