Use of two hybrid algorithms in the investigation and prediction of the values of five quantitative traits of guar beans in different deficit irrigation methods

Nowadays, deficit irrigation is of particular importance in areas facing the water shortage and drought. This study focused on the investigation and prediction of the values of five quantitative traits of guar beans under different deficit irrigation methods. Deficit irrigation methods were carried out at the initial, development, mid, and late plant growth stages. The experiment was carried out in 25 treatments each with four replications in 2018 and 2019. Initially, the values of five quantitative traits of guar beans were divided into three categories, the values of which were clustered using the K-means algorithm. Then, clusters were predicted using a combination of K-means and CART algorithms. Finally, the relationship between different deficit irrigation methods and clusters was investigated by a combination of K-means and Apriori algorithms. The results of two hybrid algorithms determined that the amount of irrigation in the mid-stage of plant growth significantly affected the five quantitative traits of guar beans. After the mid-stage of the plant growth, the amount of irrigation in the development, initial, and late growth stages had the greatest effect on the quantitative traits of guar beans. Among the deficit irrigation methods, irrigation rates of 60% in the primary stage, 80% in the development stage, 100% in the mid-stage, and 40% in the late stage of the plant growth were the best deficit irrigation methods in the four stages of growth.


Introduction
Today, some parts of the world are facing the water shortage. In recent years, the water shortage has increased in most plains of Iran. Since drought affects the production of crops every year, the use of proper crop management methods, especially deficit irrigation methods, can pave the ground to achieve acceptable yields under water shortage.
Guar (Cyamopsis tetragonoloba L.) is an annual crop and a summer grain with high resistance to the drought (Whistler and Hymowitz 1979). It is a cereal grain crop of spring and summer with resistance to drought (Ashraf et al. 2002(Ashraf et al. , 2005 that is usually cultivated in semiarid regions such as India, Pakistan, the USA, and South Africa. This crop can also be produced in other regions of the world with warm weather and water shortage (Sortino and Gresta 2007;Gresta et al. 2013). Guar can be successfully cultivated in areas where the temperature is > 30 °C in summer (Gresta et al. 2016(Gresta et al. , 2018Santonoceto et al. 2019).
The dicotyledonous seed of guar is composed of three main parts: the hull, endosperm, and germ. The germ and hull are used as a meal in the animal and poultry feed, and the endosperm is the site of gum (Lee Jason et al. 2004). Guar seeds contain galactomannan gum that has various industrial applications and form a viscous gel even in cold water (Senapati et al. 2006;Pathak et al. 2010).
Guar was first used as an industrial product and then as fodder due to its high protein (Whistler and Hymowitz 1979). Guar is used as a thickener, gel, viscosifier, and stabilizer in industrial applications owing to its chemical reaction, high flexibility, and good solubility in cold water (Wang and Zhang 2009). It is also used in drilling, color, oil operations, cosmetics, pharmaceuticals, agriculture, civil engineering, foodstuffs, and textiles (Zambrano et al. 2004;Vaughna et al. 2011;Lubbe and Verpoorte 2011). Guar has widely been used in various industrial applications in recent years (Das et al. 2011). Most the guar seeds are produced in India (80%) and Pakistan (15%). Therefore, there is a very good opportunity for the production of guar in the rest of arid and semiarid regions (Pathak and Roy 2015).
In this research, data mining algorithms were used to predict the effect of different methods of deficit irrigation on the quantitative traits of guar beans. Data mining is a process that automatically finds valuable information from data stored in large warehouses (Tan and Yu 2006). Some researchers now use data mining in different fields such as agriculture, healthcare, banking, sports, and hydrology. The tree data mining algorithm was used previously to predict variations in the depth of the aquifer (Mirhashemi et al. 2020).
In addition, some researchers have used data mining algorithm to extract association rules, which were used in India to link floods and droughts to climatic data and yielded strong relationships (Dhanya and Nagesh Kumar 2009). In a study by Mirhashemi and Mirzaei (2021), the Apriori algorithm was used to extract association rules, which were then employed to study the relationship between changes in the aquifer depth and the affecting factors.
In most plains of Iran, rainfall is usually lower in spring and summer than in the other seasons; thus, plants grown in these two seasons may be more exposed to water deficit. In this study, therefore, quantitative traits of guar were investigated in different deficit irrigation methods in spring and summer. This research aimed to predict quantitative traits of guar in different deficit irrigation methods and to investigate the relationships between different deficit irrigation methods and quantitative traits of guar by hybrid algorithms.

