Digenic Interactions on Yield in Yardlong Bean: A Generation Mean Analysis

June 2025, Volume 1, Issue I. doi: 10.5281/zenodo.15684703 Digenic Interactions on Yield in Yardlong Bean: A Generation Mean Analysis Lovely B*. Kerala Agricultural University Radhadevi D.S Kerala Agricultural University Vijayaraghava Kumar Kerala Agricultural University Abstract Vegetable cowpea [Vigna unguiculata ssp. sesquipedalis (L.) Verdc.] is a distinct form of cowpea cultivated in southern Asia and the Far East for its immature pods. Six parameter generation mean analysis of three cowpea crosses revealed complex gene action for several yield-related traits. Significant scale tests and epistasis indicated the inadequacy of the simple additive-dominance model, underscoring the role of non-allelic interactions in trait inheritance. Additive × additive, additive × dominance, and dominance × dominance effects were observed for traits such as pod length, pod yield per plant, pods per plant, and root weight. The presence of duplicate and complementary epistasis suggests that hybridization followed by selection in segregating generations would be effective for improving these traits. Traits like pod breadth, seeds per pod, and 100-seed weight, which lacked significant epistasis, can be improved using additive-dominance models. Recombination breeding is recommended for enhancing pod yield and pod weight. Keywords: vegetable cowpea, non-allelic interaction, duplicate and complementary epistasis, scale values, genetic components. 2Digenic Interactions on Yield in Yardlong Bean: A Generation Mean Analysis 1. Introduction The yardlong bean is one of the most important leguminous vegetables in Asia. Also known as the asparagus bean, string bean, snake bean, or snake pea, it was originally cultivated in West Africa and is now widely grown throughout Southeast Asia—including Malaysia, the Philippines, Indonesia, and Thailand—where it can be cultivated year-round. In India, it has been known since Vedic times (Benchasri et al. 2012). Typically harvested while still young, the yardlong bean is consumed as a green vegetable. It is an annual plant characterized by rapid growth, especially when supported by a trellis. Both tall and short climbing types exist. A member of the Fabaceae family, the plant features twining, delicate stems with a tenacious root system. It blooms in mid-summer, producing pairs of large white or purple flowers. Once pollinated, these flowers develop into slender, dark green beans that can grow up to 12 inches in just a few days. Mature beans can reach lengths of up to three feet, turning pale green and swelling as the red or black seeds ripen. The yardlong bean also contributes to soil fertility by fixing atmospheric nitrogen through nodules on its roots. It is often referred to as the “poor man’s meat” because its pods are not only rich in protein (23–32% of seed weight) but also contain essential amino acids like lysine and tryptophan, as well as significant levels of folic acid, vitamin B, and other critical micronutrients (Peyrano et al. 2016). As