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The Toda chain is the prime example of a classical integrable system with strictly local conservation laws. Relying on the Dumitriu–Edelman matrix model, we obtain the generalized free energy of the Toda chain and thereby establish a mapping to the one-dimensional log-gas with an interaction strength of order 1 /  N . The (deterministic) local density of states of the Lax matrix is identified as the object, which should evolve according to generalized hydrodynamics.

Tilletia laevis (syn. Tilletia foetida) etmeninin neden olduğu sürme hastalığı küresel düzeyde buğday üretim ve kalitesini olumsuz etkileyen önemli bir başak hastalığıdır. Bu çalışmada, 50 adet ön verim kademesinde bulunan buğday hattının, 2023-2024 yetiştirme sezonunda Antalya, Aydın, Çanakkale, Denizli, Kırıkkale, Kırşehir, Mersin ve Siirt lokasyonlarında yapay epidemi koşullarında sürme hastalığına karşı göstermiş oldukları reaksiyonları değerlendirilmiştir. Çalışmada test edilen buğday hatları tarla koşullarında, her lokasyonda tesadüf blokları deneme desenine göre üç tekerrürlü olacak şekilde gerçekleştirilmiştir. Sürme sporları her bir test edilen buğday genotiplerine yaklaşık 4 gram olacak şekilde %0.5 oranında inoküle edilmiştir. Hastalık reaksiyon değerlendirmelerinde, her bir buğday genotipi için hastalıklı ve toplam başaklar sayılmış ve yüzde (%) sürme hastalık oranı hesaplanmıştır. Ek olarak, hassas kontrol genotiplerinin hastalık reaksiyonları %90-100 olarak belirlenmiş olup, sonuçlar araştırmanın güvenilir olduğu şeklinde yorumlanmıştır. Reaksiyonlar %0 (İmmun), %0.1-10.0 (Dayanıklı), %10.1-25.0 (Orta Dayanıklı), %25.1-40 (Orta Hassas), %40.1-70.0 (Hassas) ve %70.1+ (Çok Hassas) olarak gruplandırılarak değerlendirilmiştir. Ayrıca, genotip ve genotip-çevre (GGE) etkileşimleri GGE Biplot yöntemi kullanılarak analiz edilmiş olup, analiz toplam varyasyonun %97.07'sini açıklamıştır. Reaksiyon gruplarına göre yapılan genotip sıralaması genel olarak GGE Biplot sonuçları ile tutarlılık gösterirken, GGE Biplot yöntemi ile yapılan sınıflandırmanın sürme hastalığına dayanıklı ve stabil materyallerin seleksiyonu için kullanışlı olduğu sonucuna ulaşılmıştır. Sonuç olarak, buğdayda sürme hastalığının reaksiyonlarını değerlendirmek için ölçeğin kullanımı güvenilir sonuçlar vermektedir. Bu nedenle, dayanıklı grupta belirlenen materyallerin sürme hastalığı dayanıklılık ıslah programlarında genitör olarak kullanılabilir. Bu çalışmadan elde edilen sonuçlar, sürme hastalığı ile mücadelede fungusit kullanımı azaltmak ve hastalık etmeni ile etkili bir şekilde mücadele etmek açısından önem arz etmektedir.

Lentil yield is a complicated quantitative trait; it is significantly influenced by the environment. It is crucial for improving human health and nutritional security in the country as well as for a sustainable agricultural system. The study was laid out to determine the stable genotype through the collaboration of G × E by AMMI and GGE biplot and to identify the superior genotypes using 33 parametric and non-parametric stability statistics of 10 genotypes across four different conditions. The total G × E effect was divided into two primary components by the AMMI model. For days to flowering, days to maturity, plant height, pods per plant, and hundred seed weight, IPCA1 was significant and accounted for 83%, 75%, 100%, and 62%, respectively. Both IPCA1 and IPCA2 were non-significant for yield per plant and accounted for 62% of the overall G × E interaction. An estimated set of eight stability parameters showed strong positive correlations with mean seed yield, and these measurements can be utilized to choose stable genotypes. The productivity of lentils has varied greatly in the environment, ranging from 786 kg per ha in the MYM environment to 1658 kg per ha in the ISD environment, according to the AMMI biplot. Three genotypes (G8, G7, and G2) were shown to be the most stable based on non-parametric stability scores for grain yield. G8, G7, G2, and G5 were determined as the top lentil genotypes based on grain production using numerical stability metrics such as Francis’s coefficient of variation, Shukla stability value (σi2), and Wrick’s ecovalence (Wi). Genotypes G7, G10, and G4 were the most stable with the highest yield, according to BLUP-based simultaneous selection stability characteristics. The findings of graphic stability methods such as AMMI and GGE for identifying the high-yielding and stable lentil genotypes were very similar. While the GGE biplot indicated G2, G10, and G7 as the most stable and high-producing genotypes, AMMI analysis identified G2, G9, G10, and G7. These selected genotypes would be used to release a new variety. Considering all the stability models, such as Eberhart and Russell’s regression and deviation from regression, additive main effects, multiplicative interactions (AMMI) analysis, and GGE, the genotypes G2, G9, and G7 could be used as well-adapted genotypes with moderate grain yield in all tested environments.

