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Updated: Nov 27, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Adaptability and stability analyses of plants using random regression models.

Michel Henriques de Souza1, José Domingos Pereira Júnior1, Skarlet De Marco Steckling2

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Random regression models (RRM) accurately predict common bean cultivar performance across environments, overcoming experimental imbalances. This method enhances understanding of genotype-by-environment interaction, adaptability, and stability in plant breeding.

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Area of Science:

  • Plant Breeding and Genetics
  • Quantitative Genetics
  • Agricultural Science

Background:

  • Evaluating cultivars in multi-environment trials (MET) is crucial for plant breeding, with genotype-by-environment interaction (GEI) being a key focus.
  • Traditional linear regression methods for assessing GEI, adaptability, and stability have limitations, particularly with unbalanced experimental data and heterogeneous variances.
  • Random regression models (RRM) offer an alternative by characterizing genotype behavior as reaction norms using longitudinal data and covariance functions.

Purpose of the Study:

  • To apply random regression models (RRM) for studying the behavior of common bean cultivars in multi-environment trials (MET).
  • To utilize Legendre polynomials and genotype-ideotype distances within the RRM framework.
  • To accurately quantify genotypic adaptability and stability across diverse environments.

Main Methods:

  • Application of random regression models (RRM) using Legendre polynomials.
  • Calculation of genotype-ideotype distances based on predicted genotypic values.
  • Analysis of 13 multi-environment trials classified as favorable or unfavorable.

Main Results:

  • RRM accurately predicted genotypic values in unobserved environments, effectively addressing experimental imbalance.
  • Genotypic adaptability was successfully measured by comparing reaction norms to ideotypes.
  • Cultivar stability was interpreted through the variation in ideotype behavior, enabling better performance comparisons.

Conclusions:

  • Random regression models provide a robust alternative for analyzing cultivar performance in MET, especially for quantifying adaptability and stability.
  • The RRM approach circumvents limitations of traditional methods, offering high accuracy in predicting genotypic values across environments.
  • Using ideotypes derived from real data facilitates a more precise comparison of cultivar performance and stability.