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In plant breeding and agricultural research, biplot analysis has become an important statistical technique. The goal of this study was to find the winning genotype(s) for the test settings in a part of the Southwest region of Nigeria, as well as to investigate the nature and extent of genotype × environment interaction (GEI) effects on Bambara groundnut (BGN) production. The experiment was carried out in four environments (two separate sites, Ibadan and Ikenne, for two consecutive years, 2018 and 2019) with ninety-five BGN accessions. According to the combined analysis of variance over environments, genotypes and GEI both had a substantial (p < 0.001) impact on BGN yield. The results revealed that BGN accessions performed differently in different test conditions, indicating that the interaction was crossover in nature. The results revealed that BGN accessions performed differently in different test conditions, indicating that the interaction was crossover in nature. To examine and show the pattern of the interaction components, biplots with the genotype main effect and genotype × environment interaction (GEI) were used. The first two PCs explained 80% of the total variation of the GGE model (i.e., G + GE) (PC1 = 48.59%, PC2 = 31.41%). The accessions that performed best in each environment based on the “which-won-where” polygon were TVSu-2031, TVSu-1724, TVSu-1742, TVSu-2022, TVSu-1943, TVSu-1892, TVSu-1557, TVSu-2060, and TVSu-2017. Among these accessions, TVSu-2017, TVSu-1557, TVSu-2060, TVSu-1892, and TVSu-1943 were among the highest-yielding accessions on the field. The adaptable accessions were TVSu-1763, TVSu-1899, TVSu-2019, TVSu-1898, TVSu-1957, TVSu-2021, and TVSu-1850, and the stable accessions were TVSu-1589, TVSu-1905, and TVSu-2048. In terms of discriminating and representativeness for the environments, Ibadan 2019 is deemed to be a superior environment. The selected accessions are recommended as parental lines in breeding programs for grain yield improvement in Ibadan or Ikenne or similar agro-ecological zones.

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.

Biplot analysis has emerged as a crucial statistical method in plant breeding and agricultural research. The objective of this research was to identify the best-performing genotype(s) for the environments in three distinct regions of Nigeria while also examining the characteristics and magnitude of genotype–environment interaction (GEI) effects on the yield of Bambara groundnut (BGN). The study was conducted in Ibadan, Ikenne, and Mokwa, utilizing a sample of 30 accessions. The yield of BGN was found to be significantly affected by accessions, environment, and their interaction through a combined analysis of variance, with a p-value < 0.001. Biplots were utilized to demonstrate the pattern of interaction components, specifically the genotype’s main effect and genotype–environment interaction (GEI). The initial two principal components elucidated the complete variance of the GGE model, encompassing both genetic and genotype-by-environment interaction effects (PC1 = 87.81%, PC2 = 12.19%). The accessions that exhibited superior performance in each respective environment, as determined by the “which-won-where” polygon, were identified as TVSu-2223, TVSu-2236, TVSu-2240, and TVSu-2249 in Mokwa; TVSu-2214 in Ikenne; and TVSu-2188 in Ibadan. The accessions TVSu-2207 and TVSu-2199 exhibited stability in all environments, whereas the accessions TVSu-2226, TVSu-2249, TVSu-2209, TVSu-2184, TVSu-2204, and TVSu-2236 demonstrated adaptability. In addition, the accessions TVSu-2240 and TVSu-2283 were stable and adaptable in all environments. The accessions that were chosen have been suggested as suitable parental lines for breeding programs aimed at enhancing grain yield in the agro-ecological zones that were evaluated. This study’s findings identify BGN accessions with adaptability and stability across selected environments in Nigeria, suggesting specific accessions that can serve as suitable parental lines in breeding programs to enhance grain yield, thereby holding promise for improving food security.

• As climate change transforms seasonal patterns of temperature and precipitation, germination success at marginal temperatures will become critical for the long-term persistence of many plant species and communities. If populations vary in their environmental sensitivity to marginal temperatures across a species’ geographical range, populations that respond better to future environmental extremes are likely to be critical for maintaining ecological resilience of the species. • Using seeds from two to six populations for each of nine species of Mediterranean plants, we characterized patterns of among-population variation in environmental sensitivity by quantifying genotype-by-environment interactions (G × E) for germination success at temperature extremes, and under two light regimes representing conditions below and above the soil surface. • For eight of nine species tested at hot and cold marginal temperatures, we observed substantial among-population variation in environmental sensitivity for germination success, and this often depended on the light treatment. Importantly, different populations often performed best at different environmental extremes. • Our results demonstrate that ongoing changes in temperature regime will affect the phenology, fitness, and demography of different populations within the same species differently. We show that quantifying patterns of G × E for multiple populations, and understanding how such patterns arise, can test mechanisms that promote ecological resilience.

The context‐dependent investigations of host–pathogen genotypic interactions, where environmental factors are explicitly incorporated, allow the assessment of both coevolutionary history and contemporary ecological influences. Such a functional explanatory framework is particularly valuable for describing mortality trends and identifying drivers of disease risk more accurately. Using two common North American frog species (Lithobates pipiens and Lithobates sylvaticus) and three strains of frog virus 3 (FV3) at different temperatures, we conducted a laboratory experiment to investigate the influence of host species/genotype, ranavirus strains, temperature, and their interactions, in determining mortality and infection patterns. Our results revealed variability in host susceptibility and strain infectivity along with significant host–strain interactions, indicating that the outcome of an infection is dependent on the specific combination of host and virus genotypes. Moreover, we observed a strong influence of temperature on infection and mortality probabilities, revealing the potential for genotype–genotype–environment interactions to be responsible for unexpected mortality in this system. Our study thus suggests that amphibian hosts and ranavirus strains genetic characteristics should be considered in order to understand infection outcomes and that the investigation of coevolutionary mechanisms within a context‐dependent framework provides a tool for the comprehensive understanding of disease dynamics.

