A robust AMMI model for the analysis of genotype-by-environment data

Grass pea dual purpose dry matter and seed yields in rainfed conditions across diverse environments

Grass pea (Lathyrus sativus L.) stands out as an excellent choice for sustainable agriculture, thanks to its favorable agronomic characteristics, including a robust root system that penetrates deeply into the soil and its resilience against various biotic and abiotic stressors. In this study, dry-matter yield and seed yield of 16 grass pea genotypes were evaluated in rain-fed conditions at "Gachsaran", "Mehran", "Kuhdasht", and "Shirvan-Chardavol" locations in Iran for three consecutive years. The experimental field trials were carried out using a randomized complete block design, and each experimental setup was replicated three times. The descriptive statistics showed a mean value of 4.030 (ton/ha) and 1.530 (ton/ha), with phenotypic coefficients of 54.77 and 61.56 for dry-matter yield and seed yield, respectively. The projection of geographical, climatic, and edaphic variables into yield measurements depicted remarkable divergence among the four studied environments. Elevation exerts a greater influence on both dry matter and seed yields in the Mehran location as compared to other environments. The climatic factors of rainfall and relative humidity played an important role in "Gachsaran" and "Shirvan-Chardavol", respectively. While for seed yield, the temperature-related attributes were more significant in the "Mehran" location. Low broad-sense heritability was observed, and the R2 for genotype-environment interaction showed the existence of GEI for dry-matter yield (0.126) and seed yield (0.223). Both AMMI1 and AMMI2 could recognize unstable genotypes from other ones, and both AMMI's identified genotypes G10 and G3 as high-yielding and stable genotypes. BLUP-based stability indices revealed G10 and G13 as superior genotypes for seed yield and dry-matter yield, respectively. Three and two mega-environments were identified using a GGE biplot for dry-matter yield and seed yield. For dry-matter-identified mega-environments, the G1, G13, and G2, and for seed-yield-recognized mega-environments, the G10 and G15 can be introduced. "Mehran" and "Gachsaran" out of the studied locations possessed diverse distributions considering dry-matter yield and seed yield and for further GE interaction studies, it is better to establish adaptability trials in these locations. The study concludes that for the promotion of sustainable agriculture in rain-fed regions, taking into account the influence of environmental factors, cultivation of the identified grass pea genotypes holds promise.

Unraveling genotypic interactions in sugar beet for enhanced yield stability and trait associations

The interaction between genotype and environment (GEI) significantly influences plant performance, crucial for breeding programs and ultimately boosting crop productivity. Alongside GEI, breeders encounter another hurdle in their quest for yield improvement, notably adverse and negative correlations among pivotal traits. This study delved into the stability of white sugar yield (WSY), root yield (RY), sugar content (SC), extraction coefficient of sugar (ECS), and the interplay among essential traits including RY, SC, alpha amino nitrogen (N), sodium (Na+), and potassium (K+) across 15 sugar beet hybrids and three control varieties. The investigation spanned two locations over two consecutive years (2022-2023), employing a randomized complete block design with four replications to comprehensively analyze these factors. The analysis of variance highlighted the significant effects of environment, genotype, and GEI at the 1% probability level. Notably, the AMMI analysis of GEI revealed the significance of the first component for WSY, RY, and SC, with the first two components proving significant for ECS. Within the linear mixed model (LMM), WSY, RY, SC, and ECS demonstrated significant effects from both genotype and GEI. In the WAASB biplot, genotypes 10, 8, 17, 6, 13, 14, 15, 7, 12, and 16 exhibited stability in WSY, while genotypes 9, 10, 6, 14, 7, 8, 13, 12, 18, and 15 displayed stability in RY. Additionally, genotypes 10, 15, 12, 13, 16, 17, 6, and 14 were stable for SC, and genotypes 8, 10, 7, 6, 13, 12, 16, 17, 15, 14, and 18 showcased stability in ECS, boasting above-average yield values. In the genotype by yield × trait (GYT) biplot, genotypes 15, 18, and 16 emerged as top performers when combining RY with SC, Na+, N, and K+, suggesting their potential for inclusion in breeding programs.

Genotype-by-environment interaction and stability analysis of grain yield of bread wheat (Triticum aestivum L.) genotypes using AMMI and GGE biplot analyses

Bread wheat is a vital staple crop worldwide; including in Ethiopia, but its production is prone to various environmental constraints and yield reduction associated with adaptation. To identify adaptable genotypes, a total of 12 bread wheat genotypes (G1 to G12) were evaluated for their genotype-environment interaction (GEI) and stability across three different environments for two years using Additive Main Effect and Multiplicative Interaction (AMMI) and genotype main effect plus genotype-by-environment interaction (GGE) biplots analysis. GEI is a common phenomenon in crop improvement and is of significant importance in genotype assessment and recommendation. According to combined analysis of variance, grain yield was considerably impacted by environments, genotypes, and GEI. AMMI and GGE biplots analysis also provided insights into the performance and stability of the genotypes across diverse environmental conditions. Among the 12 genotypes, G6 was selected by AMMI biplot analysis as adaptive and high-yielding genotype; G5 and G7 demonstrated high stability and minimal interaction with the environment, as evidenced by their IPCA1 values. G7 was identified as the most stable and high-yielding genotype. The GGE biplot's polygon view revealed that the highest grain yield was obtained from G6 in environment three (E3). E3 was selected as the ideal environment by the GGE biplot. The top three stable genotypes identified by AMMI stability value (ASV) were G5, G7, and G10, while the most stable genotype determined by Genotype Selection Index (GSI) was G7. Even though G6 was a high yielder, it was found to be unstable according to ASV and ranked third in stability according to GSI. Based on the study's findings, the GGE biplot genotype view for grain yield identified Tay genotype (G6) to be the most ideal genotype due to its high grain yield and stability in diverse environments. G7 showed similar characteristics and was also stable. These findings provide valuable insights to breeders and researchers for selecting high-yielding and stable, as well as high-yielding specifically adapted genotypes.