The apparent climatic extremes affect the growth and developmental process of cool-season grain legumes, especially the high-temperature stress. The present study aimed to investigate the impacts of high-temperature stress on crop phenology, seed set, and seed quality parameters, which are still uncertain in tropical environments. Therefore, a panel of 150 field pea genotypes, grouped as early ( n = 88) and late ( n = 62) maturing, were exposed to high-temperature environments following staggered sowing [normal sowing time or non-heat stress environment (NHSE); moderately late sowing (15 days after normal sowing) or heat stress environment-I (HSE-I); and very-late sowing (30 days after normal sowing) or HSE-II]. The average maximum temperature during flowering was about 22.5 ± 0.17°C for NHSE and increased to 25.9 ± 0.11°C and 30.6 ± 0.19°C in HSE-I and HSE-II, respectively. The average maximum temperature during the reproductive period (RP) (flowering to maturity) was in the order HSE-II (33.3 ± 0.03°C) > HSE-I (30.5 ± 0.10°C) > NHSE (27.3 ± 0.10°C). The high-temperature stress reduced the seed yield (24–60%) and seed germination (4–8%) with a prominent effect on long-duration genotypes. The maximum reduction in seed germination (>15%) was observed in HSE-II for genotypes with >115 days maturity duration, which was primarily attributed to higher ambient maximum temperature during the RP. Under HSEs, the reduction in the RP in early- and late-maturing genotypes was 13–23 and 18–33%, suggesting forced maturity for long-duration genotypes under late-sown conditions. The cumulative growing degree days at different crop stages had significant associations ( p < 0.001) with seed germination in both early- and late-maturing genotypes; and the results further demonstrate that an extended vegetative period could enhance the 100-seed weight and seed germination. Reduction in seed set (7–14%) and 100-seed weight (6–16%) was observed under HSEs, particularly in HSE-II. The positive associations of 100-seed weight were observed with seed germination and germination rate in the late-maturing genotypes, whereas in early-maturing genotypes, a negative association was observed for 100-seed weight and germination rate. The GGE biplot analysis identified IPFD 11-5, Pant P-72, P-1544-1, and HUDP 11 as superior genotypes, as they possess an ability to produce more viable seeds under heat stress conditions. Such genotypes will be useful in developing field pea varieties for quality seed production under the high-temperature environments.

Barley is the fourth largest grain crop globally with varieties suited to temperate, subarctic, and subtropical areas. The identification and subsequent selection of superior varieties are complicated by genotype-by-environment interactions. The main objective of this study was to use parametric and non-parametric stability measures along with a GGE biplot model to identify high-yielding stable barley genotypes in Iran. Eighteen barley genotypes (16 new genotypes and two control varieties) were evaluated in a randomized complete block design with four replications at five locations over three growing seasons (2013–2014, 2014–2015, 2015–2016). The combined analysis of variance indicated that the environment main effect accounted for > 69% of all variation, compared with < 31% for the combined genotype (G) and genotype-by-environment interaction effects. The mean grain yield of each genotype across the five test sites and three seasons ranged from 1900 to 2302 kg ha−1. Using Spearman’s rank correlation and principal component analyses, the stability measures were divided into three groups: the first included mean yield, TOP and b, which are related to the dynamic concept of stability, the second comprised θi, Wi2, σi2, CVi, \\[S_{di}^{2}\\], KR, and the non-parametric measures, S(i) and NP(i), which are related to the static concept of stability, and the third included θi and R2. The GGE biplot analysis indicated that, of the five test locations, Gonbad and Moghan had the most discriminating and representative environments. Hence, these locations are recommended as ideal test locations in Iran for the selection of superior genotypes. The numerical and graphical methods both produced similar results, identifying genotypes G12, G13, and G17 as the best material for rainfed conditions in Iran; these genotypes should be promoted for commercial production.

