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Significance and Stability Analysis of Genotype-Environment Interaction using GxEStat

Meng'en Qin, Zhe Li, Hui Huang, Xihong Liu

arXiv:2604.03337v3cs.CVstat.AP

TL;DR

G×E interactions can change genotype performance across environments, limiting reliable evaluation and selection. The paper integrates mixed-effect significance testing with multiple stability analyses in GxEStat, an interactive R platform. Applications to breeding datasets demonstrate the framework’s effectiveness for multi-environment trial analysis.

  • Problem

    G×E interactions alter genotype performance across environments, reducing phenotype predictability and complicating reliable genotype evaluation and selection.

  • Method

    The framework combines linear mixed-effect significance testing with single-genotype and multi-genotype stability models in a reproducible GxEStat workflow.

  • Results

    GxEStat integrates analysis, visualization, and interpretation while improving analytical efficiency, reproducibility, and accessibility for multi-environment trial analysis.

  • Takeaways & Limitations

    The framework supports identifying genotype adaptability, environmental representativeness, and performance consistency across environments in practical breeding research.

  • Takeaways & Limitations

    Single-genotype stability models cannot characterize interaction patterns among all genotypes and environments, while multi-trait, multi-environment, and high-dimensional genomic modeling remains an open problem.

Abstract

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Genotype-environment (GxE) interactions can influence the performance of genotypes across diverse environments, limiting the reliability of genotype evaluation and selection in breeding programs. In-depth analysis of GxE interactions is therefore essential for understanding how genetic advantages or defects are expressed under varying environmental conditions and for identifying superior and stable genotypes. This study presents an integrated computational framework for GxE analysis that combines significance and stability evaluation within a unified analytical workflow. The framework incorporates the mixed effect modeling to quantify the significance of environment, genotype, and GxE effects, together with multiple stability analysis approaches for characterizing genotype adaptability, environmental representativeness, and performance consistency across environments. To support reproducible statistical analysis, we develop GxEStat, an interactive R platform that automates model construction, parameter estimation, statistical inference, and graphical visualization. GxEStat substantially improves analytical efficiency, reproducibility, and accessibility for multi-environment trial analysis. Applications to real breeding datasets demonstrate the effectiveness of the proposed framework for practical breeding research. Codes are available at https://github.com/mason-ching/GxEStat.

1 Introduction

G×E interactions alter genotype performance across environments, complicating phenotype prediction and breeding selection. The paper reviews stability methods and introduces an integrated, reproducible framework implemented in GxEStat.

  • G×E interactions modulate genetic effects by environmental conditions, altering genotype performance and reducing phenotype predictability in target settings.
  • ANOVA and mixed-effect models support significance assessment, with fixed or random genotype treatment selected according to the inferential objective.
  • Regression-based stability evaluates trait mean, environmental response slope, and regression deviation to characterize genotype adaptability across environments.
  • Variance-based indices include Wricke’s ecovalence, Shukla’s stability variance, Kang’s yield stability index, Lin’s Pi, and Francis’s coefficient of variation.
  • AMMI and GGE provide graphically interpretable multivariate stability analyses, although researchers continue to debate appropriate methods for multi-environment breeding data.
  • GxEStat unifies significance testing, variance estimation, stability assessment, visualization, and interpretation in an interactive, reproducible R platform.

2.1 Preliminaries

The preliminaries explain fixed and random effects in mixed models and introduce PCA/SVD as tools for representing multivariate data in lower dimensions. These foundations support modeling repeated variety observations and multivariate G×E structure.

  • 2.1.1 Fixed and Random Effects: A standard regression can violate residual independence when variety-specific predictors change across repeated observations.
  • 2.1.1 Fixed and Random Effects: Random-intercept models give each variety a separate intercept, while random-intercept-and-slope models give each variety its own trajectory.
  • 2.1.1 Fixed and Random Effects: Fixed effects represent group-level intercepts, slopes, main effects, and interactions; random effects represent individual characteristic variability across samples.
  • 2.1.2 PCA and SVD: PCA maps correlated quantitative variables to orthogonal principal components ordered by explained variance, enabling lower-dimensional visualization and interpretation.
  • 2.1.2 PCA and SVD: SVD computes PCA directly on centered data and is described as more numerically stable and efficient for large or non-square matrices.
  • 2.1.2 PCA and SVD: Dimensionality reduction retains leading singular values and right singular vectors to construct a rank-k approximation of the original data.

2.2 Significance Analysis of Genotype-Environment Interaction

The framework uses mixed-effects models to represent multi-environment breeding data, estimate genotype-specific predictions, and test fixed, random, and interaction effects. Significance testing combines Type III F-tests for fixed effects with likelihood-ratio comparisons for random effects, while variance components quantify contributions to phenotypic variation.

  • Mixed Effect Model: Multi-environment trials generate G × E × R observations, with environments commonly defined by location-year combinations and treatments by genotype-environment combinations.
  • Mixed Effect Model: Fixed and random effect assignments for location, year, genotype, and replication depend on the inferential objective.Genotypes are fixed when comparing specific cultivars and random when the objective requires a different inferential treatment.
  • Mixed Effect Model: The fitted mixed-effects model provides fixed-effect estimates, standard errors, random-effect variances, and BLUP-based predictions for genotype-specific traits.The lmer function fits the model, while random effects are estimated through best linear unbiased prediction and conditional fitted values.
  • Significance Analysis: Significance analysis identifies contributing model effects and estimates variance components for genotypes, environments, and their interactions.The resulting significance assessment supports model simplification and provides the basis for subsequent stability analysis.
  • Significance Analysis: Type III F-tests using the Kenward–Roger approximation assess fixed effects, whereas likelihood-ratio tests compare nested models for random effects.Random-effect testing removes one variance component from an auxiliary model while retaining the other model terms.
  • Significance Analysis: Random-effect likelihood-ratio testing is a boundary problem because variance components are constrained to be non-negative, yielding a theoretical chi-square mixture rather than a standard asymptotic distribution.The likelihood-ratio statistic compares auxiliary and full-model maximum likelihoods, with k equal to their difference in estimated parameters.

