Abstract
BackgroundAnalysis of data on genotypes with different expression in different environments is a classic problem in quantitative genetics. A review of models for data with genotype × environment interactions and related problems is given, linking early, analysis of variance based formulations to their modern, mixed model counterparts.ResultsIt is shown that models developed for the analysis of multi-environment trials in plant breeding are directly applicable in animal breeding. In particular, the 'additive main effect, multiplicative interaction' models accommodate heterogeneity of variance and are characterised by a factor-analytic covariance structure. While this can be implemented in mixed models by imposing such structure on the genetic covariance matrix in a standard, multi-trait model, an equivalent model is obtained by fitting the common and specific factors genetic separately. Properties of the mixed model equations for alternative implementations of factor-analytic models are discussed, and extensions to structured modelling of covariance matrices for multi-trait, multi-environment scenarios are described.ConclusionFactor analytic models provide a natural framework for modelling genotype × environment interaction type problems. Mixed model analyses fitting such models are likely to see increasing use due to the parsimonious description of covariance structures available, the scope for direct interpretation of factors as well as computational advantages.
Highlights
It has long been recognised that expression of genotypes is altered by environmental conditions
Assuming genotypes and interaction effects are random, such basic model generally implies a constant variance of G × E effects and, for more than two environments, a uniform genetic correlation across all environments
Falconer [4] perceived that treating performance of genotypes in different environments as different, correlated traits provides an alternative way to model G × E effects
Summary
It has long been recognised that expression of genotypes is altered by environmental conditions. Assuming genotypes and interaction effects are random, such basic model generally implies a constant variance of G × E effects and, for more than two environments, a uniform genetic correlation across all environments. Often, this is too restrictive and a number of other models and methods have been developed, both in animal and plant breeding applications; see, for instance, Freeman [1] for a review of early approaches, Cameron [2] for an outline of more modern methods, and James [3] for a recent exposé. A review of models for data with genotype × environment interactions and related problems is given, linking early, analysis of variance based formulations to their modern, mixed model counterparts
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call