Experiments measuring the interaction between genotypes and environments measure the spatial (e.g., locations) and temporal (e.g., years) separation and/or combination of these factors. The genotype-by-environment interaction (GEI) is very important in plant breeding programs. Over the past six decades, the propensity to model the GEI led to the development of several models and mathematical methods for deciphering GEI in multi-environmental trials (METs) called “stability analyses”. However, its size is hidden by the contribution of improved management in the yield increase, and for this reason comparisons of new with old varieties in a single experiment could reveal its real size. Due to the existence of inherent differences among proposed methods and analytical models, it is necessary for researchers that calculate stability indices, and ultimately select the superior genotypes, to dissect their usefulness. Thus, we have collected statistics, as well as models and their equations, to explore these methods further. This review introduces a complete set of parametric and non-parametric methods and models with a selection pattern based on each of them. Furthermore, we have aligned each method or statistic with a matched software, macro codes, and/or scripts.

The phenolic compound contents and antioxidant activities of the leaf extracts of nine olive genotypes were determined, and the obtained data were analysed using chemometric techniques. In the crude extracts, 12 compounds belonging to the secoiridoids, phenylethanoids, and flavonoids were identified. Oleuropein was the primary component for all genotypes, exhibiting a content of 21.0 to 98.0 mg/g extract. Hydroxytyrosol, verbascoside, luteolin 7-O-glucoside, and luteolin 4′-O-glucoside were also present in noticeable quantities. Genotypes differed to the greatest extent in the content of verbascoside (0.45–21.07 mg/g extract). The content of hydroxytyrosol ranged from 1.33 to 4.03 mg/g extract, and the aforementioned luteolin glucosides were present at 1.58–8.67 mg/g extract. The total phenolic content (TPC), DPPH• and ABTS•+ scavenging activities, ferric reducing antioxidant power (FRAP), and ability to inhibit the oxidation of β-carotene-linoleic acid emulsion also varied significantly among genotypes. A hierarchical cluster analysis enabled the division of genotypes into three clusters with similarity above 60% in each group. GGE biplot analysis showed olive genotypes variability with respect to phenolic compound contents and antioxidant activities. Significant correlations among TPC, FRAP, the values of both radical scavenging assays, and the content of oleuropein were found. The contents of 7-O-glucoside and 4′-O-glucoside correlated with TPC, TEAC, FRAP, and the results of the emulsion oxidation assay.

The two most common styles to analyze genotype-by-environment interaction (GEI) and estimate genotypes are additive main effects and multiplicative interaction (AMMI) and genotype + genotype × environment (GGE) biplot. Therefore, the aim of this study was to find the winning genotype(s) under three locations, as well as to investigate the nature and extent of GEI effects on Bambara groundnut production. The experiment was carried out in the fields of three environments with 15 Bambara groundnut accessions using the randomized complete block design (RCBD) with three replications each in Ibadan, Osun, and Odeda. Yield per plant, fresh seed weight, total number of pods per plant, hundred seed weight, length of seeds, and width of seeds were estimated. According to the combined analysis of variance over environments, genotypes and GEI both had a significant (p < 0.001) impact on Bambara groundnut (BGN) yield. This result revealed that BGN accessions performed differently in the three locations. A two-dimensional GGE biplot was generated using the first two principal component analyses for the pattern of the interaction components with the genotype and GEI. The first two principal component analyses (PCAs) for yield per plant accounted for 59.9% in PCA1 and 40.1% in PCA2. The genotypes that performed best in each environment based on the \"which-won-where\" polygon were G8, G3, G2, G11, G6, and G4. They were also the vertex genotypes for each environment. Based on the ranking of genotypes, the ideal genotypes were G2 and G6 for YPP, G1 and G5 for FPW, G15 and G13 for TNPP, G3 and GG7 for HSW, G7 and G12 for LOS, and G10 and G7 for WOS. G8 was recorded as the top most-yielding genotype. G8, G4, G7, and G13 were high yielding and the most stable across the environments; G11, G14, and G9 were unstable, but they yielded above-average performance; G14, G12, G15, and G1 were unstable and yielded poorly, as their performances were below average. Bowen was the most discriminating and representative environment and is classified as the superior environment. Based on the performance of accessions in each region, we recommend TVSU 455 (G8) and TVSU 458 (G3) in Bowen, TVSU 455 (G8) and TVSU 939 (G6) and TVSU 454 (G1) in Ibadan, and TVSU 158 (G2) and TVSU 2096 (G10) in Odeda. The variety that performed best in the three environments was TVSU 455 (G8). They could also be used as parental lines in breeding programs.