Developing climate-resilient crop varieties with better performance under variable environments is essential to ensure food security in a changing climate. This process is significantly influenced, among other factors, by genotype × environment (G × E) interactions. With the objective of identifying high-yielding and stable genotypes, 20 elite durum wheat lines were evaluated in 24 environments (location–season combination) during 5 crop seasons (2010/11–2014/15). The REML (residual maximum likelihood)-predicted means of grain yield of 16 genotypes that were common across all environments ranged from 3522 kg/ha in G201 to 4132 kg/ha in G217. Results of additive main effect and multiplicative interaction (AMMI) analysis showed that genotypes (G), environments (E), and genotype × environment interaction (GEI) significantly affected grain yield. From the total sum of squares due to treatments (G + E + GEI), E attributed the highest proportion of the variation (90.0%), followed by GEI (8.7%) and G (1.3%). Based on the first four AMMI selections for grain yield in the 24 environments, genotypes G217, G219, G211, and G213 were selected in 23, 12, 11, and 9 environments, respectively. The genotype and genotype × environment biplot (GGE) biplot polygon view showed that the environments were separated into three mega-environments. The winning genotypes in these mega-environments were G217, G214, and G204. Genotypes G212, G220, G217, G215, and G213 showed low AMMI stability values (ASV), whereas genotypes G217, G220, G212, G211, and G219 showed low genotype selection index (GSI), indicating their better stability and adaptability to the test environments. The results indicated that genotypes G217, G219, G211, G213, and G220 combined both high grain yield and stability/adaptability under dry but irrigated and heat-prone environments. An in-depth analysis of the superior genotypes could help better understand the stress-adaptive traits that could be targeted to further increase durum wheat yield and stability under the changing climate.

The aim of potato breeding is to release cultivars that exhibit high and stable performance across the target population of environments. The objective of this research was therefore to investigate the use of various methods (site regression [SREG], coefficient of variation and regression deviation [σ2δ]) for determining the adaptability and stability of productive and quality traits in the Nordic region of Europe. The multi-environment trials included 256 breeding clones and released cultivars grown by EU farmers at three distinct testing sites over two years in Sweden. There was significant (P < 0.001) variation in tuber yield, starch percentage and reducing sugars in the tuber flesh among the breeding clones and cultivars, testing environments and the genotype by environment interaction (GEI). The environments were very diverse, as revealed by the SREG biplots and particularly for the GEI patterns noted in terms of their productive and quality characteristics. The percentage of stable high-tuber yielding germplasm was greater for breeding clones (23%) than for released European cultivars (2%), thus revealing the advantage of potato breeding in the target population of environments. SLU 1415001 and SLU 1314015 were the most promising breeding clones due to their stable high tuber yield. This characteristic was best for the starch potato cultivars, although none of them exhibited a significant different σ2δ. ‘Talent’ shows an almost stable good performance among low reducing sugar cultivars and breeding clones, which are often unstable in terms of their scoring across environments. Neither a breeding clone nor a cultivar was at the top for stable tuber yield, tuber flesh starch or reducing sugars in the tuber flesh, which shows the challenge faced by potato breeding while addressing the needs of different markets.

The phenotype and adaptability of an individual tree is influenced by genetic and environmental factors. In this study, the genetic parameters of growth traits for 40 poplar clones at three different sites (Lishu, Cuohai, and Fujin) in northeastern China were investigated and analyzed. ANOVAs showed that all effects were significantly different (P < 0.001). The phenotypic coefficients of variation of different traits ranged from 14.84% (height in Lishu) to 23.61% (basal diameter in Fujin). The repeatability of the different traits varied from 0.81 (height in Fujin) to 0.97 (basal diameter in Lishu). Genotype × environment interaction models showed that populations G33, G38, and G32 were stable and high-yielding clones, and Lishu was considered an ideal test environment that was representative of poplar clone populations and allowed for discrimination between traits. The stability analysis indicated that some clones showed high basal diameters but were sensitive to environmental conditions, whereas others had moderate basal diameters but were adapted to environmental conditions, which suggested that elite clones should be selected separately for different sites. Based on the growth traits, with a selection rate of 10%, four clones were selected at each site, and the genetic gains of growth traits ranged from 9.99% (height) to 25.45% (basal diameter). These superior clones will provide materials for forestland renewal in semiarid regions, and the results in the present research contribute to a theoretical foundation for the selection of poplar tree individuals.

The selection of better-evaluated genotypes for a target region depends on the characterization of the climate conditions of the environment. With the advancement of computer technology and daily available information about the weather, integrating such information in selection and interaction genotype × environment studies has become a challenge. This article presents the use of the technique of artificial neural networks associated with reaction norms for the processing of climate and georeferenced data for the study of genetic behaviors and the genotype × environment interaction of soybean genotypes. The technique of self-organizing maps (SOM) consists of competitive learning between two layers of neurons; one is the input, which transfers the data to the map, and the other is the output, where the topological structure formed by the competition generates weights, which represent the dissimilarity between the neural units. The methodologies used to classify these neurons and form the target populations of environments (TPE) were the discriminant analysis (DA) and the principal component analysis (PCA). To study soybean genetic behavior within these TPE, the random regression model was adopted to estimate the components of variance, and the reaction norms were adjusted through the Legendre polynomials. The SOM methodology allowed for an explanation of 99% of the variance of the climate data and the formation of well-structured TPE, with the membership probability of the regions within the TPE above 80%. The formation of these TPE allowed us to identify and quantify the response of the genotypes to sensitive changes in the environment.