cs.CVApr 3, 2026

Significance and Stability Analysis of Genotype-Environment Interaction using GxEStat

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

Organizations: School of Mathematics and Statistics, Henan University, Kaifeng, China. · Faculty of Computer Science and Artificial Intelligence, Shenzhen University of Advanced Technology, Shenzhen, China. · School of Nursing, Shanghai Jiao Tong University, Shanghai, China. · Shenzhen University of Advanced Technology General Hospital, Shenzhen, China.

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Abstract

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.

Figures & tables

Source of variationDegree of freedomF or R
M1M2M3M4M5M6
genotypeG−1G-1RFFRRF
locationL−1L-1RFRFRF
yearY−1Y-1RFRRFR
replication (year ×\times location)(R−1)×L×Y(R-1)\times L\times YRRRRRR
location ×\times year(L−1)×(Y−1)(L-1)\times(Y-1)RFRRRR
Table 1: Degree of freedom and effect category of variation source terms.
ModelMixed-effect model
Model 1Trait∼  1+(1∣year)+(1∣location)+(1∣genotype)+(1∣year:location)+(1∣year:genotype)+(1∣location:genotype)+(1∣year:location:genotype)+(1∣year:location:replication)\begin{aligned} \texttt{Trait}\sim\;&1+(1|\texttt{year})+(1|\texttt{location})+(1|\texttt{genotype})\\ &+(1|\texttt{year:location})+(1|\texttt{year:genotype})\\ &+(1|\texttt{location:genotype})\\ &+(1|\texttt{year:location:genotype})\\ &+(1|\texttt{year:location:replication})\end{aligned}
Model 2Trait∼  year∗location∗genotype+(1∣year:location:replication)\begin{aligned} \texttt{Trait}\sim\;&\texttt{year}*\texttt{location}*\texttt{genotype}\\ &+(1|\texttt{year:location:replication})\end{aligned}
Model 3Trait∼  1+(1∣year)+(1∣location)+genotype+(1∣year:location)+(1∣year:genotype)+(1∣location:genotype)+(1∣year:location:genotype)+(1∣year:location:replication)\begin{aligned} \texttt{Trait}\sim\;&1+(1|\texttt{year})+(1|\texttt{location})+\texttt{genotype}\\ &+(1|\texttt{year:location})+(1|\texttt{year:genotype})\\ &+(1|\texttt{location:genotype})\\ &+(1|\texttt{year:location:genotype})\\ &+(1|\texttt{year:location:replication})\end{aligned}
Model 4Trait∼  1+(1∣year)+location+(1∣genotype)+(1∣year:location)+(1∣year:genotype)+(1∣location:genotype)+(1∣year:location:genotype)+(1∣year:location:replication)\begin{aligned} \texttt{Trait}\sim\;&1+(1|\texttt{year})+\texttt{location}+(1|\texttt{genotype})\\ &+(1|\texttt{year:location})+(1|\texttt{year:genotype})\\ &+(1|\texttt{location:genotype})\\ &+(1|\texttt{year:location:genotype})\\ &+(1|\texttt{year:location:replication})\end{aligned}
Model 5Trait∼  1+year+(1∣location)+(1∣genotype)+(1∣year:location)+(1∣year:genotype)+(1∣location:genotype)+(1∣year:location:genotype)+(1∣year:location:replication)\begin{aligned} \texttt{Trait}\sim\;&1+\texttt{year}+(1|\texttt{location})+(1|\texttt{genotype})\\ &+(1|\texttt{year:location})+(1|\texttt{year:genotype})\\ &+(1|\texttt{location:genotype})\\ &+(1|\texttt{year:location:genotype})\\ &+(1|\texttt{year:location:replication})\end{aligned}
Model 6Trait∼  1+(1∣year)+location+genotype+(1∣year:location)+(1∣year:genotype)+location:genotype+(1∣year:location:genotype)+(1∣year:location:replication)\begin{aligned} \texttt{Trait}\sim\;&1+(1|\texttt{year})+\texttt{location}+\texttt{genotype}\\ &+(1|\texttt{year:location})+(1|\texttt{year:genotype})\\ &+\texttt{location:genotype}\\ &+(1|\texttt{year:location:genotype})\\ &+(1|\texttt{year:location:replication})\end{aligned}
Table 2: Mixed effect model specifications.
Figure 1: Interface of our GxEStat.
yearlocationreplicationgenotypemarketable yield
2009KN1EarlyCanada56.236
2009KN1CalhounGray74.167
2009KN1GeorgiaRattlesnake55.873
2010TN2EarlyCanada32.601
2010TN2CalhounGray74.167
2010TN2GeorgiaRattlesnake64.794
Table 3: Demo of watermelon yield trial data in the southern United States in 2009–2010.
Source of variationVarianceStandard deviationLikelihood ratio pp -value
year ×\times location ×\times genotype49.747.050.008
year ×\times location ×\times replication73.918.600.000
location ×\times genotype0.000.001.000
year ×\times genotype0.000.001.000
year ×\times location57.817.600.078
genotype111.6810.570.001
Table 4: Significance analysis of watermelon breeding data.
Source of variationMean squareFF statisticpp -value
location ×\times genotype0.4112.9890.018
genotype0.5543.5470.013
location0.3342.8560.037
residual0.156––
Table 5: Significance analysis of oat field data.
Figure 2: Scatter plots of yield predictions versus model residuals for (a) watermelon breeding data and (b) oat field random trial data.
genotypeβ1i\beta_{1i}sdi2s_{di}^{2}σi2\sigma_{i}^{2}si2s_{i}^{2}Wi2W_{i}^{2}YSiYS_{i}
CalhounGray1.301124.67061.347 ns15.761 ns279.74710+
CrimsonSweet1.3411450.035 ∗∗439.125 ns567.988 ns1488.6364
EarlyCanada0.249 ∗∗686.251 ∗∗253.230 ns285.370 ns893.7722
FiestaF11.639657.873300.285 ns385.997 ns1044.34911+
GeorgiaRattlesnake0.945220.06352.213 ns44.863 ns250.5188+
Legacy1.056428.070287.394 ns262.488 ns1003.0977+
Table 6: Single-genotype stability analysis of watermelon data.
Figure 3: (a) PC1 v.s. PC2 biplot of oat field data, (b) PC1 v.s. PC2 v.s. PC3 triplot of oat field data, (c) PC1 v.s. PC2 biplot of watermelon breeding data. (d) PC1 v.s. PC2 v.s. PC3 triplot of watermelon breeding data.
Figure 4: GGE biplots: (a) discrimitiveness v.s. representativeness, (b) yield mean v.s. stability, (c) ranking environments, (d) which won where/what, (e) ranking genotypes, (f) relationship among environments.

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