such, it serves as a key dietary staple for many of the poorest populations in developing countries. Despite its nutritional and agricultural importance, relatively little breeding work has been conducted on this crop. The development of high-yielding, stress-tolerant varieties could significantly boost its cultivation and productivity. However, as a predominantly self-pollinated crop, studies on gene action in yardlong bean remain limited. This study aims to identify gene action governing yield-related traits, which will help inform new breeding strategies to enhance crop improvement efforts. 2. Materials and methods The genetic material used in the present study consisted of hybrid (𝐹1) plants derived from three promising crosses, along with their six respective parents. The selected parental inbred lines were chosen based solely on differences in yield-related traits. Three single-cross 𝐹1 hybrids were developed using parents with contrasting characteristics. The three most promising hybrids, based on yield performance and disease resistance from a previous study, were selected for further evaluation. The 𝐹1hybrids were backcrossed to their respective parents to generate backcross (BC) generations. Simultaneously, the 𝐹1hybrids were self-pollinated to produce the corresponding 𝐹2populations. Generation mean analysis was conducted using eighteen populations in total: the three 𝐹1s, their six parents, six backcross generations, and three 𝐹2populations. The experiment was laid out in a randomized block design (RBD) with three replications in the College of Agriculture, Vellayani during Summer 2004. Standard crop management practices were followed throughout the study. Observations on yield and yield-related traits were recorded from 10 plants each for the 𝐹1, parent, and backcross generations. For the 𝐹2populations, data were collected from 30 plants per cross. Journal of Sustainable Technology in Agriculture 3 2.1. Generation Mean Analysis The six-parameter model developed by Hayman (Hayman 1958) was used for generation mean analysis. The four scaling tests (𝐴,𝐵,𝐶, and 𝐷) were determined according to the method suggested by Mather (Mather 1949). These different scales are computed using simple linear combinations as given in Equation 1to Equation 4. 𝐴 = 2𝐵1− 𝐹1− 𝑃1= 0 (1) 𝐵 = 2𝐵2− 𝐹1− 𝑃2= 0 (2) 𝐶 = 4𝐹2− 2𝐹1− 𝑃1− 𝑃2= 0 (3) 𝐷 = 4𝐹3− 2𝐹2− 𝑃1− 𝑃2= 0 or 𝐷 = 2𝐹2− 𝐵2− 𝐵1(4) Where 𝑃1,𝑃2,𝐹1,𝐹2,𝐵1, and 𝐵2are means of different generations, respectively. The variances of the quantities 𝐴,𝐵,𝐶, and 𝐷were calculated from the respective variances of different generations as given from Equation 5to Equation 8. 