Introduction

Tomato (2n=2x=24), belonging to the Solanaceae family, is an important vegetable with high nutrient content, widely cultivated throughout the world, and the second most consumed vegetable after potato^1,2. Its morphology is the subject of interest in basic studies, plant organ development, determinants for culinary purposes, market value and utilization of the harvested product. Growers demand highly profitable tomatoes, which correlates with their size^3,4.

Yield potential is a complex trait, which is influenced by yield components (RCs), and these are controlled by many genes whose expression is strongly influenced by the environment^5,6. The CRs in tomato include characters such as fruit weight, number of fruits per plant, fruit length and fruit diameter^7,8, the correlation between these and yield is important in the indirect selection of genotypes for improvement, a significant and positive correlation between 2 characters suggests that both can be improved simultaneously in a selection program, and this of one of them, translates into the selection and improvement of the other^9,10. However, selection based solely on the correlation coefficient can lead to erroneous results, since it only measures the degree of association between two variables, without taking into account the causes⁹.

Path coefficient analysis provides an effective means of discovering the direct and indirect causes of the association that allows a critical examination of the specific forces acting to produce a given correlation, and measures the relative importance of each causal factor¹¹. Thus, path coefficient analysis is a statistical analysis capable of recognizing cause and effect relationships¹¹ by displaying the correlation coefficient on the direct and indirect effects of independent variables on a dependent variable, which provides an obvious understanding of their association with fruit yield. Ultimately, this type of analysis could help to improve, design selection strategies for fruit yield and nutritional value¹².

The National Vegetable Project (PNH) of the National Institute for Agricultural and Forestry Innovation (INIAF) has been identifying genotypes with high fruit yield, quality and tolerance to adverse abiotic and biotic factors, evaluating a large number of variables to explain the yield components by means of a simple model, analyzing their numerical components, such as the number of fruits per plant (NFP), which is determined by the number of flowers (NF) that are fertilized and their final weight. The objective of this work was to analyze the main variables related to tomato yield, and to guide the selection of materials for the INIAF vegetable breeding program.

Materials and methods

INIAF, located in the municipality of Sipe Sipe, Quillacollo province, Department of Cochabamba. It is located at 17°26'24.4" south latitude; 66°20'38.9" west longitude and at an altitude of 2505 meters above sea level (m.a.s.l.) during the 2018-2019 agricultural season.

For the development of the work, 7 experimental lines of tomato were used, and 2 control varieties (Lía and Río Grande) were added to this material to compare the superiority or inferiority of the materials in terms of productivity.

The seeds were sown in multi-cell trays of 128 cells, containing rice husks, slats and topsoil as substrate. Seedlings were transplanted 36 days after sowing (dds) in open field conditions, using a planting density of 20000 pl ha-1. The plants were trellised when they reached 15 cm in height, and the lower leaves were defoliated once the fruits of the first bunch were formed. Drip irrigation was used, separated at 20 cm, with 2 daily irrigations of 20 min each, applying per plant approximately 1.13 L day-1. Fertilizers were applied by fertigation with direct aspiration through a Venturi, the daily doses were according to the phenological stage of the crop, the total applied was: 260 N-330 P-330 K. Fruit harvesting began 75 days after transplanting (ddt), by hand, once a week.

A randomised complete block design (RCBD) was used, with 9 treatments (experimental lines) and 3 replications. The experimental unit (EU) consisted of 10 plants distributed in 2 rows, 80 cm apart and 2 m long each. For harvesting purposes, 5 plants were taken per EU. Variables associated with yield components of second bunch fruit were evaluated on 5 individual plants per plot, in free competition. Table 2 describes the name of the response variables, symbol and units of measurement; these were evaluated according to the International Plant Genetic Resources Institute's manual of descriptors for tomato (Solanum lycopersicum L.)¹³ and the International Union for the Protection of New Varieties of Plants guide for tomato¹⁴.

The data of the 9 variables evaluated were subjected to analysis of variance (ANVA), considering the genotypes as fixed effects after observing the assumptions of homogeneity of variance and residual normality. When significance levels were p ≤ 0.05, averages were calculated and the Least Significant Difference (LSD) test was applied. Phenotypic correlations (r) between variables were calculated using Pearson's correlation coefficient, using the agricolae¹⁵ package, and plotted using the corrplot¹⁶ package in R¹⁷ software. Path coefficient analysis was performed, considering fruit yield as the dependent variable and yield components as independent variables, using the R¹⁷ software.

Results

The ANVA mean squares values for the traits PF, DE, DP, PFP, NFP and RTO under study, revealed highly significant differences (p≤0.01) and for NRP and NFR significant differences (p≤0.05), among the lines studied (Table 3). These results indicate that the differences are due to the intrinsic genetic conditions of each cultivar. The low coefficients of experimental variation (< 27 %) reveal the existence of experimental precision.

Table 4 shows the results of the mean test. AVTO1007, AVTO1003, L014 and Rio Grande had the highest NFR. While L015, Lía, L027 and L019, expressed the lowest amounts. For the FP variable, line L015 was superior and L027 presented the lowest data. The most outstanding lines in RTO were L015, Lía, L014 and Rio Grande.

