Evaluating direct and indirect pathways of essential yield-attributing traits for crop improvement in brinjal (Solanum Melongena L.)

Introduction

Brinjal (Solanum melongena L.) is a major solanaceous vegetable crop (2n = 2x = 24) widely cultivated across tropical and subtropical regions owing to its high yield potential, wide adaptability, and diverse fruit forms, sizes, and color profiles making it a staple dietary crop for resource-poor and rural populations hence, referred as "poor man's crop" (Kumar et al., 2023) [1] . Cultivated since ancient times, its primary center of origin and diversity is India (Thompson et al., 1957; Vavilov, 1926) [2,3] . In Indian horticulture, it remains an indispensable indigenous vegetable, rich in dietary fiber, minerals, and antioxidants. Current estimates indicate that India produces over 12.99 million metric tonnes annually from 683.1 thousand hectares (Anonymous 2023-24) [4] . Structurally, brinjal possesses hermaphrodite, actinomorphic flowers exhibiting heterostyly (Kowalska, 2006) [5] and a bicarpellary, syncarpous, hypogynous ovary with basal placentation. Although predominantly self-pollinated, natural cross-pollination of 6-10% occurs via insect vectors like bees, ants, and thrips (Mal et al. 2022) [6] . Brinjal (eggplant) is widely grown across India, particularly in Odisha, West Bengal, Bihar, Uttar Pradesh, Madhya Pradesh, Gujarat, Maharashtra, Karnataka, and Andhra Pradesh, though it struggles at high altitudes. The plant requires a long, warm growing season, with the primary harvest occurring during the autumn and winter months. Ideal growth occurs between 25 °C and 30 °C, while temperatures below 15 °C significantly hinder development. For optimal seed germination, 25 °C is ideal-though germination can occur between 15 °C and 30 °C-and seedlings transplant best at temperatures around 20 °C. (Swarup, 2014) [7] To meet escalating market demands, maximizing unit-area yield and enhancing fruit quality remain key priorities for plant breeders. However, because total yield per plant is a complex polygenic trait influenced heavily by the environment, direct selection for yield alone is often inefficient. In this context, path coefficient analysis serves as a vital biometrical tool by partitioning simple correlation coefficients into direct and indirect effects. By identifying key yield-contributing morphological and biochemical components such as fruit weight, fruits per plant, plant height, and fruit length, path analysis enables breeders to formulate effective, trait-specific direct selection strategies to accelerate the development of high-yielding brinjal genotypes.

Materials and Methods

The study was conducted at the Department of Horticulture, Babasaheb Bhimrao Ambedkar University, Lucknow, Uttar Pradesh, India, during the Rabi season. Path coefficient analysis was performed using pooled data from two consecutive years (2024-25 and 2025-26) to identify important yield-contributing traits in brinjal. Geographically, the experimental site falls under a humid, subtropical climate and is located between 24.47 0 and 26.56 0 N latitude and 82.12 0 and 83.98 0 E longitude at an altitude of 113m above mean sea level in the Gangetic Alluvial Plains of Eastern Uttar Pradesh. The soil type of the experimental site was sandy loam with an average fertility level and pH in the range of 7.5-8.5. The field of the experimental site represented an ideal spatial unit in respect of texture, makeup, and fertility status. The row-to-row spacing was 75 cm, and the plantto-plant spacing was 60 cm. Each experimental plot consisted of two rows, each 3 m long. The experiment was laid out in a Randomized Block Design (RBD) with three replications for each treatment to identify the prominent quantitative traits correlated with enhanced fruit yield in brinjal. To support optimal crop growth and development, the recommended intercultural practices and doses of fertilizers (RDF) were applied. Path-coefficient analysis was carried out according to Dewey and Lu (1959) [8] . Total fruit yield was assumed to be the dependent variable (effect) which was influenced by the 17 independent morphological and biochemical characters. The variation in fruit yield unexplained by the 17 characters was assumed to be contributed by a residual factor (X). The path coefficient was calculated using the following formula:

Where, r iy = Genotypic/phenotypic correlation coefficient between the i th character and total fruit yield per plant (Y). P iy = Direct effect of the i th character on total fruit yield per plant (Y). r ij = Inter-correlation coefficient between the i th and j th independent characters.

𝑃 jy = Direct effect of the j th character on total fruit yield per plant (Y). The above equation can be written in the form of a matrix.

