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Multi-parent populations (MPPs) are attractive for genetic and breeding studies because they combine genetic diversity with an easy-to-control population structure. Most methods for mapping QTLs in MPPs focus on the detection of QTLs in single environments. Little attention has been given to mapping QTLs in multienvironment trials (METs) and to detecting and modeling QTL-by-environment interactions (QEIs). We present mixed model approaches for the detection and modeling of consistent versus environment-dependent QTLs, i.e., QTL-by-environment interaction (QEI). QTL effects are assumed to be normally distributed with variances expressing consistency or dependence on environments and families. The entries of the corresponding design matrices are functions of identity-by-descent (IBD) probabilities between parents and offspring and follow from the parental origin of offspring DNA. A polygenic effect is added to the models to account for background genetic variation. We illustrate the wide applicability of our method by analyzing several public MPP datasets with observations from METs. The examples include diallel, nested association mapping (NAM), and multi-parent advanced inter-cross (MAGIC) populations. The results of our approach compare favorably with those of previous studies that used tailored methods.

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Combining ability status of the inbred lines is crucial information for hybrid breeding program. Diallel or line × tester mating designs are frequently used to evaluate the combining ability. In the current study a modified diallel model was used, wherein the Griffing's combining ability effects were further partitioned to understand the effects due to maternal and reciprocal. To do this, eight parental lines of maize were crossed in full diallel method and the generated hybrids along with parents were phenotyped. The field data on the quantitative traits was analyzed using both Griffing's and the modified model to determine how well the parents' and the F1 hybrids combined. For each of the traits, a sizable reciprocal and maternal variance was observed. The number of kernel rows per cob variable had a ratio of additive variance to dominance variance greater than one. All other traits including grain yield had a ratio close to zero, suggesting that non-additive gene action was primarily responsible for the genetic control of most of the traits. The narrow sense heritability was low to moderate for majority of the variables, except for number of kernel rows per cob. With the help of the improved model, it was possible to choose superior parents and cross-parent pairings with accuracy. Based on the modified general combining ability effects and maternal effects, the parental line P5 was recognized as a potential female parent and P7 as a good male parent for grain yield and yield-attributing characteristics. The cross combination of P8×P1 had the highest specific combining ability effect on grain yield. P5×P6 cross had the highest reciprocal effect. The correlation analysis implies that the Griffing's general combining ability effects and specific combining ability effects were found to be less efficient in predicting F1 performance as compared to the modified model.

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Background: Groundnut is one of the world's major food and oil crops. Being sources of nutrition and vegetable oil, rich in affordable and digestible protein, it is a strategic crop in Burkina Faso for food security, nutrition, and cash income. Understanding the nature of gene effect and genetic variation affecting yield and yield component traits will contribute to designing appropriate breeding methods for groundnut improvement and increase selection efficiency in Burkina Faso. Methods: In 2018, a total of 30 F2 progenies were generated through a 6 x 6 full diallel mating using six different and contrasting varieties. In 2019, parents and progenies were evaluated in a lattice square design in 3 replications at ICRISAT-Mali experimental field to assess the general combining ability (GCA) and specific combining ability (SCA) effects, the inheritance and the maternal and reciprocal effects for yield component traits (YCT) and oil content (OC). Results: Significant variabilities were observed among the parental genotypes and their F2 progenies for DTH, PSR, HPW, PL, PWD, SL, SWD, and OAC. Mean performance of the six parents were HPW (117.05g), HSW (57.24 g), PYH (1914.76), SYH (1312.73), PL (2.52), PWD (1,19), SL (1.38), SWD (0.83), OC (49.43), OAC (50.43) and LAC (33.61). Parent QH243C presented the highest value for SWD (1.02 cm) and OAC (60.76) while the parent ICGV09195 had the highest value of OC (50.36). Chalimbana presented the highest value of HPW (169.61 g), PL (2.98 cm), PWD (1. 41 cm), and SL (1.57 cm) while CG7 presented the highest value for HSW (75. 14 g), and SYH (1639.28 kg). Both YCT and OC are controlled by additive and non-additive gene effects with a predominance of additive gene action for HSW, SL, and SWD, whereas HPW, PL, PWD, and OAC were found to be more controlled by non-additive gene effects. Maternal effects as well as nuclear and cytoplasmic interaction effects were observed for both YCT and OC indicating that YCT and OC are influenced by a combination of genetic factors from both the maternal parent and the nuclear genome, as well as cytoplasmic factors such as mitochondrial DNA. Broad sense heritability ranged from 3.76 % to 91.56 %, and higher broad sense heritability values were recorded for pod length (91.56 %), hundred pod weight (83.71 %) and pod width (80.95 %). Conclusion: The study yields valuable insights into the inheritance of YCT and OC. The parents, Chalimbana and CG7, showed promise as good combiners for both yield component traits and oil content when used as male parents while TE3, Sh470P and QH243C can be used as female for the oil content and its components (oleic and linoleic content).