𝑉𝐴= 4𝑉𝐵1+ 𝑉𝐹1+ 𝑉𝑃1(5) 𝑉𝐵= 4𝑉𝐵2+ 𝑉𝐹1+ 𝑉𝑃2(6) 𝑉𝐶= 16𝑉𝐹2+ 4𝑉𝐹1+ 𝑉𝑃1+ 𝑉𝑃2(7) 𝑉𝐷= 16𝑉𝐹3+ 4𝑉𝐹2+ 𝑉𝑃1+ 𝑉𝑃2(8) Where, 𝑉𝑃1is the variance of the individuals within the 𝑃1family; 𝑉𝑃1is the variance of 𝑃1 (mean of the 𝑃1family); and 𝑉𝑃1=𝑉𝑃1 𝑁, where 𝑁is the number of individuals observed in the 𝑃1family. The standard error of 𝐴,𝐵,𝐶, and 𝐷is calculated by taking the square root of their respective variances. The corresponding 𝑡values are computed by dividing the values of 𝐴,𝐵,𝐶, and 𝐷by their respective standard errors. Significance of any of the four scales indicates the inadequacy of the additive-dominance model and the presence of epistasis. If the calculated 𝑡values are found to be significant, the presence of specific types of epistasis is confirmed. The significance of either one or both of the 𝐴and 𝐵scales indicates the presence of all three types of digenic interaction, namely additive × additive, additive × dominance, and dominance × dominance. The significance of scale 𝐶indicates the presence of dominance × 4Digenic Interactions on Yield in Yardlong Bean: A Generation Mean Analysis dominance type of non-allelic interaction, while the significance of scale 𝐷denotes additive × additive type of gene action. When both 𝐶and 𝐷scales are significant, it suggests the presence of both additive × additive and dominance × dominance types of gene interaction. 2.2. Estimation of gene effects Significance of any of the scales 𝐴,𝐵,𝐶and 𝐷will indicate the presence of epistatic interaction or digenic interactions. Hayman and Jinks and Jones gave a 6 parameter model for the estimation of various genetic components. The six genetic parameters were estimated using Equation 9to Equation 14. 𝑚 = 𝐹2(9) 𝑑 = 𝐵1− 𝐵2(10) ℎ = 𝐹1− 4𝐹2−𝑃1 2−𝑃2 2+ 2𝐵1+ 2𝐵2(11) 𝑖 = 2𝐵1+ 2𝐵2− 4𝐹2(12) 𝑗 = 𝐵1−𝑃1 2− 𝐵2+𝑃2 2(13) 𝑙 = 𝑃1+ 𝑃2+ 2𝐹1+ 4𝐹2− 4𝐵1− 4𝐵2(14) Where 𝑚= mean; 𝑑= additive effect; ℎ= dominance effect; 𝑖= additive x additive gene interaction; 𝑗= additive x dominance gene interaction; 𝑙= dominance x dominance gene interaction. The variances of the six genetic parameters were calculated using Equation 15 to Equation 20 (𝑚) = 𝑉𝐹2(15) 𝑉 (𝑑) = 𝑉𝐵1+ 𝑉𝐵2(16) 𝑉 (ℎ) = 𝑉𝐹1+ 16𝑉𝐹2+𝑉𝑃1 4+𝑉𝑃2 4+ 4𝑉𝐵1+ 4𝑉𝐵2(17) 𝑉 (𝑖) = 4𝑉𝐵1+ 4𝑉𝐵2+ 16𝑉𝐹2(18) 𝑉 (𝑗) = 𝑉𝐵1+𝑉𝑃1 4+ 𝑉𝐵2+𝑉𝑃2 4(19) Journal of Sustainable Technology in Agriculture 5 𝑉 (𝑙) = 4𝑉𝑃1+ 4𝑉𝑃2+ 4𝑉𝐹1+ 16𝑉𝐹2+ 16𝑉𝐵1+ 16𝑉𝐵2(20) 3. Results Generation mean analysis is a statistical technique used to estimate the components of variance and determine the predominant type of gene action controlling important traits in a crop species. This analysis assists in selecting appropriate breeding strategies for the improvement of various quantitative traits. Generation mean analysis was conducted for three cowpea crosses: • Cross 1: VS86 × VS132 • Cross 2: Kozhicode Local-2 × Thiruvananthapuram Local-12 • Cross 3: Thiruvananthapuram Local-9 × Thiruvananthapuram Local-12 The mean values of the six generations (𝑃1,𝑃2,𝐹1,𝐹2,𝐵1, and 𝐵2) for each cross are presented in Table 1. Among them, the 𝐹1of Cross 3 flowered the earliest (38.4 days), while Cross 1 was harvested the earliest (58.1 days). The 𝐹1of Cross 2 exhibited the highest pod yield per plant (454.91 g), whereas the 𝐵2generation of Cross 1 recorded the maximum yield overall (485.67 g). The scale values and genetic component estimates for the various traits across the three crosses are shown in Table 2and Table 3. The estimated mean effect (𝑚) was highly significant for traits such as days to flowering, pod length, pod breadth, pods per plant, pod