[A] 17x1 = [B] 17x17 x [C] 17x1

Where, [A] is the 17x1 column vector of correlation coefficients between independent traits and yield (r iy ) [B] is the 17x17 matrix of inter-correlation coefficients among the 17 independent traits (r ij ), and [C] is the 17x1 column vector of direct effects (P iy ) The Residual Factor was calculated as follows: P xy =√1-𝑅 2 Where, R 2 =Σ 𝑖 = 1 17 P iy r iy

In the above equations: P xy = Path coefficient of the residual variation (residual effect). R 2 = Coefficient of determination. P iy = Direct effect of the i th independent character on total fruit yield per plant (Y), where i = 1, 2 ...17. r iy = Correlation coefficient between the i th independent character and total fruit yield per plant (Y). r ij = Inter-correlation coefficient between any two independent characters (i and j), covering all possible trait combinations (r 1.2 to r 16.17 ).

Parameters recorded

There were eighteen parameters recorded for the given experiment. They are depicted below: days to 50% flowering, plant height (cm), primary branches per plant, fruit polar length (cm), fruit equatorial circumference (cm), number of fruits per plant, days to first fruit harvest, average fruit weight (g), length of calyx (cm), length of pedicel (cm), number of fruits per cluster, total soluble solids (TSS) (ºB), ascorbic acid content (mg/100g), reducing sugar (%), non-reducing sugar (%), total sugar (%), dry matter content (%), and fruit yield per plant (kg). The data recorded were analysed by analysis of variance (Panse et al., 1978) [9] . The path coefficients were calculated using the approach proposed by Wright (1921) [10] and refined by Dewey and Lu (1959) [8] .

Results and Discussion

Yield is a complex, quantitative trait strongly shaped by environmental conditions, making direct selection for yield inefficient in crop breeding. While simple correlation analysis measures the strength and direction of linear relationships between yield and its component traits, it fails to reveal cause-and-effect mechanisms or quantify the relative importance of individual direct and indirect contributions (Jakhwal et al., 2024) [11] . Path coefficient analysis (Wright 1921; Dewey and Lu 1959) [8,10] addresses this limitation by partitioning total correlation coefficients into direct and indirect effects. By untangling these cause-and-effect relationships, path analysis identifies key driving traits, allowing plant breeders to establish precise selection criteria and accelerate genetic gain.

Genotypic path coefficient analysis

The genotypic path coefficient analysis was performed using pooled data over both years, with total yield per plant as the dependent variable, to evaluate the direct and indirect influences of component characters across environments. Table 2 showed that reducing sugar had the strongest positive direct effect (0.6926) on total yield per plant. Other traits exhibiting positive direct contributions included plant height (0.6422), number of fruits per cluster (0.4860), fruit polar length (0.3731), average fruit weight (0.3033), days to 50% flowering (0.3010), length of calyx (0.2426), non-reducing sugar (0.0995), primary branches per plant (0.0351), and fruit equatorial length/circumference (0.0110). These observations indicate that direct selection for these characters-particularly reducing sugar, plant height, number of fruits per cluster, fruit polar length, average fruit weight, and days to 50% flowering-will be highly effective in achieving consistent genetic gains for total yield per plant. In contrast, the strongest negative direct effect on total yield per plant was recorded for total sugar (-0.6721), followed by dry matter content (-0.4288), total soluble solids (-0.3577), days to first fruit harvest (-0.2920), length of pedicel (-0.1775), ascorbic acid (-0.0839), and number of fruits per plant (-0.0632). These traits contributed adversely to yield through their direct pathways in the pooled evaluation. These results are in agreement with the findings of Bansal et al. (2008) [12] , Singh et al. (2011) [13] , Singh et al. (2017) [14] , Singh et al. (2020) [15] , Kumar et al. (2021) [16] , Sakariya et al., 2022) [17] , Kumar et al. (2023) [18] , and Rathod et al., 2023) [19] . Reducing sugar served as a paramount positive indirect pathway for multiple characters. High positive indirect effects on total yield per plant were expressed through reducing sugar by total sugar (0.6755), length of pedicel (0.2670), primary branches per plant (0.2402), fruit equatorial circumference (0.2175), number of fruits per plant (0.2091), fruit polar length (0.2016), plant height (0.1943), ascorbic acid (0.1743), and total soluble solids (0.1321). Additionally, plant height acted as a major positive indirect contributor to average fruit weight (0.3122), total soluble solids (0.3150), fruit equatorial circumference (0.2822), length of pedicel (0.2778), ascorbic acid (0.2068), total sugar (0.1958), primary branches per plant (0.1911), reducing sugar (0.1801), and fruit polar length (0.1716). Furthermore, number of fruits per cluster mediated substantial positive indirect contributions to number of fruits per plant (0.3043), dry matter content (0.2558), fruit polar length (0.1970), primary branches per plant (0.1558), total soluble solids (0.1299), length of calyx (0.1260), and length of pedicel (0.1218).