Materials and methods
The effects of different methods of deficit irrigation were investigated and predicted on grain yield, the number of pods m −2 , thousand-seed weight (TSW), harvest index (HI), and biomass of guar. The deficit irrigation methods were carried out in four initial, development, mid, and late stages of plant growth. The experiment was conducted in a farm in Alborz province (Iran) in spring and summer 2018 and 2019. The geographic coordinates of the experimental site are 35.8400° N, 50.9391° E with an altitude of 1.300 m from the sea level. The soil chemical and physical properties in the experimental site are shown in Table 1. According to the richness of the soil in terms of phosphorus and potassium, only 100 kg ha −1 of nitrogen (from a source of urea) was added to the soil in the development and mid-stages of plant growth. The environmental conditions of farm in four stages of growth are summarized in Table 2. There was no effective rainfall during the experiment.
The amount of irrigation water (dj) was obtained for the plant by obtaining the field capacity (F.C.) for the soil and soil moisture at the time of irrigation (Pv) using a timedomain TDR (time-domain reflectometry) installed in soil farm and obtaining the root development depth (z) in different growth stages. Accordingly, irrigation water levels of 80, 60, and 40% were defined for the other irrigation levels in normal conditions. The TDR was also used to determine suitable irrigation intervals. In this method, the device was installed in different depths of root development at each stage of plant growth. By obtaining F.C., permanent wilting point (P.W.P), and the readily available coefficient for guar beans (f), the percentage of available water was calculated to obtain the irrigation point. Irrigation operations were done based on defined treatments when soil moisture reached the irrigation point according to the TDR measurements. The surface drip system was used for irrigation.
Each experimental plot consisting of four planting lines with a length of three meters and a distance of 50 cm planting rows was selected in four replications. The distance between plants was 10 cm (Pathak and Roy 2015). The  Table 3 represents the naming of irrigation values in all four stages of plant growth.
According to the irrigation treatments (Table 4), irrigation was different in each treatment (except the control treatment) in each stage of plant growth. In the treatment of ABCD, for instance, irrigation amounts of A, B, C, and D were done at the initial, development, mid, and late stages of plant growth, respectively.
The total dry weight of the plant was measured during the harvest phase of the guar plant. To measure the biomass of guar, the aerial parts were bottom cut and incubated in an oven at 80 °C for 48 h. After drying, the total dry weight of the plant was determined by a precision scale. To measure the number of pods per plant after physiological ripeness, the total number of pods per plant and the mean of pods per plant were counted in 20 randomly selected plants. To measure the number of seeds per pod, the seeds were separated from pods, all seeds were counted, and their mean was calculated as the number of seeds per pod. The grains obtained from the grain yield were randomly weighed by a precise scale over four replication of 1000 grains and the average was calculated as the TSW for each treatment. The HI for each treatment was obtained via dividing the grain yield by the biological yield.
The K-means algorithm was used to cluster five quantitative traits of beans. To better understand the results of the K-means algorithm, all relevant data about the amount of five traits of guar beans were further categorized into three low, medium, and high categories ( Table 5). The optimal number of clusters was determined using the Silhouette index method.

Silhouette validity index (SVI)
The SVI method is defined based on the average distance of each sample of a cluster with all samples in the same cluster and the average distance of the sample in other clusters with a given cluster (Eq. 3). Based on this view, the maximum amount of dispersion and correlation of data is determined for each cluster, and the maximum values of this index are used to determine the optimal number of clusters (Rousseeuw 1987).
where a(i) is the mean distance between the ith sample and all the samples in Xi, b(i) is the minimum mean distance between the sample and all clustered samples in X k (k = l, …, c:k ≠ j). The value of SVI varies between − 1 and 1. An SVI value of 1 represents that clustering is done properly. If the SVI value is close to zero, it means that the sample can be attributed to a closer cluster and the sample position is equally distant from two clusters. An SVI value equal to − 1 means an inappropriate clustering.

