multivariate statistical methods

 Drought is one of the most important global threats to food production, in addition to that, climate change and the increase in the global population also widen the dimensions of this problem. One of the ways to solve this problem is to create new cultivars with greater tolerance to drought stress. Wheat has been one of the most important sources of human food all over the world and it is used in various food products and processing industries. Wheat together with rice and corn provide more than 60% of calories and protein needed for human nutrition. In areas like Iran, where most of the rain occurs in winter and early spring, wheat will face water shortage and drought stress at the end of the growing season. In crops, one of the effective methods that can minimize the effect of this phenomenon in combination with other methods of water deficit management is the use of high-yielding and drought-tolerant cultivars. Despite the numerous scientific sources published in this field, there are still many gaps in these studies, so studying the effects of drought stress is always a research priority. Ilam province, as one of the irrigated wheat production areas, suffers from the lack of cultivars that are resistant or tolerant to low irrigation conditions, so investigating the response of different wheat genotypes in low irrigation conditions as low input production systems is very important and is addressed in this study. 

In order to evaluate some bread wheat genotypes under normal and drought stress co ditions, 36 wheat genotypes were evaluated in the form of a randomized complete block design in three replicates in the crop year of 2019-2019 in Darehshahr city located in Ilam province. The examined traits include spike length, spike number per plant, spike length, peduncle length, sub-peduncle axis, flag leaf length, flag leaf width, number of stem nodes, plant height, number of spikes per plant, number of seeds per spike, number of seeds per plant. plant, number of tillers, hundred seed weight, single plant seed weight and seed yield. Based on performance under stress (Yp) and normal (Ys), drought tolerance indices such as average productivity tolerance index, harmonic mean, geometric meanproductivity (GMP), stress sensitivity index, stress tolerance index, performance stability index (YSI) and Relative Stability Index (RSI) and Performance Index (YI) were calculated. The mean comparison test was performed using Duncan's method and using R software. Simple correlation (Pearson), decomposition into components, decomposition into factors were also performed between the tested traits. SAS 9.1 statistical software was used for statistical analysis of traits. 

The results of the analysis of variance in drought and normal stress conditions showed that there was a significant difference between genotypes in all traits at the probability level of 1%. The most important significant correlation coefficient in both conditions between seed yield was related to the seed weight of a single plant and the number of seeds per plant. Considering the high and significant correlation of grain yield under stress and non-stress conditions with drought tolerance indices, higher productivity indices, geometric mean productivity (GMP), geometric mean  and stress tolerance index  as the best indicators. were chosen. It seems that in order to evaluate stress tolerance, the selection of genotypes should be based on several indicators. Factor analysis at the drougth stress condition indicated that the two first factors expalined a total of 97. 57% of the variance. The first factor was called the performance stability factor and the second factor was named theStability Factor. The biplot diagram also showed that the genotypes of no. 13 and 47 were placed in the vicinity of the ranges related to drought resistance indices (STI, MP, GMP, and HM) and were introduced as superior genotypes. 

According to the data obtained from analysis of variance in both normal and drought stress conditions, the genotypes were significant in terms of all traits. The significance of the studied traits indicates the existence of diversity between genotypes in terms of the studied traits, and some of these traits can be used to evaluate stress tolerance. The best genotypes had the best averages for peduncle length of genotype 33, for the number of seeds per plant of genotype 5, for seed weight of a single plant and seed yield of genotype 1. The heat map shows the relationship between drought tolerance based on different yield and drought stress toleranceindices. Considering the high and significant correlation of grain yield under stress and non-stress conditions with drought tolerance indices, average productivity indices, GMP, geometric mean and stress tolerance index were selected as the best indices that are able to distinguish tolerant genotypes from other Screen the genotypes. The yield index (YI) had the highest correlation coefficient with grain yield under stress conditions. Based on biplot results, genotypes No. 13 and 47 were the most tolerant genotypes under drought stress conditions more than other genotypes and were introduced as superior genotypes.

Rapeseed with the scientific name (Brassica napus L.) are one of the most important oilseed crops in the world. Considering the country's increasing need to import oil and the importance of rapeseed among oilseeds plants, increasing the yield and percentage of oil is very important. Therefore, identification the traits that increase seed yield, play an important role in the success of breeding programs. Yield is a complex trait that is affected by many factors. direct selection of a variety for yield is not often very effective, so investigating the relationships between grain yield and other traits for indirect selection may be effective. In such a situation, correlations may not clarify the relationships well, therefore, multivariate statistical methods and path analysis can help in understanding the nature of the relationship between traits for direct or indirect selection and improve the efficiency of selection in breeding programs plants become useful.