Genotype by environment and genotype by yield*trait interactions in sugar beet: analyzing yield stability and determining key traits association

The genotype by environment interaction significantly influences plant yield, making it imperative to understand its nature for the creation of breeding programs to enhance crop production. However, this is not the only obstacle in the yield improvement process. Breeders also face the significant challenge of unfavorable and negative correlations among key traits. In this study, the stability of root yield and white sugar yield, and the association between the key traits of root yield, sugar content, nitrogen, sodium, and potassium were examined in 20 sugar beet genotypes. The study was conducted using a randomized complete block design with four replications over two consecutive years across five locations. The combined analysis of variance results revealed significant main effects of year, location, and genotype on both root yield and white sugar yield. Notably, two-way and three-way interactions between these main effects on root yield and white sugar yield resulted in a significant difference. The additive main effect and multiplicative interaction analysis revealed that the first five interaction principal components significantly impacted both the root yield and white sugar yield. The linear mixed model results for root yield and white sugar yield indicated that the genotype effect and the genotype by environment interaction were significant. The weighted average absolute scores of the best linear unbiased predictions biplot demonstrated that genotypes 20, 4, 7, 2, 16, 3, 6, 1, 14, and 15 were superior in terms of root yield. For white sugar yield, genotypes 4, 16, 3, 7, 5, 1, 10, 20, 2, and 6 stood out. These genotypes were not only stable but also had a yield value higher than the total average. All key traits, which include sugar content, sodium, potassium, and alpha amino nitrogen, demonstrated a negative correlation with root yield. Based on the genotype by yield*trait analysis results, genotypes 20, 19, and 16 demonstrated optimal performance when considering the combination of root yield with sugar content, sodium, alpha amino nitrogen, and potassium. The multi-trait stability study, genotype 13 ranked first, and genotypes 10, 8, and 9 were identified as the most ideal stable genotypes across all traits. According to the multi-trait stability index, genotype 13 emerged as the top-ranking genotype. Additionally, genotypes 10, 8, and 9 were recognized as the most stable genotypes.

Assessment of yield performances for grain sorghum varieties by AMMI and GGE biplot analyses

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.

Identification of novel putative alleles related to important agronomic traits of wheat using robust strategies in GWAS

Principal component analysis (PCA) is widely used in various genetics studies. In this study, the role of classical PCA (cPCA) and robust PCA (rPCA) was evaluated explicitly in genome-wide association studies (GWAS). We evaluated 294 wheat genotypes under well-watered and rain-fed, focusing on spike traits. First, we showed that some phenotypic and genotypic observations could be outliers based on cPCA and different rPCA algorithms (Proj, Grid, Hubert, and Locantore). Hubert's method provided a better approach to identifying outliers, which helped to understand the nature of these samples. These outliers led to the deviation of the heritability of traits from the actual value. Then, we performed GWAS with 36,000 single nucleotide polymorphisms (SNPs) based on the traditional approach and two robust strategies. In the conventional approach and using the first three components of cPCA as population structure, 184 and 139 marker-trait associations (MTAs) were identified for five traits in well-watered and rain-fed environments, respectively. In the first robust strategy and when rPCA was used as population structure in GWAS, we observed that the Hubert and Grid methods identified new MTAs, especially for yield and spike weight on chromosomes 7A and 6B. In the second strategy, we followed the classical and robust principal component-based GWAS, where the first two PCs obtained from phenotypic variables were used instead of traits. In the recent strategy, despite the similarity between the methods, some new MTAs were identified that can be considered pleiotropic. Hubert's method provided a better linear combination of traits because it had the most MTAs in common with the traditional approach. Newly identified SNPs, including rs19833 (5B) and rs48316 (2B), were annotated with important genes with vital biological processes and molecular functions. The approaches presented in this study can reduce the misleading GWAS results caused by the adverse effect of outlier observations.

