The analysis of the variance (ANOVA) revealed significant differences among the genotypes for all traits (Table 2). Mean squares due to cross combinations (Table 3) suggested significant differences for all traits studied which indicated the presence of sufficient variability in the TTC progenies to use in recombination breeding.
Variance based \(( {\stackrel{-}{\text{L}}}_{1\text{i}}+{\stackrel{-}{\text{L}}}_{2\text{i}}-2{\stackrel{-}{\text{L}}}_{3\text{i}})\) epistatic test was done to estimate epistasis and adequacy of the testers. It was significant for all the traits. The level of significance of overall epistasis for all traits suggested the presence of inter-allelic interactions. In addition, the existence of epistasis revealed the importance of both additive and dominance components of variance in the current set of materials, which would have been biassed if the procedure had assumed epistasis was absent (Nehvi et al. 2007). Sood et al. (2007) also reported epistasis for plant height, technical height, 1000-seed weight and biological yield per plant in the linseed. In Indian mustard, Devi et al (2018) found significant epistasis for days to 50% flowering, days to 75% maturity, primary branches per plant, secondary branches per plant, plant height, 1000-seed weight, seed yield per plant and harvest index in a TTC design. The occurrence of significant epistasis for grain yield in soybean reported by Barona et al. 2012.
Further, segregation of the total epistatic interations into additive × additive [i] and additive × dominance [j] together with dominance × dominance [l] type epistasis i.e., [j + 1] type interactions indicated that [i] type epistasis was significant for days to 50% flowering, days to 75% maturity, secondary branches per plant, capsules per plant, 1000-seed weight and aerial biomass per plant. For the remaining traits, non-significant [i] type epistasis indicated that [i] type interaction is relatively trivial component of epistasis. The significant contribution of [i] type component was reported for plant height, technical height, aerial biomass per plant and 1000-seed weight in linseed (Sood et al. 2007), for 50% flowering and days to 75% maturity in mustard (Devi et al. 2018), for panicle length, 1000 grain weight, number of tillers per plant and number of productive tillers per plant in rice (Ivin et al 2021).
Mean sum of squares due to [j + 1] type interactions was significant for all the traits except seed yield per plant. Presence of significant overall epistasis but non-significant [i] type and [j + 1] type interactions for seed yield indicates that it may be due to presence of further higher order interactions as TTC cannot further bifurcate the epistasis and it tells only about the absence or presence of epistasis. In linseed, significance of [j + 1] type of interactions have been reported by Sood et al (2007) for 1000-seed weight, plant height and biological yield per plant. In addition, three traits i.e., capsules per plant, 1000-seed weight and aerial biomass per plant had higher magnitude of [i] type than [j + l] type interactions which highlights fixable component. In self-pollinated crops, breeding programs mainly focus on development of purelines and [i] type epistasis can be one of the most important factor as it is fixable in homozygous condition and it contributes to the preeminence of elite lines. The [j] and [1] types of interactions can be useful for the development of hybrids but these have limited utility in a self-pollinated crop like linseed, where commercial hybrid production is still in the future.
The mean squares due to sums \(( {\stackrel{-}{\text{L}}}_{1\text{i}}+{\stackrel{-}{\text{L}}}_{2\text{i}}+{\stackrel{-}{\text{L}}}_{3\text{i}})\) and differences \(( {\stackrel{-}{\text{L}}}_{1\text{i}}-{\stackrel{-}{\text{L}}}_{2\text{i}})\) were significant for all the traits studied (Table 5) and this gives direct test of significance for D and H component of variation. These findings concur with those of Sood et al. (2007) who found that mean squares due to the sums were significant for seeds per capsule, 1000-seed weight, plant height, technical height, seed yield per plant and harvest index whereas for the mean squares due to differences were significant for seeds per capsule, 1000-seed weight, technical height and biological yield per plant. In maize for most of the traits, significance of mean squares due to the sums and differences has been reported by Pavan et al. 2017.
The D and H component were significant for all the traits studied in linseed (Table 5). This illustrated that both additive and dominance gene actions controlling all the traits but in higher order as epistasis is also present. None of the additive or dominance variance was observed negative. If negative value observed, must be considered as equal to zero for actual value of the component (Searle 1971). The occurrence of both additive and dominant gene actions using the TTC has been reported in different plant species i.e., maize (Ming-Hua et al. 2008, Pawan et al. 2017), mustard (Devi et al. 2018), cabbage (Jabeen and Chadha 2021) and arabidopsis (Kusterer et al. 2007). In comparison to line x tester and diallel where either additive gene action or non-additive gen action reported by most of the earlier worker in the linseed viz., in diallel (Pant and Mishra 2008; Mohammadi et al. 2010; Kumar et al. 2013; Abdel-Moneam 2014; Singh et al. 2016; Kumar et al 2017; Mahto et al. 2019; Sran and Paul 2022) and in line x tester (Bhateria et al. 2006; Reddy et al. 2013). This implies the accuracy of triple test cross mating design for identifying the gene action of quantitative traits. However, greater magnitude of additive variance for most of the traits as compared to dominance variance presented in Table 5 and depicted in Fig. 1, indicates that fixable gene action prevailed.
The average degree of dominance suggests relative importance of both D and H component of genetic variance whereas general combining ability (GCA) and specific combining ability (SCA) effects could not be calculated. The average degree of dominance values were in the range of over-dominance [(H/D)1/2> 1] for plant height and 1000-seed weight indicates the presence of non-additive genetic variance (Table 5). The degree of dominance was partial [(H/ D)1/2< 1] for aerial biomass per plant, primary branches per plant, seed yield per plant, secondary branches per plant, capsules per plant, days to 50% flowering, harvest index, seeds per capsule, days to 75% maturity and technical height indicates the predominance of additive gene action implying that selection may be effective in improving these traits. Moreover, for days to 50% flowering, days to 75% maturity, secondary branches per plant, capsules per plant and aerial biomass per plant both [i] type as well as [j + l] type interactions were significant which means additive effect can be increase in the presence of epistasis (Hallander and Waldmann 2007). The results for seed yield per plant and most of its attribute traits is disagreeing with the previous researchers who have reported a prevalence of non-additive gene action in diallel and line x tester mating designs for seed yield and most of its components (Kumar et al. 2000; Patel et al. 2000; Abo El-Komsan et al. 2003; Abdel-Moneam 2014; Singh et al. 2016; Sharma et al. 2017; Mahto et al. 2019. However the results in this study shows similarities with the finding of Sood et al. (2007). In order to find the direction of dominance and types of genes exhibiting dominance, correlation coefficient was used. In this study r was non-significant for the traits for which dominance variance was significant and higher than the additive variance indicating that the alleles with decreasing and increasing effects seems to be recessive and dominant to the equal degree.
Besides this, the data were used to perform combining ability analysis using the approach of Kempthorne (1957) including F1 tester and L3i progeny families. It has been widely utilized to determine potential cross combinations and parents on the basis of their combining ability effects to get maximal genetic gain in advance generations for desirable traits. On the basis of GCA effects, KL-285 was good general combiner for seed yield (Table 6 and Fig. 2). Based on SCA effects, Hermis × JRF-1 was the promising cross combination for seed yield (Table 7 and Fig. 2).