2.3 Stability Analysis of Genotype-Environment Interaction

The framework evaluates stability through single-genotype regression and multigenotype models. Regression parameters quantify responsiveness and consistency, while AMMI and GGE use multiplicative components and graphical representations to characterize interaction patterns and adaptation.

  • Single-genotype Stability Analysis: Single-genotype stability analysis uses joint regression to quantify each genotype’s response to environmental variation.The workflow calculates genotype-environment means and constructs a regression model across environment and replication levels.
  • Single-genotype Stability Analysis: The regression coefficient β1j measures responsiveness to environmental conditions, while the deviation from regression s2_dj measures phenotypic stability.Broad adaptation corresponds to β1j not significantly different from one and s2_dj close to zero.
  • Single-genotype Stability Analysis: Genotypes with β1j > 1 respond more strongly to favorable environments, whereas genotypes with β1j < 1 tend to perform more consistently under unfavorable or stress conditions.A smaller deviation from regression indicates greater stability across environments; t-tests and F-tests evaluate the corresponding hypotheses.
  • Single-genotype Stability Analysis: Residual mean squares support calculation of Shukla’s stability variance, Wricke’s ecovalence, and Kang’s yield stability statistic.These complementary measures assess stability and help identify genotypes combining stable and high yield across environments.
  • Single-genotype Stability Analysis: Single-genotype models assess individual stability but cannot simultaneously characterize interaction patterns among all genotypes and environments.Multivariate models are therefore used to examine overall G×E structure and identify adaptation to specific or broad environments.
  • Multi-genotype Stability Analysis: AMMI combines ANOVA-estimated genotype and environment main effects with PCA of residual G×E interactions to describe dominant interaction patterns.Retained interaction principal components capture structured interaction, while remaining components represent residual variation.
  • Multi-genotype Stability Analysis: GGE combines genotype main effects and G×E interactions into one multiplicative component, enabling graphical evaluation of genotype performance, stability, and mega-environments.Its biplot is constructed using SVD of an environment-standardized genotype-by-environment matrix.
  • Multi-genotype Stability Analysis: In GGE biplots, PC1 primarily reflects average genotype performance, whereas PC2 mainly represents stability and crossover G×E interactions.

3 Experiment Results and Analysis

GxEStat applies mixed-effects significance testing and multiple stability analyses to watermelon and oat breeding datasets. The analyses identify significant genotype–environment effects, stable high-yielding genotypes, and environment-specific performance patterns.

  • Data and workflow: The study analyzes watermelon trials from 2009–2010 and oat field trials using GxEStat’s significance, single-genotype stability, and multi-genotype stability modules.The watermelon dataset includes 10 varieties, 5 locations, 2 years, and 4 replications; the oat dataset includes 6 environments and 24 varieties.
  • Significance analysis: Mixed-effects analysis found significant oat effects for genotype (F=3.547, p=0.013), location (F=2.856, p=0.037), and genotype × location (F=2.989, p=0.018).All three effects were significant at the 5% level, indicating environment-dependent relative genotype performance.
  • Significance analysis: GxEStat calculates BLUPs, yield estimates, and residuals, supporting subsequent stability analysis after genotype and genotype–environment effects are identified.The reported workflow uses significance results to motivate selection for high yield and stability.
  • Single-genotype stability: Single-genotype stability analysis reports regression slope, regression deviation, Wricke’s stability ecovalence, and Kang’s yield stability statistic.The analysis identifies CalhounGray, FiestaF1, GeorgiaRattlesnake, Legacy, and StarbriteF1 as environmentally adaptable and stable watermelon genotypes.
  • AMMI analysis: AMMI biplots depict genotype–environment interactions, with oat genotypes showing strong yields in selected environments and watermelon Gen7 and Gen9 performing particularly well in KN and TX.The biplots retain four principal components and represent interactions through genotype and environment scores.
  • GGE analysis: GGE biplots evaluate environment discrimination and representativeness, genotype productivity and stability, and which genotype performs best in each environment.Gen1, Gen5, and Gen7 are reported as stable and high-yielding, while Gen3 has the highest yield in FL, TX, CL, and KN.

4 Conclusion and Discussion

GxEStat unifies G×E significance testing and stability analysis in a reproducible, user-friendly workflow. The discussion identifies nonlinear interactions, multi-trait analysis, and heterogeneous data integration as priorities for future development.

  • GxEStat integrates linear mixed-effect significance testing with single-genotype and multi-genotype stability models.
  • The framework reduces technical barriers to G×E analysis and supports reproducible, user-friendly workflows.
  • Current linear and mixed-effects approaches may have limited capability for capturing complex nonlinear genotype-environment-management interactions.
  • Joint modeling of multiple correlated traits across environments and high-dimensional genomic data remains an open problem.
  • Future statistical software should support scalable integration of genomic, phenomic, environmental, and remote-sensing data for precision breeding.
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