yield per plant, and root weight across all crosses, indicating that these traits are quantitatively inherited. As shown in Table 3, significant negative dominant effects (ℎ) were observed for pod length and pod yield per plant, suggesting that these traits are more prominently expressed in homozygous individuals. Cross Gen 𝑋1𝑋2𝑋3𝑋4𝑋5𝑋6𝑋7𝑋8𝑋9𝑋10 𝑋11 𝑋12 Cross 1 F1 39.90 50.43 2.34 21.20 3.12 23.18 356.84 20.23 58.10 3.10 15.27 35.50 F2 44.10 45.05 2.18 16.80 2.70 25.75 481.53 19.05 59.00 3.25 19.76 39.40 P1 47.07 38.56 2.30 11.73 2.15 21.88 250.93 19.73 59.60 2.40 14.33 43.20 P2 48.27 50.75 2.30 21.69 2.94 14.68 298.07 21.27 57.80 3.60 19.34 30.20 B1 45.27 41.20 2.23 19.68 2.66 23.73 477.32 18.93 59.13 2.73 18.93 39.00 B2 45.40 47.87 2.19 21.07 2.45 19.92 485.67 19.73 60.27 3.53 17.38 39.53 Cross 2 F1 41.53 53.97 2.68 21.81 3.14 28.51 454.91 19.80 60.10 3.40 17.60 34.60 F2 43.90 50.91 2.26 15.51 2.75 29.91 465.82 18.70 58.45 3.05 19.36 30.80 P1 57.20 48.37 2.20 18.83 2.58 10.23 293.54 18.00 58.40 3.20 18.31 40.20 P2 44.00 31.89 2.17 9.40 2.31 17.99 264.54 19.73 60.80 3.00 17.92 22.00 B1 52.00 49.87 2.37 20.60 2.77 21.73 478.08 18.60 60.27 3.40 18.18 35.80 B2 44.20 43.13 2.09 14.86 2.66 24.68 376.18 18.60 60.27 2.93 14.34 33.60 6Digenic Interactions on Yield in Yardlong Bean: A Generation Mean Analysis Cross Gen 𝑋1𝑋2𝑋3𝑋4𝑋5𝑋6𝑋7𝑋8𝑋9𝑋10 𝑋11 𝑋12 Cross 3 F1 38.40 54.57 2.82 22.14 3.35 20.70 376.61 20.10 61.20 2.60 15.19 36.50 F2 44.85 52.52 2.69 20.59 2.55 27.25 484.19 18.85 61.20 2.55 18.63 38.60 P1 48.00 45.73 2.60 19.65 2.16 20.40 201.47 17.27 61.40 3.80 17.14 41.00 P2 42.53 50.73 2.61 15.64 2.91 15.81 255.33 20.73 57.80 2.80 14.30 30.40 B1 45.00 49.75 2.71 20.40 2.21 25.37 472.86 18.20 60.00 3.47 19.15 38.87 B2 42.80 51.25 2.54 16.60 2.79 23.67 400.47 18.93 59.20 2.53 17.64 38.13 Table 1: Generation mean values of the three crosses in yardlong bean} In Table 1: Gen= Generation, 𝑋1= Days to flowering, 𝑋2= Pod length (cm), 𝑋3= Pod breadth (cm), 𝑋4= Pod weight (g), 𝑋5= Pods per cluster, 𝑋6= Pods per plant, 𝑋7= Pod yield per plant (g), 𝑋8= Seeds per pod, 𝑋9= Days to first harvest, 𝑋10 = Primary branches per plant, 𝑋11 = 100-seed weight (g), 𝑋12 = Root weight (g). In Table 2:𝑋1= Days to flowering, 𝑋2= Pod length (cm), 𝑋3= Pod breadth (cm), 𝑋4= Pod weight (g), 𝑋5= Pods per cluster, 𝑋6= Pods per plant, 𝑋7= Pod yield per plant (g), 𝑋8= Seeds per pod, 𝑋9= Days to first harvest, 𝑋10 = Primary branches per plant, 𝑋11 = 100-seed weight (g), 𝑋12 = Root weight (g). Values marked with ** are significant at 1% level (𝑝 < 0.01) In Table 3:𝑋1= Days to flowering, 𝑋2= Pod length (cm), 𝑋3= Pod breadth (cm), 𝑋4= Pod weight (g), 𝑋5= Pods per cluster, 𝑋6= Pods per plant, 𝑋7= Pod yield per plant (g), 𝑋8= Seeds per pod, 𝑋9= Days to first harvest, 𝑋10 = Primary branches per plant, 𝑋11 = 100-seed weight (g), 𝑋12 = Root weight (g). 