Genotype x Environment Interaction and Stability Analysis for Grain Yield of Advanced Tef Genotypes using GGE Biplots

Selection of the most high-yielding and stable cultivars across environments are difficult because of the complex nature of genotype × environment interactions (G x E interaction). The study was conducted with the objectives to determine the G x E interaction of tef genotypes and to identify tef genotypes with high stability for grain yield using GGE biplot analysis. In the present study, 12 advanced tef genotypes and one standard check were evaluated at Holetta and Ginchi in 2014 and 2015 and at Adadi in 2014. Combined analysis of variance revealed the existence of significant G x E interaction for tef grain yield. Genotype, environment and G x E interaction explained 6.70 %, 81.03 % and 12.27 % of the variation in grain yield, respectively. The GGE model showed that the first and second principal component axis accounted for 43.2 % and 29.5 % of variability, respectively. The pattern of G x E interaction was a crossover type as revealed by differential yield ranking of the genotypes across environments. Genotype G4 (RIL77C) was both high yielding and stable across the test environments and could be considered as desirable genotype recommended for release as variety. The test environment E3 (Adadi-2014) was identified to be the most discriminating and representative environment to evaluate tef genotypes.


Experimental Design and Data Collected
The experimental design was a randomized complete block design with four replications of 2 m x 2 m (4m 2 ) plot size during the two main seasons of 2014 and 2015. The field experiment was managed as per the research recommendation of agronomic practices of the respective test locations. Grain yield (g) of each plot was measured on clean, sun dried seed and the measured grain yield value (g) has converted to kilogram per hectare for data analysis. Table1. Description of tef genotypes used for the experiment

Combined Analysis of Variance
The grain yield data were subjected to combined analysis of variance using PROC GLM in SAS using a RANDOM statement with the TEST option (SAS Institute, 2011) to determine the effects of genotype, environment and genotype × environment interaction. The combined ANOVA was done considering year-location combination as the environment. Genotype was considered as the fixed effect while environment was considered as a random effect.

GGE Biplot Analysis
GGE biplot was computed using the "GGEBiplotGUI" package of R statistical software in RStudio (Frutos et al., 2014;R Core Team, 2019) to analyze the multi-environment trial data, and evaluate the adaptability and stability of the cultivars and the effects of genotype, environment, and G × E interaction. A GGE biplot is a biplot that displays the genotypic main effect and G x E interaction of a multi-environment trial based on principal component analysis (PC1 and PC2) derived from subjecting a two way data (Genotype x environment data) to singular value decomposition (Yan et al., 2000). The GGE model used was: where Yij was the measured mean of i th genotype in j th environment; µ was the grand mean; βj was the main effect of j th environment; µ + βj was the average trait over all genotypes in j th environment; λ1 and λ2 were the singular values for the first and second principal component (PC1 and PC2), respectively; ξi1 and ξi2 were eigenvectors of i th genotype for PC1 and PC2; ηj1 and ηj2 were eigenvectors of j th environment for PC1 and PC2; and εij was the residual of the model associated i th genotype in j th environment.

Analysis of variance
The combined analysis of variance for grain yield of the 13 tef genotypes tested in five environments showed significant differences among genotypes (G), environments (E) and G x E interaction (Table 2). A large grain yield variation revealed by environments which explained 81.03 % of the total G + E + G x E variation, while the effects of the genotypes and G x E interaction contributed 6.70 % and 12.27 % of the total variation, respectively. These results in agreement with previous findings on tef (Habte et al., 2019), maize (Thokozile et al., 2014) and sorghum (Asfaw et al., 2011). Genotype mean grain yield (averaged across environments) ranged from 1874 kg ha -1 for G6 to 2429.5 kg ha -1 for G8 and Environment mean grain yield (averaged across genotypes) ranged from 1595 kg ha -1 at E4 to 3009.6 kg ha -1 at E3 (Table 3). Table 2. Combined analysis of variance for grain yield (kgha -1 ) of 12 tef genotypes grown at five environments. The presences of significant G x E interaction effect indicate variable phenotypic performance of the tested genotypes across environments because of the impact of environment on trait expression. A large G x E interaction effect compared to genotype effect suggests the possible existence of diverse mega-environments with different winner genotypes (Yan and Kang, 2003). Mega-environment was defined as group of locations that consistently share the same best cultivars (Yan and Rijcan, 2002).  Figure 1 presents a polygon view of 13 tef genotypes tested at five environments. The first two principal components (PC1 and PC2) obtained by singular value decomposition of environment-centered data of grain yield explained 72.6 % of the total effect it had on the grain yield variation with PC1 and PC2 accounted for 43.2 % and 29.5 % of variability, respectively (Figure 1) using environment centered data. The polygon view GGE biplot indicates best genotype(s) in each environment and groups of environment (Yan and Hunt, 2002). The plot is formed by connecting the vertex genotypes (located farthest away from the biplot origin) while the rest are inside Journal of Biology, Agriculture and Healthcare www.iiste.org ISSN 2224-3208 (Paper) ISSN 2225-093X (Online) Vol.10, No.21, 2020 the polygon with perpendicular lines radiating from the origin of the biplot divide the biplot into different sectors. The highest yielding genotype (winning genotype) for an environment or set of environments in a sector is the vertex genotype (Yan et al., 2010). From polygon view of GGE biplot, the polygon divided into four sectors. Three environments, E2, E4 and E5, fell in the first sector with vertex genotype G8 implying that this genotype was the winning genotype for these environments. Sector 2 comprised one environment (E3) with two genotypes (G2 and G4) where G4 was the highest yielder. The remaining environment (E1) was contained in sector 3 with G3 being high yielding genotype. Sector 4 in the polygon consisted of G6 as vertex genotype had no test environment indicating that the genotype was poor performer in all test environments. Thus, the G × E interaction was a crossover type where a change in performance ranking of the genotypes across environments observed.