In contrast, marked negative indirect effects on total yield per plant were registered through total sugar by length of pedicel (-0.3055), fruit equatorial circumference (-0.2456), fruit polar length (-0.2442), number of fruits per plant (-0.2389), primary branches per plant (-0.2350), ascorbic acid (-0.2067), and plant height (-0.2049). Additionally, dry matter content exerted adverse indirect effects through number of fruits per cluster (-0.2257), number of fruits per plant (-0.2163), and fruit polar length (-0.1480). The total soluble solids (TSS) contributed negatively through average fruit weight (-0.2192) and plant height (-0.1755). Negative indirect influences were also mediated through days to first fruit harvest by number of fruits per cluster (-0.2568), fruit polar length (-0.2543), and days to 50% flowering (-0.2313).

Phenotypic path coefficient analysis

The phenotypic path coefficient analysis was performed using pooled data over both years, with total yield per plant as the dependent variable, to determine the direct and indirect influence of component traits across environments at the phenotypic level. Table 3 showed that reducing sugar had the strongest positive direct effect (0.5921) on total yield per plant. Other traits exhibiting positive direct contributions included plant height (0.5299), number of fruits per cluster (0.4329), average fruit weight (0.3362), fruit polar length (0.3104), length of calyx (0.1602), days to 50% flowering (0.1575), non-reducing sugar (0.0977), and primary branches per plant (0.0864). These findings indicate that direct selection for these characters, particularly reducing sugar, plant height, number of fruits per cluster, average fruit weight, and fruit polar length, will be highly effective for phenotypic yield improvement. Inverse to this, the strongest negative direct effect on total yield per plant was recorded for total sugar (-0.5452), followed by dry matter content (-0.3357), total soluble solids (-0.2506), length of pedicel (-0.1786), days to first fruit harvest (-0.1498), number of fruits per plant (-0.0329), fruit equatorial length/circumference (-0.0306), and ascorbic acid (-0.0006). These traits contributed adversely to yield through their direct pathways in the pooled evaluation. Similar results have been reported by Maurya et al. (2026) [20] . Reducing sugar served as a major positive indirect conduit for multiple characters. Substantial positive indirect effects on total yield per plant were expressed through reducing sugar by total sugar (0.5706), length of pedicel (0.2215), primary branches per plant (0.1995), fruit equatorial circumference (0.1776), number of fruits per plant (0.1779), fruit polar length (0.1691), plant height (0.1550), and ascorbic acid (0.1407). Furthermore, plant height acted as a prominent positive indirect contributor to total soluble solids (0.2432), average fruit weight (0.2410), length of pedicel (0.2192), fruit equatorial circumference (0.2134), total sugar (0.1559), ascorbic acid (0.1424), reduc-ing sugar (0.1387), primary branches per plant (0.1358), and fruit polar length (0.1339). Additional positive indirect contributions were mediated through number of fruits per cluster by number of fruits per plant (0.2668), dry matter content (0.2234), fruit polar length (0.1738), primary branches per plant (0.1355), and length of calyx (0.1086), as well as through average fruit weight by total soluble solids (0.2024), fruit equatorial circumference (0.1730), length of calyx (0.1695), non-reducing sugar (0.1590), and plant height (0.1529). On the other hand, marked negative indirect effects on total yield per plant were registered through total sugar (TS) by length of pedicel (-0.2391), fruit polar length (-0.1937), fruit equatorial circumference (-0.1916), number of fruits per plant (-0.1911), primary branches per plant (-0.1818), plant height (-0.1604), ascorbic acid (-0.1530), and average fruit weight (-0.1508). Negative indirect influences were also mediated through days to first fruit harvest by number of fruits per cluster (-0.2184), fruit polar length (-0.1999), and days to 50% flowering (-0.1116). Additionally, dry matter content exerted adverse indirect contributions through number of fruits per cluster (-0.1733), number of fruits per plant (-0.1632), and fruit polar length (-0.1155), while total soluble solids (TSS) contributed negatively through average fruit weight (-0.1509) and plant height (-0.1151). The results are in confirmation with the findings of Yadav et al. (2018) [21] , Chithra et al. (2020) [22] , Gangadhara et al. (2023) [18] , and Jakhwal et al. (2024) [11] .

