AMMI and GGE Bi-plot Analysis for Seed Yield and Oil Content of Sesame ( Sesamum indicum L.) Genotypes in Tigray, Northern Ethiopia

Seventeen sesame genotypes were tested at ten environments in Tigray, Northern Ethiopia during 2014-2015 cropping seasons. Randomized Complete Block Designs (RCBD) with three replications was used in the study. According to the GGE bi-plot different sesame growing environments grouped into two mega-environments: The first mega-environment contained the favorable environments Dansha area with a vertex G4 and Sheraro area with winner G3 and the second environment included medium to low environments E2 (Humera-2), E4 (Dansha-2), E5 (Sheraro-1), E7 (Wargiba-1), E8 (Wargiba-2) and E9 (Maykadra) for seed yield. Three mega-environments identified for oil content: The 1st environment contained G12, G7 and G2 in the mega-environment group of Humera, Dansha and Gendawuha, The 2 nd environment, Sheraro location contained G9 and the 3 rd environment Wargiba, was containing G17. G1 (HuRC-4) identified as an “ideal” genotype and E1 (Humera-1) also identified as an ideal environment the most representative of the overall environments and the most powerful to discriminate genotypes. The multivariate approaches AMMI and GGEbi-plot were better for partitioning the GEI into the causes of variation. According to different stability models, G1, G7, and G3 were high yielder and the most stable both in terms of seed yield and oil content. Moreover, showed yield advantages over the released and local varieties. The stable genotypes recommended for wider areas while G14 and G4 were for specific favorable environments Sheraro and Dansha, respectively.


Introduction
Sesame (Sesamum indicum L.) is an annual, indeterminate plant with a diploid chromosome number of 2n=2x=26 and belonging to family Pedaliacea. It is a Sanjayrao Khairnar and Arjanbhai Monpara 2 plant breeder's dream crop because it presents a great genetic variability Janick and Whipkey [1]. The additive main effects and multiplicative interaction (AMMI) method integrates analysis of variance and principal components analysis into a unified approach Gauch [2]. According to Zobel, et al. [3] it can be used to analysis METs. The AMMI method is used for three main purposes. The first is model diagnoses, AMMI is more appropriate in the initial statistical analysis of yield trials, because it provides an analytical tool of diagnosing other models as sub cases when these are better for particular data sets Gauch [2]. Secondly, AMMI clarifies the GEI and summarizes patterns and relationships of genotypes and environments Zobel, et al. [3].The third use is to improve the accuracy of yield estimates. Gains have been obtained in the accuracy of yield estimates that are equivalent to increasing the number of replicates by a factor of two to five Zobel, et al. [3].
AMMI stability value (ASV) was calculated in the excel spread sheet using the formula developed by Purchase [4]:

