Assessment of genotype‐trait interaction in maize (Zea mays L.) hybrids using GGT biplot analysis

Abstract In order to investigate the interaction of genotype × trait and relationships among agronomic traits on 12 maize hybrids, an experiment was conducted in a randomized complete block design (RCBD) with three replicates in four regions of Karaj, Birjand, Shiraz, and Arak. Results of analysis of variance indicated that most of the genotypes were significantly different in terms of agronomic traits. Mean comparison by Duncan's method showed that KSC705 genotype was more favorable than other genotypes in all studied regions. SC604 genotype in Birjand and Karaj regions and KSC707 genotype in Shiraz region have higher rank than other genotypes. Correlation analysis was used to investigate the relationships between traits. In most of the studied regions, traits of number of grains in row and number of rows per ear were positively and significantly correlated with grain width and grain weight with grain yield. Graphical analysis was used to further investigate. Genotypes–trait interaction graph explained 59.27%, 61.22%, 59.17%, and 61.95% of total variance in Karaj, Birjand, Shiraz, and Arak, respectively. Based on the multivariate graph, KSC705, KSC706, and SC647 genotypes were identified as superior genotypes in all studied regions and KSC400 genotype did not show much response to change in traits. Correlation between grain width and number of rows in ear, plant height and grain length, one thousand grain weight and grain thickness, and ear diameter with number of grains in row was positive and significant. The results of classification graph of genotypes also divided the cultivars in to three groups as follows: KSC703, KSC400, and KSC706 genotypes in the first group; DC370, SC604, and SC301 in the second group; and KSC260, KSC704, KSC707, and SC301 in the third group.


| INTRODUC TI ON
The maize (Zea mays L.) is considered as one of the most important crop plants in the world, in such a way that it plays a considerable role in the provision of most of the world people's food (Panda, Behera, & Kashyap, 2004). According to the predictions, the demand for the maize in the developing countries would be twice the current demand until 2050 (Chaudhary, Kaila, & Rather, 2014). The corn breeding began since the human being has discovered the value of this plant in the provision of food, livestock, fiber, and fuel; and during the years, this plant has been changed from a wild plant to a crop one during the selection process by the farmers (Hallauer, Carena, & Miranda Filho, 2010). The main goal of plant breeding organizations is to identify the superior genotypes based on the multi-en- Generally, many genotypes are tested in different times and places based on different traits and it often is hard to identify the superiority of genotypes yield in different environments. Different methods have been applied for the perception of the interaction, and these methods usually lead is resulted in a unit conclusion for a set of specific data. GGE biplot method permits the user to study and evaluate reciprocally the data (Dehghani, Dvorak, & Sabaghnia, 2012). The GGE biplot methodology is distinguished for being a versatile and flexible analysis allowing the selection of genotypes by means of graphical representations in an easy and efficient way (Yan, 2014).
In GGE biplot method, Yan used two primary main elements which are resulted from the analysis of specific values on the data related to the yield of several environments. Anyway, this method has been introduced for the analysis of multi-spatial tests, but it can be used for any kind of data which has a reciprocal structure such as line tester, genotype by environment or genotype by trait (Yan, 2014). Yan and Rajcan (2002) used the genotype by trait (GT biplot) interaction method which is one of the GGE biplot methods for analyzing the genotype by trait data. This study revealed that GT biplot is an excellent tool for the identification of genotype by trait interactions.
The GGE biplot method also has been used for evaluating the correlation of the traits by the genotype-trait biplot graphs . The identification of correlation between different traits and also the cause and effect relation between them help the breeders to select the most appropriate and logical relation between the constituents that is resulted in the further yield (Mardi, Talei, & Omidi, 2003). Kaplan, Kokten, and Akcura (2017) in studying of 25 silage maize, concluded that GGE biplot method with different perspective, could reliably by used in assessment of silage characteristics of maize genotypes grown in various environments. Adedeji, Ajayi, Osekita, and Ogunruku (2020) in studying of genotype × trait correlation on the cowpea cultivars, concluded that the majority of traits are positive and significant correlation with grain yield trait.
In experiment done by Dolatabad, Choukan, Hervan, and Dehghani (2010) on the 14 maize hybrids in 9 research stations for studying genotype by trait (GT) biplot, clarified that correlation coefficient between grain yield components reveals a positive or negative relation between measured traits. Consequently, Gt biplot describes the interrelationships among traits and it was used to identifying hybrids that are good for some particular traits. Fan et al., (2007) in an experiment of 13 maize hybrids in 10 different regions used GGE biplot technique for studying traits correlation in various environments and concluded that yield stability should be useful in selecting superior hybrids in the absence of GGE biplot software. GGE biplot was also employed in variety evaluation of mung bean (Paramesh et al., 2016); green bean (Oliveira et al., 2018); maize (Setimela, Vivek, Banziger, Crossa, & Maideni, 2007); rice (Stanley, Samante, Wilson, Anna, & Medley, 2005); and black bean (Rocha et al., 2020).
In this study, the below aims are understudied: Estimate the level of genetic variability among 12 cultivars of corn.
The study of genotype-trait interaction analysis which may be used for corn improvement program.
Choosing of the best hybrids according to the traits in the understudied regions.
The study of correlation between traits and the relations among them.
Grouping the genotypes based on the understudied traits in various regions.