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A suite of plant traits is thought to make weed populations highly invasive, including vigorous growth and reproduction, superior competitive ability, and high dispersal ability. Using a breeding design and a common garden experiment, we tested whether such an "invasion syndrome" has evolved in an invasive range of Solidago altissima, and whether the evolution is likely to be genetically constrained. We found an overall shift in invasive phenotypes between native North American and invasive Japanese populations. The invasive populations were taller and produced more leaves, suggesting a superior ability to exploit limited resources. The populations also produced more allelopathic compounds that can suppress competitor growth. Finally, invasive populations produced more seeds, which are smaller and are released from a greater height, indicating a potential for superior dispersal ability than the native populations. Quantitative genetics analyses found a large amount of additive genetic variation in most focal traits across native and invasive populations, with no systematic differences in its magnitude between the ranges. Genetic covariances among three traits representing invasion strategies (leaf mass, polyacetylene concentration and seed size) were small. The R metric, which measures the effect of genetic covariances on the rate of adaptation, indicated that the covariance neither constrains nor accelerates concerted evolution of these traits. The results suggest that the invasion syndrome in S. altissima has evolved in the novel range due to ample additive genetic variation, and relatively free from genetic trade-offs.

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Erucic acid, more than 2 %, in mustard seed oil is considered unhealthy as edible oil, and also anti-nutritional for human consumption. The existing mustard varieties of Bangladesh contain 40-48 % erucic acid, which is a big concern for the country's nutritional, and food security and safety. Hence, to improve the seed oil quality of the existing variety, six popular cultivars of Brassica juncea mustard were crossed with a canola-grade line in 7 × 7 half diallel fashion, and the developed 21 F1 hybrids were assessed for yield contributing traits, and fatty acids composition. Variables with significant variations were found, while days to siliquae maturity, plant height, days to first flowering, and seeds per siliquae have moderate narrow sense heritability. The estimated gene action indicated that dominant or over-dominant gene action was more prominent in governing the traits. The parents, P1, P3, and P4 were discovered the best general combiners for early maturity and short phenology, whereas P2 and P7 were found to be the best general combiners for yield-attributing traits. Moreover, the hybrids P1 × P4, P1 × P6, P2 × P7, P4 × P6 and P3 × P5 were chosen as the promising hybrids due to their best specific combining ability, and desired heterotic effects on yield contributing traits. In addition, a significant decrease, on average 30-40 %, in erucic acid, but an approximately 20-25 % increase of oleic acid was found among the hybrids, in which the hybrids P1 × P6-S1, P5 × P6-S2 and P5 × P6-S4 demonstrated a better stability index. Overall, the obtained findings suggested that the hybrids, viz. P1 × P5, P1 × P6, P2 × P3, P2 × P7, P4 × P6, P5 × P6, and P6 × P7 were promising based on their early maturity, high-yielding, reduced erucic acid, and high oleic acid contents.

