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Summary Heterosis, or hybrid vigour, is a predominant phenomenon in plant genetics, serving as the basis of crop hybrid breeding, but the causative loci and genes underlying heterosis remain unclear in many crops. Here, we present a large‐scale genetic analysis using 5360 offsprings from three elite maize hybrids, which identifies 628 loci underlying 19 yield‐related traits with relatively high mapping resolutions. Heterotic pattern investigations of the 628 loci show that numerous loci, mostly with complete–incomplete dominance (the major one) or overdominance effects (the secondary one) for heterozygous genotypes and nearly equal proportion of advantageous alleles from both parental lines, are the major causes of strong heterosis in these hybrids. Follow‐up studies for 17 heterotic loci in an independent experiment using 2225 F2 individuals suggest most heterotic effects are roughly stable between environments with a small variation. Candidate gene analysis for one major heterotic locus (ub3) in maize implies that there may exist some common genes contributing to crop heterosis. These results provide a community resource for genetics studies in maize and new implications for heterosis in plants.

Copy number variation (CNV) is a major source of genetic variation and often contributes to phenotypic variation in maize. The duplication at the 27-kDa γ-zein locus ( qγ27 ) is essential to convert soft endosperm into hard endosperm in quality protein maize (QPM). This duplication is unstable and generally produces CNV at this locus. We conducted genetic experiments designed to directly measure DNA rearrangement frequencies occurring in males and females of different genetic backgrounds. The average frequency with which the duplication rearranges to single copies is 1.27 × 10 −3 and varies among different lines. A triplication of γ27 gene was screened and showed a better potential than the duplication for the future QPM breeding. Our results highlight a novel approach to directly determine the frequency of DNA rearrangements, in this case resulting in CNV at the qγ27 locus. Furthermore, this provides a highly effective way to test suitable parents in QPM breeding. Liu et al. measured the frequency of DNA rearrangements at the qγ27 locus and linked it to the variation in the maize endosperm texture. Through a series of genetic and RNAi experiments, they were able to identify the mechanism to improve maize’s nutritive value.

Heterosis, a key technology in modern commercial maize breeding, is limited by the narrow genetic base which hinders breeders from developing superior hybrid varieties. By integrating big data and functional genomics technologies, it becomes possible to create new super maize inbred lines that resemble hybrid varieties through the aggregation of multiple QTL parental advantage loci. In this study, we utilized a combination of resequencing and field selfing selection methods to develop three pyramiding QTL lines (PQLs) (PQL4, 6, and 7), each containing 15, 12, and 12 QTL loci respectively. Among the three PQLs, PQL6 (266.78 cm/119.39 cm) demonstrated hybrid-like performance comparable to the hybrid (276.96 cm/127.02 cm) ( P  < 0.05). Testcross between PQL6 and the parental lines revealed that PQL6 had accumulated and fixed advanced parent alleles for superior traits in plant and ear height. The significant increase in PQL6 plant height primarily resulted from the aggregation of two major effective QTL ( qEH2-1 and qEH8-1 on chromosomes 2 and 8), indicating that the aggregation of major effective QTL is a key selection indicator. Furthermore, PQL6 exhibited slow vegetative growth but experienced a rapid height increase during the reproductive stage, particularly in the 1–2 weeks before flowering, when its growth rate accelerated and surpassed that of the hybrid varieties. Our study explored the time period and key parameter indicators for molecular breeding of maize, providing a theoretical concept and practices for further complex multi-trait design and aggregation.

Copy number variation (CNV) is a major source of genetic variation and often contributes to phenotypic variation in maize. The duplication at the 27-kDa γ-zein locus (qγ27) is essential to convert soft endosperm into hard endosperm in quality protein maize (QPM). This duplication is unstable and generally produces CNV at this locus. We conducted genetic experiments designed to directly measure DNA rearrangement frequencies occurring in males and females of different genetic backgrounds. The average frequency with which the duplication rearranges to single copies is 1.27 × 10 and varies among different lines. A triplication of γ27 gene was screened and showed a better potential than the duplication for the future QPM breeding. Our results highlight a novel approach to directly determine the frequency of DNA rearrangements, in this case resulting in CNV at the qγ27 locus. Furthermore, this provides a highly effective way to test suitable parents in QPM breeding.

Heterosis, or hybrid vigor, is a key phenomenon in genetics research and agricultural production, and has been primarily attributed to non-additive genetic effects such as dominance — a prevailing consensus shaped by decades of empirical research and theoretical debate. Although dominance may arguably arise from distal modifiers, their selective advantage is debated due to presumably small individual effects. To address this long-standing question, particularly how genetic dominance manifests at the transcriptomic level and contributes to phenotypic heterosis, we integrated transcriptomic and phenotypic data from a large population of maize hybrids and their inbred parents. We found that ∼ 30% of the expressed seedling genes in a significant proportion of hybrids exhibited expression patterns deviating from the average of the two parents, indicative of non-additivity. Further analysis suggests that while hybrid gene expression per se is primarily regulated by cis-eQTLs, expression dominance (or non-additivity) is disproportionately controlled by trans-eQTLs. These trans-eQTLs cluster into hotspots that regulate the non-additivity of hundreds of target genes, mostly within co-expression networks, and are notably enriched for transcription factors (TFs). Focusing on one such hotspot, we functionally validated a classical maize gene ZmR1, a basic helix-loop-helix (bHLH) TF associated with multiple seedling trait heterosis, as a candidate regulator of expression dominance across hundreds of genes. Overexpression of ZmR1 enhances expression dominance of downstream genes and increases phenotypic heterosis in both seedling and adult traits. Further experiments confirmed its direct regulatory role in modulating genes involved in anthocyanin biosynthesis and lignin metabolism, driving transcriptome-level dominance. These results provide empirical support for the modifier hypothesis under an omnigenic model, suggesting that heterosis arises not from the modification of a single gene’s inheritance but through the coordinated regulation of hundreds of phenotype-associated genes, thereby helping to reconcile the long-standing debate over the genetic basis of dominance in heterosis.

In the reliability optimization design field of CNC machine tools, reliability allocation plays a significant part, which has the characteristics of high complexity and strong uncertainty. Traditionally, reliability allocation methods have the disadvantages of a single allocation influence factor, too subjective or too objective, not flexible enough, etc. To solve the related problems, a novel reliability allocation method for machine tools is proposed, which combines subjective and objective weightings, and a variety of influencing factors are considered comprehensively. To deal with the characteristic of uncertainty and fuzziness in machine tool reliability analysis, different intuitionistic trapezoidal fuzzy numbers (ITrFNs) are allocated according to the importance of influencing factors. As the subjective method, the analytic hierarchy process (AHP) can reflect the decision maker’s subjective preferences of machine tool influence factors, while the grey relational method (GRA) can analyze the relationship between data which is adopted as an objective weighting method. The reliability of each subsystem is obtained by combining the two methods. Finally, the validity of the proposed method is proved by an illustration analyzing and comparing it with the traditional AHP method and fuzzy allocation methods.