In this study, eight genotypes of spring rapeseed (SPN-202, SPN-204, SPN-206, SPN-207, SPN-217, SPN-225, SPN-227, SPN-182) along with 56 rapeseed hybrids (F1) were planted in a randomized complete block design with three replications in 2019-2020 crop years in the research farm of Gorgan Agricultural Research Station. During the experiment, phenological, morphological traits, yield and yield components were recorded. The normality of the data was evaluated based on the Kolmogorov-Smirnov method. In order to understand the relationships between traits and to identify the traits affecting on grain yield, at first, correlation coefficients were estimated, then stepwise regression were done. Then, path analysis based on correlation coefficients was used to determine the direct and indirect effects of traits. Finally, all traits were grouped based on principal component analysis.

The results of analysis of variance indicate a significant difference for all studied traits at the probability level of one percent. The coefficient of variation (C.V) for the traits varied from 1.37 (physiological maturity) to 10.31 (number of sub-branches), which indicates that there is sufficient accuracy in conducting the research. The results of correlation evaluation showed that number of pod per lateral branches (0.864), number pods per Plant (0.865), number of lateral branches (0.466), physiological maturing (0.329) and number of grain per pod (0.358) had a positive and significant correlation with grain yield (P<0.01). Stepwise regression analysis showed that the traits of number of pods per plant, number of grain per pod and 1000-grain weight has a decisive role on grain yield. Based on the results of path analysis, number of pods per plant had the most direct effect (0.881) and number of grain per pod had the most indirect effect (0.053) through the number of pods per plant on grain yield. In order the results of principal component analysis, four components were able to explain 75.91% of the changes in the measured data of 64 rapeseed varieties.

Results of the path analysis showed that number of pods per plant, number of grain per pod and 1000-grain weight had a direct positive effect on grain yield. Also, the stepwise regression analysis showed that the stated traits have the highest regression coefficients. Therefore, selection for these traits can be very effective in achieving high performance

Pollution and declining quality of water resources reduce usable water resources, weaken economic development and threaten human health. In this study, groundwater quality was studied and analyzed in Ardabil aquifer. For this purpose, 32 samples of groundwater sources in the Ardabil plain were collected and the concentrations of major ions, minor ions and some heavy metals were measured. Then, hydrogeochemical factors affecting the groundwater quality of the study area were analyzed using multivariate statistical methods, including correlation coefficients and factor analysis. According to the correlation matrix, the concentrations of metals such as arsenic, barium, scandium, silicon, zinc and vanadium indicated a little correlation with the main ions. Therefore, it can be concluded that the entry of these elements into groundwater is due to human activities. In factor analysis, the groundwater quality changes were affected by four main factors with 77.31% of the total variance of data in Ardabil plain. The results of factor analysis showed that the first factor was lithogenic, the second and third factors were lithogenic and anthropogenic, and the fourth factor was just anthropogenic. The results showed that the concentrations of heavy metals such as arsenic, barium, scandium, silicon, vanadium and zinc did not have a high correlation with the main ions, so the presence of these elements could be due to human activity. Also, the greatest effect on groundwater hydrochemistry in the study area was related to magnesium, sodium, calcium ions and electrical conductivity.

Due to the increasing need of the country to imported edible oil and rapeseed importance among oilseeds, efforts to increase its grain yield and oil content are of high importance. Therefore, recognizing the traits that increase grain yield of rapeseed has an important role in the success of breeding programs. Thus, sixteen rapeseed genotypes were evaluated in a randomized complete block design with three replications in three regions with different climatic conditions in Iran, including Karaj, Isfahan, and Hamadan in 2016-2017. Traits such as number of pods per plant, number of seeds per pod, grain yield, 1000-grain weight, plant height, height of the first branch, stem diameter, oil percent, number of days to flowering, number of days to the end of flowering, duration of flowering, and number of days to maturity were measured. Stepwise regression analysis showed that number of grain/pod, number of days to maturity and number of pods/plant (R2 = 97.7), number of pods/plant and number of days to maturity (R2 =78.4) and number of days to maturity and number of grains/pod (R2 = 45.5) accounted for total variations of grain yield in Karaj, Isfahan and Hamadan, respectively. The results showed that the number of days to maturity, number of pods/plant, number of grain/pods, stem diameter and plant height had the greatest positive effect on grain yield and oil content. Therefore, these traits can be used as suitable selection tools for increasing grain and oil yield in winter rapeseed breeding programs

Drought stress is a major constraint for the production and stability of crop yields. Analysis of reproductive traits and their response to drought can be useful to identify drought tolerant rice genotypes. The aim of this study was to evaluate the morphological behavior of some rice genotypes under different environmental conditions in the reproductive stage.

