Garlic (Allium sativum L.), is from the genus Allium and family  Alliaceae   grown  as  edible  bulbous  crop  in  the world. It is originated in Central Asia (Brewster, 1994). It is a diploid with the basic chromosome number  of  2n=16 oldest cultivated vegetable and second most extensively species of obligated apomixes, therefore its reproduction system is vegetative through its cloves. Garlic is the produced Allium next to onion (Batth et al., 2013; Diriba, 2016; Dejen, 2018). It is used for seasoning in many ingredients as well as for medicinal and spiritual purposes (Tewodros et al., 2014). It is extensively cultivated throughout the world including Ethiopia. In Ethiopia, 15381.01 ha of land have been underneath of garlic cultivation with a production of about 1386643.07 tones (CSA, 2017).

Garlic is the most widely cultivated bulbous crop in Ethiopia and it has a wide range of climatic and soil adaptation. However, its production and productivity are very low due to many biotic and abiotic bottlenecks such as lack of high yielding varieties, non-availability of quality seeds, imbalanced fertilizer use, lack of irrigation facilities, lack of appropriate disease and insect pest management and other agronomic practices, low storability, and lack of appropriate marketing services (Getachew and Asfaw, 2010; Mohammed et al., 2014). Therefore, multi environment variety trials (MET) on different crops including garlic are essential, because of the existence of genotype × environment (GE) interactions (Gauch and Zobel, 1997). The development of high yielding varieties with wide adaptability is the basic target of plant breeders. Genotype by environment interaction evaluation is important for genotype selection and cultivar recommendation, and to identify appropriate production and test environments (Singh et al., 2016; Habte et al., 2019; Ngailo et al., 2019). Bulb yield and days to maturity of garlic is disposed to environmental changes resulting in variable yield due to the significant effect of genotype-by-environment interaction (Tewodros et al., 2014).

Assessment of different genotypes across locations and over years is now not only essential to select and recommended high-yielding cultivars but also to identify suitable areas that represent the ideal environment (Yan et al., 2001). Moreover, the efficiently developed high-yielding new cultivar must have a stable overall performance and broad adaptation over a wide range of environments. A genotype is considered as stable if it has adaptability for a trait of economic significance throughout diverse environments. The environmental factor (E) usually represents the biggest issue in analyses of variance, however, it is not applicable to cultivar selection; only G and GE are relevant to significant cultivar comparison and ought to be viewed simultaneously for making selections (Yan and Kang, 2003). As there are no studies on G x E in garlic crop in Ethiopia particularly in Tigray regional state, the importance of conducting such studies throughout principal garlic producing locations have been suggested. Genotype x location (GL) interaction effects are of special interest for breeding programmes to identify adaptable, stable and high yielding genotypes and test locations. Additive    main    effects   and   multiplicative   interaction (AMMI) analysis and genotype plus genotype by environment interaction (GGE) biplot analysis were widely used a multivariate technique for interaction investigation (Gauch et al., 2008; Mohammadi et al., 2010). AMMI biplot evaluation is regarded to be a high quality tool to diagnose GEI patterns graphically. AMMI analysis can also be used to find out the stability of the genotypes across locations using the (principal component axis (PCA) scores and AMMI stability value (ASV). Purchase (1997) developed the AMMI stability value primarily based on the AMMI model’s principal components axis 1 and 2 scores for each cultivar, respectively.

Another powerful statistical model GGE biplot model combines the two principal effects, that is, genotypes (G) plus the G × E interaction (GE). This method is proven to be beneficial to decide which-won-where pattern of the multi-locational trials facts thereby figuring out high-yielding and stable cultivars and the power to discriminate and become aware of representative test environments (Yan, 2001). Now-a-days, it is a common practice through crop breeders to use GGE models in explaining G × E interaction and analyzing the overall performance of genotypes and test environments (Yan et al., 2007; Ngailo et al., 2019). GGE biplot, especially, is useful, to graphically represent the GE interaction, and to rank the studied genotypes and environments (Ngailo et al., 2019). According to the GGE biplot, a highly stable genotype would have a shorter projection on to the average environment coordinate (AEC) abscissa, irrespective of its direction (Yan and Kang, 2003). These two statistical analyses (AMMI and GGE) have broader relevance for agricultural researchers because they pertain to any two way data matrices, and such data emerge from many kinds of experiments (Gauch, 2006). In Ethiopia, there is no ample information on the genotype by environment interaction effects on bulb yield and yield related traits of garlic. Therefore, the objective of this study were:  to assess the stability and yield performance of garlic genotypes over years and across locations; and to identify stable and high yielding candidate genotype(s) for possible release. 