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Breeding resistant wheat cultivars to Fusarium head blight (FHB), caused by Fusarium spp., is the best method for controlling the disease. The aim of this study was to estimate general combining ability (GCA) and specific combining ability (SCA) for FHB resistance in a set of eight genetically diverse winter wheat cultivars to identify potential donors of FHB resistance for crossing. FHB resistance of parents and F1 crosses produced by the half diallel scheme was evaluated under the conditions of artificial inoculation with F. graminearum and natural infection. Four FHB related traits were assessed: visual rating index (VRI), Fusarium damaged kernels (FDK), and deoxynivalenol and zearalenone content in the harvested grain samples. Significant GCA effects for FHB resistance were observed for the parental cultivars with high FHB resistance for all studied FHB resistance related traits. The significant SCA and mid-parent heterosis effects for FHB resistance were rare under both artificial inoculation and natural infection conditions and involved crosses between parents with low FHB resistance. A significant negative correlation between grain yield under natural conditions and VRI (r = -0.43) and FDK (r = -0.47) under conditions of artificial inoculation was observed in the set of the studied F1 crosses. Some crosses showed high yield and high FHB resistance, indicating that breeding of FHB resistant genotypes could be performed without yield penalty. These crosses involved resistant cultivars with significant GCA effects for FHB resistance indicating that that they could be used as good donors of FHB resistance.

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Unraveling the genetic sources of gene expression variation is essential to better understand the origins of phenotypic diversity in natural populations. Genome-wide association studies identified thousands of variants involved in gene expression variation, however, variants detected only explain part of the heritability. In fact, variants such as low-frequency and structural variants (SVs) are poorly captured in association studies. To assess the impact of these variants on gene expression variation, we explored a half-diallel panel composed of 323 hybrids originated from pairwise crosses of 26 natural Saccharomyces cerevisiae isolates. Using short- and long-read sequencing strategies, we established an exhaustive catalog of single nucleotide polymorphisms (SNPs) and SVs for this panel. Combining this dataset with the transcriptomes of all hybrids, we comprehensively mapped SNPs and SVs associated with gene expression variation. While SVs impact gene expression variation, SNPs exhibit a higher effect size with an overrepresentation of low-frequency variants compared to common ones. These results reinforce the importance of dissecting the heritability of complex traits with a comprehensive catalog of genetic variants at the population level.

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Gene expression variation, an essential step between genotype and phenotype, is collectively controlled by local (cis) and distant (trans) regulatory changes. Nevertheless, how these regulatory elements differentially influence gene expression variation remains unclear. Here, we bridge this gap by analyzing the transcriptomes of a large diallel panel consisting of 323 unique hybrids originating from genetically divergent Saccharomyces cerevisiae isolates. Our analysis across 5,087 transcript abundance traits showed that non-additive components account for 36% of the gene expression variance on average. By comparing allele-specific read counts in parent-hybrid trios, we found that trans-regulatory changes underlie the majority of gene expression variation in the population. Remarkably, most cis-regulatory variations are also exaggerated or attenuated by additional trans effects. Overall, we showed that the transcriptome is globally buffered at the genetic level mainly due to trans-regulatory variation in the population.

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Given the increasing problems of water and soil contamination with cadmium (Cd), it is necessary to investigate the genetic and physiological mechanisms of tolerance to this metal in different crops, which can be used for the development of effective crop management strategies. This study aimed to assess the potential of grafting as a strategy to increase Cd tolerance and reduce absorption in tomato by evaluating the contribution of the root system and aerial parts for tolerance mechanisms. To this end, reciprocal grafting and diallel analyses were used to examine the combining ability of contrasting tomato genotypes under exposure to 0 and 35 µM CdCl2. Roots and above-ground parts were found to have specific mechanisms of Cd tolerance, absorption, and accumulation. Grafting of the USP15 genotype (scion) on USP16 (rootstock) provided the greatest synergism, increasing the tolerance index and reducing the translocation index and Cd accumulation in leaves. USP163 exhibited potential for breeding programs that target genotypes with high Cd tolerance. In tomato, both Cd tolerance and accumulation in aerial parts are genotype- and tissue-specific, controlled by a complex system of complementary mechanisms that need to be better understood to support the development of strategies to reduce Cd contamination in aerial parts.