Mean vs. stability and genotype comparison with ideal genotype views of GGE biplot
Ranking of 14 tef genotypes based on their mean yield and stability performance are presented in figure 2. The average environment coordinate (AEC) view based on genotype-focused singular value partitioning (SVP = 1) and mean value can be referred as the "mean vs. stability" view of GGE biplot (Yan et al., 2007). The single arrowed line shown on AEC abscissa points to higher mean yield across environments. Hence, genotype G8 had the highest mean grain yield followed by G1 and G4 while genotype G6 had the lowest. The stability of the genotypes are determined by their projection on to the AEC vertical axis with the most stable genotype was located on the AEC horizontal axis and had minimum projection on the AEC vertical axis. Thus, genotype G10 and G12 were the most stable followed by G4 and G2. While genotype G3 followed by G6 and G9 were the least stable for grain yield. Yan and Tinker (2006) reported that stability is important only when coupled with high trait mean. Hence, an ideal genotype would be one that has both high mean yield performance and high stability across environment. The "comparison with ideal genotype" view of GGE biplot has concentric circles with the ideal genotype in the inner circle ( Figure 3). It permits to visualize the distance between each genotype and the ideal genotype; a genotype is more desirable than others if it is located closer to ideal genotype. Therefore, G4 was the most desirable genotype and could be considered as widely adaptable genotype.

.3.3 Discriminative vs. representativeness and ranking environments relative to an ideal environment
Evaluation of test environments is crucial to identify the most desirable genotypes for a mega environment in variety performance trial. Figure 4 shows the "discriminating ability vs representativeness" view of the GGE biplot. The distance between the markers of the environment to the biplot origin, is a measure of its discriminating ability (Frutos et al., 2013). Test environments with longer vectors are more discriminating of the genotypes whereas a test environment marker with a short vector provides little information about the genotypes differences (Yan et al., 2007). Hence, among the five environments evaluated, E3 followed by E5 were the most discriminating of the genotypes while E4 was the least discriminating of all test environments.
According to Yan and Tinker (2006), the representativeness of testing environment is visualized by the angle between environment vector and abscissa of average environment axis. The smaller the angle, the more representative of the test environment would be (Yan et al., 2007). Thus, E4 followed by E3 were identified to be more representative environments. The ideal test environment is one that is most discriminating for genotypes and Journal of Biology, Agriculture and Healthcare www.iiste.org ISSN 2224-3208 (Paper) ISSN 2225-093X (Online) Vol.10, No.21, 2020 38 is representative of the target environments (Yan and Kang, 2003). The comparison with the ideal environment view of GGE biplot ( Figure 5) has concentric circles with the ideal environment in the inner circle. An environment is more desirable and discriminating when located closer to the ideal environment (Naroui et al., 2013). Therefore, E3 was more representative and discriminating environment.

Conclusions
The present study showed that tef grain yield was highly impacted by environment followed by G x E interaction and by the differences among genotypic effects. Presence of G × E interaction for grain yield indicates influence of environment on the expression of the trait. GGE biplot model was effective for analyzing and visualizing pattern of G x E and identifying the most high-yielding and stable cultivar as well as discriminating ability and representativeness of the test environments. The G × E interaction was a crossover type where a change in performance ranking of the genotypes across environments observed. The test environment Adadi-2014 (E3) was more representative and discriminating environment. The GGE biplot showed that genotype G4 (DZ-Cr-387 x Gealmie (RIL-77C)) was high yielding and stable across the test environments. Therefore, this genotype could be considered as widely adaptable genotype and can be recommended for release as variety.