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Cited by 623Genetics and Plant BreedingAgriculture, Soil, Plant ScienceOptimal Experimental Design Methods

The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches

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SMITH, A. B., CULLIS, B. R., THOMPSON, R.·2005·The Journal of Agricultural Science
DOI 10.1017/s0021859605005587
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Abstract

The analysis of series of crop variety trials has a long history with the earliest approaches being based on ANOVA methods. Kempton (1984) discussed the inadequacies of this approach, summarized the alternatives available at that time and noted that all of these approaches could be classified as multiplicative models. Recently, mixed model approaches have become popular for the analysis of series of variety trials. There are numerous reasons for their use, including the ease with which incomplete data (not all varieties in all trials) can be handled and the ability to appropriately model within-trial error variation. Currently, the most common mixed model approaches for series of variety trials are mixed model versions of the methods summarized by Kempton (1984). In the present paper a general formulation that encompasses all of these methods is described, then individual methods are considered in detail.

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Registry

Crossref · 10.1017/s0021859605005587

Cites

52 of 52 references verified0 citation errors · 0 not checkable

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  • Smith et al. (2001a, 2005) extended the G × E analysis by employing Factor Analytic Multiplicative Mixed (FAMM) models.

    “Smith et al. (2001a, 2005) extended the G × E analysis by employing Factor Analytic Multiplicative Mixed (FAMM) models.”

    From Multi-environment trials data analysis: linear mixed model-based approaches using spatial and factor analytic models (2025) · cites this paper as Smith et al., 2005

    The section “Mixed models with regressions on environmental means” (page unavailable) describes a mixed-model approach to variety-by-environment interaction with a factor-analytic variance structure and multiplicative terms. It calls this an extension of the Smith et al. (2001b) approach, however, not Smith et al. (2001a); the cited 2005 paper presents the approach in an overview rather than establishing that the 2005 work originated it. (LLM, conf=0.82)

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  • The ANOVA-based analysis commonly follows a two-stage modeling approach, first analyzing the data within each environment, then combining the results across environments for the G × E interaction analysis.

    “Furthermore, the ANOVA-based analysis commonly follows a two-stage modeling approach. This involves first analyzing the data within each environment, followed by a second stage of combining the results across environments for the G × E interaction analysis (Piepho et al., 2012; Smith et al., 2005).”

    From Multi-environment trials data analysis: linear mixed model-based approaches using spatial and factor analytic models (2025) · cites this paper as Smith et al., 2005

    The Additional information section (page unavailable) says many authors use a two-stage approach: they analyze individual trials, then combine variety means for an overall analysis. It describes that second stage as a mixed-model analysis, however, and does not establish that ANOVA-based analysis commonly follows this procedure. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • FAMM models assume random genotype effects and fixed environment effects, and use a one-stage analysis approach, where the models for residual effects are estimated simultaneously with the models for G × E effects.

    “These models assume random genotype effects and fixed environment effects, and use a one-stage analysis approach, where the models for residual effects are estimated simultaneously with the models for G × E effects.”

    From Multi-environment trials data analysis: linear mixed model-based approaches using spatial and factor analytic models (2025) · cites this paper as Smith et al., 2005

    In “Mixed models with regressions on environmental means” (page unavailable), the paper describes a factor-analytic model with random variety effects and fixed environment effects, but also describes a factor-analytic model with the converse assumptions. “Additional information” (page unavailable) explicitly defines one-stage analysis as estimating residual-effect and variety-by-environment-effect models simultaneously. The claim is therefore supported for the former model, but overstates the effect assumptions as applying to these models generally. (LLM, conf=0.83)

    Experimental — accuracy not yet measured

  • In a plant improvement program, it is more common to see environment fitted as fixed and genotype as random.

    “In a plant improvement program, it is more common to see environment fitted as fixed and genotype as random (Smith et al., 2005) which ties in with quantitative genetics theory (Falconer and Mackay, 1996).”

    From Incorporating environmental covariates to explore genotype × environment × management (G × E × M) interactions: A one-stage predictive model (2023) · cites this paper as Smith et al., 2005

    In “Variety effects: fixed or random?” (page unavailable), the paper says random variety effects are appropriate for breeding data and explicitly describes a model with random variety and fixed environment effects. It does not establish that this combination is more common in plant improvement programs; the authors present it as a modeling choice, not a measured pattern of practice. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • The two-stage ANOVA-based approach can lead to a loss of information and less effective extraction of insights from complex MET datasets.

    “This approach can lead to a loss of information and less effective extraction of insights from the complex MET datasets.”

    From Multi-environment trials data analysis: linear mixed model-based approaches using spatial and factor analytic models (2025) · cites this paper as Smith et al., 2005

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Cites

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Research works printed but not linked: 5

  1. FINNEY, D. J. (1980). Contribution to the discussion of: Statutory recommended list trials of crop varieties in the United Kingdom. Journal of the Royal Statistical Society Series A 143, 245-246.
  2. MARDIA, K. V., KENT, J. T. & BIBBY, J. M. (1988). Multi- variate Analysis. London: Academic Press.
  3. PAPADAKIS, J. S. (1937). Methode statistique pour des experiences sur champ. Bulletin Scientifique, Institut d'Amelioration des Plantes a Thessaloniki (Grece), 23, 12-28.
  4. PATTERSON, H. & NABUGOOMU, F. (1992). REML and the analysis of series of crop variety trials. In Proceedings from the 16th International Biometric Conference, pp. 77-93. Hamilton, New Zealand.
  5. TALBOT, M. (1984). Yield variability of crop varieties in the UK. Journal of Agricultural Science, Cambridge 102, 315-321.

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Authors
SMITH, A. B., CULLIS, B. R., & THOMPSON, R.
Affiliations
Rothamsted Research (GB)
ORCID
Venue
The Journal of Agricultural Science
Publisher
Cambridge University Press (CUP)
Published
2005-09-20
Volume
143
Issue
6
Pages
449-462
ISSN
  • 0021-8596 (ISSN-L)
  • 1469-5146
DOI
10.1017/s0021859605005587
OpenAlex
W2129192099
Cited by
623
References
52
Citations by year
2026: 43 · 2025: 40 · 2024: 52 · 2023: 42 · 2022: 38 · 2021: 40 · 2020: 48 · 2019: 33 · 2018: 33 · 2017: 29 · 2016: 40 · 2015: 27 · 2014: 34 · 2013: 24 · 2012: 18
FWCI
12.03
Type
journal article
Language
en
Open access
Licence
www.cambridge.org/core/terms (unspecified)
Locations
  • The Journal of Agricultural Science (publishedVersion)
  • Rothamsted Repository (Rothamsted Repository) (submittedVersion)
  • Research Online (University of Wollongong) (submittedVersion)
  • Figshare (submittedVersion)
Funders
  • Grains Research and Development Corporation
  • Directorate for Biological Sciences
  • Biotechnology and Biological Sciences Research Council
Topics
  • Life Sciences › Agricultural and Biological Sciences › Plant Science › Genetics and Plant Breeding
  • Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Agriculture, Soil, Plant Science
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
Keywords
cultivar evaluation, mixed models, multiplicative model, missing data, general formulation

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