Correlation Evaluation and Path Coefficient Analysis of Traits Related to Fruit Yield in Iranian Pepper (Capsicum annum L.) Populations

Pepper is a rich source of essential vitamins and minerals. Like tomatoes, pepper plays an important role in preventing heart diseases due to its high amount of antioxidants. Fruit yield is a complex trait that is not only controlled by several genes, but also greatly influenced by the environment. On the other hand, fruit yield is affected by a large number of other traits and their interaction. Therefore, it is very important for plant breeders to know the relationships between these traits and their interaction effects. The path coefficient analysis is a method that clarifies the relationships between traits and their direct and indirect effects on fruit yield. In this method, the correlation coefficient between two attributes is divided into components that measure direct and indirect effects. Considering the limited studies regarding the evaluation of relationships between fruit yield and other traits affecting fruit yield in pepper, this research was conducted with the aim of identifying these important relationships and evaluating their direct and indirect effects in Iranian pepper populations.
 
In order to carry out this research, the seeds of 30 Iranian pepper accessions were collected directly from the farmers. The experiment was conducted in the form of pot cultivation in the research greenhouse of the Faculty of Agriculture of Urmia University in a completely randomized design with five replications during 2015-2016. After the flowering stage, the desired traits were estimated. Variance analysis was estimated, after examining the basic hypotheses of variance analysis by SAS9.4, as well as the genotypic and phenotypic correlation between traits based on the restricted maximum likelihood (REML) procedure in the SAS9.4 software. Step-by-step regression analysis was used to determine the traits with the most variation justified the fruit yield. The Durbin-Watson test was performed to investigate the independence of experimental errors. Analysis of path coefficients was performed based on the results of stepwise regression and genotypic correlation of traits in the R V.4.0.5.
 
In order to understand the relationships between traits and use them in breeding programs, the phenotypic correlation was estimated.  In this study based on the results of phenotypic correlation, leaf width and leaf length (0.651), single fruit weight and fruit circumference (0.784), fruit circumference and fruit diameter (0.625) and pulp weight and fruit diameter (0.610), showed positive and significant correlation. The purpose of estimating genotypic correlation coefficient is to determine relationships in conditions which in environmental factors are not involved. In the investigation of genotypic correlation, a positive, strong and significant relationship between fruit yield and pulp weight (0.907), fruit circumference (0.891), fruit diameter (0.697), single fruit weight (0.646) and around the plant (0.381) were observed. Given that most of these traits are factors contributing to fruit yield, the presence of such positive and significant genotypic correlation coefficients is reasonable. It can be inferred that pepper accessions with higher fruit characteristics, encompassing factors such as plant density and branching, are likely to exhibit higher fruit yields as well. It's important to note that correlation coefficients are mathematical tools used to measure the linear relationship between two variables. Their significance lies in their mathematical interpretation, and as such, they alone do not provide sufficient proof of a cause-and-effect relationship. Utilizing the results of stepwise regression, less impactful traits or those with minimal effects were eliminated from the model. As a result, seven key traits were identified as the most influential factors affecting fruit yield: pulp weight, plant density, fruit diameter, fruit count, plant height, total seed weight, and branch count.The first characteristic was pulp weight, which was included in the model and explained 78.8% of the fruit yield changes between genotypes. The second characteristic (around the plant) along with pulp weight explained 80.9% of the fruit yield variations. Fruit diameter, together with the previous two characteristics, explained 81.5% of fruit yield variations. In total, the traits included in the model for fruit yield justified 84.6% of the total changes in fruit yield in 30 pepper accessions. In order to better understanding and more accurately interpret of the results, as well as to know the direct and indirect effects and the effect of the traits that were entered into the model through stepwise regression, the path coefficient analysis method was used in this research. Fruit diameter (0.709) and pulp weight (0.289) respectively showed the most positive and direct effect on fruit yield. Fruit pulp weight through fruit diameter had the most positive indirect effect (0.595) on fruit yield. Around the plant showed an indirect positive effect on fruit yield through pulp weight (0.157), fruit diameter (0.392) and number of branches (0.080).
 
In the present study, the trait of fruit diameter had a positive, strong and significant genotypic correlation (0.697) with fruit yield, and it also showed a positive direct effect (0.709) on fruit yield, these two coefficients can be considered equal, Approximately. Therefore, direct selection based on fruit diameter proves to be a valuable strategy for enhancing fruit yield. The magnitude of residual effects serves as an indicator of the model's accuracy in path analysis. When this value is substantial, it may be advisable to incorporate additional causal variables into the model. In the current study, the residual effects value (0.213) affirms the model's optimal accuracy.This research highlights the effectiveness of employing stepwise multivariate regression and path coefficient analysis to gain a deeper understanding of the fundamental relationships between traits. It underscores that relying solely on correlation relationships is insufficient for comprehensively justifying the associations between these traits.