Decision tree algorithm
In addition to quantitative variables, the decision tree algorithm can predict qualitative variables. This method was first introduced by Breiman et al. (1984). The decision tree algorithm tries to minimize the diversity or variety (in terms of the target attribute) in the nodes. This lack of uniformity in the nodes is measurable using the impurity measures, and the Gini index is the most important and widely used one (Yoneyama et al. 2002). The difference of various kinds of decision trees is in the impurity measure, the splitting method, and pruning of tree nodes. In this study, the decision tree model was used to investigate and predict the five quantitative traits of guar beans. Therefore, the results of the three types of tree algorithms (CART, CHAID, and C5.0) were evaluated to predict the results of cluster classification of quantitative traits of guar beans.

CART (classification and regression tree) algorithm
The CART is a binary recursive tree that exactly splits the parent nodes into two offspring groups and continues recursive splitting until another branch cannot be built. In recursive splitting of data into subgroups, it supports only two subgroups and is a fast algorithm with backward pruning (Chattamvelli 2011).

CHAID (Chi-squared automatic interaction detector) algorithm
The CHAID algorithm was presented by Morgan and Sonquist (1963). The algorithm was promoted to an algorithm for analyzing nominal-scale dependent variables by Morgan and Messenger (1973) and was converted to the CHAID algorithm by Kass (1980).

C 5.0 algorithm
This algorithm is a single-variate decision tree and the improved form of the C4.5 algorithm. Similar to CART, this algorithm first creates an almost full tree, but its pruning strategy is quite different. It performs the classification by splitting data into subsets containing more uniform records than their parents (Chattamvelli 2011). In this study, five clusters as dependent variables (objective function) and deficit irrigation methods were introduced as independent variables to tree algorithms. Agrawal et al. (1993) used the association rules to determine the important and hidden affiliations of a database. These association rules predict the occurrence of an object based on the occurrence of other objects. Therefore, the algorithms of finding association rules find all possible association rules within a database. A set of "If-then" rules, which expresses the connections between the simultaneous occurrence of a set of objects, is an important outcome of this approach. This algorithm expands the set of rules obtained from data and extracts the rules with the highest level of information.

Apriori model
This algorithm was first introduced by Agrawal and Srikant (1994) and is one of the most important findings in the mining of association dependency rules (Zhao and Bhowmick 2003). This algorithm requires the classification of all input and output fields as it is optimized for this type of data (Cheung et al. 1996).

Confidence
This coefficient determines the accuracy of a rule and suggests that if the exchange controls the antecedent conditions, then it will also obtain the consequent conditions. This measure was introduced by Agrawal et al. (1993).

Support
This parameter expresses the possible coexistence of A and B in the A → B rule. This measure was also introduced by Agrawal et al. (1993).

Lift
This is a criterion for evaluating the correlation value of two data sets. If the amount of lift is lower than one, the two sets have a negative correlation; if it is greater than one, the two data sets have a positive correlation; and if it is equal to one, the two sets have no correlation and are independent. This is one of the most commonly used measures of fitting rules introduced by Brin et al. (1997). In this study, deficit irrigation methods and the types of clusters were selected as the antecedent and consequent sets.

Results and discussion
First, the data about five quantitative traits of the guar plant in both 2018 and 2019 were analyzed by IBM SPSS Statistics. According to Tables 6 and 7, the quantitative traits of guar beans in different deficit irrigation methods were significant at a 1% level. Figures 1, 2 and 3 show the average  According to these figures and the coefficient of variation (CV) in Tables 6 and 7, the biomass of guar beans and the TSW of guar beans had the highest and the lowest CVs, respectively, relative to the other quantitative traits of guar beans in different deficit irrigation methods. The K-means algorithm was used to cluster the data related to quantitative traits of guar beans. At each run of the K-means algorithm, the clustering results were evaluated by the SVI. In the end, five clusters were achieved as the most optimal number of clustering with the highest SVI value of 0.90 (Fig. 4).
Five clusters were formed for five quantitative traits of guar beans using the K-means algorithm. The highest contribution percentage of quantitative traits classified in cluster formation is shown in Fig. 5. In the first cluster, for example, the highest contribution of the five quantitative traits belongs to the C category where the contribution of TSW, biomass of guar, and the number of pods was equal to 100%, with 92 and 72% for the HI and the yield, respectively. In the first cluster, the C category showed the most contribution of quantitative traits of guar beans, suggesting that this cluster possesses the greatest values of quantitative traits compared to the other clusters.
In the third cluster, the A category has the utmost contribution of quantitative traits of guar beans, indicating that this cluster contains the least values of quantitative traits relative to the other clusters. All quantitative traits of the second cluster, except the grain yield, are in the B category, implying that this cluster is at a medium level in terms of quantitative traits. The fourth cluster is superior to the fifth cluster in terms of the values of traits and includes B and C clusters. In this research, the five formed clusters were arbitrarily named based on the quantitative traits. Accordingly, the first, fourth, second, fifth, and third clusters have very good, good, medium, bad, and very bad values of quantitative traits, respectively. According to the size of five clusters in Fig. 6, the highest and the least sizes belong to the first (36%) and fourth (7%) clusters, respectively, among the other ones.
In the next step, the clusters in different deficit irrigation methods were predicted using a combination of tree and clustering algorithms. In this way, the results of the clustering algorithm and deficit irrigation methods as input data of the tree algorithm. Three tree algorithms, including CHAID, CART, and c5, were used for this stage. The results of performance evaluation of tree algorithms in the prediction of clusters (Table 8) indicate that the CART algorithm has the best performance in the prediction of clusters.
The CART algorithm predicted five clusters obtained from the results of the K-means algorithm (Fig. 7). The data about each branch were discussed separately to better understand the tree diagram. The tree diagram has two main branches. The third cluster and the other clusters are