√[ ]
Where, ASV= AMMI ٬ s stability value, SS=sum of squares, IPCA1=interaction of principal component analysis one, IPCA2 = interaction of principal component analysis two. Similarly Yield stability index (YSI) was also computed by summing up the ranks from ASV and mean seed yield Farshadfar, et al. [5]: YSI= RASV+RGY Where: RASV is rank of AMMI stability value and RGY is rank of mean seed yield to statistically compare the stability analysis procedures used in the study, the Spearman's coefficient of rank correlation (r s ) Steel and Torrie [6] was estimated using SPSS version 16 statistical software.
The seed yield data were subjected to AMMI analysis, which combines analysis of variance (ANOVA) with additive and multiplicative parameters in to a single model Gauch [2]. After removing the replicate effect when combining the data, the genotypes and environments observations are partitioned in to two sources: Additive main effects for genotypes and environments; and non-additive effects due to genotype by environment interaction. A biplot showing the genotype and environmental means against IPCA1 was also performed via this model using GenStat (V16). The AMMI model is: ∑ Y ij is the observed mean yield of i th genotype in the j th environment; µ is the grand mean; G i is the i th genotypic effect; E j is the j th environment effect; is the eigen value of the principal component analysis (PCA) axis k; and are the i th genotype j th environment PCA scores for the PCA axis k; is the residual; n is the number of PCA axes retained in the model. The number n is judged on the basis of empirical consideration of F-test of significance GGE bi-plot is a data visualization tool, which graphically displays a G x E interaction in a two way table Yan and Rajcan [7]. GGE bi-plot is an effective tool for: 1) mega-environment analysis (e.g. "which-won-where" pattern), whereby specific genotypes can be recommended to specific mega-environments Yan and Kang [8], 2) genotype evaluation (the mean performance and stability), and 3) environmental evaluation (the power to discriminate among genotypes in target environments). Sabaghnia, et al. [9] and Farshadfar, et al. [10] in wheat; Munawar, et al. [11] and Fiseha, et al. [12] in sesame are among the many authors who used GGE bi-plot to identify mega environments, to evaluate the genotypes and to test the environments. GGE bi-plot is able to show the best genotype with the highest yield in a quadrant containing identical locations (Mega-Environments), genotype average performance and stability, ideal genotype and ideal location to increase yield and specific location. Visualization of GGE biplot is very useful to evaluate and find the most stable genotypes Farshadfar, et al. [10]. Genotypes laid in the concentric area are the most stable compared to the genotypes laid outside, even though the environmental effect was very strong Untung, et al. [13]. An ideal genotype is defined as one that is the highest yielding across test environments and absolutely stable in performance (that ranks the highest in all test environments Farshadfar, et al. [14]. Although such an "ideal" genotype may not exist in reality, it could be used as a reference for genotype evaluation Mitrovic, et al. [15]. A genotype is more desirable if it is located closer to "ideal" genotype Mitrovic, et al. [15] and Kaya, et al. [16].

Materials and Methods
The experiment was conducted in Tigray, Northern Ethiopia presented below ( Table 2)

Experimental Genotypes
Seventeen sesame planting materials were used in the study presented (Table 3).

Experimental Design and Management
The experiment was laid out in randomized complete block design (RCBD) with three replications. Each genotype was randomly assigned and sown in a plot area of 2m x 5m with 1m between plots and 1.5m between blocks keeping inter and intra row spacing of 40cm and 10 cm, respectively.

Data Analysis
Analysis of variance for each environment, combined analysis of variance over environments and AMMI analysis were computed using GenStat statistical softwre16 th edition GenStat [20]. Unbalanced design was used for combined analysis of variance because of different locations and years in the study. The model employed in the analysis was; Yijk = μ + Gi + Ej + Bk + GEij + εijk where: Yijk is the observed mean of the i th genotype (Gi) in the j th environment (Ej), in the k th block (Bk); μ is the overall mean; Gi is effect of the i th genotype; Ej is effect of the j th environment; Bk is block effect of the i th genotype in the j th environment; GEij is the interaction effects of the i th genotype and the j th environment; and εijk is the error term.

Mean of Genotypes for Seed Yield and Oil Content Across Ten Environments
The mean seed yield of the environments in 2014-2015 and oil content during 2015 main seasons was highly significant at (p<0.001). Overall mean seed yield over ten environments was 649.35 kg/ha and the mean seed yield of genotypes across environments ranged between 238.5 kg/ha in E2 to 1123.8 kg/ha in E3. Among high yielded genotypes, G1, G7, and G3 showed 18.85%, 7.30% and 1.34% yield advantage over the recently released and 34.25%, 22.75% and 16.75% over the local varieties, respectively. Changing sesame yield performance with environments reported by Fiseha, et al. [12], Mekonnen, et al. [21] and Mohammed [22] in sesame.

