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Testing multiplicative terms in AMMI and GGE models for multienvironment trials with replicates

  • Waqas Ahmed MalikEmail author
  • Johannes Forkman
  • Hans-Peter Piepho
Original Article
  • 47 Downloads

Abstract

Key message

For analysing multienvironment trials with replicates, a resampling-based method is proposed for testing significance of multiplicative interaction terms in AMMI and GGE models, which is superior compared to contending methods in robustness to heterogeneity of variance.

Abstract

The additive main effects and multiplicative interaction model and genotype main effects and genotype-by-environment interaction model are commonly used for the analysis of multienvironment trial data. Agronomists and plant breeders are frequently using these models for cultivar trials repeated across different environments and/or years. In these models, it is crucial to decide how many significant multiplicative interaction terms to retain. Several tests have been proposed for this purpose when replicate data are available; however, all of them assume that errors are normally distributed with a homogeneous variance. Here, we propose resampling-based methods for multienvironment trial data with replicates, which are free from these distributional assumptions. The methods are compared with competing parametric tests. In an extensive simulation study based on two multienvironment trials, it was found that the proposed methods performed well in terms of Type-I error rates regardless of the distribution of errors. The proposed method even outperforms the robust \( F_{R} \) test when the assumptions of normality and homogeneity of variance are violated.

Abbreviations

AMMI

Additive main effects and multiplicative interaction

GGE

Genotype and genotype environment interaction

MET

Multienvironment trial

SVD

Singular value decomposition

Notes

Acknowledgements

This work was supported by the German Research Foundation (DFG), Grant No. PI 377/17-1. The authors acknowledge support by the Baden-Württemberg high-performance computing (bwHPC) cluster.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standards

The authors declare that the experiments comply with the current laws of the countries in which the experiments were performed.

Supplementary material

122_2019_3339_MOESM1_ESM.txt (20 kb)
Supplementary material 1 (TXT 19 kb)
122_2019_3339_MOESM2_ESM.txt (4 kb)
Supplementary material 2 (TXT 4 kb)
122_2019_3339_MOESM3_ESM.txt (15 kb)
Supplementary material 3 (TXT 14 kb)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Waqas Ahmed Malik
    • 1
    Email author
  • Johannes Forkman
    • 2
  • Hans-Peter Piepho
    • 1
  1. 1.Biostatistics Unit, Institute of Crop ScienceUniversity of HohenheimStuttgartGermany
  2. 2.Department of Crop Production EcologySwedish University of Agricultural SciencesUppsalaSweden

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