Phenotypic correlations between variables were calculated using Pearson's correlation coefficient. Such correlations constitute a measure of the magnitude of the linear association between 2 variables without considering cause and effect between them independently of the units. In Figure 1, the values of the simple correlations obtained between pairs of variables are presented. Among the performance component variables, the highest correlation corresponded to the PF with the DP (r=0.80**), these variables, in their order, are highly correlated with the PF and DP (r=0.68** and r=053**). The positive correlations of NFI with NRP (r=0.92**), and DE (r=-0.42**) indicate that plants tend to have a greater development of these characteristics causing fruits of smaller diameter.

Figure 1 Correlogram of the degree of association between fruit yield and its components in experimental lines of tomato, evaluated during the 2018-2019 cropping season 

Among the variables that are highly correlated with the RTO in fruit, are the PF per plant (r=0.93**), average PF (r=55**), DE of the fruit (r=0.63**) and DP of the fruit (r=0.47*). Indicating that lines with higher DE and polar development tend to have higher fruit weights.

Figure 2 shows the plot of the estimated path coefficients (PC) of the direct and indirect effects of the variables evaluated on the RTO in tomato, according to the path analysis. The main positive direct effect was exerted by NFP (CS=0.57). In addition, the other variables that exerted a relevant positive direct effect were PF (CS=0.46) and DP (CS= 0.33), together with a highly significant correlation with fruit yield. The main positive indirect effects on RTO were exerted by DE via PF (CS=0.72) and PFP via NFP (CS=0.63). Other positive indirect effects on RTO were exerted by DE via NFP (CS=0.22). On the other hand, the following variables exerted a negative indirect effect on RTO: NFR via DP (CS=-0.16) and DE via DP (CS=-0.37).

Figure 2 Plot of the path analysis indicating the direct and indirect effects of yield components on the yield of tomato experimental lines, evaluated during the 2018-2019 cropping season 

Discussion

The ANVA (Table 3) shows differences between lines for the variables related to the RTO, probably due to the expression of these characters during their development, which have had genetic and environmental influence. The low experimental coefficients of variation (< 27 %) reveal the existence of experimental precision, which guarantees the validity of the conclusions drawn. According to the comparison of means (Table 4), the differences in FP values between the genotypes are due to the genetic constitution of each line and the influence of the environment¹⁸. Lines L015, Lia, Rio Grande and L014 are statistically equal (p<0.05) and superior to lines AVTO1003, AVTO1007, L027 and L019 in RTO values. The presence of this difference is important, because success for any crop improvement depends on variation and, to a greater extent, on the parameter that is heritable^19-21.

On the other hand, highly significant positive phenotypic correlations were observed for the variables recorded (Figure 1). This relationship is generally due to the presence of linkage and pleiotropic effect of different genes. It was also found that the NFP is associated with morphological parts and the NFI, so that the number depends to a large extent on the type of inflorescences that the cultivars have, whether they are simple or compound²². The correlation identified between FP with fruit PD corroborates similar results reported by Kaushik & Dhaliwal²³. However, Escalante²⁴ indicated that the larger the fruit size, the lower the number of fruits. This is corroborated by the characteristics of each cultivar since the photosynthates assimilated by the plant in some cases increase the number of fruits and in others increase their size. The negative correlation between FP and NFI is related to what was reported by Antonio²⁵, who, by increasing the FP, reduced the number of fruits per plant, and there was a negative correlation. Cancino²⁶ pointed out that fruit size (closely related to FP) depends on 3 to 5 pairs of genes, an aspect that agrees with Ashcroft et al.²⁷, in which fruit size is controlled by genetic factors, as well as physiological factors, such as ripening, stalking and defoliation. Tiwari & Upadhyay²⁸ reported that plant height, fruit diameter and fruit length were directly responsible for the determination of fruit RTO in tomato. Haydar et al.²⁹ also observed that FP exerted a high positive and direct effect on RTO of fruit per plant.

Path analysis is a reliable statistical technique, designed by Wright¹¹, that helps to determine the traits that contribute to performance and is therefore useful in indirect selection. It predicts possible explanations for the observed correlations between a dependent variable and a number of independent variables, separating the direct effects of one variable on another and the indirect effects of one variable on another via one or more independent variables and helps the breeder to determine the components of performance. In this regard Singh & Chaudhary³⁰, indicated that being positive (both direct effects and correlation coefficients), the correlation explains the true relationship between these traits and a direct selection through these traits will be effective. The path analysis coefficients in Figure 2 indicated that PF, NFP and DP had maximum direct contribution along with highly significant correlation with fruit yield. The traits exhibiting high direct effect on RTO per plant indicating that direct selection could be effective in improving RTO based on selection of these traits. Similar results were obtained by Monamodi et al.²¹, who evaluated 6 lines of determinate habit tomato and observed that RTO per plant was positively correlated with NFR (r=0.59), NRP (r=0.87), NFP (r= 0.90), fruit weight per bunch (r=0.59). Souza et al.³¹ also reported that fruit yield per plant was positively related to the variables NFP (r=0.94), average fruit weight (r=0.53), NRP (r=0.72) and NFR (r=0.82).

Path coefficient analysis was that the number of fruits per plant had the highest positive direct effect on fruit yield, fruit weight and polar diameter which have significant correlation and direct effect on fruit yield emerged as the components with coefficients 0.57, 0.33 and 0.46, respectively. These traits may be relevant within the selection criteria in the development of new varieties.