Deficit irrigation (A) in the mid-stage of plant growth (I3)
The amount of irrigation was as high as 40% of full irrigation (A). The third cluster is the predicted one.
To further understand this branch, we used the data of frequencies and surrogates, which are not shown in the tree diagram (it is in the lower part of the software) ( Table 9). The lower part of the software contains the surrogates, frequencies,   and the history of each branch. Frequency is active in discrete target data and represents the percentage of each discrete value of the objective function in the target branch so that the dominant frequency is introduced as the estimated value of that branch. The surrogates represent other rules governing the branches of interest depending on their priority. This priority indicates the ability of the rule to make purity in sub-branches. Frequencies refer to more data about the leaves (results), and surrogates are about data of the branches (rules).
According to Table 9, the first main branch predicts the fifth cluster, in addition to the third cluster, but with a very lower likelihood than the third cluster. Table 9 also reveals that in addition to irrigation (A) at the stage (I3), the C and B irrigation in the stages of I1 and I2 also affects the prediction of the third cluster. The amount of irrigation decreases from the I1 to I3 stages, and the plant experiences more water stress at each stage than the previous one. The third and fifth clusters have the lowest values of quantitative traits (very bad and bad values) compared to the other clusters, which demonstrate the large negative effect of deficit irrigation (A) of the quantitative traits in the mid-stage of plant growth.

Deficit irrigation (B) in the mid-stage of plant growth (I3)
In the second main branches, the second and fifth clusters are predicted by the tree diagram when deficit irrigation is done in the I3 stage. So when the deficit irrigation B and A, respectively, occur in the I3 of I1 stages, the second cluster, but if irrigation D is done at the I1 stage, the fifth cluster will be predicted by the tree diagram. As there were no surrogates, only the frequencies data were used in these two branches. According to frequencies data, the second and fifth clusters in these two branches are predicted by different percentages.
The second cluster has a better condition with medium quantitative traits than the fifth cluster with slightly bad traits. However, the branch that predicted the second cluster has less irrigation level in the initial growth stage than the branch that predicted the fifth cluster. Considering that four Fig. 7 The tree diagram of the CART algorithm in predicting five clusters     (Table 10).

The third deficit irrigation (C) in the mid-stage of plant growth (I3)
In the next branch, when deficit irrigation C was done in the I3 phase, clusters 1, 2, and 4 were predicted by a tree diagram.
In the first case, when deficit irrigation occurs in C and A cases in the mid-and development stages of plant growth, respectively, the second cluster is predicted by the tree diagram. Frequencies and surrogates data were used for further information about this branch.
Given that full irrigation (D) was done in the I1 stage, it had no effect on the selection of very good and good (first and fifth) clusters, and deficit irrigation A at the I2 stage had a greater effect on the reduced values of quantitative traits and the choice of the second cluster (medium values of quantitative traits) (Table 11).
In the second case, when deficit irrigation C and B are applied in the I3 and I2 stages, respectively, the fourth cluster is predicted by the tree diagram. The irrigation in the I2 stage in this branch has increased compared to the previous branch and is placed in case B. The predicted cluster is also in a better position than the previous branch cluster. According to the rules of Table 12, the variation of irrigation amounts A and D in the stages of I1 and I4 does not affect the changes in cluster prediction.
In the third case, when the deficit irrigation of C and D is performed in the I3 and I2 stages, respectively, the first and fourth clusters are predicted at 60 and 40%, respectively, by the tree diagram. The very good and good conditions of the first and the fourth clusters, respectively, indicate the positive effect of additional irrigation in the I2 stage compared to I1 and I4 stages. Although full irrigation in the previous branch was done in the initial and late stages, the first cluster (very good) is not predicted (Table 13).