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Abstract Combining ability analysis provides useful information for the selection of parents, also information regarding the nature and magnitude of involved gene actions. Crops improvement involves strategies for enhancing yield potentiality and quality components. Targeting the improvement of respective characters in bitter gourd, combining ability and genetic parameters for 19 characters were estimated from a 6×6 full diallel analysis technique. The results revealed that the variances due to general combining ability (GCA) and specific combining ability (SCA) were highly significant for most of the important characters. It indicated the importance of both additive and non-additive gene actions. GCA variances were higher in magnitude than SCA variances for all the characters studied indicating the predominance of the additive gene effects in their inheritance. The parent P2 (BG 009) appeared as the best general combiner for earliness; P1 (BG 006) for number of fruits, average single fruit weight and fruit yield; P4 (BG 027) for node number of first female flower and days to seed fruit maturity; P3 (BG 011) for fruit length and thickness of the fruit flesh; P5 (BG 033) for 100-seed weight; and P6 for number of nodes per main vine. The SCA effect as well as reciprocal effect was also significant for most of the important characters in different crosses.

Resumo A análise da capacidade de combinação fornece informações úteis para a seleção dos pais, também informações sobre a natureza e a magnitude das ações dos genes envolvidos. A melhoria das safras envolve estratégias para aumentar a potencialidade da produção e os componentes de qualidade. Visando ao aprimoramento dos respectivos caracteres em cabaça-amarga, capacidade de combinação e parâmetros genéticos para 19 caracteres, foram estimados a partir de uma técnica de análise dialélica completa 6 × 6. Os resultados revelaram que as variâncias, devido à capacidade geral de combinação (GCA) e capacidade específica de combinação (SCA), foram altamente significativas para a maioria dos caracteres importantes. Indicou a importância das ações gênicas aditivas e não aditivas. As variâncias GCA foram maiores em magnitude do que as variâncias SCA para todos os caracteres estudados, indicando a predominância dos efeitos do gene aditivo em sua herança. O pai P2 (BG 009) apareceu como o melhor combinador geral para o início; P1 (BG 006) para número de frutos, peso médio de um único fruto e produção de frutos; P4 (BG 027) para número de nó da primeira flor fêmea e dias para a maturidade do fruto da semente; P3 (BG 011) para comprimento do fruto e espessura da polpa do fruto; P5 (BG 033) para peso de 100 sementes; e P6 para o número de nós por videira principal. O efeito SCA, bem como o efeito recíproco, também foi significativo para a maioria dos personagens importantes em cruzamentos diferentes.

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Abstract Combining ability analysis provides useful information for the selection of parents, also information regarding the nature and magnitude of involved gene actions. Crops improvement involves strategies for enhancing yield potentiality and quality components. Targeting the improvement of respective characters in bitter gourd, combining ability and genetic parameters for 19 characters were estimated from a 6×6 full diallel analysis technique. The results revealed that the variances due to general combining ability (GCA) and specific combining ability (SCA) were highly significant for most of the important characters. It indicated the importance of both additive and non-additive gene actions. GCA variances were higher in magnitude than SCA variances for all the characters studied indicating the predominance of the additive gene effects in their inheritance. The parent P2 (BG 009) appeared as the best general combiner for earliness; P1 (BG 006) for number of fruits, average single fruit weight and fruit yield; P4 (BG 027) for node number of first female flower and days to seed fruit maturity; P3 (BG 011) for fruit length and thickness of the fruit flesh; P5 (BG 033) for 100-seed weight; and P6 for number of nodes per main vine. The SCA effect as well as reciprocal effect was also significant for most of the important characters in different crosses.

Resumo A análise da capacidade de combinação fornece informações úteis para a seleção dos pais, também informações sobre a natureza e a magnitude das ações dos genes envolvidos. A melhoria das safras envolve estratégias para aumentar a potencialidade da produção e os componentes de qualidade. Visando ao aprimoramento dos respectivos caracteres em cabaça-amarga, capacidade de combinação e parâmetros genéticos para 19 caracteres, foram estimados a partir de uma técnica de análise dialélica completa 6 × 6. Os resultados revelaram que as variâncias, devido à capacidade geral de combinação (GCA) e capacidade específica de combinação (SCA), foram altamente significativas para a maioria dos caracteres importantes. Indicou a importância das ações gênicas aditivas e não aditivas. As variâncias GCA foram maiores em magnitude do que as variâncias SCA para todos os caracteres estudados, indicando a predominância dos efeitos do gene aditivo em sua herança. O pai P2 (BG 009) apareceu como o melhor combinador geral para o início; P1 (BG 006) para número de frutos, peso médio de um único fruto e produção de frutos; P4 (BG 027) para número de nó da primeira flor fêmea e dias para a maturidade do fruto da semente; P3 (BG 011) para comprimento do fruto e espessura da polpa do fruto; P5 (BG 033) para peso de 100 sementes; e P6 para o número de nós por videira principal. O efeito SCA, bem como o efeito recíproco, também foi significativo para a maioria dos personagens importantes em cruzamentos diferentes.