 

 

Study sites and planting materials

The field experiments were conducted in four diverse garlic growing environments in Tigray region, northern Ethiopia (Ahferom, Hagere selam, Hatsebo and Ofla). The study areas represent low to high altitudes and vary in agro-ecological conditions (Table 1). The genotypes were obtained from Debre Zeit Agricultural Research Center and Axum Agricultural Research Center (Table 2). The experimental design used was a randomized complete block with three replications at each location and year. The experimental plots consisted of 6 rows of 3 m length each. Row-to-row and plant-to-plant distances were kept at 30 and 10 cm, respectively at all the locations.   The   genotypes   were   planted  in  the   first   week   of November for two consecutive years (2017 to 2018/2019) under irrigation. Di-ammonium phosphate (DAP) as a source of phosphorus was applied at the rate of 200 kg ha^-1 during planting and nitrogen fertilizer was applied in the form of Urea at the rate of 150 kg ha^-1 in splits, half during transplanting and the rest as side dressing at 45 days after transplanting. Furrow irrigation method, scheduled at 8-12 days interval (AxARC, 2016) was used.  Weeding and other management practice have been accomplished as required for each site. Data were recorded on 90% physiological maturity, plant height, bulb diameter, bulb weight, number of cloves per bulb and bulb yield per hectare. The yield harvested from four central row of each net harvestable plot in kg was once transformed into tha^‑1.

 

 

 

Where: represents the weighted value assigned to the first interaction principal component score due to its high contributions in the GE model,SSIPCA1 and SSIPCA2  are the sum squares of  for IPCA1 and IPCA2 ,respectively. And also IPCA1 and IPCA2 are the first and second IPCA scores for each genotype. The larger ASV the more specifically adapted the genotype is to a certain environment and the smaller ASV indicates a more stable genotype across environments (Purchase, 1997; Ngailo et al., 2019). The GGE biplot were constructed from the first two principal components (PC1 and PC2) derived by subjecting the environment centered yield data (which contains G and GE) to singular valued composition (SVD) (Yan, 2000; Yan et al., 2007). Based on singular value decomposition of the first two principal components, is:

Yij – µ – aj = e1 b1 cj1 + e2 b2 cj2 + εij

 Where, Yij is the measured mean of genotype i in environment j, µ is the grand mean, aj is the main effect of environment j, i +aj is the mean yield across all genotypes in environment j, e1 and e2 are the singular values for the first and second principal components, respectively b1 and b2 are eigenvectors of genotype i for the first and second principal components, respectively, cj1 and cj2 are eigenvectors of environment j for the first and second principal components, respectively, εij is the residual associated with genotype i in environment j. AMMI and GGE biplot were performed using R software program Version 3.4.4.

Yield stability index (YSI) and Rank-Sum (RS)

The new approaches known as YSI and RS were calculated by the following formulas:

YSI = RASV + RY

Where RASV is the rank of AMMI stability value and RY is the rank of mean bulb yield of genotypes (RY) across environments. YSI incorporate both mean yield and stability in a single criterion.  Low value of this parameter shows desirable genotypes with high mean

yield and stability. Rank sum (RS) = Rank mean (R) + Standard deviation of rank (SDR). RS incorporate both yield and yield stability in a single non-parametric index. Genotypes with the least RS are considered stable with high bulb yield under irrigated conditions. Standard deviation of rank (SDR) was measured as:

Where R_ij is the rank of X_ij within the j_th environment, Ri. (R), is the mean rank across all environments for the ith genotype and SDR= (S²i) ^0.5.