𝑚= mean, 𝑑= additive effect, ℎ= dominance effect, 𝑖= additive × additive, 𝑗 = additive × dominance, 𝑙= dominance × dominance Journal of Sustainable Technology in Agriculture 7 Character A B C D 𝑋19.22 12.64** 15.61 -3.12 𝑋22.41 2.50 44.87** 19.98** 𝑋321.63** 3.14 2215.00** -1.31 𝑋4-0.01 -0.01 0.01 0.01 𝑋50.14 0.04 0.83 0.33 𝑋618.15** 24.75** 79.66** 18.38 𝑋752.10** 106.67 422.48** 131.86** 𝑋80.88 0.62 1.17 -0.16 𝑋91.23 5.34 6.62 0.02 𝑋10 0.59 0.17 0.86 0.06 𝑋11 0.59 0.79 5.31 1.97 𝑋12 3.32 5.15 84.94** 38.23** (a) Cross 1 Character A B C D 𝑋115.81** 4.03 23.75** 1.95 𝑋21.72 13.30 46.84** 15.91** 𝑋33.88 20.15 35.12** 5.54 𝑋40.02 0.03 0.24 0.09 𝑋50.13 0.13 0.83 0.29 𝑋620.79** 2.69 168.67** 72.60** 𝑋7149.71** 59.86** 394.68** 92.56** 𝑋80.65 0.24 0.77 -0.06 𝑋9-0.34 -0.66 16.01 8.50 𝑋10 0.08 0.55 1.15 0.26 𝑋11 0.84 2.17 3.89 0.44 𝑋12 26.19** 33.31** 90.80** 15.65 (b) Cross 2 Character A B C D 𝑋118.89** 1.28 25.83** 2.83 𝑋20.34 1.27 20.39** 9.39 𝑋35.04 9.54 22.37** 3.90 𝑋4-0.04 -0.06 -0.03 0.03 𝑋50.07 0.08 0.98 0.42 𝑋666.42** 33.77** 113.43** 6.62 𝑋7658.19** 469.98** 1332.00** 101.92 𝑋80.68 0.75 4.43 1.50 𝑋9-0.31 2.13 1.24 -0.29 𝑋10 0.10 0.10 0.99 0.40 𝑋11 1.29 0.43 3.97 1.12 𝑋12 2.65 5.21 15262.00** 72.38** (c) Cross 3 Table 2: Estimates of scaling and genetic components (A to D) for traits 𝑋1to 𝑋12 in three yardlong bean crosses. 8Digenic Interactions on Yield in Yardlong Bean: A Generation Mean Analysis Trait 𝑚 𝑑 ℎ 𝑖 𝑗 𝑙 𝑋15.19 -0.58 5.45 6.24 -1.71 -28.10 𝑋211.74 -0.36 -39.95 -39.96 -0.05 35.05 𝑋36.15 8.84 2.00 2.63 9.24 -27.40 𝑋40.02 -0.01 -0.06 -0.02 -0.01 0.04 𝑋50.21 0.05 -0.66 -0.66 0.05 0.48 𝑋623.79 0.80 -38.27 -36.76 -3.30 -6.14 𝑋7113.33 -30.32 -271.71 -263.71 -27.29 104.96 𝑋80.45 0.13 0.33 0.32 0.13 -1.83 𝑋92.10 -1.81 0.05 -0.04 -2.05 -6.53 𝑋10 0.39 0.21 -0.28 -0.13 0.21 -0.63 𝑋11 1.48 -0.10 -4.00 -3.94 -0.10 2.56 𝑋12 24.04 0.28 -75.97 -76.46 -0.92 67.98 (a) Cross 1 Trait 𝑚 𝑑 ℎ 𝑖 𝑗 𝑙 𝑋17.19 5.17 -5.56 -3.91 5.89 -15.93 𝑋212.27 -5.73 -31.16 -31.81 -5.79 16.79 𝑋39.42 -8.53 -11.07 -11.08 -8.14 -12.95 𝑋40.07 -0.02 -0.21 -0.19 -0.01 0.14 𝑋50.21 0.01 -0.58 -0.57 0.01 0.33 𝑋649.66 7.54 -134.56 -145.19 9.05 121.71 𝑋7104.44 47.98 -187.63 -185.11 44.92 -24.46 𝑋80.41 0.13 0.40 0.12 0.21 -1.01 𝑋95.25 0.01 -16.12 -17.01 0.16 18.01 𝑋10 0.55 -0.36 -0.56 -0.52 -0.24 -0.11 𝑋11 1.06 -0.63 -0.82 -0.88 -0.66 -2.14 𝑋12 25.16 -4.48 -33.35 -31.31 -3.56 -28.19 (b) Cross 2 Trait 𝑚 𝑑 ℎ 𝑖 𝑗 𝑙 𝑋17.03 8.51 -5.92 -5.66 8.81 -14.51 𝑋25.67 -0.40 -19.23 -18.78 -0.47 17.17 𝑋36.54 -2.05 -6.60 -7.79 -2.25 -6.80 𝑋40.03 -0.01 -0.13 -0.06 0.01 0.16 𝑋50.25 -0.01 -0.82 -0.83 -0.01 0.68 𝑋629.19 16.38 -13.57 -13.25 16.32 -86.94 𝑋7477.49 -7.18 -322.17 -203.83 94.11 -924.33 𝑋81.33 -0.04 -2.86 -3.00 -0.04 1.57 𝑋91.40 -0.96 1.93 0.59 -1.22 -2.41 𝑋10 0.45 0.01 -0.71 -0.79 0.01 0.60 𝑋11 1.06 0.38 -2.28 -2.24 0.43 0.52 𝑋12 40.04 -1.60 -142.43 -144.76 -1.28 136.91 (c) Cross 3 Table 3: : Estimates of genetic components of the three crosses for the various characteristics Journal of Sustainable Technology in Agriculture 9 Discussion The significance of scales 𝐴and 𝐵for most traits indicates that the simple additive-dominance model is inadequate for explaining their inheritance, as reported by Thakare et al. (2016) and Kudiabor et al. (2023). Non-allelic interactions, alongside additive and dominance components, were