Abstract
Genotype-by-environment interaction (GEI) is an important phenomenon in plant breeding. This paper presents a series of models for describing, exploring, understanding, and predicting GEI. All models depart from a two-way table of genotype by environment means. First, a series of descriptive and explorative models/approaches are presented: Finlay–Wilkinson model, AMMI model, GGE biplot. All of these approaches have in common that they merely try to group genotypes and environments and do not use other information than the two-way table of means. Next, factorial regression is introduced as an approach to explicitly introduce genotypic and environmental covariates for describing and explaining GEI. Finally, QTL modeling is presented as a natural extension of factorial regression, where marker information is translated into genetic predictors. Tests for regression coefficients corresponding to these genetic predictors are tests for main effect QTL expression and QTL by environment interaction (QEI). QTL models for which QEI depends on environmental covariables form an interesting model class for predicting GEI for new genotypes and new environments. For realistic modeling of genotypic differences across multiple environments, sophisticated mixed models are necessary to allow for heterogeneity of genetic variances and correlations across environments. The use and interpretation of all models is illustrated by an example data set from the CIMMYT maize breeding program, containing environments differing in drought and nitrogen stress. To help readers to carry out the statistical analyses, GenStat® programs, 15th Edition and Discovery® version, are presented as “Appendix.”
Highlights
PHENOTYPE, GENOTYPE, AND ENVIRONMENT The success of a plant breeding program depends on its ability to provide farmers with genotypes with guaranteed superior performance in terms of yield and/or quality across a range of environmental conditions
This paper explores several strategies to model Genotype-by-environment interaction (GEI), starting with simple methods that have been historically popular within the plant breeding community
While here we focus in this paper on mixed model QTL detection, this is certainly not the only method for multi-environment QTL mapping
Summary
PHENOTYPE, GENOTYPE, AND ENVIRONMENT The success of a plant breeding program depends on its ability to provide farmers with genotypes with guaranteed superior performance (phenotype) in terms of yield and/or quality across a range of environmental conditions. Managed stress trials are not a default option in plant breeding, because stress type and level can be difficult to implement and because the relationship between phenotype and stress is complex, with genes and environmental stress(es) interacting throughout the various developmental phases In those situations, a common way for plant breeders to screen for genotypic reactions to environmental factors is by “multi-environment trials” (METs). The norms of reaction of genotypes will be parallel (Figure 1A) Another important aspect is that, the parameters in the model suggest that something intrinsically genetic and something intrinsically environmental is determining the trait, the genotypic and environmental effects purely follow from a convenient way of partitioning phenotypic variation from a statistical point of view.
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