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Bayesian factor analytic model: An approach in multiple environment trials.

Joel Jorge Nuvunga1,2, Carlos Pereira da Silva1, Luciano Antonio de Oliveira1,3

  • 1Department of Statistics (DES), Federal University of Lavras, Lavras, Minas Gerais, Brazil.

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A new Bayesian approach improves genotype-by-environment interaction (GEI) analysis in plant breeding. This method offers robust GEI quantification and superior prediction for multi-environment trials (MET).

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Area of Science:

  • Plant breeding
  • Statistical genetics
  • Quantitative genetics

Background:

  • Genotype-by-environment interaction (GEI) poses challenges in plant breeding for selecting superior genotypes across diverse environments.
  • Traditional factor analytic (FA) mixed models for GEI analysis face inferential issues like non-identifiability (Heywood cases) and lack uncertainty measures in biplots.

Purpose of the Study:

  • To introduce a Bayesian framework for factor analytic (FA) models to address GEI quantification in plant breeding.
  • To enhance the identifiability and robustness of GEI analysis using direct sampling of factor loadings via spectral decomposition.

Main Methods:

  • Developed a Bayesian FA model utilizing spectral decomposition for direct sampling of factor loadings, ensuring identifiability without ad hoc constraints.
  • Applied the proposed Bayesian method to simulated and real data from multi-environment trials (MET).
  • Compared the Bayesian FA model with traditional FA mixed models under controlled unbalanced conditions.

Main Results:

  • The Bayesian FA model demonstrated robustness across various simulated levels of unbalanced data in MET.
  • The Bayesian approach exhibited superior predictive ability for missing data compared to traditional FA mixed models.
  • Classical FA mixed models encountered parametric convergence and estimation failures in some scenarios, highlighting their limitations.

Conclusions:

  • Bayesian factorial models offer a robust and reliable alternative for analyzing genotype-by-environment interactions in multi-environment trials (MET) within plant breeding programs.
  • The proposed Bayesian method overcomes limitations of traditional FA models, providing better identifiability and predictive performance.