Overall Ranking of Genotypes Using Various Stability Models
G1, G7 and G3 including the released variety (G16) and local (G17) were found the most stable and ranked 1 st , 2 nd , 3 rd , 4 th and 9 th . While, G4, G8 and G15 were unstable and7 th , 17 th and 8 th for seed yield, respectively (Table 6). According to those models, the oil content was also varied from one environment to another. G2, G15 and G16 were the most stable and ranked 6 th , 3 rd and 4 th . On contrary, G6, G10 and G9 were the most unstable and ranked16 th , 14th and 13 th formean oil content across the tested locations, respectively (Table 6).
. AMMI analysis of variance of ten environments for seed yield and six locations were presented in (7). Showed highly significance variation at (P<0.001) among genotypes, environments and GEI for seed yield and oil content. From the total variation, 69.73%, 14.68%, 9.58% were explained by environments, GEI and genotypes for seed yield and 61.6%, 13.64%) and 6.55%) for oil content, respectively. The result is agreed with the previous findings Mohammed, et al. [29] and Mekonnen, et al. [21] in sesame. This showed that the significances influence of environments on yield and oil content performance of sesame genotypes in different locations of northern Ethiopia indicating the need to test sesame genotypes under various environments. The four IPCAs were highly significant leading to a cumulative 99.8% variation and the rest 2.62% was contributed due to noise for seed yield and three IPCs significance leading to a cumulative contribution of 83.7% variation and the rest due to noise for oil content. AMMI with only the two interaction principal component axes was the best predicative model for both seed yield and oil content. This is in harmony with Zobel, et al. [3]. G15, G1, G16, G3, G4, G5, G14, G17 and G7 recorded seed yield above grand mean in the favorable environments, while eight genotypes G12, G8, G10, G2, G13, G6, G9 and G11 were below the grand mean and low yield in the unfavorable environments (Figure 1). Stable genotypes were adaptive to wider areas and give consistency mean yield across the test locations. G1, G7, G2, G3, G6, G9 and G16 were found nearly closer to the origin and the most stable with little responsive to the GEI. Genotypes far from the origin are sensitive to environmental changes. Hence, G4, G10, G8, G11, G12, G13, G17, G15 and G14 were the unstable. In contrast, G1, G7, G 16 and G3 were the most stable in the favorable environments. G8 and G11 were unstable with low yield in the unfavorable environments. Therefore, genotypes with high yield and wider stability performance are the most desirable for wider area.

'Which-Won-Where' Pattern and Mega-environment Identification
The ten environments fell into six sectors with different winner genotypes and the bi-plot showed that four vertex genotypes, G4, G15, G1 and G8. From winner genotypes except G8 were high yielding in favorable environments. The GGE biplot identified two different sesame growing mega-environments. The first megaenvironment containing overlapping environments with highest yielding environment (E3) in Dansha area with a vertex genotype G4 and the higher yielding environment (E6) in Sheraro area with winner genotype G3; and second environment includes medium E1 and E10 to low yielding E2, E4, E5, E7, E8 and E9 environments, respectively with the winner genotype G1 ( Figure 5).

Summaryand Conclusion
According to the GGE bi-plot different sesame growing environments grouped into two for yield production: The first environment containing the favorable environment Dansha area with a vertex G4 and Sheraro area with winner G3; and second environment includes medium to low environments E2 (Humera-2), E4 (Dansha-2), E5 (Sheraro-1), E7 (Wargiba-1), E8 (Wargiba-2) and E9 (Maykadra). GGE bi-plot classified three different sesame growing mega-environments for oil content production: The 1 st environment containing G12, G7 and G2 in the mega-environment group of Humera, Dansha and Gendawuha. The 2 nd environment, Sheraro containing G9 and the 3 rd environment Wargiba contained G17. AMMI model and GGE bi-plot were better for partitioning the GEI into the causes of variation. G1, G7, and G3 were high yielder and the most stable both in terms of seed yield and oil content. Moreover, showed yield advantage over the standard and local check. Hence, G1, G7 and G3 were recommended for wider environments and G14 and G4 for favorable environments Sheraro and Dansha, respectively.