Abstract
ABSTRACT The additive main effects and multiplicative interaction (AMMI) model is frequently applied in plant breeding for studying the genotype × environment (G × E) interaction. One of the main difficulties related to this method of analysis is the incorporation of inference to the bilinear terms that compose the biplot representation. This study aimed to incorporate credible intervals for the genotypic and environmental scores in the AMMI model by using an informative prior for the genotype effect. This approach differs from the Bayesian methods that have been presented so far, which assume the same restrictions as the fixed effects model. The method was exemplified by using data from a study with 55 maize hybrids in nine different environments for which variable being studied was the yield of unhusked ears. Our results demonstrated that the credible intervals allowed for the identification of genotypes and environments that did not contribute to the G × E interaction. In addition, it facilitated recognition of homogeneous subgroups of genotypes and environments (with respect to the effect of the interaction) and the adaptability of genotypes to specific environments of great interest to breeders. The posterior distributions of singular vectors were bimodal but with the same density peaks in absolute value. This reflects the arbitrary choice of signs of the main component that was used in different mathematical algorithms. Although our data set was based on unrelated single cross hybrids, the choice of genotypes as random effects enabled the Bayesian AMMI to accommodate the additive and nonadditive relationship matrices. Additionally, the flexibility of the analysis facilitated working with unbalanced data and the incorporation of heterogeneity of variances.
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Claims 5
Claim · model-written summary
Credible intervals identified genotypes and environments that did not contribute to genotype by environment interaction.
- Outcome
- identification of genotypes and environments that did not contribute to the G × E interactione0
- Comparator
- genotypes and environmentse0
Zea maysOrganisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the credible intervals allowed for the identification of genotypes and environments that did not contribute to the G × E interaction”
e1“55 maize hybrids”
Claim · model-written summary
The method identified homogeneous subgroups and genotype adaptability to specific environments.
- Outcome
- recognition of homogeneous subgroups of genotypes and environmentse0
- Comparator
- genotypes and environmentse0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“it facilitated recognition of homogeneous subgroups of genotypes and environments (with respect to the effect of the interaction) and the adaptability of genotypes to specific environments”
e1“55 maize hybrids”
Claim · model-written summary
Posterior distributions of singular vectors were bimodal with equal absolute density peaks.
- Outcome
- posterior distributions of singular vectorse0
- Comparator
- same density peaks in absolute valuee0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The posterior distributions of singular vectors were bimodal but with the same density peaks in absolute value”
e1“55 maize hybrids”
Claim · model-written summary
Random genotype effects enabled Bayesian AMMI to accommodate additive and nonadditive relationship matrices.
- Outcome
- accommodate the additive and nonadditive relationship matricese0
- Comparator
- additive and nonadditive relationship matricese0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the choice of genotypes as random effects enabled the Bayesian AMMI to accommodate the additive and nonadditive relationship matrices”
e1“55 maize hybrids”
Claim · model-written summary
The analysis allowed unbalanced data and heterogeneous variances.
- Outcome
- working with unbalanced data and the incorporation of heterogeneity of variancese0
- Comparator
- unbalanced datae0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the flexibility of the analysis facilitated working with unbalanced data and the incorporation of heterogeneity of variances”
e1“55 maize hybrids”