| Experimental design
In this study, every experimental plot was designed with 4 rows, with 75 cm distance from each other. The seeds were planted with 10 cm distance from each other, and during the crop season, all the harvest operations such as the irrigation, weeding, and thinking were done consecutively and different crop traits were recorded. Also, irrigation system was similar for all experimental location. The names and codes of hybrids are represented in Table 1. Average of annual rainfall and codes and geographical parameters of under studied regions are represented in Table 2.

| Data analysis
Analysis of variance and other genetic parameters help to formulate a suitable breeding parameter and being prerequisites for any effective method of crop improvement (Osekita & Ajayi, 2013).
Analysis of variance and mean comparison base Duncan multiple range test were used for investigation of traits in four environments.
Relationships between different traits were examined using Pearson correlation coefficients. These analyzes were performed using SAS v.9.1 software for each environment. The genotype-trait interaction (GT biplot) investigated using principle component analysis. In this research, three biplot graphs were created with data matrix of the environment and genotypes by using GenStat software v12. These For studying the genotype × trait interaction, Yan and Rajcan (2002) method was used as below (Equation 1): Where α ij : average amount of genotype i for every trait j, β j : average amount of all the genotypes for the traits, σ j : standard deviation of the trait j in the average genotypes ε ij : amount of genotype i remained in the trait j, λ n : certain amount for the main element (PC n ), ξ i : amount of PC n for the genotype i, and η jn : amount of PC n for the genotype j.