Full irrigation (D) in the mid-stage of plant growth (I3)
Finally, when the amount of irrigation D is at the I3 stage, the tree diagram predicts the first cluster. According to Table 14, full irrigation in the mid-stage and irrigation C at the development stage of plant growth had significant effects in the prediction of very good and good clusters. Table 14 also indicates that the best-deficit irrigation methods should be applied in the initial, development, mid, and late stages of plant growth in the order of B, C, D, and A, respectively, for large amounts of quantitative traits.   Figure 8 shows the importance of irrigation in the four stages of plant growth in predicting the five clusters. Accordingly, irrigation in the I3 stage with a relatively high difference from the other irrigation phases has the greatest importance in predicting clusters.

Results of the Apriori and K-means hybrid algorithm
To extract the association rules, it is necessary to introduce the antecedent and consequent data to the Apriori algorithm. For this purpose, clusters and the amount of irrigation in four stages of plant growth were introduced as the consequent and the antecedent, respectively, to the Apriori algorithm. The rules with the highest validity relative to the other rules were used among the extracted rules (Tables 15, 16 , 17, 18, 19). The rules are sorted in descending order of confidence percentage, decreasing from the first to the last rule. In Table 15, the rules extracted by the Apriori algorithm are related to the first cluster.
Most of the rules in Table 15 have a 100% confidence interval that specifies the high validity of the rules. For example, the first rule can be defined in such a way that the values of quantitative traits of guar beans belonged to the first cluster in 100 cases where irrigation amounts B and D were applied in I2 and I3, respectively. Furthermore, a support coefficient of 8% reveals that irrigation amounts B and D in the I2 and I3 stages, respectively, occurred at the same time with the first cluster in 8% of the total irrigation factors influencing the values of the first cluster. Given that the support value is the percentage of simultaneous occurrence of consequent and antecedent factors, lower values of antecedent factors result in a higher percentage of support.
The positive value of lift also marks a positive correlation between antecedent and consequent factors. Therefore, there is a positive correlation between consequent and antecedent factors in all rules in Table 15.
In rule 14, full irrigation (D) is done in all stages of the plant growth; hence, it has 100% confidence associated with the first cluster (very good values of quantitative traits). The values of the three assessment indices in rules 9-13 are equal to those of rule 14. Therefore, the irrigation rules of 9-13 can be applied to achieve very good values of quantitative traits as in rule 14.
Rule 15 consists of an antecedent factor (the amount of irrigation D in the I3 stage) and the maximum support value (28%). In addition to rule 15, the amount of irrigation D is carried out at the I3 stage in all rules of Table 2, which further confirms the great correlation of irrigation D in the I3 stage with very good values of quantitative traits.
In Table 16, the confidence level of the first rule is greater than the other rules. In this rule, irrigation amounts B, A, C, and D were done in the stages of I1, I2, I3, and I4, respectively. Considering that the second cluster has moderate values of quantitative traits and the duration of irrigation A is 30 days in the I2 stage, it is appropriate in terms of water saving and the increase in the values of quantitative traits.
The support value is 24% in all rules involving an antecedent factor, except for rule 23 with the maximum support of 28%. In this rule, irrigation D was done in the I1 stage. The support coefficient states that irrigation D in the I1 stage occurred simultaneously with the second cluster in 28% of the total set of irrigation values affecting the second cluster.
In Table 16, the I3 stage only includes the irrigation amounts B and C, further demonstrating the correlation of almost medium (B and C) irrigation in the I3 phase with the second cluster (medium).
As shown in Table 17, irrigation A was carried out in the I3 phase in five rules with a 100% confidence value. Given that the values of quantitative traits in the third cluster are in a very bad condition, irrigation A in the mid-stage had a significant effect on reducing the values of quantitative traits in guar beans. Although full irrigation (D) was carried out in I1 and I4 stages in these five rules, it did not affect the increase in the values of quantitative traits. Therefore, irrigation A should not be performed at the I3 stage due to its high reducing effect on the quantitative traits of guar beans.
In addition, among the rules in which antecedent factors contain one element, rules 11 and 19, respectively, have the highest percentages of confidence and lift. In these rules, the antecedent factor of irrigation amounts A and B occurred at the I3 and I2 stages, respectively. These rules demonstrate the importance of irrigation amounts A and B in the I3 and I2 stages, respectively, in the values of quantitative traits in guar beans.
In Table 18, the highest percentages of confidence and lift belong to the first rule. Given that the fourth cluster has good values of quantitative traits, the first rule irrigation pattern is suggested for regions with deficient in water (when the goal is the fourth cluster). Irrigation D should be done because the water demand in the plant and the duration of irrigation are not high in the I1 stage. Irrigation B and C should, respectively, be done at the developmental and mid-stages of plant growth when the duration of the plant growth is longer than the other growth stages, and irrigation A is appropriate in the late stage of growth. In all the rules of Table 18, irrigation C was carried out at the I3 stage, indicating a high correlation between irrigation C in the I3 phase and the fourth cluster. The lowest percentages of confidence and lift are related to the last rule; thus, irrigation A in the I1 stage is not highly correlated with the fourth cluster (good values of quantitative traits). According to Table 19, the highest percentage of confidence is related to rules 1-3, where irrigation amounts A and B were carried out in the I2 and I3 stages, respectively. The fifth cluster has slightly bad values of quantitative traits relative to the other clusters, which further shows the relationship of irrigation A and B in the I2 and I3 stages, respectively, with slightly bad values of quantitative traits.
The values of the evaluation index are equal in the fourth and fifth rules, but irrigation amounts C and D are different in the I4 phase of the two rules. Thus, irrigation amounts C or D in the I4 stage and irrigation B at the I3 stage have the same relationship with the fifth cluster. In terms of water saving, therefore, it is best to do irrigation C instead of irrigation D in the fourth stage after applying irrigation B at the I3 stage (when the goal is the fifth cluster).
Irrigation B was done in all the rules where the antecedent elements involve the I3 phase. In this table, therefore, Irrigation B in the I3 stage has a high correlation with the fifth cluster (bad values of quantitative traits).