observed in the expression of several traits, similar to the findings of Edematie et al. (2021) and Akombo et al. (2021). Significant additive × additive (𝑖) interactions were found for pod length, pods per plant, pod yield per plant, and root weight, suggesting complementary or duplicate epistasis. Non-allelic interactions were also evident in traits like days to first flowering. Here, additive effects were highly significant, and additive × dominance (𝑗) interactions were also observed. Dominance × dominance (𝑙) interactions acted in a favorable negative direction in all hybrids. Similar epistatic interactions for early flowering and duplicate epistasis for traits like days to 90% pod maturity in cowpea were reported by Patel et al. (2013), Thakare et al. (2016), and Owusu et al. (2022). These findings imply that earliness in cowpea could be improved through hybridization followed by the selection of promising recombinants in later generations, particularly in crosses governed by duplicate epistasis. The significance of scales 𝐶and 𝐷for pod length further supports the involvement of dominance × dominance and additive × additive interactions in this trait. Significant additive (𝑑) and dominance (ℎ) effects for pod length were also reported by Rashwan (2010) and Thakare et al. (2013). Among epistatic interactions, dominance × dominance (𝑙), additive × additive (𝑖), and additive × dominance (𝑗) were observed in different crosses. In the case of pod weight, both dominance effects and additive × additive interactions were significant but acted in a negative direction. However, the positive significance of dominance × dominance interactions suggests that hybridization followed by selection would be an effective strategy for improving this trait. All three types of digenic interactions (𝑖,𝑗,𝑙) were observed for pods per plant. While additive × dominance (𝑗) was positive and significant, both dominance (ℎ) and additive × additive (𝑖) effects acted in the negative direction. The presence of non-allelic interactions for this trait aligns with the findings of Thakare et al. (2016) and Edematie et al. (2021). Significant positive dominance (ℎ) and dominance × dominance (𝑙) interactions suggest the presence of complementary epistasis. In contrast, the negative significance of dominance × dominance (𝑙) for pod yield per plant implies limited potential for improvement through heterosis breeding for this trait. The direction of dominance and dominance × dominance interactions indicated duplicate gene action in the expression of traits such as pod weight, pod breadth, pods per cluster, seeds per pod, root weight per plant, and days to first harvest. Dominance was found to play a role in all traits, especially pod length, as reported by Santos et al. (2024) and Pallavi et al. (2019). Both additive × additive and dominance × dominance interactions were significant for root weight per plant, while the insignificance of all four scale tests (𝐴,𝐵,𝐶,𝐷) for traits like pod breadth, pods per cluster, seeds per pod, days to first harvest, primary branches per plant,