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Updated: Apr 26, 2026

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Analysis of linear and non-linear genotype × environment interaction.

Rong-Cai Yang1

  • 1Alberta Agriculture and Rural Development Edmonton, AB, Canada ; Department of Agricultural, Food and Nutritional Science, University of Alberta Edmonton, AB, Canada.

Frontiers in Genetics
|August 8, 2014
PubMed
Summary

Non-linear functions improve the analysis of genotype × environment (G × E) interactions, especially with wide environmental ranges. This approach enhances the detection of G × E variation compared to traditional linear models.

Keywords:
barleyenvironmental indexestimationgenotype × environment interactionnon-linear functionsquantitative trait loci

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Area of Science:

  • Plant breeding
  • Quantitative genetics
  • Agricultural science

Background:

  • Genotype × environment (G × E) interaction analysis typically uses linear models.
  • Linear models can obscure non-linear genotypic responses across diverse environmental conditions.
  • Detecting G × E variation is crucial for crop improvement.

Purpose of the Study:

  • To explore non-linear functions (logistic, parabola, normal, Cauchy) for modeling G × E.
  • To investigate how non-linear modeling affects the estimation of genetic effects across environments.
  • To compare the power of non-linear versus linear models in detecting G × E variation.

Main Methods:

  • Applied four non-linear functions to model genotypic responses to environmental changes.
  • Analyzed barley cultivar trial data (Data A) and North America Barley Genome Mapping Project data (Data B).
  • Compared G × E variation captured by non-linear functions against linear models.

Main Results:

  • The Cauchy function captured over 40% of G × E variation in Data A.
  • Non-linear functions can reveal more G × E variation than linear models.
  • Data B showed largely linear genotypic responses but strong QTL × environment interactions.

Conclusions:

  • Non-linear functions are valuable for analyzing multi-environmental trials with broad environmental variation.
  • QTL × environment interactions can stem from varying effect sizes across environments.
  • Considering non-linear responses improves the understanding of G × E interactions in crop breeding.