The augmented design concept, a methodology that emphasizes two primary assessments, the evaluation of line variance and the comparison between lines and checks [56, 57], is not just significant but highly effective. This approach is predicated on the expectation that the lines developed will exhibit substantial diversity and distinctiveness compared with the check varieties, thereby enhancing the effectiveness of line selection. The augmented design concept, in particular, allows for a comprehensive evaluation of the diversity and distinctiveness of the developed lines, which is crucial in the context of maize breeding and production. According to the results of this study, nearly all growth characteristics, except the male flowering age, anthesis‒silking interval (ASI), ear diameter, and number of rows of seeds per ear, satisfy the criteria for character assessment in the augmented design. These four characteristics exhibited insignificant responses to line diversity, a finding corroborated by Akfindarwan et al. [55] and Makmur et al. [26] in their evaluations of maize lines in the S2 and S3 generations. Both studies reported no significant effects of line diversity on these characteristics. This suggests that evaluating TS is sufficiently robust to exclude these four characteristics from further analysis. Therefore, all growth characteristics, except for male flowering age, ASI, ear diameter, and the number of seed rows per ear, can be incorporated into subsequent correlation and cross-sectional analyses.
Correlation and path analyses are critical for determining selection criteria and represent systematic techniques for identifying potential criteria that support production [19, 38]. Various studies have documented this approach, including those by Baye et al. [58], Khan et al. (2022), Thuy et al. [59], and Anshori et al. [38], with similar methodologies applied to maize [19, 60, 61]. The results of these analyses indicate that ear weight and grain yield serve as secondary selection criteria that complement the potential of seed weight per plant. The efficacy of these criteria in maize evaluation has been demonstrated by Mendes-Moreira et al. [62], Sah et al. [63], Mousavi and Nagy [64], and Dermail et al. [65], highlighting their significant regression effects in determining yield potential [62, 64]. Consequently, combining ear weight and seed yield with seed weight per ear was effective in the validation of S4 TS maize.
The evaluation of the TS against the established selection criteria involves a significant transformation. The three selection criteria were converted into a ratio, providing a methodological solution for comparisons on the basis of morphometric principles [66]. This ratio concept aligns with the comparative approach used in this study. Compared with self-pollinated transgressive lines, maize hybrid varieties generally exhibit superior growth potential [26, 37, 46]. This disparity renders direct comparisons between the two unfair. Hence, the three selection criteria were converted into a ratio representing the general potential of the ear.
In this study, the comparative ratio was focused primarily on ear length. Generally, ratio comparisons can be performed through volume measurements [67, 68], where the ear's length and diameter serve as the basis of the ratio. However, in this analysis, ear diameter exhibited an insignificant response to the segregant lines. In contrast, ear length showed a significant response, suggesting that ear length is the most appropriate metric for ratio comparisons among the tested genotypes. The results indicate that certain segregant lines demonstrated superior ratio potential compared with some comparator varieties. This contrasts with the performance of the three selection criteria before transformation, where the comparator varieties generally outperformed the lines regarding ear potential. However, it is crucial to note that relying solely on the ratio for assessment is ineffective without considering the variability within lines. This aligns with previous findings indicating that transgressive lines should be evaluated based on intraline variability [38]. Narrow variability within a line indicates that segregants may have reached their homozygous potential [39–41], necessitating the correction of the ratio comparison to a standardized value that accounts for this variation. A high standardized value can reflect strong performance potential and uniformity within a line [26, 38, 55, 65]. The comparison of standardized values to simple ratios reveals significant differences, indicating that uncorrected mean values can lead to misinterpretations [69, 70]. However, further refinement of the standardization process is needed to assess the potential of TS accurately, which could be recommended for developing hybrid maize varieties [38]. Therefore, the potential of TS was standardized and transformed via the best linear unbiased prediction and selection index methodologies
The development of best linear unbiased prediction (BLUP) analysis and selection indices represents a practical methodology for assessing channelization. This approach has been documented in various studies [71–74], including applications in maize research [75–77]. The BLUP concept primarily accounts for potential random effects and the genetic variance of genotypes [73, 78, 79]. The potential random effect is determined in augmented designs relative to the comparison variety [80–82]. This random effect serves as a correction factor for the performance potential of the tested lines within each block. The effectiveness of the BLUP approach in augmented designs has also been corroborated by Molenaar et al. [83], Burgueño et al. [81], and Amaral et al. [82]. In this study, a comprehensive correction was applied to the standardized values of each genotype relative to their best linear unbiased prediction (BLUP) values, enhancing the precision of the evaluation process. The BLUP-derived values were subsequently utilized with a selection index, which was the final component in evaluating the TS. However, before the development of the selection index, the BLUP values were also transformed into standardized values and relative fitness metrics to ensure accurate assessment.