Conclusion

The phenotypic and genotypic path coefficient analyses highlighted the primary role of reducing sugar, plant height, number of fruits per cluster, average fruit weight, and fruit polar length as key drivers of total fruit yield per plant in brinjal. Furthermore, reducing sugar, plant height, and fruits per cluster emerged as major indirect pathways through which associated morphological and biochemical attributes contribute to overall productivity. Therefore, an integrated selection strategy focusing simultaneously on these essential traits provides a highly effective and reliable approach for accelerating genetic gain and developing high-yielding brinjal cultivars in future breeding programs. .000 NPB -0.0479 0.1358 0.0864 0.1291 -0.0059 -0.0096 0.0492 0.0462 0.0141 -0.0789 0.1355 -0.0106 0.1995 0.0050 -0.1818 -0.000 FPL -0.1014 0.1339 0.0359 0.3104 -0.0090 -0.0231 0.0964 0.0769 0.0387 -0.0636 0.1738 -0.0247 0.1691 0.0328 -0.1937 -0.000 FEC -0.0253 0.2134 0.0167 0.0913 -0.0306 -0.0081 0.0037 0.1730 0.0383 -0.0440 -0.0140 -0.0655 0.1776 0.0246 -0.1916 -0.000 NFP -0.0697 0.0625 0.0252 0.2179 -0.0075 -0.0329 0.0813 0.0463 0.0225 -0.0490 0.2668 -0.0097 0.1779 0.0252 -0.1911 -0.000 DFFH 0.1173 -0.0353 -0.0284 -0.1999 0.0008 0.0179 -0.1498 -0.0935 -0.0411 0.0386 -0.2184 0.0341 -0.1215 -0.0369 0.1563 0.000 AFW -0.0378 0.2410 0.0119 0.0710 -0.0158 -0.0045 0.0417 0.3362 0.0807 -0.0578 0.0624 -0.1509 0.0999 0.0462 -0.1508 -0.000 LC -0.0615 0.0983 0.0076 0.0750 -0.0073 -0.0046 0.0385 0.1695 0.1602 -0.0071 0.1086 -0.1044 0.0513 0.0150 -0.0650 -0.000 LP -0.0206 0.2192 0.0382 0.1105 -0.0075 -0.0090 0.0324 0.1088 0.0063 -0.1786 0.1033 -0.0604 0.2215 0.0323 -0.2391 -0.000 NFPC -0.0507 -0.0087 0.0270 0.1246 0.0010 -0.0203 0.0756 0.0484 0.0402 -0.0426 0.4329 -0.0663 0.0642 0.0219 -0.0860 0.000 TSS 0.0127 0.2432 0.0037 0.0306 -0.0080 -0.0013 0.0204 0.2024 0.0668 -0.0430 0.1145 -0.2506 0.1118 0.0314 -0.1380 -0.000 RS -0.0092 0.1387 0.0291 0.0886 -0.0092 -0.0099 0.0307 0.0567 0.0139 -0.0668 0.0469 -0.0473 0.5921 0.0028 -0.5254 -0.000 NRS -0.0391 0.0772 0.0044 0.1044 -0.0077 -0.0085 0.0565 0.1590 0.0246 -0.0592 0.0971 -0.0806 0.0170 0.0977 -0.1400 -0.000 TS -0.0181 0.1559 0.0288 0.1103 -0.0108 -0.0115 0.0429 0.0930 0.0191 -0.0783 0.0683 -0.0634 0.5706 0.0251 -0.5452 -0.000 AC -0.0299 0.1424 0.0114 0.1306 -0.0124 -0.0074 0.0220 0.0955 0.0349 -0.0599 0.0292 -0.0577 0.1407 0.0235 -0.1530 -0.000 DMC -0.0394 0.0518 0.0236 0.1068 -0.0008 -0.0160 0.0423 0.0069 0.0414 -0.0090 0.2234 -0.0025 0.0146 -0.0141 0.0068 0.000 Residual effect = 0.258; *, ** significant at 5% and 1% levels, respectively

Acknowledgement

AcknowledgementThe authors gratefully acknowledge the Professors of the Department of Horticulture, School of Agricultural Sciences and Technology, Babasaheb Bhimrao Ambedkar University (A Central University), Lucknow, UP, for sharing their pearls of wisdom with us during the course of this research and for providing insight and expertise that greatly assisted the research. We would also like to show our gratitude to the IIVR, Varanasi, U.P., for providing the research material for the research work.

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21. How to cite this article: Mitra DS, Kumar S, Yadav G, Kumar Meena D, Kumar Rawat S, Kumar Pal R, et al. Evaluating direct and indirect pathways of essential yield-attributing traits for crop improvement in brinjal (Solanum melongena L.). International Journal of Advanced Biochemistry Research. 2026;SP10(10):635-641. doi: https://www.doi.org/10.33545/26174693.20