This study was conducted in greenhouse of Sari Agricultural Sciences and Natural Resources University, a factorial experiment based on a completely randomized design in 2018. The experimental factors included rice genotypes (IR64, drought sensitive and Dinorado and Moroberecan, drought tolerant) and drought stress levels (normal irrigation and re-watering).

Analysis of variance of data showed that the effect of genotype, drought stress and genotype × drought stress interaction on studied traits was significantly different, indicating that rice genotypes behave differently under different environmental conditions. Comparison of simple correlation coefficients between different traits of rice genotypes under normal irrigation showed that yield had a positive and significant correlation with tiller number (r = 0.97). However, under drought stress, yield with tiller number (r = -0.66) was negatively correlated with flag leaf length, length and weight of panicle, number of primary and secondary spikelet, number of filled grains in panicle and percentage of panicle fertility percentage were positive and significant had. The results of stepwise regression to justify the variation of yield of rice genotypes based on morphological traits under normal irrigation conditions, tiller number, 100 seed weight and Number of secondary spikelet traits, and in drought stress conditions, the number of filled grains in the panicle and panicle weight as the most important traits explaining variations seed yields. Comparison of path coefficients of yield and yield components showed that in normal irrigation conditions the number of tillers (0.652), however, under drought stress conditions; number of filled grains in panicle (1.513) had the most direct effect on yield. The highest correlation coefficient was observed in the number of filled grains in the panicle with grain yield (r = 0.931) under drought stress.

In general, IR64 genotype (susceptible control), under the influence of drought stress showed a significant decrease in yield and yield components (such as panicle length, panicle weight, number of filled grains in the panicle and percentage of panicle fertility percentage) than tolerant genotypes.

Khoy plain is one of the main industrial and agricultural centers in West Azerbaijan province that the water requirement for agriculture, industry and drinking water is generally supplied by groundwater. Therefore, the quality of available water seems very important in this area. Groundwater quality is generally dependent on hydrogeochemical processes that regnant the water resources system. For this purpose, in order to better understand the hydrochemical processes in Khoy plain aquifer, graphical and multi-variable statistical methods were used to interpret the results obtained from the analysis of 54 samples taken in September 2016 from groundwater resources. The results of the Piper diagram and the expanded Durov diagram shows that the groundwater type in the region is mostly calcium and magnesium carbonate, sodium chloride and the mixed type. In hierarchical cluster analysis, the samples are placed in two main clusters and five sub-clusters. The Stiff graphs identified eight general groups with saline, calcareous, basaltic, igneous and calcareous composition, Saline shale composition, shale and lime composition (Marne) and mixed type. The results of the factor analysis method suggested a three-component model for the data. In the first component, sodium, chloride, sulfate, bicarbonate, calcium and magnesium were interdependent; in the second component, nitrate and arsenic were linked; while in the third component, iron was partially related to the others. The first and third factors have geogenic sources and the second factor shows both geogenic and anthropogenic sources for groundwater contaminants.

Terminal heat stress has been recognized as the most widespread and detrimental type of heat stress in the world. In southern regions of Iran like Khuzestan, delay in planting date causes pollination and grain filling stages to be exposed to high temperatures, resulting in yield reduction. Developing heat tolerant cultivars is one of the ways to deal with heat stress. In this study, to identify resources of heat tolerance in wheat germplasm, a total of 203 bread wheat accessions with three control cultivars were planted in normal and delayed planting dates as an augmented experimental design in Ahwaz and the agronomic traits were evaluated. The results showed that almost all the evaluated traits were reduced in heat stress conditions compared to normal conditions. In both normal and heat stress conditions, some superior accessions were identified in terms of the studied traits compared to the control cultivars. In the biplot based on the principal components under heat stress conditions, 64 accessions along with control cultivars were located in the area of superior characteristics in terms of grain weight of five spikes, number of florets per spike, number of grains per spike, number of spikelets per spike, spike length and plant height. The studied accessions were divided into five groups by cluster analysis. The results showed a high diversity in the studied genetic material and the accessions superior to the control cultivars in terms of the studied traits were identified which can be used in future breeding programs.