Developing standardized and relative fitness values is crucial for equalizing dimensions across traits and refining the selection process. Although each parameter has been transformed into internal ratios and standardized values, this approach has been applied only within each genotype. Population-wide standardization has not yet been implemented. Such standardization would reveal the potential of a genotype relative to the overall population response, thereby identifying genotypes with greater selection potential than others in the population [38, 84, 85]. The selection process is further refined via roulette wheel selection or the relative fitness approach, which compares the potential of a genotype against the population's highest-performing genotype [86, 87]. However, in this study, the concept was modified using standardized values as fitness benchmarks so that relative fitness only pertains to comparisons between genotypes and the best comparator. This modification aligns with the inherent concept of TS, where TS in cross-pollinated plants is expected to exhibit equal or superior potential to that of their parents or comparators. Thus, the potential of each transgressive segregant line must be corrected relative to the maximum potential of the comparator variety [38–40]. This approach narrows the range of standardized values, making the selection process more stringent than relying on standardized values alone. Consequently, these two approaches serve as intermediate steps preceding index selection.
The assessment based on the selection index concept is intricately linked to the weighting of each selection criterion involved. According to this study, the weight of each selection criterion can be estimated via the direct effect value derived from path analysis. The effectiveness of employing direct effect values as a basis for selection indices has been documented in studies by Sabouri [88], Alsabah et al. [85], and Fadhilah et al. [57], including in maize [18]. However, the direct effect value must be corrected with the determination value. This results in the following relative fitness BLUP-based selection index:
Indeks = 0.83*0.64*BTK + 0.37*0,64*RB + Yield
Indeks = 0.53 BTK + 0.24 RB + yield
Based on the index selection results, lines SG4.27.5, SG2.25.6, SG2.7.14, SG3.10.1, SG4.24.13, CB1.37.14, CB2.23.1, SG2.19.6, SG3.35.12, SG4.11.12, and SG4.41.4 have been identified as potential S4 maize TSs owing to their positive index values. This aligns with Paternelli et al. [84] and Anshori et al. [38], who suggested that a positive index value indicates potential in index-based selection. Among these, four lines exhibit superior potential to the SINHAS variety, an open-pollinated variety with generally lower heterosis than hybrid varieties [5, 6, 16, 20]. Thus, these four lines are anticipated to have substantial potential as hybrid parents. However, further investigation is needed to determine the effectiveness of the selection concept and the potential of the identified TS.
The results from the evaluation of three-way cross hybrids between TS and F1 testers showed promising potential, especially for crosses involving F1 JH 37. This finding indicates that JH 37 is a good tester for assessing the potential of TSs on the basis of the concept of three-way cross-analysis. In addition, the graph between the TSI and TWCI showed a quadratic response pattern with good determination. This is common in cross-pollinated plants, which focus on heterozygous and heterosis patterns and have the potential for inbreeding depression. The action of dominant genes strongly influences the concept of heterosis in cross-pollinated plants. This gene action causes the concept of the two indices' response to be not additive, so it does not follow a linear curve. This differs from self-pollinated plants, dominated by the concept of additive gene action, so the response pattern is relatively linear [16, 20, 30, 89]. On this basis, the concept of transgressive segregation developed in this study can be a good consideration when selecting maize hybrid elders. In addition, the maize crosses SG 3.35.12 X JH37 and CB 2.23.1 X JH37 can also be recommended as promising three-way crosses, and the transgressive segregant CB2.23.1 can be used as a potential parent in the maize hybrid assembly.