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A Bayesian Shrinkage Approach for AMMI Models.

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This study introduces a Bayesian approach for genotype-by-environment interaction (GEI) analysis in maize breeding. The Bayesian shrinkage AMMI model effectively selects parsimonious models, retaining key GEI patterns and improving selection accuracy.

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Area of Science:

  • Agricultural Science
  • Biometrics
  • Plant Breeding

Background:

  • Genotype-by-environment interaction (GEI) is crucial in plant breeding for developing stable and high-yielding varieties.
  • Additive main effects and multiplicative interaction (AMMI) models are widely used for GEI analysis, but selecting the number of multiplicative terms remains a challenge.
  • Shrinkage estimators offer a potential solution for selecting GEI components in AMMI models.

Purpose of the Study:

  • To develop and evaluate a Bayesian approach combined with AMMI and shrinkage estimators for GEI analysis.
  • To compare the performance of traditional Bayesian AMMI and Bayesian shrinkage AMMI models.
  • To assess the model selection criteria and the ability to retain GEI patterns.

Main Methods:

  • A Bayesian approach was integrated with the AMMI model incorporating shrinkage estimators for principal components.
  • Fifty-five maize genotypes were evaluated across nine environments using a randomized complete block design with three replicates.
  • Model selection was based on posterior distribution of singular values and compared with traditional methods like the Cornelius F-test and cross-validation.

Main Results:

  • The traditional Bayesian AMMI model showed limited shrinkage but accurately determined credible intervals.
  • Bayesian shrinkage AMMI models demonstrated stronger shrinkage of principal components, leading to more parsimonious models.
  • Selected models using the Bayesian shrinkage approach were comparable to those from traditional F-tests and cross-validation, retaining more GEI pattern in fewer components.

Conclusions:

  • The Bayesian shrinkage AMMI model provides a robust method for selecting parsimonious GEI models in plant breeding.
  • This approach effectively retains significant GEI patterns while discarding noise, without relying on Gaussian assumptions.
  • The method facilitates credible interval estimation for AMMI biplots and offers a data-driven model selection criterion.