Cross-Validation for Lower Rank Matrices Containing Outliers

Several statistical techniques for analyzing data matrices use lower rank approximations to these matrices, for which, in general, the appropriate rank must first be estimated depending on the objective of the study. The estimation can be conducted by cross-validation (CV), but most methods are not designed to cope with the presence of outliers, a very common problem in data matrices. The literature suggests one option to circumvent the problem, namely, the elimination of the outliers, but such information removal should only be performed when it is possible to verify that an outlier effectively corresponds to a collection or typing error. This paper proposes a methodology that combines the robust singular value decomposition (rSVD) with a CV scheme, and this allows outliers to be taken into account without eliminating them. For this, three possible rSVD’s are considered and six resistant criteria are proposed for the choice of the rank, based on three classic statistics used in multivariate statistics. To test the performance of the various methods, a simulation study and an analysis of real data are described, using an exclusively numerical evaluation through Procrustes statistics and critical angles between subspaces of principal components. We conclude that, when data matrices are contaminated with outliers, the best estimation of rank is the one that uses a CV scheme over a robust lower rank approximation (RLRA) containing as many components as possible. In our experiments, the best results were obtained when this RLRA was calculated using an rSVD that minimizes the L2 norm.

Techniques for Robust Imputation in Incomplete Two-Way Tables

We describe imputation strategies resistant to outliers, through modifications of the simple imputation method proposed by Krzanowski and assess their performance. The strategies use a robust singular value decomposition, do not depend on distributional or structural assumptions and have no restrictions as to the pattern or missing data mechanisms. They are tested through the simulation of contamination and unbalance, both in artificially generated matrices and in a matrix of real data from an experiment with genotype-by-environment interaction. Their performance is assessed by means of prediction errors, the squared cosine between matrices, and a quality coefficient of fit between imputations and true values. For small matrices, the best results are obtained by applying robust decomposition directly, while for larger matrices the highest quality is obtained by eliminating the singular values of the imputation equation.

Simulated data from a genotype-to-phenotype crop growth model for pepper

The data in this article includes 300 simulated two-way data tables with 200 genotypes in the rows and 12 environments in the columns each. The yield data was obtained from a genotype-to-phenotype crop growth model that was adapted for pepper. The genotypes were characterized by 237 markers covering all the 12 chromosomes, and the environments were obtained as a combination of: (i) two levels of radiation based on historical data; (ii) three levels of daily average temperatures, 15, 20 and 25 °C; and (iii) two countries, Spain and The Netherlands. 100 two-way data tables were obtained for each of the three levels of heritability in the environments, 0.3, 0.5 and 0.8. The data is available as supplementary material of this paper.

Robust estimation of heritability and predictive accuracy in plant breeding: evaluation using simulation and empirical data

BACKGROUND

Genomic prediction (GP) is used in animal and plant breeding to help identify the best genotypes for selection. One of the most important measures of the effectiveness and reliability of GP in plant breeding is predictive accuracy. An accurate estimate of this measure is thus central to GP. Moreover, regression models are the models of choice for analyzing field trial data in plant breeding. However, models that use the classical likelihood typically perform poorly, often resulting in biased parameter estimates, when their underlying assumptions are violated. This typically happens when data are contaminated with outliers. These biases often translate into inaccurate estimates of heritability and predictive accuracy, compromising the performance of GP. Since phenotypic data are susceptible to contamination, improving the methods for estimating heritability and predictive accuracy can enhance the performance of GP. Robust statistical methods provide an intuitively appealing and a theoretically well justified framework for overcoming some of the drawbacks of classical regression, most notably the departure from the normality assumption. We compare the performance of robust and classical approaches to two recently published methods for estimating heritability and predictive accuracy of GP using simulation of several plausible scenarios of random and block data contamination with outliers and commercial maize and rye breeding datasets.

RESULTS

The robust approach generally performed as good as or better than the classical approach in phenotypic data analysis and in estimating the predictive accuracy of heritability and genomic prediction under both the random and block contamination scenarios. Notably, it consistently outperformed the classical approach under the random contamination scenario. Analyses of the empirical maize and rye datasets further reinforce the stability and reliability of the robust approach in the presence of outliers or missing data.

CONCLUSIONS

The proposed robust approach enhances the predictive accuracy of heritability and genomic prediction by minimizing the deleterious effects of outliers for a broad range of simulation scenarios and empirical breeding datasets. Accordingly, plant breeders should seriously consider regularly using the robust alongside the classical approach and increasing the number of replicates to three or more, to further enhance the accuracy of the robust approach.

The Decomposition and Forecasting of Mutual Investment Funds Using Singular Spectrum Analysis

Singular spectrum analysis (SSA) is a non-parametric method that breaks down a time series into a set of components that can be interpreted and grouped as trend, periodicity, and noise, emphasizing the separability of the underlying components and separate periodicities that occur at different time scales. The original time series can be recovered by summing all components. However, only the components associated to the signal should be considered for the reconstruction of the noise-free time series and to conduct forecasts. When the time series data has the presence of outliers, SSA and other classic parametric and non-parametric methods might result in misleading conclusions and robust methodologies should be used. In this paper we consider the use of two robust SSA algorithms for model fit and one for model forecasting. The classic SSA model, the robust SSA alternatives, and the autoregressive integrated moving average (ARIMA) model are compared in terms of computational time and accuracy for model fit and model forecast, using a simulation example and time series data from the quotas and returns of six mutual investment funds. When outliers are present in the data, the simulation study shows that the robust SSA algorithms outperform the classical ARIMA and SSA models.