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In this study the pattern of color of inheritance based on Mendel's laws on the Clarias gariepinus strain was evaluated, to ascertain the different traits of albino, normally pigmented, and a combination of both traits that could be passed across from the parent stocks to the progenies. Since albinism is caused by a series of genetic abnormalities resulting in the reduction of melanin production, partial diallel cross between normally pigmented and albino fish was carried out using two females (albino and normal pigmented brood fish) weighing 2.5 kg and 3 kg, respectively; they were used in crossing two males (albino and normal pigmented brood fish) that weighed 1.5 kg and 1 kg, respectively. They were paired with normal pigmented (♂Np × â™€Np) and albino C. gariepinus (♂Ae × â™€Ae) fish to produce a pure strain of normally pigmented and albino strain, respectively. To produce the hybrids, they were paired (♂Np × â™€Ae) and (♂Ae × â™€Np), respectively. The outcomes of this study showed that crossbreeding between normally pigmented females and albino males produced all normally pigmented F1 generation, while some quantity of albino (36.67%) at crossing male albino to normally pigmented females were produced. However, the pure strains breed true (100%). Each hybrid exhibits heterosis after 56 days of rearing compared to the normal strain that was crossed, although the normally pigmented fish gives a better SGR. Hence, there is a need to investigate if sex is linked with albinism.

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Combining ability is referred to as the hybridization value of the parental genotypes involved in the crossing to develop hybrids. The best parents are selected through combining ability methods and subsequently used to produce high yielding and resistant hybrids. Thus, the objectives of this study were to (i) understand the nature and action of genes controlling water deficit tolerance, and (ii) identify superior genotypes from the genetic breadth provided by hybridization in cowpea. Twenty-four genotypes were subjected to normal irrigation and water deficit condition to examine combining ability, genotypic and phenotypic correlations for traits directly related to water deficit (proline and chlorophylls), grain yield and yield components. The results showed the presence of the action of additive and non-additive genes under both water regime conditions. However, there was the predominance of the action of additive genes for most of the traits studied under both conditions. The parents KVX61-1, IT06K242-3, IT07K-211-1-8, Kpodjiguèguè, IT99K-573-1-1, Tawa and IT97K-206-1-1 were observed to be good general combiners for proline content, chlorophyll content and traits associated with yield, while KVX61-1 × KVX396-18, IT06K242-3 × KVX396-18, IT07K-211-1-1 × KVX396-18, Kpodjiguèguè x KVX396-18, KVX61 -1 × IT97K-206-1-1, IT06K242-3 × IT97K-206-1-1, IT07K-211-1-1 × IT97K-206-1-1 and Kpodjiguèguè x IT97K-206-1-1 were proven to be the best specific combiners for traits directly related to water deficit tolerance and yield. It should be noted that number of days to pod maturity, pod length, number of pods per plant and weight of hundred seeds were highly heritable traits in this study.

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The development of hybrid plants can increase the production and quality of blue corn, and, thus, satisfy its high demand. For this development, it is essential to understand the heterotic relationships of the germplasm. The objectives of this study were to determine the effects of general (GCA) and specific (SCA) combining ability, as well as the reciprocal effects (REs) on the yields of 10 blue corn lines, and to select the outstanding lines. Diallel crosses were generated with 10 lines and evaluated at the Valle de México Experimental Station in Chapingo, Mexico, and Calpulalpan, Tlaxcala, Mexico. There were differences (p ≤ 0.01) in the hybrids, Loc, effects of GCA, SCA, and REs, and in the following interactions: hybrids × Loc, GCA × Loc, SCA × Loc, and RE × Loc. For GCA, lines Ll, L4, L6, and L9 stood out, with significant values of 3.4, 2.9, 2.9, and 3.1, respectively. For SCA, the hybrids featured were L4 × L10, L2 × L10, L1 × L10, L7 × L8, and L2 × L6, with values of 3.0, 2.5, 2.3, 2.3, and 2.2, and yields of 11.2, 10.2, 10.4, 10.4, and 10.5 t ha-l, respectively. There were no significant REs in these lines. Considerable effects of GCA and SCA were detected; therefore, we concluded that native populations had favorable dominance and additive genetic effects that could be used to support the development of high-yielding lines and hybrids.