 

 

Analysis of variance

The combined analysis of variance (Table 3) for bulb yield and yield related traits showed highly significance differences (P≤0.01) among genotypes, locations and presence of significance G×E interaction, indicating variation of environments and the presence of genetic variability among genotypes. The analysis of variance also indicated that there was highly significant variation (P<0.01) among the genotypes in plant height (cm), bulb diameter (mm), bulb weight (g), number of cloves per bulb, days to 90% physiological maturity and bulb yield (tha^‑1). This showed variability among the genotypes for these characters. The overall mean bulb yield of the locations was ranged from 5.58 to 8.39 tha^‑1 (Table 4), therefore, the eight environments (Location × year) showed broad variation in their yield production potential. The mean bulb yield of genotypes was 6.64 tha^‑1  (Tables 3 and 4). The performance of genotypes in all yield associated characteristics was different both in each and throughout locations. This indicated that the efficiency of a breeding program aimed only at yield enhancement resulted in inconsistent performance of genotypes  due to significant genotype- by- environment interaction effect, which complicates the procedure of crop variety development particularly when varieties are chosen in one environment and used in others (Singh et al., 2016).

 

 

 

AMMI analysis of variance for bulb yield

Combined analysis of variance for bulb yield of the nine garlic genotypes examined across eight environments is presented in Table 5. The main effect differences among genotypes, environments, and the interaction results were highly significant (P < 0.01) of the whole variance of bulb yield. The environment impact accounted for 61.84%, whereas genotype and G × E interaction results accounted for 11.86 and 11.52% of the total variation, respectively (Table 5). The maximum environmental sum square indicated that there was a huge difference among the testing locations causing unique genotypes to perform in another way across the testing environments and the excessive percentage of the environment is an indication that the main factor that influence yield performance of garlic genotypes in Ethiopia is the environment. Genotypes revealed highly significant (P<0.001) variations for bulb yield. This shows that there was genetic difference among genotypes for this trait. This variation is beneficial when intending to find out about the consequences of G×E interaction, as properly as to consider the phenotypic stability of genotypes. The magnitude of the GEI sum of squares used to be rather similar with that  of  the  genotypes,  indicating  that  there was by some means comparable response of some of the genotype across environments.

 

 

The results of AMMI model for bulb yield are presented in Table 5. As it is viewed from Table 5, the mean square of the three IPCA was highly significant (P<0.001). The AMMI biplot, which accounted for 73.5% of the G×E interaction, gives the interaction principal component rankings of the 1^st and 2^nd IPCA. The first PC axis (PC1) score explained 55.1% of the variant in GEI, while the 2^nd PC axes accounted for18.4% of the variability. Many researchers witnessed that the best accurate AMMI model prediction can be made by using the first two IPCAs (Yan et al., 2000). Therefore, the dataset obtained from the interaction of 9 genotypes examined at eight environments were well predicted through the first two IPCAs. On the other hand, the IPCA scores of a genotype in the AMMI analysis are indication of the stability of a genotype throughout environments (Purchase, 1997). Accordingly, the closer the IPCA scores to zero (origin), the more stabile the genotypes are across all environments (Purchase, 1997). The IPCA1 used to be plotted on x-axis whereas IPCA2 was plotted on y-axis for bulb yield and yield components (Figure 1). The greater the IPCA scores (positive or negative) as it is a relative value, the greater especially adapted a genotype is to certain environments. The greater IPCA scores approximate to zero, the more stability the genotype is throughout environments sampled (Purchase, 1997). The IPCA1 and IPCA2 rankings of bulb yield for each genotype and the corresponding AMMI stability value (ASV) are presented in Table 6. According to ASV ranking, genotype 2 had the lowest value indicating its high stability, while genotypes 9 and 7 were extraordinarily unstable. Purchase (1997) pointed out that the closer the genotypes score to the center of the biplot the genotype is broadly adapted and the reverse is true. Regarding the position of the environments in the biplot graph, locations E2  (Ofla)  and E4 (Ahferom) were the most discriminating environments as they have long distance between their marker and the biplot origin (Figure 1). However, due to their massive IPCA2 score, genotypic variations discovered at these environments may not precisely show the genotypes average yield across locations. The interaction principal component one (IPCA1) and the interaction principal component two (IPCA2) scores in the AMMI model are indications of stability.

