Bayesian GGE model for heteroscedastic multienvironmental trials

Abstract

The dissection of genotype × environment interaction (GEI) is a crucial aspect of the final stages of plant breeding pipelines and recommendation of cultivars. Linearbilinear models used to analyze this interaction, such as the additive main effects and multiplicative interaction (AMMI) and genotype plus GEI (GGE), often assume homogeneity of the residual variances across environments which affects the estimates and therefore, interpretations and conclusions. Our main objective was to propose a GGE model that considers heteroscedasticity across environments using Bayesian inference and to evaluate its implications in the interpretation of real and simulated data. The GGE model assuming common variance was also fitted for comparison purposes. The great flexibility of the Bayesian inference is transferred to the biplots, allowing the construction of credible regions for genotypic and environmental scores. The inference on the stability and adaptability of genotypes might change when heteroscedasticity is ignored. When real data are used, different patterns of correlations between environments also affect the representativeness and discrimination of the target environment. The modeling of heteroscedasticity allowed the clustering of environments into subgroups, with similar effects for GEI. The proposed GGE model was more adequate and realistic to deal with scenarios of heterogeneous variance in multienvironment trials, which can be useful for exploiting the GEI.Abbreviations: AE, average environment; AEA, axis of the average environment; AEC, average environment coordination; AMMI, additive main effects and multiplicative interaction model; BGGE, Bayesian GGE model under homogeneity of residual variances across sites; BGGEH, Bayesian GGE model under heterogeneity of residual variances across sites; FA, Factor-Analytic Model; G, Genotype; GEI, Genotype × environment interaction; GGE, Genotype main effect + genotype × environment interaction; HPD, Highest posterior density; IG, ideal genotype; MCMC, Markov chain Monte Carlo; MET, Multienvironmental trial; MLM, mixed linear model; SS GGE , total sum of squares for G + GEI; SVD, Singular value decomposition.

Response of African Sorghum Genotypes for Drought Tolerance under Variable Environments

“…Its analysis is an essential step for cultivar recommendation. To quantify the effects of genotype, environment, and GEI, several statistical methods are used, including the additive main effects and multiplicative interaction (AMMI) and genotype-by-environment (GGE) biplots [26][27][28][29]. Of the two methods, AMMI analysis is recommended as the most effective due to its ability to illustrate the complex interaction between genotypes and environments accurately and graphically [27].…”

An investigation of the impact of imbalance on the analysis of the US crop variety evaluation program data

“…(2019) and De Oliveira et al. (2022), incorporated Bayesian methods to address heteroscedasticity across environments, and they offered wide flexibility in modeling complex covariance structure of GEI. However, these models would require more balanced data to obtain accurate estimation and prediction (Smith et al., 2015).…”

“…However, such a strong assumption might not be realistic and a class of more complex and informative models, the factor analytic model, was proposed to accommodate both heterogeneous variances and between-environment correlation (Kelly et al, 2007;Nuvunga et al, 2015;Piepho et al, 1998;Smith et al, 2005). Several recent works, such as Silva et al (2019) and De Oliveira et al (2022), incorpo-rated Bayesian methods to address heteroscedasticity across environments, and they offered wide flexibility in modeling complex covariance structure of GEI. However, these models would require more balanced data to obtain accurate estimation and prediction (Smith et al, 2015).…”

Assessing the stability and adaptability of corn hybrid yield with the Bayesian AMMI model

“…The Markov chains for all model parameters were generated using a Gibbs sampler with the help of the ammiBayes package (OLIVEIRA et al, 2022) which was adapted to the model used by Crossa et al (2011) to estimate a general mean and does not use specific priors for the variance of the genotype effect.…”