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Gene expression variation, an essential step between genomic variation and phenotypic landscape, is collectively controlled by local (cis) and distant (trans) regulatory changes. Nevertheless, how these regulatory elements differentially influence the heritability of expression traits remains unclear. Here, we bridge this gap by analyzing the transcriptomes of a large diallel panel consisting of 323 unique hybrids originated from genetically divergent yeast isolates. We estimated the broad- and narrow-sense heritability across 5,087 transcript abundance traits and showed that non-additive components account for 36% of the phenotypic variance on average. By comparing allelic expression ratios in the hybrid and the corresponding parental pair, we identified regulatory changes in 25% of all cases, with a majority acting in trans. We further showed that trans-regulation could underlie coordinated expression variation across highly connected genes, resulting in significantly higher non-additive variance and most likely in some of the missing heritability of gene expression traits.

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Unraveling the genetic sources of gene expression variation is essential to better understand the origins of phenotypic diversity in natural populations. Genome-wide association studies identified thousands of variants involved in gene expression variation, however, variants detected only explain part of the heritability. In fact, variants such as low-frequency and structural variants (SVs) are poorly captured in association studies. To assess the impact of these variants on gene expression variation, we explored a half-diallel panel composed of 323 hybrids originated from pairwise crosses of 26 natural Saccharomyces cerevisiae isolates. Using short- and long-read sequencing strategies, we established an exhaustive catalog of single nucleotide polymorphisms (SNPs) and SVs for this panel. Combining this dataset with the transcriptomes of all hybrids, we comprehensively mapped SNPs and SVs associated with gene expression variation. While SVs impact gene expression variation, SNPs exhibit a higher effect size with an overrepresentation of low-frequency variants compared to common ones. These results reinforce the importance of dissecting the heritability of complex traits with a comprehensive catalog of genetic variants at the population level.

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Nitrogen is crucial for plant growth and development, and improving nitrogen use efficiency (NUE) is a viable strategy for reducing dependence on nitrogen inputs and promoting sustainability. While the benefits of heterosis in corn are well known, the physiological mechanisms underlying this phenomenon in popcorn are less understood. We aimed to investigate the effects of heterosis on growth and physiological traits in four popcorn lines and their hybrids under two contrasting nitrogen conditions. We evaluated morpho-agronomic and physiological traits such as leaf pigments, the maximum photochemical efficiency of PSII, and leaf gas exchange. Components associated with NUE were also evaluated. N deprivation caused reductions of up to 65% in terms of plant architecture, 37% in terms of leaf pigments, and 42% in terms of photosynthesis-related traits. Heterosis had significant effects on growth traits, NUE, and foliar pigments, particularly under low soil nitrogen conditions. N-utilization efficiency was found to be the mechanism favoring superior hybrid performance for NUE. Non-additive genetic effects were predominant in controlling the studied traits, indicating that exploring heterosis is the most effective strategy for obtaining superior hybrids to promote NUE. The findings are relevant and beneficial for agro farmers seeking sustainable agricultural practices and improved crop productivity through the optimization of nitrogen utilization.