Pigeonpea [Cajanus cajan (L.) Millspaugh] is a widely grown pulse with high seed protein content that contributes to food and nutritional security in the Indian subcontinent. The majority of pigeonpea varieties cultivated in India are of medium duration (<180 days to maturity), which makes it essential for breeders to focus on the development of stable high-yielding varieties. The diverse agroecological regime in the Indian subcontinent necessitates an efficient multi-environment study by taking into consideration genotype (G) × environment (E) interaction (GEI) that has a significant impact on traits like grain yield (GY) in developing high-yielding and widely adaptable varieties. In the present study, 37 pigeonpea genotypes were evaluated during the 2021 rainy season at ARS Badnapur, ARS Tandur, BAU Ranchi, GKVK Bengaluru, and ICRISAT Patancheru. The GEI was significant on the grain yield (p < 0.01), and hence, genotype + genotype × environment (GGE) and additive main effects and multiplicative interaction (AMMI) biplots along with AMMI stability value (ASV) and yield relative to environmental maximum (YREM) statistics were used to identify stable high-yielding genotypes. The interaction principal component analysis 1 and 2 (IPC1 and IPC2) explained 40.6% and 23.3% variations, respectively. Based on the rankings of genotypes, G37 (ICPL 20205), G35 (ICPL 20203), G8 (ICPL 19404), G17 (ICPL 19415), and G9 (ICPL 19405) were identified as ideal genotypes. Discriminativeness vs. representativeness identified GKVK Bengaluru as an ideal environment for comprehensive evaluation of test genotypes. However, ICPL 19405 was identified as the potentially stable high-yielding genotype for further testing and release across the test environments based on its mean grain yield (1,469.30 kg/ha), least ASV (3.82), and low yield stability index (YSI) of 13.

Grain sorghum is an exceptional source of dietary nutrition with outstanding economic values. Breeding of grain sorghum can be slowed down by the occurrence of genotype × environment interactions (GEI) causing biased estimation of yield performance in multi-environments and therefore complicates direct phenotypic selection of superior genotypes. Multi-environment trials by randomized complete block design with three replications were performed on 13 newly developed grain sorghum varieties at seven test locations across China for two years. Additive main effects and multiplicative interaction (AMMI) and genotype + genotype × environment (GGE) biplot models were adopted to uncover GEI patterns and effectively identify high-yielding genotypes with stable performance across environments. Yield (YLD), plant height (PH), days to maturity (DTM), thousand seed weight (TSW), and panicle length (PL) were measured. Statistical analysis showed that target traits were influenced by significant GEI effects ( p < 0.001), that broad-sense heritability estimates for these traits varied from 0.40 to 0.94 within the medium to high range, that AMMI and GGE biplot models captured more than 66.3% of total variance suggesting sufficient applicability of both analytic models, and that two genotypes, G3 (Liaoza No.52) and G10 (Jinza 110), were identified as the superior varieties while one genotype, G11 (Jinza 111), was the locally adapted variety. G3 was the most stable variety with highest yielding potential and G10 was second to G3 in average yield and stability whereas G11 had best adaptation only in one test location. We recommend G3 and G10 for the production in Shenyang, Chaoyang, Jinzhou, Jinzhong, Yulin, and Pingliang, while G11 for Yili.