Conclusions
Most plains in Iran have been plagued by water shortage and drought in the last few years. Accordingly, this study sought to investigate and predict five quantitative traits of guar beans in different deficit irrigation methods. For this purpose, various deficit irrigation methods were applied in the first four growth stages of the guar bean plant. First, five quantitative traits of guar beans were clustered by the K-means algorithm, the results of which consisted of five optimal clusters selected by the SVI. According to the results of clustering, the first and third clusters, respectively, had the highest and lowest values of quantitative traits in guar beans compared to the other clusters.
According to the results of the CART-K-means hybrid algorithm, the third cluster is predicted when irrigation A (40% of full irrigation) occurs at the mid-stage of the guar bean growth. The first cluster (with the maximum values of quantitative traits) was predicted in two modes. The first mode was when full irrigation was performed at the midstage of plant growth, and the second was when full irrigation and 80% of full irrigation (irrigation C) occur in the development and mid-stages of plant growth, respectively. The order of the importance of irrigation amounts in different stages of growth in the prediction of clusters was determined as the mid-, development, initial, and late stages of plant growth, respectively, by the CART-K-means hybrid algorithm.
Furthermore, the Apriori-K-means hybrid algorithm determined the relationship between different irrigation levels in the four stages of plant growth with the clusters. According to the results, the irrigation amount in the midstage of plant growth had the greatest relationship with the clusters. In the mid-stage of plant growth, the highest relationships were observed between irrigation amounts D (full irrigation) with the first cluster, B (60% of full irrigation) and C with the second cluster, A with the third cluster, C with the fourth cluster, and B with the fifth cluster, respectively.
According to the results of this study, the best method of irrigation in the initial, development, mid-, and late stages of plant growth is in order of B, C, D, and A, respectively, to increase the values of quantitative traits in the guar bean plant.
Funding The authors received no specific funding for this work.

Conflict of interest
The corresponding author states that there is no conflict of interest.
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