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Las variedades de habichuela cultivadas en Colombia presentan un bajo potencial de producción, por lo que se hace necesario adelantar programas de mejoramiento, cuya ejecución depende del conocimiento de la habilidad combinatoria de los cultivares disponibles. Con el objetivo de evaluar la acción génica predominante en caracteres de importancia económica, se evaluaron 15 híbridos directos y seis progenitores. Las habilidades combinatorias general (HCG) y específica (HCE), se estimaron con el Método 2 modelo 1 de Griffing, que considera a los progenitores y sus cruzamientos directos. Se midieron los caracteres: número de vainas y producción por planta, peso promedio y longitud de la vaina. Los resultados indicaron efectos genéticos aditivos para longitud de la vaina; por el contrario, el número de vainas y producción por planta, se vieron influenciados por efectos genéticos no aditivos, mientras que el peso promedio de la vaina fue controlado por efectos genéticos, tanto aditivos como no aditivos. Los progenitores 1 y 6 mostraron efectos positivos más altos de HCG, para el peso promedio y longitud de la vaina, mientras los progenitores 5 y 6, lo fueron para la producción de vainas por planta y los progenitores 4 y 5, para el número de vainas por planta. La estimación de HCE más alta para todos los caracteres, se presentó en el hibrido 1x2, siendo la más adecuada para mejorar la producción de la habichuela.

Green bean varieties grown in Colombia have low production potential, therefore it is necessary to carry out plant breeding programs, which execution depends on the knowledge of the combinatorial ability of the available cultivars. To evaluate the predominant gene action in economically important traits 15 direct hybrids and six parents were evaluated. General combining ability (GCA) and specific combining ability (SCA) were estimated with Griffing's Method 2 model 1, which considers parents and their direct crosses. The characters: number of pods and yield per plant, average weight and pod length were measured. The results indicated additive genetic effects for pod length. In contrast, pod number and yield per plant were influenced by non-additive genetic effects, while average pod weight was controlled by both additive and non-additive genetic effects. Parents 1 and 6 showed higher positive effects of HCG for average pod weight and pod length, while parents 5 and 6 for pod yield per plant and parents 4 and 5 for number of pods per plant. The highest ECGH estimation for all traits was found in the 1x2 hybrid, being the most suitable for improving bean production.

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The current theoretical knowledge concerning the influence of epistasis on heterosis is based on a simplified multiplicative model. The objective of this study was to assess how epistasis affects the heterosis and combining ability analyses, assuming additive model, hundreds of genes, linkage disequilibrium (LD), dominance, and seven types of digenic epistasis. We developed the quantitative genetics theory for supporting the simulation of the individual genotypic values in nine populations, the selfed populations, the 36 interpopulation crosses, 180 doubled haploids (DHs), and their 16,110 crosses, assuming 400 genes on 10 chromosomes of 200 cM. Epistasis only affects population heterosis if there is LD. Only additive × additive and dominance × dominance epistasis can affect the components of the heterosis and combining ability analyses of populations. Epistasis can have a negative impact on the heterosis and combining ability analysis of populations, leading to wrong inferences regarding the identification of superior and most divergent populations. However, this depends on the type of epistasis, percentage of epistatic genes, and magnitude of their effects. Except for duplicate genes with cumulative effects and non-epistatic genic interaction, there was a decrease in the average heterosis by increasing the percentage of epistatic genes and the magnitude of their effects. The same results are generally true for the combining ability analysis of DHs. The combining ability analyses of subsets of 20 DHs showed no significant average impact of epistasis on the identification of the most divergent ones, regardless of the number of epistatic genes and magnitude of their effects. However, a negative effect on the assessment of the superior DHs can occur assuming 100% of epistatic genes, but depending on the epistasis type and the epistatic effect magnitude.

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A multi-parental population is an innovative tool for mapping large numbers of loci and genetic modifications, particularly where they have been used for breeding and pre-breeding in crops. Frost injury is an environmental stress factor that greatly affects the growth, development, production efficiency, and geographical distribution of crops. No reported study has focused on genetic mapping and molecular marker development using diallel populations of potatoes. In this study, 23 successful cross combinations, obtained by a half diallel cross among 16 parents, including eight frost-tolerant advanced breeding lines and eight cultivars, were used to map the genetic loci for frost tolerance and to create a molecular marker-assisted selection (MAS) system. Three candidate regions related to frost tolerance on chromosomes II, V, and IX were mapped by bulked segregant analysis (BSA). Furthermore, six SNP markers associated with frost tolerance from candidate regions were developed and validated. Above all, a MAS system for the frost tolerance screening of early breeding offspring was established. This study highlights the practical advantages of applying diallel populations to broaden and improve frost-tolerant germplasm resources.

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