Considering the first interaction principal component (IPCA1), the genotype G5, was the most stable genotype with IPCA1 value (-2.53). When the second interaction principal component (IPCA2) was considered, G5 was the most stable genotype with interaction principal component value (-2.07) followed by the genotype G6 with the IPCA2 value (-1.94). The two principal components have their own extremis, however calculating the AMMI ASV is a balanced measure of stability (Purchase, 1997). The genotype with lower ASV values is viewed stable and genotypes with higher ASV are unstable. Based on the value of ASV, genotype G2 was the most stable with an ASV value of 0.67 followed with the genotypes G1 and G6 with ASV value of 0.84 and 3.59 of bulb yield respectively. Genotypes G7, G9 and G5 were the most unstable with ASV value of 12.71, 12.64 and 7.86 of bulb yield respectively (Table 6).

 

 

 

Yield stability index (YSI)

Stability is not the only criterion for selection, due to the fact that most stable genotypes would no longer necessarily provide the best yield across environments (Mohammadi et al., 2010), consequently there is a need for approaches that comprise both mean yield and stability in a single index number of authors introduced extraordinary standards for simultaneous selection of yield and stability rank-sum, modified rank-sum and  yield stability (Farshadfar et al., 2011). In this regard, ASV takes into account both IPCA1 and IPCA2 and justifies most of the variation in the GEI. The genotype with least YSI is regarded as the most stable with high yield mean. It was utilized to identify high yielding and stable genotypes in cereal crops like durum wheat (Mohammadi et al., 2010).  Based on YSI, the most stable genotype with high bulb yield is genotype G9 with YSI of 9 accompanied via G7 and G6 YSI of 11 and 11, respectively .The highest YSI indicate that G4, G5 and G8 were unstable genotypes. Rank-sum (RS) showed that genotype G9 produced high bulb yield and followed via genotype G7 indicating that they were the most stable genotypes with high bulb yield. Both YSI and RS confirmed that genotype G7 gave high bulb yield.

Analysis of GGE biplot for bulb yield

GGE Biplot analysis shows “which-won-where” pattern, ranking of cultivars on the basis of yield and stability, and correlation vectors among environments. Angles between environment vectors were used to judge correlations (similarities/dissimilarities) between pairs of environments (Yan and Kang, 2003; Yan, 2011). GGE biplot is visualized on the basis of consequences defined for the first two principal components (Yan et al., 2001). In the current study, the first two principal components of GGE biplot explained 84.13% (PC1=74.52 and PC2=9.61%) of the whole variations (Figure 2). In the polygon, genotypes located far away from the origin are the vertex genotypes having  the  highest  yield  in  the  region  (Esayas  et  al., 2019; Habte et al., 2019). In this study, genotypes G9, G7, G5 and G3 had the highest yield in their respective sector.

 

 

 

 

 

 

 

 

 

From the current study, it is concluded that multiple methods were employed to analyze stability. The AMMI and GGE biplot methods can be effectively utilized for the identification of the suitable genotypes for suitable environments. The results of AMMI analyses indicated that garlic bulb yield performances was highly affected by environmental effect followed by the magnitude of GEI, but  genotype contributed the minimum effect. The AMMI and GGE biplot analysis permitted estimation of interaction effect of a genotype in each environment and they helped to identify genotypes best suited for specific environments. The GGE biplot analysis shown that the genotypes G9, G7, G5 and G3 were corner genotypes and suited to specific environments. The polygon views of the GGE biplot grouped in two possible mega environments. The first mega environment consisted of six environments (E2, E3, E4, E6, E7 and E8); and the second mega environment consisted of two environments (E1 and E5). In addition, the discriminating power vs. representativeness view of the GGE biplot has been an effective tool for test environments evaluation. Environment E2 (Ofla) and E4 (Ahferom) were the most discriminating for bulb yield of the tested garlic genotypes. According to the AMMI and GGE biplot models, considering simultaneous average yield and stability, G9 (Bora-1/16) and G7 were the best genotypes.  Therefore,   these    genotypes    should    be released for Tigray region and others similar agro-ecologies to enhance the productivity of garlic.

 

The authors have not declared any conflict of interests.

 

The authors grateful appreciate the Tigray Agricultural Research Institute (TARI) and Axum Agricultural Research Center (AxARC) for financial support and are also indebted to Horticulture staffs at Alamata Agricultural Research Center and Mekelle Agricultural Research Centers for provision of experimental fields, technical support and data collection during the experiments were conducted.