Redefining the context for GxE studies; attempts to integrate statistical, physiological and genetical models
by
Fred van Eeuwijk
Dept of Plant Sciences, Wageningen University, The Netherlands

Many texts consider genotype by environment interaction (GxE) as a central problem to plant breeding. In the case of cross-over interaction, by many authors considered as the most severe form of GxE, GxE leads to rank changes of genotypic performances between environments. Less severe forms of GxE can then be imagined to consist of convergence and divergence of the phenotypic responses for various genotypes. When the phenotype is understood as a complex, development-dependent, non-linear function of genetical and environmental factors, integrated over time, presence of GxE should be the norm and absence of GxE the exception. The real questions with respect to GxE thus seem not to concern existence (testing), but, earlier, description (estimation) of GxE. The issue is to built a reliable model for phenotypic expression in relation to genetic and environmental information.

Traditional approaches focussed rather heavily on tests for GxE. One class of approaches, models the phenotypic responses for different genotypes by non-parallel regressions, by which the test for GxE becomes a test for (non-)parallelism. Another class of statistical models focusses on variance parameters for individual genotypes, making the test for GxE a test for heterogeneity of variance. Finally, lack of correlation between responses in different environments is considered to provide a firm indication of the existence of GxE.

The last decade, new developments in mixed model methodology have made the distinction between the regression, variance and correlation approach obsolete. When modelling phenotypic data in relation to genotype and environment, both expectation and variance-covariance structure should be taken into account. The choice of model and the choice of model terms as fixed or random should be determined by the specific question at hand. Investigating GxE means, constructing a (mixed) model that allows specific questions to be answered. For example, which genotypes will be superior in particular environments, what is the probability that a particular genotype’s yield will exceed a predefined threshold, what would be a reasonable design for the selection of high yielding genotypes for particular conditions?

Model building in a pure mixed model framework can still be cumbersome. A useful complement to formal model building, is provided by graphical procedures related to various forms of singular value decomposition and multilinear modelling.

Recent improvements to statistical models for phenotypic responses are both statistical and non-statistical. On the statistical side, the developments in mixed model theory and multilinear modelling have contributed. On the non-statistical side, the construction of relevant genetic and environmental covariables has greatly advanced the quality of models for phenotypic expression, and, by implication, for GxE. More detail in the genetic dimension of models for phenotypic expression is visible in the introduction of so-called quantitative trait loci (QTLs) in models for GxE. Statistically, this is equivalent to the inclusion of nominal covariables on the levels of genotypic factor(s). Detail in the environmental dimension follows from the use of crop-growth models for the description of environmental stresses. Statistically, this means the inclusion of quantitative covariables on the levels of the environmental factor(s), where the values for the environmental covariables are outputs from crop-growth models.

In the presentation, I will touch upon classical models/tests for GxE, multilinear approaches, graphical analyses, mixed models, extension to models for QTLxE, and use of crop-growth models.

Date received: October 22, 2002