Path and biplot analysis based on linear and bilinear models, respectively, are of the effective statistical methods for expressing relationships between traits in plant. In order to study of effective traits on seed yield of bitter vetch, 20 ecotypes were evaluated in a randomized block design with three replications during 2017-2018 growing season in the Research Field of Faculty of Agriculture at Vali-e-Asr University of Rafsanjan. The analysis of variance revealed significant differences among the ecotypes for 16 studied traits except plant and root height in maturity stage and one seed pod length suggesting high variation among the ecotypes for the majority of the studied traits. Correlation analysis showed that there were a positive and significant correlation between seed yield and the most of traits except phenological traits including days to 50% flowering and days to maturing start and days to 50% maturing and two morphological traits including root height in maturity stage and two seed pod length. Stepwise regression analysis indicated that thousand kernel weight, number of seed per plant and number of lateral branch entered into model and explained about 65.7 of the total variation. The results obtained from path analysis demonstrated that thousand kernel weight had the most direct effects on seed yield (an increase of 0.657 g in seed yield per 1 g increase in thousand kernel weight). Biplot of first two components divided the successful ecotypes into two groups and identified the most effective traits association with the success of each group.

Sesame is one of the oldest and most important oilseeds in Iran and the world due to its nutritional value. In the present study, 25 sesame landraces collected from different regions of the country were evaluated in terms of phenological, morphological and physiological traits in Urmia climate. The ANOVA results showed that there was a statistically significant difference between the landraces in terms of all traits at 1 % probability level. The results of descriptive statistics also confirmed this. Leaf index, number of branches per plant and number of capsules per plant had the highest phenotypic and genotypic diversity coefficient, while day to flowering and capsuling along with oil percentage had the lowest value for these coefficients. Seed yield as the most important trait had a moderate general heritability. The studied sesame landraces were divided into three groups by cluster analysis. The landraces in the first group were in good condition in terms of yield and yield components traits, and if the goal is to select high-yield genotypes, selection from this group will be more effective. In contrast, the third group, which included only one landrace, showed lower values in terms of yield and yield components and had longer-term phenological stages. In principal component analysis, the first component showed positive correlation with yield and yield components except of two hundred grains weight. The results of the present study can be used in sesame future breeding programs.

In order to evaluate the genetic diversity in 115 rice mutant genotypes of Tarom Jalodar, a randomized complete block design with three replications was conducted at Sari Agricultural Sciences and Natural ResourcesUniversity. Eleven quantitative traits were evaluated. Analysis of variance showed that there is a significant difference between the genotypes for the morphological traits.The correlation coefficients between traits showed that flag leaf width, number of tillers, number of grains and 100-grain weight had a positive and significant correlation with grain yield.Based on cluster analysis, rice genotypes were divided into three groups. Stepwise regression analysis showed that panicle length, 100-grain weight and number of unfilled grain explain 58.9 % of variation of yield Results of path analysis showed that the most direct and positive effects obtain from number of tillers (0.59) and 100-grain weight (0.37).Results of the main principle component analysis (PCA) reveaed that the four main components justify 70.15% of the total data variation.In general, the results showed that genotypes 109, 64 and 75, due to the more number of tillers, higher length of panicle, the more100-grain weight and less number of unfilled grain were chosen as desirable genotypes, they can be used in the following program

In order to evaluate effect of deficit irrigation and application of water superabsorbent and determining principal components in water use efficiency of common bean, sesame and maize a split plots experiment based on RCBD design with three replications was conducted during 2015-2016 growing season, in Ferdowsi University of Mashhad, Iran. Irrigation levels (50 and 100% of water requirement) and application and non-application of water superabsorbent assigned to main and sub plots, respectively. Principal components analysis for three plant species resulted in two principle components with the most considerable variances. The first component explained 73, 60 and 80% of variables variance in bean, sesame and corn, respectively. In bean, variables of seed yield, biological yield, seed weight, plant height, crop growth rate and soil nitrogen, phosphorous content and pH were assigned to the first component and leaf area index, EC and water use efficiency were assigned to the second component. In sesame, variables of seed yield, biological yield, seed weight, plant height, crop growth rate and soil phosphorous and pH had the highest load on the first component and variables of leaf area index, soil nitrogen content, EC and water use efficiency had the highest load on the second component. In corn, variables of seed yield, biological yield, seed weight, plant height, leaf area index, crop growth rate and soil nitrogen and pH were in the first component and variables of soil phosphorous and EC and water use efficiency in the second component had the highest load.

