Relationships among analytical methods used to study genotypic variation and genotype-by-environment interaction in plant breeding multi-environment experiments

Following the recognition of the importance of dealing with the effects of genotype-by-environment (G ×E) interaction in multi-environment testing of genotypes in plant breeding programs, there has been substantial development in the area of analytical methodology to quantify and describe these interactions. Three major areas where there have been developments are the analysis of variance, indirect selection, and pattern analysis methodologies. This has resulted in a wide range of analytical methods each with their own advocates. There is little doubt that the development of these methodologies has greatly contributed to an enhanced understanding of the magnitude and form ofG ×E interactions and our ability to quantify their presence in a multi-environment experiment. However, our understanding of the environmental and physiological bases of the nature ofG ×E interactions in plant breeding has not improved commensurably with the availability of these methodologies. This may in part be due to concentration on the statistical aspects of the analytical methodologies rather than on the complementary resolution of the biological basis of the differences in genotypic adaptation observed in plant breeding experiments. There are clear relationships between many of the analytical methodologies used for studying genotypic variation andG ×E interaction in plant breeding experiments. However, from the numerous discussions on the relative merits of alternative ways of analysingG ×E interactions which can be found in the literature, these relationships do not appear to be widely appreciated. This paper outlines the relevant theoretical relationships between the analysis of variance, indirect selection and pattern analysis methodologies, and their practical implications for the plant breeder interested in assessing the effects ofG ×E interaction on the response to selection. The variance components estimated from the combined analysis of variance can be used to judge the relative magnitude of genotypic andG ×E interaction variance. Where concern is on the effect of lack of correlation among environments, theG ×E interaction component can be partitioned into a component due to heterogeneity of genotypic variance among environments and another due to the lack of correlation among environments. In addition, the pooled genetic correlation among all environments can be estimated as the intraclass correlation from the variance components of the combined analysis of variance. WhereG ×E interaction accounts for a large proportion of the variation among genotypes, the individual genetic correlations between environments could be investigated rather than the pooled genetic correlation. Indirect selection theory can be applied to the case where the same character is measured on the same genotypes in different environments. Where there are no correlations of error effects among environments, the phenotypic correlation between environments may be used to investigate indirect response to selection. Pattern analysis (classification and ordination) methods based on standardised data can be used to summarise the relationships among environments in terms of the scope to exploit indirect selection. With the availability of this range of analytical methodology, it is now possible to investigate the results of more comprehensive experiments which attempt to understand the nature of differences in genotypic adaptation. Hence a greater focus of interest on understanding the causes of the interaction can be achieved.