Genotype by environment interaction (GxE) is considered by many texts to constitute one of the most pressing and persistent problems in plant breeding. Among plant breeders it is easier to find agreement on the consequences of GxE than on the underlying mechanisms. The major consequence of the occurrence of GxE can be captured in the observation that phenotypic evaluations on a set of genotypes as obtained in one or more specific trials are at best only partially predictive for the performance of the same genotypes in other conditions. Two broad classes of approaches have been developed to deal with this imperfect predictability. On the one hand, methodology has been proposed to model the phenotypic responses across environments in a genotype-specific way with the aim of being able to predict responses also for environments that were not in the original set of test-environments. Principally, regression models are involved in this approach, where the effort is placed on finding the right regressors. Genotypes then differ in sensitivity with respect to certain environmental variables, or they differ in adaptability. Good examples are the Finlay-Wilkinson model (regression on environmental mean) and factorial regression models (regression on climatological and/ or soil variables). To some extent, additive main effects and multiplicative interactions (AMMI) models can also be placed under this description. Alternatively, the occurrence of GxE may be accepted and then the modeling effort is directed at a satisfactory description of the genotype-dependent uncertainty in the response. All kinds of stability statistics fit within this philosophy,like the Eberhart-Russell and Shukla stability variances. A curious property of many of the adaptability and stability statistics is that they seem to be presented detached from a clear model- and-inference framework. Consequentially, interpretations of GxE are reduced to ranking genotypes on a one- or low-dimensional set of descriptors. As phenotypic responses can be thought of as originating from a multi-dimensional non-linear integration of genetic and environmental factors over time, it seems hard to believe that ranking genotypes on mean yield and some adaptability and stability statistics provides enough information to breeders for making selections. Worse, adaptability and stability statistics are highly dependent on the set of genotypes and environments included in the trials and may represent more of a statistical artifact than something intrinsically genetic. A natural choice for a modeling framework that allows the combined modeling of genotype dependent mean responses with genotype dependent variances, is the class of mixed models. Using mixed models, inferences on adaptability and stability can be done within a unifying likelihood context. The presentation will contain an example of this type of inference on adaptability and stability. Inclusion of co-variables on genotypes and environments in a regression setting leads to factorial regression models. In these models GxE is written as one or more products of genotypic descriptors (sensitivities, susceptibilities, tolerances, resistances) and environmental descriptors (climate, soil, infection pressures). Extending factorial regressions to mixed factorial regressions produces a very powerful type of model for dealing with GxE problems, giving attention to both adaptability and stability aspects. Again, inference can be determined by likelihood considerations. Principles will be illustrated by means of an example. The step from modeling GxE to quantitative trait loci (QTL) by environment interaction, or QxE, is a small one for users of mixed factorial regression models. QTL effects can be modeled by the introduction of a special type of genotypic co-variable, i.e., co-variables containing probabilities for QTL genotypes given the flanking markers. As soon as QTL expression becomes environment dependent, QxE appears. The identification of QTIs, with and without environment dependent expression, is most fruitfully considered an exercise in model selection. A straightforward extension of QxE models in mixed factorial regression form is the incorporation of environmental co-variables that determine the amount of QTL expression. For example, a QTL expression could be linearly related to temperature. Use of mixed factorial regression models for QxE will be illustrated on yield data from the North American Barley Genome Project. When responses are intrinsically non-linear, standard mixed factorial regression will no longer be sufficient for adequate modeling of mean responses and variances. For those cases various non-linear generalizations exist. An application of a non-linear mixed model to senescence data in potato, where individual genotypes show a logistic senescence curve in time, will close the presentation.

English

0309|AGRIS 0301|AL-Wheat Program|AL-Maize Program

Juan Carlos Mendieta

CIMMYT Publications Collection