| RE SULT AND D ISCUSS I ON
Analysis of variance indicated that the genotype effect was significant for ear length, ear diameter, number of grains per row, grain width, and grain yield in all locations. Genotype effect was significant for thousand grain weight in Shiraz and Karaj. Genotype effect was significant differences for grain thickness in Arak and Birjand.
The most and least percentage of coefficient of variation was related to the grain thickness and ear length, respectively (Table 3).  it had negative and significant correlation with the trait grain width and grain yield. The traits grain width and weight of thousand grains also had positive and significant correlation with the trait grain yield (Table 6). It can be concluded that the genotypes KSC705, KSC706, and SC647 were recognized as the superior hybrids, since they had higher performance in comparison with the other genotypes in all the studied stations. As well, it was revealed that in all the studied stations, the genotypes DC370 and KSC706, respectively, had higher performance in the traits grain thickness and plant height in comparison with the other genotypes and the genotype KSC400 did not show considerable reaction to different traits.
The correlation graphical analysis was used for evaluating the correlation between the traits. In this biplot graph, the cosine of the angle between the traits vectors is indicative of the correlation intensity between the traits. If the angle between the two traits vectors be less than 90˚, equal to 90˚, and 180˚, the correlation between the vectors would be +1, 0, and −1, respectively. Kaplan et al. (2017) and Dolatabad et al. (2010) had used this type of graph for studying maize varieties, and Adedeji et al. (2020) had used this type of graph for studying cowpea. Accordingly, in Karaj region, the ear length, number of rows in ear, and grain width vectors had positive and significant correlation with each other since the angle between them was less than 90˚. So, they were categorized in one group. In addition, the traits "plant height and grain length," "grain yield, grain thickness, and one thousand grain weight," and "ear diameter and number of grains in row" were categorized in the second, third, and fourth groups, respectively. Accordingly, it can be concluded that the vectors of two traits grain thickness and number of rows in ear had negative and significant correlation with each other since they had 180˚ angle. In addition, the plant height, ear diameter, and number of grains in row had negative and significant correlation with each other (Figure 2a).
In Birjand region, with regard to the angle between the vectors, "grain thickness, grain length, and one thousand grain weight," "grain yield, plant height, and grain length," "number of rows in ear and grain width" and "ear diameter and number of grain in row," respectively, were categorized into the first, second, third, and fourth groups and had positive and significant correlation with each other. Since the traits "number of rows in ear with grain thickness" and "grain yield with grain width" has 180˚ angle between two vectors, they had negative and significant correlation with each other (Figure 2b).
In the study of Shiraz regions, "grain yield, grain length, and grain thickness," "plant height and grain length," "number of rows in ear and grain width," and "one thousand grain weight, ear diameter, and number of grain in row," respectively, were categorized into the first, second, third, and fourth groups and had positive and significant correlation with each other. In addition, with regard to this matter that the angle between two vectors in the traits number of rows in ear and grain thickness, grain width and grain yield, and one thousand grain weight and grain length was 180˚, they had negative and significant correlation with each other (Figure 2c). Also, in Arak region, the "grain length, plant height, and grain yield," "ear length, number of rows in ear, and grain width," "ear diameter and number of grain in row" and "grain thickness and one thousand grain weight" were categorized into the first, second, third, and fourth groups and had positive and significant correlation with each other. In addition, the traits "one thousand grain weight and grain yield," "grain thickness and number of rows in ear," and "number of grains in row and grain length" had negative and significant correlation with each other (Figure 2d). It can be concluded that in all the studied regions, the traits "grain width  For evaluating the classification between the genotypes in terms of the traits, the graph related to the classification between the genotypes was used (Figure 3).
Based on the Figure 3 (Figure 3c). In the study done on Arak station, 61.95% of data total variance was explained by this graph that 34.88% and 27.07% of that were respectively related to the first and second principal components. The genotypes were categorized into four groups: The first group included the genotypes KSC360, KSC707, SC302, and KSC704; the second group included the genotypes KSC703 and KSC705; the third group included the genotypes KSC400 and KSC706; and the last group included the genotypes SC604, DC370, and SC301. Genotype SC647 was not in the same group with other genotypes (Figure 3d). With regard to the obtained data, it can be concluded that in all the studied regions, the genotypes "KSC703, KSC400, and KSC706," "DC370, SC604, and SC301," and "KSC260, KSC704, KSC707, and SC301," respectively, were categorized into the first, second, and third groups. KSC705 and SC647 were not in the same group with other genotypes. Dolatabad et al., (2010) had used this type of graph for studying maize.

| CON CLUS ION
GT biplot technique allowed essential and reliable assessment, examined traits in various environments. Based on this technique, it clarified how traits are changed in genotypes and different environments and describes the interrelationships among traits.
Result indicated that investigating different genotypes in various environments, KSC400, KSC706, and SC647, were identify superior hybrids. The traits grain thickness-one thousand grain weight, grain length-plant height, grain width-number of rows in ear, and number of grains in row-ear diameter had positive and significant correlation in the majority of the regions. Based on the classification between genotypes, the genotypes were categorized into three groups.
The highest grain yield in all locations belonged to KSC707 cultivar at 6.9 t/ha followed by SC604 with 6.7 t/ha. *, **, and ns: significant at 5%, 1%, and not significant.