Phaseolous vulgaris is highly important among bean species. China, Iran and Japan are the most important countries producing bean in Asia. According to reported information, cultivated area of bean was 94000 ha in Iran which 17841 ha located in Lorestan province. Improvement of new cultivar with high genetic potential for grain yield is the final goal in many breeding programs. To achieve this goal, many characteristics should be considered. Positive and negative significant correlation has been reported between traits in common bean. Various, traits had different direct and indirect effects on grain yield which should be considered. In addition to path analysis, evaluation and relationship of traits by other multivariate statistical methods such as cluster and factor analysis have been studied for better understanding of these relationships. This study aimed to investigate superior lines, study the relationship between important traits with seed yield by some univariate and multivariate statistical methods, and provide functional recommendation to breeding programs.
 

Elite lines obtained from red common bean (Phaseolus vulgaris L.) local populations of Lorestan province and suburbs, Iran, including 14 lines belonged to Azna (2 lines), Aligudarz (4 lines), Aleshtar (1 line), Borujerd (1 lines), Durood (2 lines), Shazand (2 line) and Nourabad (2 lines), with two control cultivars Goli and Sayyad were evaluated in randomized complete block design (RCBD) with 4 replications in Borujerd station, Lorestan, Iran, in 2011. Plant height, node number, stem number, pod length, pod number per plant, seed number per plant, 100 seed weight and seed yield characteristics were measured. Data were normalized by Kolmogorov-Smirnov test at 0.01 probability level. Error, genetic and phenotypic variances, and broad sense heritability pertreatment mean were estimated. Pearson correlation coefficient was used to determine the relationship between traits. Cluster analysis based on UPGMA was performed and Wilks' lambda statistic was used for cutting dendrogram. Then, a code was allocated to each group and these groups were compared. However, in order to fix type I error, Hotelling’s T2 test was used at 0.05 probability level. Before that, the assumption of homogeneous variance-covariance matrix was tested by BOX test at 0.01 probability level. Then, traits were compared. Seed yield was considered as dependent variable (y) and regression analysis was performed by stepwise method. Traits, that had significant standardized coefficient, were used in path analysis. For statistical analysis, Excel, SPSS and MSTAT-C software were used.
 

The results of ANOVA showed that the lines had significant difference for all studied traits. Mean comparison by Duncan test showed the highest and lowest seed yield belonged to Aligodarz-3 line (6058 Kg ha-1) and Goli cultivar (3175 Kg ha-1), respectively. All of the genotypes that were located in high seed yield group by cluster analysis belonged to elite lines that indicated the local red common bean populations, as a heterozygote germplasm source that been mixed of homozygous genotypes, had high potential to selection of superior lines in the breeding program. Comparison between groups by Hotelling-T2 statistics indicated seed number per plant and had significant difference at 0.01 probability level. The highest and lowest significant correlation coefficient was observed for seed number per plant with seed yield (0.91**) and node number with stem number (0.27*), respectively. The results of multiple regression for seed yield as dependent variable showed that seed number per plant and 100 seed weight had significant standardized regression coefficient. While, 100 seed weight had no significant correlation coefficient with seed yield that breeders should be considered different aspect of trait relationships. Path analysis results showed seed number per plant with direct effect 1.03 had more effect on seed yield than 100 seed weight with direct effect 0.43. While, both seed number per plant and 100 seed weight had negative indirect effect on seed yield by each other. The results of factor analysis showed four factors explained 93% of total variation. The first and second factor were called yield and yield component, and phenological type explained 60% of total variation. The lines that located in high yield group had the highest value for yield and yield components factor. While, the lowest score for mentioned factor belonged to Goli cultivar that showed factor analysis can be used both to summarize many dependent variables (traits) into little independent variables (factors) and to selective genotypes based on factor value. According to reports, the genetic base of bean cultivars has been limited. One of the useful results of multivariate analysis is the investigation of genotypes that locate at the end of distribution for several traits and these genotypes can be used as parents for better utilizing of probably heterosis. Heterosis and crossing one of the sustainable agricultural goals would improve germplasm, increase human food, promotion of farmer’s livelihoods and provide food.
 

Local populations of red common bean should be considered by breeders to select superior lines because of its potential and adaptation. Some studied traits had high diversity that could be exploited in breeding programs. While, other traits need to increase diversity by breeding strategies. Considering that each of studied analysis showed the different aspects of traits relationships and genotypes potential. So, the results should be considered simultaneously by breeders to better interpretation. Among the studied traits seed number per plant, according to high heritability, the identification of groups with different grain yield, high correlation and positive direct effect on grain yield was appropriate to increase seed yield. Multivariate analysis can be used to evaluate desirable genotypes and accumulate favorable alleles in breeding programs. The results of this study can be useful for breeders to investigate and utilize both traits and genotypes in breeding programs.